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Electrostatic Analysis of and Improvements to Electrophotographic Solid Freeform Fabrication


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ELECTROSTATIC ANALYSIS OF AND IMPROVEMENTS TO ELECTROPHOTOGRAPHIC SOLID FREEFORM FABRICATION By JAMES EDWARD FAY JR. A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2003

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Copyright 2003 by James Edward Fay Jr

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Dedicated to my family and friends.

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ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Ashok Kumar, for his help and advice in this study. I would also like to thank my committee members, Dr. John Schueller and Dr. John Ziegert, for their assistance in preparing and evaluating this thesis. I appreciate all the assistance and guidance I have gotten from my fellow researchers at the Design and Rapid Prototyping Laboratory. I would finally like to thank my family and friends for helping me to make it this far. iv

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TABLE OF CONTENTS Page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES...........................................................................................................viii LIST OF FIGURES...........................................................................................................ix ABSTRACT......................................................................................................................xii CHAPTER 1 INTRODUCTION........................................................................................................1 Overview.......................................................................................................................1 Goals.............................................................................................................................2 Outline..........................................................................................................................3 2 BACKGROUND ON RAPID PROTOTYPING SYSTEMS.......................................5 Overview of Rapid Prototyping Technologies.............................................................5 Laminated Object Manufacturing.................................................................................6 Fused Deposition Modeling..........................................................................................8 Stereo Lithography.......................................................................................................9 Selective Laser Sintering............................................................................................10 Three Dimensional Printing........................................................................................11 3 BACKGROUND ON ELECTROPHOTOGRAPHY.................................................13 Introduction.................................................................................................................13 Photoconductor Materials...........................................................................................14 Dark Decay..........................................................................................................14 Charge Acceptance..............................................................................................14 Image Formation Time........................................................................................15 Image Stability.....................................................................................................15 Residual Image....................................................................................................15 Material Selection................................................................................................15 The Electrophotographic Process...............................................................................16 Charging..............................................................................................................16 Corona..........................................................................................................17 Charging roller.............................................................................................17 v

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Imaging................................................................................................................18 Development........................................................................................................18 Toner transport.............................................................................................20 Toner charging.............................................................................................23 Transfer................................................................................................................24 Fusing..................................................................................................................24 Cleaning...............................................................................................................25 Case Study: The Hewlett-Packard LaserJet 4.............................................................26 4 ELECTROPHOTOGRAPHIC SOLID FREEFORM FABRICATION.....................32 Introduction.................................................................................................................32 Development of an ESFF testbed system...................................................................32 Motion Control....................................................................................................33 Printing................................................................................................................34 Fusing..................................................................................................................34 Software...............................................................................................................34 Development of a Charge Measurement Apparatus...................................................35 5 MODELING OF THE ESFF PROCESS....................................................................39 Introduction.................................................................................................................39 Electrostatic Voltmeter Testing..................................................................................40 Corona Charging.........................................................................................................42 Transfer.......................................................................................................................47 Agreement of Model with Experimental Data............................................................53 Conclusions.................................................................................................................56 6 PATTERN PRINTING...............................................................................................59 Introduction.................................................................................................................59 Theoretical Model.......................................................................................................59 Experimental Results..................................................................................................65 Conclusions.................................................................................................................71 Future Work................................................................................................................72 7 DESIGN OF AN ELECTROPHOTOGRAPHIC DEVELOPER SYSTEM..............74 Introduction.................................................................................................................74 Developer System Fundamentals...............................................................................75 Powder Storage....................................................................................................75 Powder Charging.................................................................................................75 Corona charging...........................................................................................75 Injection charging.........................................................................................76 Triboelectric charging..................................................................................76 Powder Transport................................................................................................76 Magnetic transport........................................................................................77 vi

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Cascade transport.........................................................................................77 Powder Transfer..................................................................................................78 Evolution of ESFF Developer Design........................................................................79 Experimental Analysis of the Two-Roller Developer................................................85 Conclusions.................................................................................................................86 8 DESIGN OF A NEW ESFF TESTBED.....................................................................88 Reasons for New Design............................................................................................88 Design Concept...........................................................................................................89 The Photoconductor Plate....................................................................................90 The Developer System........................................................................................92 The Imaging System............................................................................................94 Imaging System Analysis...........................................................................................95 Imaging System Control.............................................................................................99 Future Work..............................................................................................................100 9 CONCLUSIONS AND FUTURE WORK...............................................................102 Conclusions...............................................................................................................102 System Modeling...............................................................................................102 Pattern Printing..................................................................................................102 Developer Design..............................................................................................103 New ESFF Testbed............................................................................................103 Future Work..............................................................................................................103 System Modeling...............................................................................................103 Pattern Printing..................................................................................................104 Developer Design..............................................................................................104 New ESFF Testbed............................................................................................104 Overview...................................................................................................................105 APPENDIX CODE FOR MATLAB EFFICIENCY SIMULATION.............................106 LIST OF REFERENCES.................................................................................................108 BIOGRAPHICAL SKETCH...........................................................................................110 vii

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LIST OF TABLES Table page 5-1 Parameters for numerical simulation...........................................................................54 6-1 Results of varying the discharged area width..............................................................64 6-2 Results of varying the charged area width...................................................................64 6-3 Pattern printing experimental results...........................................................................66 6-4 Pattern printing rank table...........................................................................................67 8-1 DC controller connections chart..................................................................................97 viii

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LIST OF FIGURES Figure page 2-1 The rapid prototyping process.......................................................................................6 2-2 Schematic of a typical LOM system..............................................................................7 2-3 Schematic of metal foil LOM system............................................................................8 2-4 Schematic of a typical FDM system..............................................................................9 2-5 Schematic of a typical SLA system.............................................................................10 2-6 Schematic of a typical SLS system..............................................................................11 2-7 Schematic of a typical three-dimensional printing system..........................................12 3-1 Schematic of a typical drum electrophotography system............................................17 3-2 A typical shielded corotron..........................................................................................18 3-3 The imaging process....................................................................................................19 3-4 A typical development system.....................................................................................19 3-5 A cascade development system...................................................................................21 3-6 A typical magnetic brush development system...........................................................22 3-7 The transfer process.....................................................................................................25 3-8 The LaserJet 4 printing system....................................................................................26 3-9 Diagram of LaserJet 4 control architecture.................................................................27 3-10 LaserJet 4 imager diagram.........................................................................................29 3-11 LaserJet 4 developer schematic.................................................................................31 4-1 The ESFF testbed.........................................................................................................33 4-2 Flowchart of the ESFF process....................................................................................36 ix

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4-3 Schematic of the charge measurement apparatus........................................................37 5-1 Model of the voltage measurement stage....................................................................41 5-2 Corona charging schematic.........................................................................................43 5-3 Model of the corona charging stage............................................................................44 5-4 Model of the printing stage..........................................................................................48 5-5 Results of simulation of printing model......................................................................55 5-6 Experimental printing build rates................................................................................56 6-1 Solid area printing model............................................................................................60 6-2 Solid area printing model results.................................................................................61 6-3 Pattern printing model.................................................................................................61 6-4 Pattern printing model results......................................................................................62 6-5 Print with no pattern....................................................................................................68 6-6 Print with a 1/72-inch black and white line pattern.....................................................68 6-7 Print with a 4/72-inch black line and 1/72-inch white line pattern.............................69 6-8 Print with a 4/72-inch black and white line pattern.....................................................69 6-9 Pattern printing parts, 250 prints.................................................................................70 6-10 Further pattern printing parts, 250 prints...................................................................71 6-11 Comparison image of parts from Figure 6-10 without pattern printing....................71 7-1 Development system schematic...................................................................................74 7-2 Cross-section of original developer design.................................................................80 7-3 Cross section of improved developer design...............................................................81 7-4 Cross-section of two-roller developer design..............................................................83 8-1 Conceptual schematic of the new ESFF testbed..........................................................89 8-2 Conceptual schematic of new developer.....................................................................93 8-4 Imager control diagram...............................................................................................96 x

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8-4 Imaging control architecture........................................................................................99 xi

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Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ELECTROSTATIC ANALYSIS OF AND IMPROVEMENTS TO ELECTROPHOTOGRAPHIC SOLID FREEFORM FABRICATION By James Edward Fay Jr. December 2003 Chair: Ashok V. Kumar Major Department: Mechanical and Aerospace Engineering Electrophotographic solid freeform fabrication (ESFF) is a method for rapid prototyping under research at the University of Florida. This system uses laser printing technology to build parts by depositing successive layers of a powdered material. The material is deposited through the use of electrostatic charge, giving electrophotography its name. There are four main areas of research in this thesis. First, several stages of the ESFF process were modeled to help understand the results of printing as they relate to controlled system parameters. This modeling provides a basis for understanding and eliminating several part defects caused by uneven printing across the layer. The reasons for the uneven printing are explored. Solutions are provided where applicable, and limitations of the technology caused by these defects are discussed. Second, a new method of printing line patterns in the cross section instead of a solid area is discussed. The technique is intended to solve an issue of uneven printing whereby the edges of a part grow faster than the center area. The process is examined xii

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using finite element analysis to test the theoretical validity of the solution. Experimental research is next presented to validate the results of the finite element analysis. The advantages and problems presented by this method are discussed in relation to both the finite element analysis and the experimental results. Third, a novel design for a device called a developer is presented. This device is used in electrophotography to charge powder so that it can be used to form an image. The theory of developer design is reviewed. A history of the various versions of the device designed in this research is presented. The practical issues with the device are discussed in light of a new design for the overall ESFF process that will be more accommodative to developer design. Finally, a new design for the ESFF test apparatus is presented. The issues this new design is intended to resolve are discussed. The conceptual design of several components is presented. A control system for imaging that will remove many current technological restrictions is presented and discussed. xiii

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CHAPTER 1 INTRODUCTION Overview Electrophotographic solid freeform fabrication (ESFF) is a new method for rapid prototyping under development at the University of Florida. Like other rapid prototyping technologies, ESFF adds material in layers to form parts in an arbitrary shape. This allows the production of prototype-quality parts without the need for expensive, time-consuming tooling operations. While slower than some traditional machining methods for mass production, rapid prototyping technologies can produce parts with prohibitively complex geometries and very fine features. The ESFF technique attempts to expand the rapid prototyping field by allowing for the production of very fine tolerance parts in a variety of materials. Rapid prototyping technologies are currently limited in their ability to produce parts with very small features, and are generally reliant on polymers as modeling materials. There are a variety of methods currently used for the production of rapid prototyping. ESFF introduces a new technology to the field, that of electrophotography. This technology, which is the basis for laser printers, uses charge and field attraction to move powder and special materials to create an image using a laser beam. The powder transportation method holds the possibility of creating parts in a wider variety of materials than previously available. The theoretical limits of the imaging system are also much finer than current technologies, even finer than traditional machining. 1

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2 To date, much progress has been made on realizing a working ESFF system. A hardware testbed and a software control system have been developed. In early tests a build height limitation of approximately 1 mm was found. This problem was analyzed by physical modeling and solved by the addition of a surface charging system. The physical characteristics of a number of powders have been studied and their relationship with the ESFF process modeled. Detailed models of some stages of the ESFF process have been constructed. Several challenges have not been overcome, and some new problems have emerged as the technology progressed. A poor understanding of some of the stages of the ESFF process that had not been modeled created a difficulty in trying to solve problems and improve performance. A problem in all electrophotography is the uniform imaging within a solid area, due to changes in field strength. A solution to this problem had been proposed but not tested. While powders had been examined, a system for using these powders to create parts was still needed. Finally, a new design for the ESFF system was needed to improve printing with alternative materials and remove the reliance on a particular printing system. Goals The goal of this study was to find solutions wherever possible to the outstanding issues in the ESFF process. This goal involved a number of specific objectives, namely: Modeling of poorly understood stages of the ESFF process and construction of more detailed models in some areas. Testing and evaluation of the pattern printing system to solve the problem of solid-area development. Design, testing, and evaluation of a development system to print new powder materials.

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3 Overall design of a new ESFF hardware system, with study of an imaging system for use in the new design. Outline Chapter 1 is a short introduction to the overall work. This contains a brief description of the place of ESFF in the manufacturing field. It also provides a description of the current state of ESFF research and the problems yet to be overcome. Chapter 2 is an overview of the history of the rapid prototyping field. Issues related to the field are discussed. Several prototyping technologies are described and their relative merits and drawbacks presented. Chapter 3 is a description of electrophotography technology. This technology is covered in some detail in order to lay the groundwork for later. An example of the technology, the LaserJet 4 printer used in the ESFF system, is described in detail. Chapter 4 deals with work to date on the ESFF system. This chapter describes ESFF technology in detail in preparation for later chapters. This chapter also serves to document the work done to date to some extent for other projects. Problems in the technology are described to show the importance of the work presented here. Chapter 5 presents the modeling work done for this thesis. Three main stages of the process were modeled: voltage measurement, corona surface charging, and powder transfer. The first two stages mentioned had not been previously modeled, which led to many difficulties in understanding experimental results and attempting to solve problems. The third stage was modeled in more detail than in previous works to account for areas of interest not studied in those models. The agreement of the models with observed behavior is discussed.

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4 Chapter 6 discusses the experimental results of a study of pattern printing. Sivakumar Bhaskarapanditha (2003) first proposed the basis of this process. His work is reviewed, along with the theoretical background. Experimental testing of the system is presented, along with further modeling of the process. The advantages and problems this system entails are discussed. Chapter 7 is a discussion of the design of a new developer system to be used for printing new powders. The iterations of system design are discussed to show the reasons for the aspects of the final design. A theoretical model of the final design is shown. The problems associated with this system are discussed. Chapter 8 describes the new ESFF testbed design. The reasons this design is necessary are enumerated. An overview of the design is presented. The results of system modeling of the imager system from the current testbed are shown, along with the control architecture used to use this system alone without the need for the complete printer. Finally, Chapter 9 will provide conclusions to the research and describe future work to be done. The conclusions presented in Chapters 5 through 8 will be summarized to provide an overview of the research as a whole.

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CHAPTER 2 BACKGROUND ON RAPID PROTOTYPING SYSTEMS Overview of Rapid Prototyping Technologies Rapid prototyping, also known as solid freeform fabrication or layered manufacturing, is a new but well-established tool in the manufacturing field. The technology allows for the creation of individual prototype-quality items in little time without the need for expensive tooling. In some applications the technology can also be used to quickly produce specialized tools or casts for traditional manufacture. The parts are first generated as computer models, then sent to the prototyping machine of choice. The generation of tool paths is performed automatically. The prototyping machine builds the part, which may then require post-processing treatments such as curing or support material removal. A flowchart of this process is shown in Figure 2-1. There are several important characteristics of a rapid prototyping technique. The speed at which a given technique is able to build parts is of course important, as is the accuracy with which those parts can be produced. Another important factor is the material used to produce the parts. Some technologies require the use of a special material that may be expensive or may have undesirable mechanical properties, other technologies can use multiple materials. To date most rapid prototyping technologies have used polymers of some variety as their build materials, and there is much research underway to produce technologies that can build with metals or ceramics. 5

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6 Computer Model of Desired Part Software Interface Prototyping Machine Finished Part Post-Processing Figure 2-1. The rapid prototyping process There are many rapid prototyping technologies currently available commercially. There are also several experimental technologies that offer promise for the future. This chapter will give a brief overview of some of these technologies. Laminated Object Manufacturing Laminated object manufacturing (LOM) is a straightforward technology that produces a part by cutting cross sections out of a film using a laser and joining them. Both the part cross section and the surrounding paper are left in place after division, with the end result being a cube that can easily be separated into the part and waste material. This provides the support material needed for overhanging sections. The production rate is very quick for parts with large cross sections, because the system only needs to trace the edge of the cross section with a laser rather than place material or fill in the area

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7 (Cooper 2001). The finished part has mechanical properties similar to pressed wood. A schematic of a typical LOM system is shown in Figure 2-2. Figure 2-2. Schematic of a typical LOM system (Kochan 1993) Unfortunately, the LOM system requires a material that can be formed into a film, which is not always desirable. There is also a large amount of material waste in the system, since not only the part but also the surrounding area must be removed, and the resulting webbing is not reusable. Because paper is a common choice for the LOM process the costs associated with material waste are not generally great, but there is a certain amount of smoke produced in the laser cutting operation that must also be carried away when paper is used (Cooper 2001). A similar technology is currently under research that uses sheets of metal foil as the material (Doumanidis and Gao 2002). The material is compressed onto previous layers using a magnetic field, then the cross section shapes are cut with a diamond bit and joined by ultrasonic spot welding. This technology has some of the same drawbacks seen in traditional LOM, but offers the ability to quickly prototype metal parts with large cross

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8 sections, which would be a significant advance. A schematic of the system is shown in Figure 2-3. Figure 2-3. Schematic of metal foil LOM system (Doumanidis and Gao 2002) Fused Deposition Modeling Fused deposition modeling (FDM) is a very popular commercial rapid prototyping technology. An actuated head moves in two axes to build a planar cross section on a build platform, which is capable of translating in a third direction to give the part height. The part is built using material extruded from a nozzle on the head, which traces the outline of the part then fills in the solid area with cross-hatching. A typical FDM build head has two nozzles, one for the part material and one for a support material. The material is stored as a spooled filament, extruded into the heated nozzle and then cools and solidifies once placed. A large number of materials can be extruded in this manner, although to date almost all FDM technology is based on plastics and waxes because the heat required to melt and extrude metal is prohibitive from both safety and energy perspectives. Even so,

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9 this grants a fairly broad amount of freedom in the type of material used. A typical FDM system is depicted in Figure 2-4. Figure 2-4. Schematic of a typical FDM system (Kochan 1993) FDM technologies are not as fast as LOM systems, because they must trace the cross-hatching for each section, and because they require the movement of a physical head to build the part rather than laser cutting. However, FDM systems can use a variety of plastics, as well as waxes that can be used to make molds for casting. Furthermore, FDM systems have far less material waste, because they build support structures only where needed. Stereo Lithography Stereo lithography (SLA) systems are the oldest rapid prototyping technology. The system features a build platform immersed in a liquid polymer bath. The part is built by tracing a cross section with a laser in the thin layer of liquid polymer on top of the build platform, which solidifies the special polymer used. This technique requires cross-hatching of the section, and the construction of supports is problematic. These supports are usually constructed by building a network of fine mesh in the desired areas that

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10 require a significant amount of post-processing to remove. A typical SLA system is shown in Figure 2-5. Laser Part Build Platform Liquid Polymer Figure 2-5. Schematic of a typical SLA system The main drawback of this technology is the special polymer material used. The material is a proprietary polymer, and is much more expensive than the materials used in other technologies. Earlier technologies also used a material that was somewhat hazardous, though there are now build materials that are much safer (Cooper 2001). Selective Laser Sintering Selective laser sintering (SLS) is another popular commercial technology. In this system, a thin layer of powder is spread uniformly over the build platform. A laser then fuses the powder into a solid by heating it to just below the melting point. This technology is able to create parts form a large number of materials, mostly polymers and waxes. However, recently the technology has been used to build parts from metal powders in which the particles have been coated with polymer. This produces a metal part with green strength sufficient to be processed in a furnace. If a fully dense metal part

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11 were desired a post-processing step is needed to infiltrate the metal part with copper to fill the gaps between sintered particles. Another way to achieve fully dense metal parts is to use the system to make a blank for a mold, then cast the part. The powder bed is full, so there is no need for support material, much like LOM. However, once the part is finished the excess powder can be recovered and reused, significantly reducing waste costs. A typical SLS system is shown in Figure 2-6. Powder Build Platform Part Laser Levelling Roller Figure 2-6. Schematic of a typical SLS system Three Dimensional Printing Three-dimensional printing is very similar to SLS. Thin layers of powder are spread over the build area, then joined into a cross section. In this case, however, the cross section is joined using an inkjet head that disperses a resin onto the powder. This allows the technology to build parts from virtually any material that can be powdered. However, the building speed is slower than SLS, since a print head must be moved to create the cross section rather than tracing it with a laser. The parts may need additional post-processing as well, as the resin may not provide the part with as much mechanical

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12 strength as in the sintering process. A depiction of a three-dimensional printing system is shown in Figure 2-7. Figure 2-7. Schematic of a typical three-dimensional printing system (Kochan 1993)

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CHAPTER 3 BACKGROUND ON ELECTROPHOTOGRAPHY Introduction Electrophotography, sometimes called xerography because of its early development by the Xerox Corporation, is a widespread method for the creation of printed documents. Laser printers and copiers are based on the technology, as are some types of imaging systems used to digitally capture x-ray scans. The technology was first developed by Chester Carlson (Carlson 1942). The first experiments in electrophotography involved a charge image created in a glass slide, which was used to pick up powder and transfer it to wax paper. Such permanent slide methods are still sometimes used, as in mass printing of journals and the like, in a manner analogous to typeset printing. Modern electrophotography uses a much different technique. A uniform charge is deposited on a photoconductive surface with a grounded backing. This surface is then selectively exposed to light of a specific wavelength, turning the substrate conductive and thus discharging the surface at specified points. Depending on the printing technique, a powder called toner is picked up either in the charged or discharged area. This allows for the creation of a temporary image and the reuse of the imaging medium. The toner itself is charged in a device called a developer, which also brings the toner near the imaging surface to create a toner image using the latent charged image. The toner image is then transferred to an external medium, usually paper. The toner powder is then fused to the paper, making the image permanent. Finally, any excess toner that was not transferred is cleaned from the imaging surface. 13

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14 Photoconductor Materials There are a number of materials used in photoconductive imaging. The two most common materials are amorphous selenium, which was used in many early imaging systems, and organic photoreceptors, used in most printers today. The common property they share, photoconductivity, denotes that a certain wavelength of incident radiation causes a large decrease in their resistivity. The exact chemical mechanism by which this occurs is not within the scope of this thesis. The major characteristics of a photoconductor that are of interest here are dark decay, charge acceptance, image formation time, image stability, and residual image. Dark Decay Dark decay is essentially the permanence of an charge image on the photoconductor. Even in the absence of light, the photoconductor is not a perfect insulator and will slowly shed its charge. The time needed for the photoconductor to shed half its charge is referred to as the depletion time. Organic photoreceptors typically have much shorter depletion times than amorphous selenium (Diamond 1991). Charge Acceptance The surface charge density that can be deposited on the photoconductor by a given voltage is the charge acceptance. This characteristic is determined primarily by the dielectric properties of the photoconductor. So long as the charge acceptance is high enough to sustain a charge that will allow transfer of toner from the developer to the charge image, the photoconductor material is adequate. A charge acceptance much higher than this necessary minimum will lead to a large force holding the toner to the imaging surface, thus making the transfer to paper problematic.

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15 Image Formation Time The image formation time is the amount of time necessary for the imaging light source to discharge the photoconductor. In point of fact, a more proper term would be the image formation energy, but since the intensity of light is considered a given in a specific electrophotography application, it is the time that is considered the variable. This time is critical to the speed of the printing system, and thus is one of the more important characteristics of the photoconductor. Image Stability Image stability refers to the tendency of the charge image to migrate and spread across the imaging surface. Some image instability is due to the inability of the photoconductor medium to sustain a highly localized area of discharge. Surface contamination also plays a role, allowing charge to move or dissipate on the surface itself. Residual Image Residual image is due to residual charge on the imaging surface that is not discharged in the printing process. There are a number of reasons this can occur, and the effect is especially noticeable after many prints, when ghost images can begin to appear. Printers typically feature a discharging cycle after each print to alleviate the problem, but with high rates of printing it can be problematic to completely eliminate latent charge. Material Selection As mentioned above, the tendency in commercial electrophotography systems has been moving from amorphous selenium photoconductors towards organic photoreceptors. At first this would seem counterintuitive. Organic photoreceptors are softer and thus more prone to wear. They also do not hold an image for as long as amorphous selenium,

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16 and suffer gradual breakdown from environmental exposure. However, organic photoreceptors are significantly less expensive, even considering the need for frequent replacement. Printer design has minimized the impact, since the imaging drum in most printers is now part of the toner cartridge, which is sent for recycling periodically as the toner is depleted. During the recycling of the cartridge the drum can be inspected and, if necessary, re-coated. The issue of image duration is not of major significance in current printers, because printing speed has now reached the point where even the shorter image duration seen in organic photoreceptors is more than sufficient. Amorphous selenium has a fairly broad range of acceptable wavelengths, making it suitable for many applications but meaning it must be protected from light, while organic photoreceptors function only with light in the ultraviolet spectrum, meaning that these materials do not require as much shielding. The Electrophotographic Process As described earlier, there are six main steps in the electrophotographic cycle: charging, imaging, development, transfer, fusing, and cleaning. In most printers this process is carried out on a drum, which minimizes space, allowing for the current generation of small laser printers for desktops. A depiction of a drum electrophotography system is shown in Figure 3-1. Charging The first stage of the electrophotography process is to charge the surface of the imaging system. It is of the utmost importance to the picture quality that this charge be uniform across the surface. There are two main methods to accomplish charging, a corona and a charging roller.

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17 Laser Heated FusingRollers TonerReceptacle Cleaning Blade PhotoconductorDrum Developer Charging Roller Charging Roller Figure 3-1. Schematic of a typical drum electrophotography system Corona A corona charging system is essentially an ion jet. Most current printers use a shielded corotron charger. In this arrangement, a wire at high voltage is surrounded by a metal shield at the same voltage, generally around 7000 volts (Schaffert 1975). The wire produces ions by dielectric breakdown of air. The ions with the same sign as the wire are repelled away in all directions. The shield serves to deflect these ions in one specific direction. This produces a steady stream of ions and a regular charge. However, the high voltage required by the corotron, as well as its somewhat bulky size, has caused these systems to fall out of favor. A typical shielded corotron is shown in Figure 3-2. Charging roller Roller charging is the preferred method for charging the photoconductor drum in current printers. The system is more compact than a corotron, and requires a much lower

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18 voltage. The charge roller is made up of a metal axis surrounded by a layer of relatively conductive polymer foam. The shaft is subjected to a DC-biased AC voltage. This causes an intense electric field, leading to small discharges between the irregular polymer surface and the photoconductor drum (Hirakawa and Murata 1995). Figure 3-2. A typical shielded corotron Imaging Once the photoconductor surface is charged, the next step is to selectively discharge areas to produce an image. A polygonal mirror, where each face is one scan line, reflects a laser of the appropriate wavelength onto the photoconductor surface. The laser is switched on and off at high speeds to discharge specific dots. The resolution of the image is determined by the wavelength of the beam and the switching speed. A depiction of the process is shown in Figure 3-3. Development Development is the process of charging the toner powder and transferring it to the latent charge image. This is by far the most complex part of the electrophotography process. The toner powder is metered by a doctor blade to ensure a thin, uniform layer of toner is constantly brought out. The toner is charged, and brought near the photoconductor drum so that electrostatic force may draw the toner off onto the latent

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19 charge image. The topic of development is explored in greater detail in Chapter 7. A schematic of a typical developer is shown in Figure 3-4. + + + + + + + + + Laser Beam Photoconductor Layer Conductive Layer DischargedArea Figure 3-3. The imaging process Stirring Rod Doctor Blade Developer Roller Toner Hopper Figure 3-4. A typical development system

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20 Toner transport One of the most difficult parts of development is constantly providing a thin, uniform layer of toner for the photoconductor drum. To accomplish this goal, development systems progressed from cascade development, to insulative magnetic brush development, to conductive magnetic brush development (Schein 1988). All of these systems used a two-component toner, composed of carrier particles crucial to transport and charging as well as the toner particles that were ultimately transferred. Cascade development was a very simplistic mechanism whereby charged powder was brought across the photoconductor surface by mechanical force. In the earliest days of electrophotography the photoconductor was a plate, and a powder of carrier particles coated with toner was simply poured or cascaded across its face, giving the development system its name. Because toner was attracted by field force rather than by charge itself, solid area development was problematic (Schein 1988). Large charged areas have no field in the center, and thus toner was only attracted to the edge of an image. Another problem with this development system was the number of forces acting on free-flowing powder. Charge force was only one of many forces that may attract or repel toner from the photoconductor surface, and as such it was difficult if not impossible to control powder behavior. Cascade development also tended to have a great deal of powder loss and spillage. For these reasons, cascade development was largely abandoned when magnetic development systems were invented. A depiction of an early cascade system is shown in Figure 3-5. Insulative magnetic brush development was a significant step forward. In an insulative brush system, a stationary magnet inside the developer roller attracted iron in the carrier particles, which were coated in toner particles. This provided a counter-force

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21 to the charge force, and served to nullify a number of minor forces that disrupt control in cascade development. A roller rotated around this stationary magnet, carrying the toner by friction. The carrier particles formed chains in the magnetic field, such that the roller appeared to be a brush. Charged toner was carried across to the photoconductor drum when the electric field force was greater than the friction force holding the toner onto the carrier. The carrier beads were spherical, and the transfer of toner was limited by a balance of charge between the photoconductor surface and the carrier particles (Schein 1988). A depiction of a magnetic brush development system is shown in Figure 3-6. Figure 3-5. A cascade development system Conductive magnetic brush development was the most successful form of two-component development. The major change was that the carrier was now composed of irregular particles that were more capable of transmitting current across the development gap. This meant that there was not a balancing charge buildup in the carrier particles, and thus that much more powder could be transferred (Kasper and May 1978). This lead to darker lines and text, and more regular solid area development. The need for two

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22 component toner, however, was undesirable, as this lead to larger toner cartridges that had to be refilled more frequently. DevelopmentRoller CarrierParticles PhotoconductorDrum TonerParticles Figure 3-6. A typical magnetic brush development system Most printers currently use a mono-component toner that is insulative and magnetic. In this system, the toner, usually a polystyrene powder, is doped with iron compounds to make it magnetic. Thus the same advantages of force cancellation and control are present as in two-component magnetic development. The toner particles on the developer roller are charged, and thus may be stripped off the roller by the force of attraction with the image field. To aid in this process, an alternating current is applied to the developer roller, causing the charged toner particles to bounce back and forth from the roller surface, forming a cloud. An exception to this trend is in color printing where

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23 cascade development is still used, because the iron compounds that provide magnetic force would prevent proper coloration. Toner charging There are several methods for charging toner. The method used depends on the nature of the toner itself. Some methods use the characteristics of the toner itself to charge, while others create the charge externally. The toner may self-charge due to either triboelectric effects or chemical effects. Two-component toners often charge triboelectrically, with the contact friction between the carrier and toner particles causing an opposing charge on each particle. Liquid toners, used for applications involving extremely fine resolution prints due to the difficulty of handling very fine powders, are charged chemically, with charge transfer occurring between the toner and the liquid in which it is suspended. Chemical charging is also used to some degree in monocomponent toners, which are doped with charge control agents that have a similar effect, but these agents can only induce a part of the charge needed to print. The main purpose of the charge control agents is to render the toner susceptible to external charging. There are also several charging methods that allow charge to be applied to the toner by the developer. The most direct system of this kind is corona charging, identical to corona charging of the photoconductor. In addition to the normal problems of corona charging, the corona wire may become coated with toner particles, rendering it inoperable. The toner can be charged by triboelectric effects from rubbing with parts of the developer. This method is now very popular because the charge control agents in mono-component toners can make the toner particles triboelectrically active (Schein 1988). If the toner is conductive it can induce charge by passing through an electric field.

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24 Finally, insulating toner particles can be injected with charge by moving it rapidly around the developer roller through an electric field, though the exact mechanics of this process are poorly understood (Nelson 1978). If the charge per unit mass on the toner is too low, there will be insufficient electrostatic force to strip the toner from the magnetic roller. If the charge per unit mass is too high, a very thin layer of toner will cancel the image charge and make a light image. Thus the optimum design is to charge toner to the critical threshold value, which will depend on the magnetic field strength of the developer roller. Transfer Once the image is developed in toner powder, the next step is to transfer the toner to the paper. This transfer is accomplished by a mix of electrostatic and mechanical transfer force. An elastic charge roller presses the paper against the photoconductor drum, while depositing a charge opposite to that of the toner on the back face of the paper. The paper is sufficiently insulative for this charge to form a field across the paper width with the toner, helping to hold the toner onto the paper as it is pressed against the photoconductor drum. A schematic of the transfer stage is shown in Figure 3-7. Fusing The image on the paper is not yet in a permanent form. The charge force is sufficient to hold the toner to the paper lightly, but it must be fixed permanently so that it will not wipe off as soon as the paper is handled. In early electrophotography the toner powders were specialized powders, and wax paper was used as the fixing mechanism. In current printers toner technology has advanced significantly, and the toner has been adapted to the role of fixing agent so that ordinary paper may be used. The toner is mostly composed of polystyrene, which has a low melting point. The paper with the toner

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25 image is heated, causing the toner to melt. Some printers use a radiant heater, but many now opt for a heating roller that can both melt the toner and press it into the paper for better image fixing. The disadvantage of a heating roller is that it may pick up some toner, which will then smudge later pages. Nonstick coatings such as teflon are used on the heating rollers for this reason. + + + + + + Photoconductor Drum Developer Roller Figure 3-7. The transfer process Cleaning The final step in the cycle is to clean the photoconductor drum for later prints. In current desktop printers cleaning actually occurs within the cycle, as the photoconductor drum goes through several rotations for each page. The toner is scraped from the drum by a flexible blade and captured in a receptacle. This receptacle must be emptied periodically, but is usually designed to be large enough that it needs to be emptied less frequently than the toner must be replenished, so that the end user does not need to take the cartridge apart themselves.

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26 Case Study: The Hewlett-Packard LaserJet 4 The LaserJet 4 printer used in the Electrophotographic Solid Freeform Fabrication system is a typical example of the current generation of desktop laser printers. The LaserJet 4 uses an organic photoreceptor drum charged by roller. The imaging system is based on an ultraviolet laser and produces an image with a maximum resolution of 600 dots per inch (dpi). The developer is a mono-component magnetic insulative system. Fusing occurs by heating rollers. A diagram of the LaserJet 4 printing system is shown in Figure 3-8. Figure 3-8. The LaserJet 4 printing system (Hewlett-Packard 1996) The print is sent to the LaserJet 4 via a normal print cable and arrives at a computer board called the formatter. The formatter reads in the data and communicates the necessary information to other printer components. The formatter is also responsible for taking in settings from the printer control panel. The electromechanical control aspects of

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27 printing are then handled by another computer board, the DC controller. As well as sending control signals to the imaging system, the motor, the fuser, and the paper control system, this board reads in signals from a variety of sensors and sends messages back to the formatter as needed, such as when a paper jam is detected. The DC controller is also responsible for breaking the data stream from the formatter into a series of pulses that are transmitted to the imaging system, turning the laser on and off. A diagram of the printer control architecture is shown in Figure 3-9. Figure 3-9. Diagram of LaserJet 4 control architecture (Hewlett-Packard 1996)

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28 A single motor provides the drive to the paper handling system, the photoconductor drum, and the developer through a system of gears. This motor is equipped with its own dedicated control circuit for managing speed and acceleration, and requires only power and an on/off signal from the DC controller. The paper handling system uses a number of rollers to feed paper through the printer from the paper tray. A series of photosensors make sure that paper is feeding through properly and send paper jam warnings to the DC controller. There are two power units, one that takes in the voltage from the power socket of the printer, and another that breaks this voltage down into a number of high voltages for the various printing components. There are several components such as the charge rollers and heating system that use voltages so high that they must be isolated from the printer circuitry to prevent damage. There is a feedback system that ensures that voltage is being applied to the photoconductor drum, developer, and heating roller by resistance measurement. This signal is returned to the DC controller. The imaging system of the LaserJet 4 was designed to produce high-resolution images in a compact environment. At the time of the design the 600-dpi resolution was considered high for laser printers, though today there are higher resolution systems. The laser is a standard ultraviolet source with its own control board. This board takes in the laser pulse signal and status signals and outputs an error signal if necessary. The laser beam makes its way to the photoconductor drum by way of a rotating polygonal mirror that turns the laser stream into a scanning beam moving along the length of the photoconductor drum. The beam passes through two lenses to be focused and is then reflected by an angled mirror because the imager is at an angle to the drum. The

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29 polygonal mirror motor has its own control system and is turned on and off by the DC controller. The final part of the imager system is a photosensor that detects the start of each scan line, analogous to a homing sensor on a motor control system. A diagram of the LaserJet 4 imager is shown in Figure 3-10. Figure 3-10. LaserJet 4 imager diagram (Hewlett-Packard 1996) The developer system is based on insulative magnetic mono-component toner technology. The toner itself is a polystyrene powder base doped with charge control agents, iron compounds for magnetism, and carbon black for color. A stirring rod is present to keep the powder moving in a pseudo-fluid flow. The toner is primarily charged triboelectrically by rubbing with the material on the doctor blade. A DC-biased AC signal on the developer roller forms a powder cloud. The LaserJet 4 developer system is shown in Figure 3-11. The toner image is transferred to the paper using the elastic roller method described earlier. Once the image has been transferred the reverse side of the paper is discharged to

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30 prevent the paper form picking up any loose toner that may be present in the paper handling system. The paper is then fed through a pair of heating rollers for fusing before being sent out of the printer. A cleaning blade removes excess toner from the photoconductor drum.

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31 Figure 3-11. LaserJet 4 developer schematic (Hewlett-Packard 1996)

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CHAPTER 4 ELECTROPHOTOGRAPHIC SOLID FREEFORM FABRICATION Introduction Electrophotographic solid freeform fabrication (ESFF) is a recent innovation in the field of rapid prototyping developed at the University of Florida (Kumar 2000). The concept is to use the technology of electrophotography to deposit layers of powder imaged to form the cross sections of a part, then fuse them together. This combines the advantages of many existing freeform fabrication technologies. Using the speed of laser imaging and a rotating drum, the technology can deposit a layer of powder in seconds. The build material is also flexible, as any powder that can be charged and fused is usable. Powders which cannot be fused could still be used, but would require an additional binder layer. The resolution is very fine, as there are commercially-available printing systems which can image at resolutions well above 1000 dots per inch, and if the technology were to be applied specifically to this application there is no reason why imaging could not be performed at even finer resolutions. The main drawback ESFF is that the process is very complex and difficult to control. Development of an ESFF testbed system The first stage of ESFF research was the creation of a system that would allow for experimentation with ESFF technology. The system required a two-axis movement platform, a printing system, and some mechanism for fusing the imaged powder (Zhang 2001). A model of the ESFF testbed is shown in Figure 4-1. 32

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33 Figure 4-1. The ESFF testbed (Dutta 2002) Motion Control A Parker automation system was used to provide the motion and control. This system provides translation in two axes and a frame to mount the components of the ESFF apparatus. A Galil control system actuates the motors, as well as serving as an input/output junction between the computer and the various controls and sensors. The system includes a software control mechanism and an interface that allows the system to be controlled from within C++ programs. The build platform this system actuates is a spring-mounted plate with flanges to clip on the paper for printing. The springs allow the platform to be pushed against the photoconductor drum for better transfer without damage, and alleviate any issues related to the platform mounting not being perfectly horizontal. Finally, the platform allows control of the pressure of fusing during compaction by compressing the springs to a

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34 selected distance. A position sensor measures when this compression is reached and sends a signal to the Galil controller. There is also a connection to the voltage source so that the platform can be electrified in order to attract charged powder during printing. Printing The printer selected was a Hewlett-Packard LaserJet 4. This printer has a resolution of 600 dots per inch. To work within the ESFF testbed the printer required significant modification. Much of the printer had to be stripped apart so that the build platform would have access to the photoconductor drum. The internal sensors that detected the mechanical status of the printer had to be bypassed or controlled in order to simulate operation under normal conditions. Several communication signals within the printer also had to be intercepted so that the build platform and the printer could work together seamlessly. A schematic of the Hewlett-Packard LaserJet 4 was shown in Figure 3-8. Fusing The original fusing system used a radiant heater to melt the plastic toner powder. However, there are always slight variations in the amount of powder deposited across an image, so a compaction system was desired to level the powder during fusion. The heating system was thus changed to a compaction plate warmed by a mica strip heater. Recently a teflon-coated plate was added to the compaction and fusing system in order to prevent part damage due to sticking. Software To control this hardware, a software system was developed that would automate the process of building a part. A flowchart of the system and its controls is shown in Figure 4-2. There are several levels of programming in the software. There is a specific programming language of commands for the Parker automation system. Scripts

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35 programmed in this language may be called from C++ programs, which are stored in a dynamic link library. Finally, the SolidSlicer program developed in Java for the ESFF testbed reads in model files created in CAD software, divides them into cross sections, allows for positioning of the parts on the build platform, automates the process of building the part, and stores a log of each build (Bhaskarapanditha 2003). This ESFF apparatus provides a suitable mechanism for basic testing. A variety of parameters within the printing process can be varied. The qualities of the printed image can be manipulated through software, which will be touched on in a later chapter. Furthermore, a variety of analysis and sensor equipment can be installed within the testbed to evaluate different stages of the process and the effects of manipulating those stages. However, there are areas within the process that are essentially black box technology. The printer in particular has issues with process stages that are not transparent to an outside observer. For this reason, further test equipment and modeling is needed. Development of a Charge Measurement Apparatus One of the most important parts of the printing process is the charging of toner powder. The powder must be charged effectively enough that it can transfer an even layer onto the latent charged image, but not so charged that a tiny amount of powder can cancel the charge of the latent image. This testing would be very difficult, if not impossible, on the ESFF testbed because of the difficulty of testing charge within the framework of that system, as well as problems of recovering the powder. For this reason, a separate system was created which could test the charge and mass of printed powder. This system is shown in Figure 4-3.

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36 Figure 4-2. Flowchart of the ESFF process (Dutta 2002)

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37 Figure 4-3. Schematic of the charge measurement apparatus (Gokhale 2001) The charge measurement apparatus replaces the printer drive mechanism and photoconductor drum, and provides an attachment point for a developer. The developer cartridge is attached to a fabricated stand and attached to a voltage source. A photoconductor drum is attached and grounded through an Keithley electrometer that has the ability to integrate current over time, thus measuring the amount of charge flowing to the ground (Keithley Instruments 1995). When toner is deposited on the surface of the drum, the grounded metal on the opposite side of the insulator induces an equal and opposite charge that flows out through this ground. The photoconductor drum is removed and its mass measured before and after printing in order to determine the mass of powder deposited. Printing area may be normalized by controlling the time of operation through computer control of the drive motor.

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38 This system was initially used to optimize printing using the standard LaserJet 4 developer cartridge. It has also been used to test development systems created for research of the charging characteristics of other powders. The function of the system is the same in all cases. The design of such development systems is discussed in detail in a Chapter 7. The main problem with this measurement system is the measurement of powder mass. Removing the photoconductor drum mechanically causes powder to be lost, making the readings less accurate. A more accurate system would be possible if the measurement could be made in place, but this is problematic in practice. Another alternative currently being explored is to include a system for cleaning the powder from the photoconductor drum into a container, which could be removed and tested without loss of powder.

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CHAPTER 5 MODELING OF THE ESFF PROCESS Introduction The electrophotographic printing process used in ESFF is an extremely complex transfer method. In order to understand and optimize the process it is necessary to construct a detailed model of each step, as what seems intuitive will often prove wrong when analyzed further. It is also important to take into account the ways in which different stages of the ESFF process are interconnected. There were several areas in which it was desirable to perform a detailed analysis of the process. The first was the relationship between the surface voltage of a part measured by an electrostatic voltmeter and the charge state of the part. This is important because an electrostatic voltmeter is used experimentally to gauge both surface charge and volumetric charge, and it was necessary to understand what its readings indicated in regards to both values. The second stage of interest for modeling was the characteristics of corona charging. As a part builds, it is necessary to charge the surface in order to continue attracting charged powder. This is done in the ESFF platform using a corona charger. It was desirable to understand how the various characteristics of a building part such as thickness and charge state would effect the level of surface charge as the part builds, since this will determine both how well a part can be built and how consistently new layers will be deposited. 39

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40 The final stage to be modeled was the transfer of powder from the photoconductor drum onto the part. The results of the corona charging model were relevant here, because the surface charge deposited by the corona serves to enhance transfer. It was important to see what system parameters would alter both the consistency of a print within a layer and the amount of powder being transferred overall. Electrostatic Voltmeter Testing An electrostatic voltmeter is the best tool for measuring the surface voltages that are the basis of electrostatic transfer. The voltmeter determines the surface voltage by altering the voltage applied to a vibrating reed until the induced current is negated, showing that there is no field and thus that the reed and surface voltages are equal. The probe is calibrated to be held in air a specified distance from the surface being tested, which allows this field to be converted to a voltage on the surface. When the measurement involves a simple charged surface as the probe is designed for, the meaning of the measured voltage is clear. When used in a more complex measurement such as measuring the charge on the surface of a part that may contain a volumetric charge, it is necessary to do some analysis to ascertain what the reading given by the voltmeter indicates in regards to the contributing charges. First a model must be constructed to approximate the system, and then the field that the voltmeter probe detects must be derived as a function of the parameters of interest. In order to construct a model of the situation in probe testing on the ESFF system, several assumptions and simplifications had to be introduced. The system was modeled as a Gaussian series of parallel planes, with each plane representing a material layer in the system. The layers are the part itself, the paper substrate the system builds on, an air gap introduced to assess the effects of irregularities below the substrate, and the grounded

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41 metal plate on the build platform. Because the cross sectional area of a typical printed part is many orders of magnitude larger than the thickness, it was assumed that the various layers were infinite. Along with the material properties of the various layers, a surface charge t and volumetric charge t were assumed to be present on the part. This simulates a part wherein the surface charge has not been totally nullified by charged powder deposition and the volumetric charge has not been totally dissipated, both of which are common situations in the part building process. The field above the part was taken as zero, as would be the case if the voltmeter probe is behaving properly. The system model is shown in Figure 5-1. Plate Ground Air (da, a) Paper (d p p) Toner (d t t t t ) 0 2 1 3 Electrostatic VoltmeterProbe 4 dx: Thickness of layer x: Relative permissivity of layer material x: Surface charge density on layer x: Volumetric charge density in layer Figure 5-1. Model of the voltage measurement stage First, boundary conditions must be defined. The voltage on the metal plate is known to be ground as shown in Equation 5.1. 00V (5.1) The surface voltage is the total potential drop across all the layers, shown in Equation 5.2. 303VVVVs (5.2)

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42 By integrating the fields as shown in Equations 5.3 through 5.5 and summing the potential differences as shown in Equation 5.6, the surface voltage V s was found, and is presented in Equation 5.7. tdtttttttttdddxxVV00200322 (5.3) pdppttpptptttddddxdVV000021 (5.4) adaattaatatttddddxdVV000010 (5.5) sVVVVVVVVV 03102132 (5.6) aappttttaapptttsdddddddV210 (5.7) Most of these parameter values are either documented or can be determined experimentally. This equation shows that in order to use the voltmeter to measure surface charge it is necessary to first test the part before charging to find the portion of the voltage contributed by volumetric charge. Measuring this value and knowing the system parameters allows the surface charge t to be found using the voltmeter probe, which is very valuable in areas such as corona charging optimization experiments. Corona Charging The voltmeter probe simulation allowed for better understanding of experimental measurements of the corona charging process, among other things. It was also desirable to have a more detailed understanding of the charging process itself. The corona produces a stream of ions of both charge signs due to field breakdown of air around a high voltage wire. These ions are either attracted or repelled to the corona

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43 wire due to their sign and the sign of the wire voltage. The wire itself repels opposite charged ions in all directions, however in a corona charging device there is a metal shield around the wire at the same voltage, which subsequently repels the ions deflected in its direction. This shield has an opening at one side, and the ions are thus deflected out through this opening. Many corona charging systems also use a metal grid or a number of wires across the opening held at the same voltage as the corona wire, which serve to nullify velocities in all directions except that normal to the plane of the grid surface. The corona may thus be deemed for purposes of modeling a plane with a fixed flux of charge. A corona charge system is shown in Figure 5-2. Corona wire, shield, andgrid wires held at samevoltage Figure 5-2. Corona charging schematic The charge will deposit onto another surface until that surface becomes saturated. The saturation takes place due to the fact that eventually the surface has so much charge that it becomes repulsive to new particles. If the charge particles are depositing onto a conductive surface that has been grounded, the charging can go on more or less indefinitely. If the ions are depositing onto an insulative surface, there is a finite limit.

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44 Placing a grounded plate behind the insulative surface has the effect of suppressing the field the ions create and thus extends the charge capacity of the surface. The model used for the corona charging simulation is very similar to the one used in the voltmeter simulation. A new layer has been introduced, which models the air gap above the part filled with ions of a constant charge density c The corona itself is seen as a plane at a fixed voltage. The model is taken at equilibrium once charging has stopped, which was assumed to occur when field in the corona gap dropped to a critical magnitude. The charging causes an induced field in the build platform, modeled by a surface charge b The corona voltage is a known value. The model of the charging process is shown in Figure 5-3. Plate ( b ) Ground Air (da, a) Paper (d p p ) Toner (dt, t, t, t) 0213 Vcorona 4 Corona Gap (dc, a, c) Figure 5-3. Model of the corona charging stage First, boundary conditions were defined. The conditions in this case were the ground voltage on the bottom plate and the applied voltage on the corona, V corona The boundary conditions are shown in Equations 5.8 and 5.9. 00V (5.8)

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45 coronaVV4 (5.9) As before, the field in each layer was integrated to find the potential difference across the layer. This process is shown in Equations 5.10 through 5.13. adaababddxVV00010 (5.10) pdppbpbddxVV00021 (5.11) tdttttttttbtbttddddxxVV002000322 (5.12) cdaccacttactacbacbtttddddddxxdVV0020000432 (5.13) The next step was to sum the potential differences as shown in Equation 5.14. This equation was then expanded with the calculated potential differences to yield Equation 5.15. 1021324304VVVVVVVVVVVCorona (5.14) accacttttactttttppacabCoronaddddddddddV22120 (5.15) To determine the field in the corona gap, it was necessary to solve for the induced charge in the platform in terms of the system parameters, as shown in Equation 5.16. ttppacaaccacttttactttCoronabddddddddddV2220 (5.16) Finally, the field at the top surface of the part was computed using this charge. The result is shown in Equation 5.17.

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46 020022aaccttttppaatppaaCoronaatttbcCdddddddVdE (5.17) Using the equilibrium assumption of a zero field at this surface and simplifying the equation for the surface charge density t results in a solution for the maximum charge density on the surface, t,max shown in Equation 5.18. ppaattppaattCoronaacctddddddVd2202max, (5.18) It is desirable that this value be large and positive. Although the charge density in the corona gap was assumed to be constant, it is in fact a function of the corona voltage, with an optimum value determined by the mechanics of the corona itself. This relationship was not known precisely, so the constant value was used. Equation 5.4 demonstrates that it would be ideal to use either the optimum voltage, or if this was not attainable, the maximum voltage that could be provided. At first glance it would appear that the volumetric charge should be minimized, but the sign of this charge density will be opposite that of the charge being deposited. Thus the negatively charged part in fact enhances positive corona charging. As the part grows and d t becomes larger, the volumetric charge density of the part will dominate the equation. With the mechanics of corona charging determined, it became possible to examine the mechanics of the printing process itself in a very detailed manner.

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47 Transfer The transfer stage of the ESFF system is both the most critical and most complex stage of the entire process. It is necessary to model this system in order to find the parameters that will insure that the amount of powder transferred is maximized, and that the printing of each layer remains consistent. This will create a better build rate, and improve part quality. The system model was again a Gaussian series of infinite planes. This is more of an approximation in this case than previously, because the photoconductor drum and the model layers that are attached to it are in fact cylindrical. However, the radius of curvature of these layers is orders of magnitude larger than the thickness of the layers, so the approximation is a reasonable one. Furthermore, this model is too complex to be a realistic numerical simulation, because too many parameters involved are either not known with any useful precision or vary too widely over time for a realistic numerical snapshot to be constructed. For this reason, the error introduced by the parallel planes approximation is of little importance given the overall numerical uncertainty of the simulation. This is not to say, however, that the model itself is not useful. It is enough to know that the optimum system performance can be obtained by maximizing or minimizing certain variables without necessarily finding numerical values for those parameters. This model again sought to simulate a system at equilibrium. It was assumed there was an initial layer of powder on the photoconductor drum of thickness d 1 which was transferred with efficiency An air gap was introduced between the photoconductor drum and the part to simulate irregularities in the part surface. Two layers of toner are

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48 now present on the build platform, the fused powder which has both a surface charge and residual volumetric charge, and the fresh toner transferred during printing which has only a volumetric charge of density l The model of the system is shown Figure 5-4. Plate Vplatform Air (da, a) Paper (d p p) Toner (df, t, t) 0 2 1 3 Gap (d g a) Toner ((1dl, t, l) Insulation (di, i) Metal Drum ( d ) Ground 4 5 6 Toner (dl, t) 7 Figure 5-4. Model of the printing stage The boundary conditions here are the voltages on the platform and photoconductor drum backing, shown in Equations 5.19 and 5.20. platformVV0 (5.19) 07V (5.20) Again, the voltage drop across the model was found by integrating the fields as shown in Equations 5.21 through 5.27 then summing as in Equation 5.28. 00067iiddidddxVVi (5.21) ldtllltldtldddddxxVV100200562211 (5.22) gdagllagdglldddddxdVV00005411 (5.23)

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49 ldtlltldtlllddddxxdVV00220043221 (5.24) fdtfttfttflltfdtttlldddddddxxdVV0020000322 (5.25) pdppttpptppllppdptttllddddddddxddVV00000021 (5.26) adaattaataallaadatttllddddddddxddVV00000010 (5.27) aapptfftaapptftppaagtflllppaagtfliidplatformdddddddddddddddddddVVV21222211006 (5.28) The next step was to solve for the induced charge d shown in Equation 5.29. aapptfftaapptftppaagtflllplatformppaagtfliiddddddddddddddVdddddd212222110 (5.29) To manage this complex equation, coefficients are defined as shown in Equation 5.30. PdNMdLVfttllplatformd 0 (5.30)

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50 The next step was to solve for the field in the printing gap, E c in terms of the defined system. This field equation is shown in Equation 5.31. 000 afttllplatformalldcPdNMdLPVdE (5.31) Only the l coefficient contains so expanding P -L will allow for solution in terms of First, the field equation is solved in terms of this quantity, shown in Equation 5.32. llfttplatformcaddNMVEPLP 00 (5.32) Next, the quantity P-L is expanded. Because the L term contains the equation is separated to isolate the efficiency term. The result is shown in Equation 5.33. ppaagtfltagtappaagtfliiddddddddddddLP2221 (5.33) Substituting Equation 5.33 into Equation 5.32 yields a solution for shown in Equation 5.34. tagtappaagtfliillppaagtflllfttplatformcadddddddddddddddNMVEP222100 (5.34) Substituting the value for t found in Equation 5.18, an equation for the efficiency in terms of both printing and corona-charging parameters is obtained. This result is shown in Equation 5.35.

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51 ttfppaaaapptfcacppaaaapptfllppaagtflcappaagtfliiCoronappaaaapptfplatformlltagtappaagtfliiddddddddddddddddddEddddddVdddddVdddddddd220002222211 (5.35) In order to make this equation more manageable, constants are defined. This is shown in Equation 5.36. ltclcCoronaplatformCCCCECVCV 6543210 (5.36) Now that the model solution for printing is solved, the next phase is to analyze this result and learn what it means. The constant thicknesses and material properties may be ignored, since they are unalterable. The platform voltage, corona voltage, and critical transfer field E c are all multiplied by the permissivity of free space, 0 Because this constant has a value of 8.85x10 -18 C 2 V 2 / mm 2 the magnitude of these three contributions will be orders of magnitude less significant than other factors. For this reason the impact of these three variables can reasonably be assumed to be negligible.

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52 The contribution of the volumetric charge density in fresh toner, l is complex, especially in that it has a contribution both to the numerator and the denominator. The numerator contribution will grow with d l the initial toner layer thickness brought out by the photoconductor drum. It will also grow with the fused part thickness d f Finally, the numerator contribution will grow proportionally with the transfer gap d g and the substrate irregularity gap d a The contribution of the denominator term will follow these trends as well. The multiplier of the denominator term should be larger in general, so the magnitude of the charge density in fresh toner should be small to increase the amount of toner transferred. This is reasonable, since a more highly charged toner will require less transferred mass to cancel the field. The corona gap charge density c is more straightforward. This term exists only in the numerator, so it should be as large as possible. The multiplier of this term will grow with fused toner thickness, because as seen earlier the charge in the fused part can attract more charge from the corona. There is also a dependency on the air gap thickness, but this term exists in both the numerator and denominator of the multiplier term. As such the impact of the air gap in this term will be mitigated to a degree. The final term to be considered is the volumetric charge in the fused toner. The charge density t has a negative sign, and its multiplier is positive. This means the overall contribution of the fused toner charge will be negative, despite its effects in the corona charging process. The contribution of this charge density grows very quickly with part height, and shows variation with substrate adhesion.

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53 Agreement of Model with Experimental Data In order to evaluate the model of the printing stage, a computer simulation was constructed based on the model. The print cycle was then simulated over a range of volumetric charge densities in the fused toner to study the impact of discharging the fused powder on the part build rate. The values for the variables were the known values were applicable. Many values are unknown, however, or vary greatly. For these variables, values were selected that were deemed realistic. As such, the simulation is not an accurate numeric depiction of expected results, but such a depiction was not expected. The value in the simulation lies in showing the trends that occur as certain parameters vary. The values used in the simulation are provided in Table 5-1. The computational method used in the simulation was fairly simple. The part height began at zero. For the parameters used, the transfer efficiency was calculated, then an assumed value for the amount of toner brought out by the photoconductor drum was used to calculate the amount of toner transferred. This process was repeated over 500 prints. The charge density in fused toner was varied to analyze the changes in the system due to the efficiency of discharge. The other parameters were held constant. This is an unrealistic assumption, but provides an understanding of the impact of a specific variable. The results of the simulation are shown in Figure 5-5. The part height is given in inches for comparison with experimental data below. The code for the program is provided in the Appendix.

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54 Table 5-1. Parameters for numerical simulation SymbolMeaningValueSourcedaMean substrate irregularity thickness0.1 mmEstimateddcCorona gap thickness10.16 mmMeasureddfFused toner layer thicknessVariable-dgMean printing gap thickness due tosurface irregularity0.05 mmEstimateddiInsulation layer thickness0.01 mmMeasureddlInitial drum toner layer thickness0.02 mmEstimateddpPaper Thickness0.25 mmMeasuredEcElectric field in printing gap at whichadhesion and electrostatic forces areequal50 V / mmEstimatedVcoronaVoltage applied to corona5000 VControlledVoltage applied to platform duringprinting1000 VControlledPermissivity of free space8.85x10-18 C2 V2mm-2ScientificConstantaRelative permissivity of air1EstimatediRelative permissivity of insulation3EstimatedpRelative permissivity of paper2EstimatedtRelative permissivity of toner3.42MeasuredTransfer efficiency over printing gapVariable-cCharge density in corona gap2x10-6 C mm-3EstimatedlCharge density in fresh toner-7.28x10-9 Cmm-3EsitmatedtCharge density in fused toneron platformVariable-tCharge density on fused toner onplatformVariableVplatform

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55 Figure 5-5. Results of simulation of printing model For all charge states the build rate was quicker for the first few layers, where the field generated by the platform voltage still had a major impact. The build rate then experienced a falloff. For full discharge this falloff was very minor, but if the discharge was less efficient the falloff was significant, almost creating a plateau. This result was consistent with observed behavior over a very large number of samples in ESFF testing. The number of prints is obviously simple to control, but the charge density is problematic to vary, or even to measure after the discharge during printing. However, many of the parameters such as the relative permittivity of the materials can be reasonably assumed to vary only slightly. Discharge would vary over a greater range, so its impact should be more noticeable. The experimental data are shown in Figure 5-6.

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56 Part Height vs. Number of Prints0.00E+002.00E-034.00E-036.00E-038.00E-031.00E-021.20E-020510152025Number of Prints Build 1 Build 2 Build 3 Build 4 Build 5 Average Figure 5-6. Experimental printing build rates The experimental data shows that the prints began with a similar build rate, which then decreases over time. They also show that the variance in the different part models becomes greater as the number of prints increases. This data is consistent with the above simulation results for variations in build rate due to differences in discharge. Undoubtedly there were variations in many of the parameters taken as constants in the simulation, but it is reasonable to assume that the charge state varied more significantly, since the dielectric properties of materials are regular, and the variations in thickness of the layers would be randomized across the area of the print. Conclusions Overall, it would appear that the part would continue to build indefinitely with adequate corona charging, but that the average build rate would decrease drastically after

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57 several prints. This is in line with many observations over long printing times. These results indicate the need for consistent discharge of the part in the current transfer model. Inconsistencies in the adhesion of the substrate to the build platform will yield a warped part surface. This is, of course, undesirable. This effect has been observed in part builds in the past. It is difficult to overcome this problem in the current system, because the paper substrate is merely clipped onto the build platform. For the moment this effect seems to be beyond solution for the project. Ultimately, it would be desirable to have a build platform machined that would have a much smaller tolerance for surface irregularities. Adhesion of the paper substrate more tightly to the platform is also difficult. An adhesive backed paper would mar the build platform and be difficult to remove. A vacuum system would solve these problems, but would be expensive, difficult to install, and might leave vent holes behind the paper which would exacerbate the problem. Another troublesome result of the analysis was the problem presented by irregularities in the printed part surface. Not only are such irregularities undesirable in the first place, they appear to have a self-propagating nature. There are finite limitations on the ability to print a part regularly no matter how well the process is managed, and this result shows that over a large number of prints the quality of the part will decrease. The solution to this issue is to create a planar surface on the top of the part after every print. This is in fact the purpose of the compaction during the fusing stage. However, the compaction pressure needed to reduce irregularities in the part surface is also sufficient to deform the part under heating. To allow proper compaction, it would be necessary to surround the part with another powder to provide the needed support during

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58 fusing and compaction. Printing the background of each layer in another powder would accomplish this. The building part would then be encased in a block of secondary powder, which would provide a support structure as well as allow proper compaction. The secondary powder could be selected to allow easy removal during post-processing. It is also necessary to read between the lines of the analysis. The charge densities were assumed to be constant. However, in real life these densities will vary both between prints and across the cross section of the part. Variations in powder charge across a cross section could easily have the same self-propagating impact mentioned above, as not only the amount of powder developed at a given location for a given print but also the residual charge at that spot in subsequent prints would be impacted. Corona charge density would not have as much of a long-term impact, but would impact a given layer, which is a self-propagating situation in and of itself.

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CHAPTER 6 PATTERN PRINTING Introduction One of the major problems in electrophotographic printing is the phenomenon of edge printing, where the edges of a solid print area are dark but the center appears faded. This effect is due to the fact that the electric field gradient at the edge of the image is of much higher magnitude than that in the center. This effect is not seen in the printing of thin lines because the entire print area is within the range of the strong field gradient. For electrophotographic solid freeform fabrication, this is a subject of special importance. If the edges of a solid area consistently build faster than the center, soon there will be a gap between the center of the print area and the photoconductor drum, causing even less toner to transfer in successive images until only the edges build at all. For this reason, it is desirable to use thin lines for ESFF in order to assure a more consistent print across the cross section. However, it is unrealistic to develop a rapid prototyping technology around a specific type of cross section, as this would severely limit the number of applications. Therefore it was decided to create a pattern of thin lines within the cross section in order to break up the solid area and hopefully take advantage of the properties of thin line printing. Theoretical Model The effect behind edge printing is well documented. The exact characteristics, like many things in electrophotography, are very dependent on the individual characteristics 59

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60 of the system. For this reason the simplest way to study the problem is finite element analysis. The effect in this electrophotography system was first modeled by Sivakumar Bhaskarapanditha, and it was found that a dramatic peak in field did indeed occur at the very edge of a solid area image, with the center of the area having only a very slight field (Bhaskarapanditha 2003). The physical model of the system is shown in Figure 6-1, with the simulation results shown in Figure 6-2. The left half of the figure is the image area. Although the field in the middle of the image here appears to be zero, it is in fact roughly 3.6x10 7 N/C, several orders of magnitude smaller than the value at the edge but still positive. This large difference in electric field will lead to much faster growth at the edges. This was followed by a study of an alternating line pattern with lines of width 0.2 mm. A unit of the repeating pattern was modeled with several elements along the length of both the charged and discharged areas. The model used by Mr. Bhaskarapanditha in this simulation is shown in Figure 6-3, with the simulation results in Figure 6-4. The charged area is in the center, with the discharged image areas on either side. Figure 6-1. Solid area printing model (Bhaskarapanditha 2003)

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61 Figure 6-2. Solid area printing model results (Bhaskarapanditha 2003) Figure 6-3. Pattern printing model (Bhaskarapanditha 2003)

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62 Figure 6-4. Pattern printing model results (Bhaskarapanditha 2003) This simulation shows much preferable field effects. The edge effect is much less noticeable, and there is a near-uniform field across the image area, meaning a more consistent transfer of toner in regards to image field. Thus pattern printing offers at least the possibility of an end to the edge effect. The next step would be optimizing the pattern print in terms of both hardware and software for the actual system and testing how it worked when applied. Due to the programming language used to create the cross section images from solid areas, the line widths have a set resolution of 1/72 inches (roughly 0.35 mm), and all line patterns must be based on increments of that resolution. The patterns are created by first creating an image using the part files as usual. The image is then overwritten with a series of white lines. Finally, the outline of the part cross section is traced again in order to maintain part cohesion.

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63 A new analysis was necessary to find the ideal width of both the black lines in the print and the white lines dividing them in order to maximize field and prevent any areas of low field within the solid area. The new finite element analyses followed those previously performed as closely as possible. The insulation layer was modeled with a thickness of 10 micrometers, with a permissivity of 2.6553x10 -11 F/m. The toner layer was specified to have a thickness of 30 micrometers, a permissivity of 3.09785x10 -11 F/m, and a volumetric charge density of .058 C/m 3 The charge deposited on the insulation was specified as 1x10 -4 C/m 2 The bottom of the insulation was specified as a ground, and the top of the toner layer was specified as the developer roller mean voltage of V. These values were all taken from Mr. Bhaskarapandithas thesis. Two sets of analysis were performed, one holding the thickness of the charged area constant and varying the thickness of the discharged area, the other holding the thickness of the discharged area constant and varying the thickness of the charged area. This models altering the white and black line widths in the printed pattern. Presenting the entirety of the resulting data would be tedious and unnecessary. For the purposes of this evaluation, the values of importance were the median field in the charged and discharged regions, which govern powder transfer and image clarity. The strength of the peak values near the edge of the pattern was also of interest, as these would govern the uniformity of the print. The results of the two analyses are shown in Tables 6-1 and 6-2, respectively.

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64 Table 6-1. Results of varying the discharged area width Black Line Width (1/72 inches)White Line Width (1/72 inches)Discharged Center Field (N/C)Discharged Peak Field (N/C)Charged Center Field (N/C)Charged Peak Field (N/C)111.272E+091.276E+09-2.557E+09-2.557E+09211.260E+091.260E+09-2.466E+09-2.473E+09311.224E+091.224E+09-2.542E+09-2.542E+09411.295E+091.295E+09-2.473E+09-2.473E+09 Table 6-2. Results of varying the charged area width Black Line Width (1/72 inches)White Line Width (1/72 inches)Discharged Center Field (N/C)Discharged Peak Field (N/C)Charged Center Field (N/C)Charged Peak Field (N/C)411.295E+091.295E+09-2.473E+09-2.473E+09421.229E+091.229E+09-2.538E+09-2.547E+09431.229E+091.231E+09-2.530E+09-2.616E+09441.229E+091.375E+09-2.530E+09-2.681E+09 The discharged field strength in the center of the line seemed to vary only slightly with changes in the discharged area, with less than a 6% change overall. No change was observed in this value due to varying the charged area. This would indicate that in the range evaluated in the test, this field strength is more or less constant. Under the circumstances, it is always desirable to maximize the amount of the part cross section being printed, so the thickest line would be the best choice.

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65 The peak of the discharged field strength also had little variation in relation to the discharged line width. There was a very slight peak in the thinnest line width, but its strength was negligible. In varying the charged area widths, however, the peaks quickly became noticeable as the white line width increased. This indicates that as the black lines are separated, they act more and more like large solid areas. This would indicate the best prints would come from having thin white lines breaking up the solid area. As for the charged area field strength and its peaks, they were of lesser concern. Had there been a large reduction in this field strength it could have meant that under certain conditions the white area of the print would lose its field strength, possibly resulting in significant background development. This did not occur, but there was a slight increase in field strength magnitude and a significant increase in peak strength when increasing the white line width. This would mean that in printing a larger white line in the pattern would yield sharper, more differentiated lines. This would offset the above disadvantage due to discharged peak magnitude. Experimental Results In order to verify the results of the finite element analysis, an experiment was conducted to test the various characteristics of pattern printing. A particular set of parts was printed multiple times with different patterns as well as with normal solid area printing. The height and mass of the part were measured, and the various prints were ranked in terms of print quality. The print quality rankings were by necessity a subjective measure, but unfortunately there was not a readily measurable metric available to compare the various prints in terms of how well the pattern overcame the solid area printing issue. The subjective quality of the prints was based predominantly on whether and to what degree they overcame the very noticeable gaps caused by the edge effect,

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66 however, so the assessment was based on readily visible and discernable characteristics. In the end, these quality rankings did not diverge greatly from the other metrics regardless. It was decided that the testing pattern would be to vary the black line width between 1/72 and 4/72 inches in order to keep the test space to reasonable bounds. The width of white lines would be varied between 1/72 and the width of a given black line, because it was not desired to depart significantly from a fully dense part. The part was then printed for roughly 15 layers to allow the results of the pattern to sufficiently emerge while minimizing test time. The experimental results are presented in Table 6-3. Table 6-3. Pattern printing experimental results Black line width (1/72 inch)White line width (1/72 inch)Average layer height (inch/print)Average layer mass (g/print)115.5E-045.53E-02215.9E-045.14E-02225.7E-045.30E-02315.7E-045.50E-02326.2E-045.22E-02336.0E-045.19E-02415.6E-045.12E-02425.8E-046.55E-02436.4E-045.72E-02446.5E-046.60E-02SolidN/ A 5.7E-045.63E-02Average:5.9E-045.59E-02Deviation:3.3E-055.27E-03 This amount of data is difficult to analyze simply by looking at it. The best print in terms of the two quantitative metrics was roughly two standard deviations above the average in both measurements, indicating a significant improvement in print quality. Traditional solid area printing was near the average in both metrics, implying that many patterns were improving the printing process. To find the optimal pattern a ranking table was constructed, with a subjective metric added based on visual print quality. An average

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67 of the height, mass, and quality rankings was used to compare the various patterns. The ranking table is presented in Table 6-4. Table 6-4. Pattern printing rank table Black line width (1/72 inch)White line width (1/72 inch)Height RankMass RankQuality rankAverage Rank111159215105229773176103238333491411011810426264323444112SolidN/ 878855531 A 84118 For demonstration purposes, some of the resulting pattern prints are shown below. Some digital editing was done to the images to reduce background print density for better visibility. A print with no pattern is shown in Figure 6-5. A print with a white and black line width of 1/72 inches is shown in Figure 6-6. A print with a black line width of 4/72 inches and a white line width of 1/72 inches is shown in Figure 6-7. Finally, a print with a white and black line width of 4/72 inches is shown in Figure 6-8. The solid circular part is 0.75 inches in diameter. As can be seen in Table 6-4, there are several patterns that produce prints superior to the solid area print. It can also be seen that the very fine patterns did not perform as well as the solid area. From what was seen in the resulting parts it would appear that the fine patterns do not have sufficient gaps between the lines to overcome the solid area effect, and thus suffer the same setbacks, along with an additional disadvantage of only part of the cross section being filled. It is also likely these parts suffered from mechanical failure during fusing, since very thin lines would have difficulty tolerating compaction.

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68 The prints with broader white lines seemed to overcome the solid area issue and print more like lines. This is advantageous in terms of both print quality and mass. In terms of height, it has been known from previous efforts that fine lines tend to collapse during compaction as part height increases. Thus a wider black line yields a superior part in the long run. Figure 6-5. Print with no pattern Figure 6-6. Print with a 1/72-inch black and white line pattern

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69 Figure 6-7. Print with a 4/72-inch black line and 1/72-inch white line pattern Figure 6-8. Print with a 4/72-inch black and white line pattern

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70 There are boundaries to these trends, however. At some point, a sufficiently broad black line will become subject to the solid area problem itself. The benefits of a white line will suffer diminishing value once the black lines are sufficiently isolated to prevent solid area printing issues, and further white line width will merely serve to decrease the amount of printed material. To study the effects of pattern printing over a larger number of prints, as occurs in part building, a group of parts were studied over a printing range of 250 prints. Based on the earlier findings, a pattern of 4/72-inch white and black lines was selected. This included some large solid parts to study the efficacy of pattern printing at overcoming the solid area printing issue. Also included were some parts with small details, a critical test of the pattern printing method as it applies to rapid prototyping applications. The printed parts are shown in Figures 6-9 and 6-10. For comparison purposes, an image of the parts in Figure 6-10 printed without patterns is shown in Figure 6-11. Background printing has again been digitally removed for visibility. Figure 6-9. Pattern printing parts, 250 prints

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71 Figure 6-10. Further pattern printing parts, 250 prints Figure 6-11. Comparison image of parts from Figure 6-10 without pattern printing (Dutta 2002) The results of this test were mixed. Solid area parts continued to build consistently, with no appearance of edge effect. This verified the purpose of pattern printing. Parts with fine detail, however, have significant problems in print quality when the pattern printing method was used. The pattern broke up the fine details, either eliminating them entirely or preventing the parts from surviving the fusing and compaction process. This would indicate that pattern printing should only be used for parts with large solid areas. Conclusions The experimental results indicate that pattern printing can indeed provide a superior part to solid area printing, both qualitatively and quantitatively. From the results it would

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72 appear that a broad black line with a broad white line seems to be the best pattern. It is probable that the current set of experiments did not find the optimum pattern, given that the best results were found at the limits of the test space. However, these results will serve to improve the quality of printing, so they are useful. The experimental results did not entirely agree with the finite element modeling. Increasing the black line width within the test range did result in superior printing. However, increasing the white line width did not appear to cause any edge development. It is possible that the variance in field change predicted by the finite element analysis was so small that its effects were not noticeable, and that the positive effects of stronger charged area field differentiating the black lines in this case was more significant. The printing of finely detailed parts showed a significant problem with pattern printing. The pattern method proved more problematic than useful in this application. To be used with finely detailed parts, as would be necessary in rapid prototyping, the patterns would either have to be made finer depending on the part detail, or they would have to only be applied to parts with large solid cross sections. This would prove difficult in the current software arrangement, but would not be infeasible. Future Work A larger test space would obviously be advantageous. Also, refining the control program in order to allow for finer resolution could allow a better result to be found. Both of these would be too time-consuming for current project goals, however. Another line of research that could prove fruitful would be to study the effects of patterns other than a simple alternating line pattern. A grayscale could be used to counteract the edge effect and yield a uniform part, or a dot pattern might allow sufficient isolation of black areas with a printed area percentage. However, there are any number of

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73 possible patterns, and a better theoretical understanding of the process would be desirable rather than randomly testing patterns to see which work. Also, it would be useful if a fully dense part could be created by printing the normal pattern on one print, and filling in the white spaces on the next print. This was originally planned as part of the pattern printing system, but unfortunately hardware problems with the current system prevented it. There was an issue with the imaging system not returning to precisely the same origin after each print. Thus a subsequent print would be offset by a fraction of the software resolution. After several prints of this the portion of the part where several prints had overlapped would be much thicker than surrounding areas, leading to the same issues as with edge printing. A better-controlled printing system would solve this issue, but would require more time and money than is devoted to this project. This alternating printing arrangement could offset the problems associated with finely detailed parts.

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CHAPTER 7 DESIGN OF AN ELECTROPHOTOGRAPHIC DEVELOPER SYSTEM Introduction The developer system in a printer is the system responsible for transferring powder to the proper areas of the photoconductor drum. A typical development system stores the powder, charges the powder, transports the powder, and transfers the powder to the photoconductor drum. A simplified schematic of a development system is shown in Figure 7-1. PhotoconductorDrumTransferRollerDoctor Blade PowderHopper Figure 7-1. Development system schematic The main components of a developer system are labeled in Figure 7-1. The powder hopper is a receptacle filled with toner powder. The doctor blade is a metering device used to control the thickness of the powder layer being brought out of the hopper, and is often a part of the charging system. The transfer roller serves to move the powder and bring it near the photoconductor drum. 74

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75 Developer System Fundamentals Powder Storage The storage of powder is a very straightforward part of the development process. In general, developers will have a hopper of some variety filled with toner powder. Some contain a stirring apparatus to prevent the very fine toner powder from agglomerating into a solid mass. Many commercial systems will also have specially designed access points to allow for refilling of the cartridge during recycling, and some new developers contain electronic safeguards to prevent unauthorized recyclers from tampering with the cartridge. The main concerns in this stage are that powder be prevented from leaking, and that it be possible to replenish the powder supply when necessary. Powder Charging The proper charging of powder is critical to the electrophotographic imaging process. If powder is not adequately charged, it will not transfer to the image areas. If it is too highly charged, a very thin layer of powder on the image will be sufficient for charge cancellation and the image will be very faint. If the powder is not charged consistently there will be noticeable variations in imaging between prints or even within an image. If powder charges to the wrong sign, there will be background printing in the final result. There are currently three main methods used for powder charging: corona charging, injection charging, and triboelectric charging. Corona charging Corona charging of powder works on the simple principle of subjecting a powder layer to a stream of ions. The physics of corona charging have been covered at length elsewhere in this paper, so they will not be discussed in detail here. The fundamental

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76 problem with corona charging of toner is that powder particles may be airborne in the developer and may then coat the corona wire, preventing it from being effective. Injection charging Injection charging is a very straightforward method for charging a wide variety of powders. The powder particles are exposed to a significant voltage. This is often accomplished by applying a voltage to a metallic foil attached to the doctor blade, which powder must rub against as it passes by. The outer surface of the insulative toner material will take on charge as it rubs against the surface. This is a very effective and popular means for powder charging, with the minor issue of requiring the use of a high voltage power source. Triboelectric charging Triboelectric charging is used in most current-generation printers, often in conjunction with injection charging. In this charging method, electrons jump from one material to another, causing a resultant positive and negative charge on the two bodies. The triboelectric effect occurs between specific materials, so when used in development the toner and triboelectric surface must be chosen carefully. This surface is usually a film on the doctor blade, where it is known the toner particles will rub against the surface. The excess charge on the film can be dissipated by means of a connection to ground. Special charge control agents added to the toner powder cause it to charge triboelectrically. Powder Transport The movement of powder from the hopper to the photoconductor drum is a very important and very difficult step in the development process. For proper imaging, a consistent layer of powder must be moved to the photoconductor drum without spilling. The doctor blade helps to maintain a consistent layer thickness so long as the transfer

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77 roller is initially bringing out a layer thicker than the doctor blade is designed to meter out. There are two main methods currently used for powder transport: magnetic and cascade transport. Magnetic transport Magnetic transport is by far the most popular method for transporting powder. In this method, the toner particles are doped with a magnetic substance, usually an iron oxide compound, and the transport roller has a magnetic core that provides an attractive force for the particles. Either the magnetic core itself or an outer frictional roller revolves, circulating the powder with it. This method of transport virtually eliminates spilling, keeps powder flow consistent, and makes it fairly easy to predict the amount of powder the roller will draw out. There is the added advantage that in the transfer stage, the particles must overcome the magnetic force by electric field force, which greatly reduces the transfer of wrong-sign charged toner. However, there is one notable disadvantage to this method, and that is the requirement of a magnetic material. In printing this means the method is only useful for black toners, and the method is not favorable for ESFF because it introduces significant restrictions on the toner material. Cascade transport Cascade transport is so named because in the very early days of electrophotography, images would be developed by pouring or cascading charged toner down a plate with a latent charge image. Toner would stick to the image areas due to electrostatic force, forming an image that could be transferred for permanent printing. In a modern system this process is a bit more complex. Toner is brought out of the hopper by mechanical force, usually friction, by a roller. A layer of the toner on the transfer

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78 roller then passes near the photoconductor drum, where particles are attracted to the properly charged areas. Because there is no adhesive force between the transfer roller and the toner, the doctor blade can knock off more powder than it is meant to meter, causing uneven prints. There are also unavoidable spilling problems. This development method is necessary for color printing with electrophotography, but with ink-jet printers becoming comparably fast to laser printers the drawbacks of the system are preventing it from being used. This system is needed for ESFF using a traditional drum printer, however, because it can develop arbitrary powders. Powder Transfer The final step of the development process is to transfer powder to the image on the photoconductor drum. The quality of this process in a given system is fundamentally a balance of forces. There is the electrostatic force pulling the charged particles towards the image, the attractive forces which draw the particles towards the surface to which they are most closely adhered, and the attractive forces between particles. Ideally, there would be a strong tendency for particles to stay on the transfer roller due to attractive forces except where drawn off by electrostatic effects. This produces a clear image with minimal transfer in the background areas. This is easily accomplished in magnetic powder transport because of the strong magnetic attractive force. The charged powder is caused to jump on and off the roller by an AC field, creating a cloud of powder around the roller. The magnetic strength of the roller and the AC voltage can be varied to optimize printing. Cascade transport suffers more difficulties in this area. Because of the high surface area to density ratio of most toners, especially polymer toners, the electrostatic and van der Waals forces are orders of magnitude larger than forces pertaining to mass. This

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79 means that these powders will not be firmly adhered to the transfer roller, and that interparticular attraction will be very significant. For this reason, cascade systems will have significant background printing. Also, if the toner from previous prints is not adequately cleaned from the photoconductor drum, it can act as a seed to attract powder in subsequent prints due to the interparticular attraction. Evolution of ESFF Developer Design In past work with the ESFF testbed, it has been necessary to use standard printer toner to build parts because of the lack of a system to print other powders. This is disadvantageous, in that the toner powder used in laser printing produces brittle parts, and that simply printing small plastic parts would not be a significant advancement in the field of rapid prototyping. For reasons of construction simplicity and flexibility in terms of which powders would be printed, it was decided to use a design based on cascade transport and injection charging. This combination allows for development of nearly any insulative powder. The first developer design is shown in Figure 7-2. The first design for this developer was a very simplistic device involving a powder hopper, a developer roller, and a cantilevered doctor blade actuated by a screw plate. Plastic pieces were built to encase the transfer roller on the sides and bottom. A press fit piece in one side allowed the roller to be removed laterally through a large opening. The roller itself pressed against the photoconductor drum directly. It was believed this would balance forces causing powder to adhere to the surfaces, leading to better development. The LaserJet 4 photoconductor drum is roughly 1.2 inches in diameter.

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80 Photoconducto r Drum Developer Roller Screw Plate Powder Hopper Doctor Blade Figure 7-2. Cross-section of original developer design This design suffered from a number of shortcomings. The plastic casing was not adequate to prevent leaks. The doctor blade was not rigid enough to maintain a consistent powder flow across its length. Finally, the direct contact between the transfer roller and the photoconductor drum led to powder being sheared off at the intersection of the rollers, causing an unacceptable spillage rate. The bottom lip of the developer was also insufficient, because it sat too high and too close to the transfer roller to catch any powder which spilled off the bottom side of the roller due to gravity. The distance between the roller and the mouth of the powder hopper often caused powder flow to cut off, but was necessary for the cantilevered doctor blade. Measures were taken to try and correct these problems within the context of the same basic design. The second design of the developer is shown in Figure 7-3. The plastic casing had foam gaskets added to reduce leaking. The roller was assembled by

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81 sliding it into narrow, baffled fittings. The bottom lip was brought as close as possible to the photoconductor drum to catch any falling powder. Offset rollers were added to provide a small gap between the transfer roller and the photoconductor drum, thus preventing spilling due to powder shear. The doctor blade was changed to a leaf-spring actuated design wherein powder would have to slide past the blade over a longer distance, leading to more consistency regardless of particle size. Also, small protrusions were added to the side of the casing which were meant to keep powder from reaching the side connections, further reducing leaking. PhotoconductorDrum Develo p er Roller Doctor Blade Leaf Spring Powder Hopper Figure 7-3. Cross section of improved developer design

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82 This design suffered from some of the same problems as the previous design, but showed improvement in many areas. Powder leaking from the casing itself was greatly reduced, almost to the point of being eliminated. The offset rollers used were not consistent enough in providing a gap and allowing proper rotation of the roller, and had to be abandoned. This reintroduced the shearing problem seen before. The extended bottom lip was still not able to catch all falling powder. The doctor blade had improved consistency, but was more difficult to actuate if a different flow rate was desired. The side protrusions added a great deal of friction, making the developer difficult to drive. It was clear at this point that a different design path was needed. This resulted in another design, shown in Figure 7-4. Successful ideas like gaskets and baffled fittings were kept and expanded, with almost all fittings now being baffled and gaskets added wherever desirable. A printing gap was included to prevent spilling due to shearing of powder in the printing interface. Instead of offset rollers, the gap in this system would be provided by tapes on a metal developer roller, providing a very thin and very consistent gap. A two-roller design was introduced, in hopes that by including an initial electrostatic transfer across a gap, the amount of powder brought out by the system could be reduced, and that the powder could then be effectively recirculated. It was also hoped this would give greater control over the charge density on the powder that would form the toner image. This final design greatly increased the complexity of the process. The doctor blade opening, the gaps between the two rollers and between the second roller and the photoconductor drum, and the charge voltage can all be varied. This is advantageous, in that it gives a great deal of control over the transfer process. However, there is a

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83 significant drawback in that these variables must be controlled precisely and consistently in order to maintain proper development. Photoconducto r Drum Secon d DeveloperRoller FirstDeveloperRoller Doctor Blade Powder Ho pp er Figure 7-4. Cross-section of two-roller developer design The doctor blade gap is on the surface a straightforward control system. The wider the gap, the more powder is brought out. However, there are complications in controlling this aspect of the developer. Because this developer system has two transfer stages, it will be inherently less efficient than a single-transfer developer design. Therefore, enough powder must be brought out to compensate for the loss in the process. If too much

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84 powder is brought out, however, it will not be possible to recirculate all the excess powder, and the device will clog. Furthermore, it is critical that the amount of powder brought out be uniform. To achieve uniformity, precise control of the gap is necessary, as are rigidity in the doctor blade and manufacturing tolerances. The transfer gap between the two developer rollers serves as a control over the charge density in the powder presented for final development. Powder will be attracted across this gap by induced field on the second metal roller, caused by the field between the developer voltage source and the grounded photoconductor drum. This field will cause the metal roller to take a median charge state between the two rollers, attracting powder from the first roller but being less attractive than the photoconductor drum. The larger the gap between the developer rollers, the higher the charge in the transferred powder must be to be attracted across the gap. Thus a small gap will serve to screen out particles with the wrong charge sign, or with insufficient charge. If the gap is made too large, only highly charged particles will be transferred, which will decrease the transfer mass both as a matter of charging statistics and because a small mass of highly charged particles can cancel out a large field. If the gap is too small, a larger mass of particles will be transferred, and the layers of powder on the two developer rollers may contact each other. Both of these trends could result in clogging of the developer. The transfer gap between the second roller and the photoconductor drum is also of critical importance. This gap will control the amount of powder transferred to the toner image. The larger this gap is, the less powder will be transferred. If the gap is too small, however, there may be shearing of powder between the two rollers. Furthermore, the amount of powdered carried over from the first transfer is also important, since the

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85 thicker the layer of powder on the second developer roller the larger the final gap must be to prevent shearing. The final control characteristic is the charging voltage. This voltage has two effects, first in controlling the amount of powder charge, and second in determining the field present between the photoconductor drum and the developer. As far as powder charging, a higher voltage will result in a higher average charge density in the toner. As mentioned earlier, to maximize the transfer mass it is necessary to charge the powder to a critical threshold value, as too little charging will result in an inability to transfer, and too much charging will result in a small powder mass being adequate to cancel the field. Thus from the charging perspective, there is an optimal voltage. In establishing the overall field across the entire development process, it would be ideal to have an arbitrarily high voltage, since this will maximize the field and with it the mass of toner transferred. Experimental Analysis of the Two-Roller Developer Once the system was built, the next step was to analyze the performance of the developer. The system would first be tested on the charge-measuring unit (Gokhale 2001). The unit allows the testing of charge and mass, such that the performance of a particular toner powder or developer system could be measured and optimized. If this testing was successful, the developer would then be used in the ESFF testbed itself, where it could be used to actually deposit imaged layers. Some success was seen in charging and transferring powder. Preliminary testing with nylon powder showed that the device could transfer a powder layer across the printing gap onto a grounded drum after charging. This showed the capacity for electrophotographic development of an arbitrary insulative powder in its most basic form.

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86 There were several major problems with the design, however. The complex design was difficult to manufacture and assemble properly, making for improper fits and uneven gaps. There was significant friction in the system, which made driving the developer difficult and caused some jumping during motion. The powder flow was uneven across the length of the developer, meaning that any toner images produced by the developer would be badly uneven across their area, leading to deformation of cross sections as well as significant difficulties in the printing of multiple layers. The gap between the rollers proved difficult to control to sufficient resolution. When the gap was too small, there would be additional friction from the rollers touching and the powder between them getting compacted, as well as an overabundance of powder being brought out. When the gap was too large, powder would not transfer to the second roller, preventing printing. All in all, even after many enhancements the design of an effective cascade developer proved unmanageable. The underlying difficulties of cascade developer design, which plague even professionally manufactured systems, could not be overcome in the lab. Conclusions While no cascade developer proved useful for placement in the ESFF testbed for part building, the developers did yield many insights into the printing process. Powder leakage could be ignored in charge measurement tests, and the final generation of single roller developer found use in a new charge measurement apparatus designed by Ajay Das. Early testing also disproved a notion of field transfer to the grounded photoconductor drum. It was demonstrated that surface charging of the drum was needed for transfer, not just a grounded backing. This led to a reworking of the charge measurement system to accommodate surface charging.

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87 Although the developers performed poorly, this is not completely attributable to their designs. These developers were manufactured on a fused deposition modeler in order to produce a test part faster and to reduce costs. As such, the manufacturing tolerances were not as rigidly controlled as they would have been if the parts had been machined. Most parts were also plastic, which greatly reduced strength and rigidity. In the long run, a method for developing new powders is critical to the project. Once it was seen that conventional cascade development would not be capable of achieving satisfactory development, it was decided to fundamentally alter the ESFF testbed to accommodate a new development system that would seek to overcome these new challenges. This design is discussed in Chapter 8.

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CHAPTER 8 DESIGN OF A NEW ESFF TESTBED Reasons for New Design As mentioned in Chapter 7, there has been a failure to achieve a system for printing arbitrary toner powders in the ESFF printing system. The cascade developer technology is too simplistic to achieve the desired goals in this application. Powder spilling from the cascade arrangement could jam moving parts of the system as well as cause heavy background development on the build platform. The uneven flow of powder would cause an equally uneven toner layer, which has been shown in Chapter 5 to heavily impair part building over many layers. A new developer concept is needed to circumvent these difficulties. Furthermore, the current testbed system has problems in the area of transfer already mentioned. Small variations in part thickness or the platform surface can greatly impact the electric field used for transfer, preventing the even building of a part. Variations in the charge deposited on the part surface can have this effect as well, which is a cause for concern since it is impossible to deposit charge by corona without some degree of variation. Finally, there are practical reasons to move to a new design. The current ESFF testbed relies on a heavily modified printer as described in Chapter 4. When parts break or a change in the system setup is desired, there is a great deal of intensive work that goes into adapting the printer and control system. Debugging such a complex system is time-consuming and difficult. The learning curve for new members of the project is also a 88

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89 problem, requiring months to understand the workings of the system. The printer used is now outdated, and the difficulty in modifying a new printer to the purpose would shut down research for some time. There is also the economic consideration of maintaining a stock of parts. In the end, the only reason to use the printer is for its imaging system, which would be difficult to construct in the lab. Design Concept To overcome the aforementioned problems, a new design was formulated for the ESFF testbed. A conceptual schematic of this design is shown in Figure 8-1. Y Build Platform Developer Photoconductor Plate Cleaner LaserJet 4Ima g in g S y stem Charge Roller X Figure 8-1. Conceptual schematic of the new ESFF testbed The current two-axis motion system would be used, but instead of moving the printing platform it would be attached to a photoconductor plate. The plate would move in the X axis of the figure. The plate would also be moved in the Y axis to compensate for part height on the build platform. The photoconductor plate would first move over a charge roller, depositing charge on its surface. Next it would pass over the imaging system, selectively discharging the part image. Then the plate would move over the developer, picking up powder electrostatically. The plate would then move over the build

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90 platform and lower itself for transfer. After transfer the plate would scrape off excess powder using the cleaner, then return to begin another cycle. The new design would abandon the use of an entire printer, and would instead take the imaging unit from the current LaserJet 4 printer and control it directly. This would reduce part stocking expenses and greatly reduce the complexity of the imaging system. The developer would now print vertically onto the platform, instead of horizontally. This would allow the use of cascade technology that brings out powder by friction, only now gravity would be advantageous, acting in the same way magnetic force does in commercial developers. This could solve powder spilling problem and even allow the use of a powder cloud for development. The transfer of the imaged powder to the build platform could be accomplished by charge deposition on the part surface, as in the current system. Another method would be repulsion using a back-plate behind the photoconductor system. This would ensure that the field will be nearly constant each print, with no dependency on part height. Cleaning could be accomplished simply enough using a flexible doctor blade. The mechanism for fusing remains open at this point. A heated compaction plate like the one currently used would serve the purpose for plastic parts, or an ultrasonic or electric discharge system could enable direct fusing of metal powders without the need for post-processing. The Photoconductor Plate The use of a plate photoconductor imaging system has several benefits. First, it allows for translation during the printing process instead of rotation. This spreads the various components of the printing system out, making design simpler as the components no longer need to be extremely compact. This is a reversion to earlier electrophotographic

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91 technology, because the advances developed in the technology to make printers smaller and faster are not advantageous in the current application. Another advantage of the photoconductor plate is in transfer to the build platform. An entire layer can be imaged, then deposited at once. This allows the use of the repulsion method mentioned earlier. In a photoconductor drum, one part of the drum is involved in charging, one in imaging, one in development, and one in transfer, all at the same time. For this reason, the metal cylinder of the drum must be grounded, as any other field effects on the drum at any point would effect all parts of the process. In the plate system, the back-plate can be grounded during the charging, imaging, and development steps. Then, when the plate is brought over the build platform, the back-plate can be electrified to repulse the charged powder uniformly over its surface. This method would drastically improve and simplify the process. As seen earlier, the current transfer stage is too complex to be adequately controlled. Using the repulsion technique, small variations in factors like the build platform surface and the part thickness would no longer be an issue. The ability to evenly deposit charge on the part would also cease to be a limiting factor. The transfer process would be the same for all stages of part building, and would rely only on the evenness of powder image deposition on the plate and the regularity of the photoconductor layer. There is one important consideration in the design of the photoconductor plate, and that is the photoconductor material of choice, amorphous selenium or an organic photoreceptor. There are several considerations to be taken into account in this choice. The first is commercial availability. It would be impractical to manufacture the plates in the lab, because the deposition equipment is expensive. Organic photoreceptor

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92 materials are more widely available than amorphous selenium, which is considered an outdated material for most commercial applications of electrophotography. Another important factor is dark decay. The time for which the charged image will remain on the surface is very important. Organic photoreceptors have a very short period of decay, while amorphous selenium can hold an image for considerably longer. The importance of dark decay is ameliorated by the fact that the charging, imaging, and development can occur very close together. Once the toner powder is deposited into an image, the decay is no longer a matter of since discharged area printing is used. The final consideration is the spectrum of light used to image the plate. Organic photoreceptors are imaged with light in the ultraviolet spectrum. Because this is the spectrum of light used in the LaserJet 4 printer, use of an organic photoreceptor would ensure proper imaging. Amorphous selenium has a very broad spectrum of light it can accept, and thus would likely function with the LaserJet 4 image system as well. There is a significant drawback to the wide light-spectrum of amorphous selenium, however. An amorphous selenium plate would need to be protected from room lights during printing, as visible light could also discharge the plate. The Developer System A schematic of the new developer concept is shown in Figure 8-2. The new developer system is, in appearance, very similar to the previous design. A single roller brings out powder by friction. The roller has a doctor blade and a recirculation extension that catches excess powder and brings it back into the developer. A pressure plate holds powder against the roller.

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93 T o n er Pressure Plate Recirculation Gap Roller Doctor Blade Figure 8-2. Conceptual schematic of new developer Unlike the previous designs, the problem of powder spilling is no longer a substantial issue. The powder is held to the developer roller by gravity in the same way magnetic mono-component development uses magnetic attraction with iron particles in the toner. Also like magnetic development, the powder can be formed into a cloud using a DC-biased AC signal, because there is now a force drawing the toner back onto the roller. Charged powder will hop on and off the roller as the field changes, making it easier for the charge image on the photoconductor plate to pick up powder and allowing fine tuning of the transfer. Powder recirculation is easier to achieve in the vertical developer for two reasons. First, gravity pulls the powder down into the recirculation opening, rather than the powder having to be moved through this opening by friction. Second, the lip of the opening is no longer very near the photoconductor surface, so the opening can be widened significantly to ensure that powder does not spill beyond the lip. If any spilling did occur, the powder would spill away from the photoconductor plate and a receptacle could be provided for catching spilled powder if needed, greatly reducing the problems associated with this issue.

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94 Another major difference is the doctor blade. In the new design, the powder would not require the same degree of metering. In the horizontal developer system gravity caused the powder in the hopper to flow out wherever possible, and only the doctor blade held it back. In vertical development, gravity will hold the powder back from flowing out, and only the powder that is carried out by friction with the developer roller will be brought out. This means that the powder flow should be more uniform, as the friction with the roller is much more regular than the opening a doctor blade could produce. The doctor blade will still be used in charging of the powder, however. A major challenge of the new system is ensuring that powder is constantly provided to the developer roller. In the previous developer, gravity would pull the powder against the roller. In this case, however, the force will have to be provided. A spring-loaded or actuated pressure system could serve the purpose of holding powder against the roller. This system will have to be designed to keep pushing the powder towards the roller as the powder level decreases during printing. The Imaging System The imaging system is taken entirely from a Hewlett-Packard LaserJet 4 printer. This system uses an ultraviolet laser to discharge the photoconductor. The laser is pulses on and off with a maximum resolution of 600 dots per inch. The scan moves along a line as it is reflected by a polygonal mirror, which is rotated by a stepper motor. At the start of each line, another mirror bounces the laser onto a photosensor, which acts in a manner equivalent to a home switch on a motor. This alerts the control system when the laser scan is at a specific position, allowing the print image to be synchronized from line to line. This signal also alerts the system when to switch the laser signal from one line to

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95 another (Hewlett-Packard 1996). A schematic of the LaserJet 4 imaging system was shown in Figure 3-10. The practical advantages of maintaining a stock of only one part of the printing system were outlined above. It is also much easier to document one relatively simple component for future training. The use of only the imager also gives more control than was previously available. Whereas before all control over the final image was through a software interface written without consideration of the current application, direct control of the imaging system allows for the creation of a new software interface specific to the process. This could allow an easier change to the resolution of a print, which caused problems in the pattern printing tests. It could also allow for the creation of simple gray-scaling algorithms that might allow the benefits of pattern printing without some of the drawbacks. The direct control aspect is also problematic however, in that all control software will have to be written directly. When the printer was used as a whole, the imaging system existed as part of a black box. A predefined command was given to print an image. The formatting of this image was set up through the printer driver software, passed to the formatter, and turned into control signals by the onboard control system. The project-written software needed only create an image. For early testing the control system can be set up to simply print a given pattern that remains the same for each line. For real freeform fabrication, however, the image created by the slicing software will have to be processed into a series of image signals. Imaging System Analysis The first step to controlling the imager directly was to analyze input and output signals. The imager system actually has three control components. The first is for the

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96 beam detection sensor, the second is the motor control card, and the third is the laser control card. The imager with the control connections is shown in Figure 8-4. The numbers and markings shown are those used on the imager printed circuit boards. Mirror Polygonal Mirror on Stepper Motor Beam Detection Sensor Laser Diode 1 2 3 4 5 Feedback Motor Enable Switch 24V Supply Speed Control Ground Supply 123 5V Supply Sensor Feedback Ground Supply Ground Supply PD LD GND Laser Diode Photosensor Diode Figure 8-4. Imager control diagram The beam detection and motor control connections are separate at the imaging unit, but are joined together at the DC controller. The analysis of the signals was performed with an oscilloscope, checking the behavior of the circuit during different stages of printing with the components attached or not. When an understanding of the component was believed to have been reached, control was attempted, and the theory of operation was refined. The beam detection sensor is the simplest of the components. The device has three connections. Two of these are power connections for the ground and five volt bus lines

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97 used by the sensor. The third connection is the sensor output. The sensor output is at five volts while inactive, and drops to ground when the laser strikes the photosensor. During printing in the LaserJet 4 the frequency of the sensor signal change was observed to be approximately 1.1 kHz. This frequency is determined by the speed of the stepper motor driving the polygonal mirror. The motor control signal is also straightforward. The power connections in this device were a ground and 24-volt line. This device has three signal lines. The first is the stepper motor speed control, which delivers a series of controlled pulses. The frequency of these pulses determines the motor speed. In the LaserJet 4, the pulse speed on this line was measured as roughly 3 MHz. Another signal is the motor enable switch, which turns the motor on and off. This switch is active low. The final signal is a motor ready feedback, which gives a low signal once the motor has finished accelerating. This allows for proper timing, and also serves as a validation that the device is functioning correctly. As mentioned, these two connections are joined at the DC controller. For documentation purposes, Table 8-1 lists the connections as numbered on the DC controller circuit board. Table 8-1. DC controller connections chart PinInactive statePrinting StateFunction10 V0 VGround bus25 V5 V with 50 s pulse to ground at 1.1 kHzBeam sensor35V5 V5 V bus40 V0 VGround bus5Same as print5 V pulsing to ground at 3 MhzMotor speed control624 V24 V24 V bus75 V0 VMotor enable switch85 V0 V once motor has acceleratedMotor ready feedbackBeam DetectionMotor Control

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98 The control of the laser is much more complex. There are seven connections to the laser control card. Testing showed early on that it would be prohibitively difficult to use the trigger pattern for this card. However, the laser diode itself can be controlled directly without using the card as an intermediary. It was necessary to determine the control signal pattern from the control card, however. This was accomplished by printing a variety of pages, and using the signal on the card to determine the control parameters. Of interest were the active and inactive voltages for the laser diode, and the frequency of the control signal. The voltages were easily determined as two volts to activate the laser and a ground connection to turn it off. The control frequency was determined by printing a series of lines. By observing the on and off patterns that corresponded to the lines in the images, it was found that one inch of image width corresponded to 90 microseconds of on time for the laser. Given the operating resolution of 600 dots per inch, the control frequency was found as shown in Equation 8.1. MHz 67.6ss 101sinch901 inchdots 6006controlf (8.1) There is a simpler method for control in the case where the synchronization is handled as part of the control system. The laser control circuit is connected to a laser diode. This connection is very simple, having only three pins. These pins are labeled LD, PD, and GND. This is a common control system for laser diodes (Power Technology 2003). The GND pin is a connection for the circuit ground. The LD pin is a connection to the laser diode itself. The PD pin is a connection to a photodiode. This photodiode provides feedback and can be used to adjust the current of the laser diode to regulate brightness. In the LaserJet 4 the PD pin mirrored the feedback signal described above.

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99 Imaging System Control With the workings of the imaging system analyzed, the next step was to construct a control system using the Galil controller. The output and input signals would be used to synchronize the timing of the system. The laser scan image would be a very simple predetermined on/off pattern. The control would be verified by measuring the output at the beam detection sensor. A flowchart of the control architecture is shown in Figure 8-4. Switch on five volt andground signals Set motor speed controlto 3 MHz Enable motor and waitfor acceleration Send control signal tolaser Use beam detect sensorto verify function and asa switch for line image Figure 8-4. Imaging control architecture In testing, control of the laser system for imaging was confirmed. When the laser was set on, the beam detection signal had a pattern of peaks at 1.1 kHz, as in printing. This confirmed that the laser was on and that the motor control was indeed operating at the same speed as in printing. When the laser was set off, no signal was seen on the beam detection sensor, confirming that the previous results were not a misunderstanding. As

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100 mentioned, the laser switching frequency is most likely well below that needed for high-resolution imaging. The motor speed is controlled, however, so the scan rate could be slowed down to match the laser switching frequency. The problem with this approach is that the dark decay rate of the organic photoconductor used in this application would not allow imaging at a very slow pace. For the moment this is not an issue, because the Galil control does not allow accurate high speed switching regardless. The final test was to use the printer equipment to image in toner, allowing a visual verification of control. For this to occur, the printer motor that drives the photoconductor drum, developer, and paper feed system would have to be controlled. This is a simple matter already accomplished for use in the charge measurement apparatus described in Chapter 4. High voltages for various parts of the electrophotographic system must also be provided. These voltages are known and documented as well (Zhang 2001). The imaging system control can then be tested by attempting to print pure black or white, or by sending regular signal to the laser. This would demonstrate that the current control system removes the printer as an uncontrolled black box. This test proved successful. The control system was used to operate the printer, producing imaged pages. The Galil control lacks the speed to synchronize the output signal with the beam detection sensor feedback, but controlled imaging was still possible. First, a full black and a full white page were printed to demonstrate that the laser was in fact being controlled. Two high-frequency signals were sent to the laser switch, creating distinct random patterns on the page. Future Work With the imaging system control demonstrated, several additional steps are needed to finish the new testbed. The vertical developer system must be designed, built, and

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101 tested. The photoconductor plate must be obtained. A transfer system must be decided and developed. Fusing will still be needed, and will have to be implemented as well. Finally, a cleaning device must be constructed. These steps will mark the construction of the system. The software and control system needs work as well. The motion control system can be accomplished with minor alterations to current equipment and software. The imaging process itself will require new software as well. As mentioned, the Galil control system does not have adequate speed to control high-resolution imaging, or even for proper synchronization of the image signal with the beam detection feedback. A microprocessor or control card capable of high speed switching will be needed. A more difficult part of the system will be the software to turn computer models into a stream of control data. This will require substantial software development.

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CHAPTER 9 CONCLUSIONS AND FUTURE WORK Conclusions Many conclusions can be drawn from the research presented in this thesis. The conclusions will be divided into those drawn from system modeling, pattern printing, developer design, and the new ESFF testbed design. System Modeling The results of the modeling process showed that it is possible to continue building a part indefinitely with corona surface charging so long as the part is sufficiently discharged. However, many factors can adversely impact the uniformity of the print. Irregularities in the substrate adhesion to the build platform will cause variations in the transfer of powder. Irregularities in the part surface will cause a decrease in the amount of powder transferred to subsequent layers. This is a very troubling result in that irregularities always occur, and this shows these irregularities will very quickly degrade part quality. Pattern Printing On the whole, pattern printing was successful at eliminating the problems associated with edge development. Printing was improved for solid area cross sections in terms of quality and average build rate. However, in printing parts with fine features there were significant problems related to the pattern printing method. Pattern printing broke up these features to such an extent that they did not survive the fusing process. Thus it 102

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103 would appear that pattern printing is only useful for specific parts, or at the least requires improvements to make it generally applicable. Developer Design Unfortunately, the current design concept of a cascade developer built around the LaserJet 4 printer was not only a limited success. The research did provide a basis for charge measurement testing of new powders. The possibility of printing these powders was also demonstrated. The developer systems were not sufficiently usable to be put into use, however. A far better understanding of developer function was attained, which will be very useful in continued developer design for the new ESFF system. New ESFF Testbed The new ESFF design concept seems to solve many of the problems with the current system. The developer will have gravity in place of magnetic force to prevent powder spilling and allow the formation of a powder cloud. The use of only the imager from the LaserJet 4 printer will decrease the complexity of the system greatly, and reduce overhead costs associated with stocking large numbers of spare parts. The imager control testing showed that the laser and motor could be controlled as desired. The feedback signals could also be interpreted to analyze the behavior of the device. Future Work There is still much work to be done in ESFF research. This section will be divided as before. System Modeling The problems due to irregularities in the part surface are not easily resolved, but the causes of these irregularities can be addressed. A better method for fixing the substrate to the build platform would be beneficial. Another possible improvement would be a means

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104 for leveling the part surface after each print. This was the purpose of the compaction that takes place during fusing, but clearly this is not sufficiently effective. It is necessary to surround the part in a secondary powder that can be separated in post processing, thus allowing a compaction pressure capable of leveling the surface. Pattern Printing There are many several improvements that could be made to the pattern printing method. A software change could enable higher resolutions, which in turn would enable finer control over the white and black line widths in the pattern. Software could also be used to select parts that are appropriate for patterns. Finally, hardware improvements, especially with direct control of the imaging system, could resolve the issue preventing alternating patterns from being printed, which would eliminate many of the issues involved. Developer Design The knowledge gained in developer design can be applied to new designs to be used on the revised ESFF testbed. The problems with powder leakage and spilling provide insight into how to take advantage of the vertical transfer direction. The knowledge gained in charge measurement testing can also provide valuable information about the charging characteristics of various powders. Much information has also been learned about powder flow that can be applied to the new system. New ESFF Testbed There is much work left on the new ESFF testbed. With the imaging system controlled, the next step is to develop a fast switching system that can be used to synchronize the imaging process. This will then need to be integrated into the SolidSlicer control program so that actual parts can be imaged. The developer for this system needs

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105 to be designed and tested. A fusing system is still needed, and there are improvements to be made in the transfer process as well. Overall, the new ESFF testbed is still in its very early stages, but the design holds great promise for the future. Overview Many advancements have been made in ESFF technology. The system is now more capable of printing parts than previously, and is much closer to a working rapid prototyping system. Despite the improvements, several outstanding issues remain. Transfer irregularities due to part height variations pose a serious problem that is not easily solved. The inability to print new powders is also a serious limitation to the technology. It remains to be seen how the new ESFF testbed will be impacted by these issues, and what new issues will be raised. However, ESFF technology is advancing far beyond where it has been in the past.

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APPENDIX CODE FOR MATLAB EFFICIENCY SIMULATION % efficiency_simulation.m % Copyright James Fay, 2003 % % Uses hard-coded parameters to compute and plot efficiency for an electrostatic transfer % process. dp = 0.25; %% paper thickness, mm da = 0.10; %% air irregularity, mm di = 0.01; %% insulation thickness, mm dl = 0.02; %% initial drum layer thickness, mm dc = 10.16; %% corona gap, mm dg = 0.05; %% printing gap, mm kp = 2; %% paper dielectric ka = 1; %% air dielectric ki = 3; %% insulation dielectric kt = 3.42; %% toner dielectric V_platform = 1000; %% platform voltage, V V_corona = 5000; %% corona voltage, V Ec = 50; %% critical transfer field strength, V mm^-1 e0 = 8.85e-18; %% permissivity of free space, C^2 N^2 mm^-2 rho_l = -7.28e-9; %% charge density in drum toner, C mm^-3 rho_c = 2e-6; %% corona gap charge density, C mm^-3 %% Now establish a vector of values for fused toner charge density as a simulation variable num_steps = 500; %% number of simulation values rho_max = -9e-5; %% maximum charge desnity magnitude, C mm^-3 d_rho = rho_max/num_steps; %% step magnitude, C mm^-3 rho_t = 0:d_rho:rho_max-d_rho; %% fused toner charge density, C mm^-3 %% Initialize simulation parameters num_prints = 500; %% total number of prints in simulation 106

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107 print_num = 1:num_prints; %% axis vector for graph height = zeros(num_prints, num_steps); %% Perform the simulation and store part heights as a fucntion of the print number and fused toner charge density for i = 1:num_steps df = 0; %% fused powder thickness, mm, initialized for each curve for j = 1:num_prints sigma_t = 0; sigma_t = (rho_c*dc*dc)/(2*ka); sigma_t = sigma_t + (e0*V_corona); sigma_t = sigma_t ((rho_t(i))*df*((da/ka)+(dp/kp)+(df/(2*kt)))); sigma_t = sigma_t / ((da/ka)+(dp/kp)); M = (df/kt)+(dp/kp)+(da/ka); N = (df/(2*kt))+(dp/kp)+(da/ka); P = (di/ki)+((dl+df)/kt)+((dg+da)/ka)+(dp/kp); eff = 0; eff = (e0*V_platform)+(N*df*(rho_t(i)))+(P*ka*e0*Ec)+(M*sigma_t); eff = eff/(rho_l*dl); eff = eff + ((1+(2*dl)+(2*df))/(2*kt))+((dg+da)/ka)+(dp/kp); eff = eff/(P-((ka-(kt*dg))/(ka*kt))); df = df + (eff_norm*dl); %% update part thickness height(j,i) = df; %% store thickness to matrix end end %% Now display the results as a surface plot mesh(rho_t,print_num,height/25.4) title('Part height as a function of number of prints and charge density in fused toner') xlabel('Charge density magnitude in fused toner (C mm^-3)') ylabel('Print number') zlabel('Part height (inch)') colormap(gray)

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LIST OF REFERENCES Bhaskarapanditha, Sivakumar V., Solid Slicing and Electrostatic Analysis for Electrophotographic Rapid Prototyping Machine. MS thesis, University of Florida, Gainesville, Florida, 2003. Carlson, Chester F., Electrophotography, US Patent 2297691, 1942. Cooper, Kenneth G., Rapid Prototyping Technology: Selection and Application. Marcel Dekker, New York, New York, 2001. Diamond, Arthur S., Handbook of Imaging Materials. Marcel Dekker, New York, New York, 1991. Doumanidis, Charalabos and Yuan Gao, Mechanical Analysis of Ultrasonic Bonding for Rapid Prototyping. Journal of Manufacturing Science and Engineering, Volume 124, Pg. 426-434. May, 2002. Dutta, Anirban, Study and Enhancement of Electrophotographic Solid Freeform Fabrication. MS thesis, University of Florida, Gainesville, Florida, 2002. Gokhale, Samit, Study and Implementation of Electrophotographic Solid Freeform Fabrication and Charge Measurement Apparatus. MS thesis, University of Florida, Gainesville, Florida, 2001. Hewlett-Packard, LaserJet 4 Printer Manual. Hewlett-Packard, Boise, Idaho, 1996. Hirakawa, H., and Y. Murata, Mechanism of Contact Charging Photoconductor and Insulator with DC-biased Conductive Roller. IEEE, 1995. Kasper, G. P., and J. W. May, Conductive Magnetic Brush Development, US Patent 4076847, 1978. Keithley Instruments, 6517A Electrometer Manual. Keithley Instruments, Cleveland, Ohio, 1995. Kochan, D., Solid Freeform Manufacturing: Advanced Rapid Prototyping. Elsevier, Amsterdam, New York, 1993. Kumar, A. V., Solid Freeform Fabrication Using Powder Deposition, US Patent 6066285, 2000. Nelson, K, Injection Charging of Toner, US Patent 4121931, 1978. 108

PAGE 122

109 Power Technology, Inc., Pin Configuration for Common Laser Diodes, http://www.powertechnology.com/LDINFO/PDCONFIG.ASP?PDType=LDC+to+PDC July 31, 2003. Schaffert, R. M., Electrophotography. Focal Press, New York, New York, 1975. Schein, L. B., Electrophotography and Development Physics. Springer-Verlag, New York, New York, 1988. Zhang, Hongxin, Design and Implementation of a Testbed for Electrophotographic Solid Freeform Fabrication. MS thesis, University of Florida, Gainesville, Florida, 2001.

PAGE 123

BIOGRAPHICAL SKETCH James Fay was born in Pensacola, Florida, in 1978. In 2001 he received a Bachelor of Mechanical Engineering degree from the Georgia Institute of Technology. Following this degree he began research on electrophotographic solid freeform fabrication at the University of Florida. 110


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ELECTROSTATIC ANALYSIS OF AND IMPROVEMENTS TO
ELECTROPHOTOGRAPHIC SOLID FREEFORM FABRICATION













By

JAMES EDWARD FAY JR.


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2003

































Copyright 2003

by

James Edward Fay Jr

































Dedicated to my family and friends.















ACKNOWLEDGMENTS

I would like to thank my advisor, Dr. Ashok Kumar, for his help and advice in this

study. I would also like to thank my committee members, Dr. John Schueller and Dr.

John Ziegert, for their assistance in preparing and evaluating this thesis. I appreciate all

the assistance and guidance I have gotten from my fellow researchers at the Design and

Rapid Prototyping Laboratory. I would finally like to thank my family and friends for

helping me to make it this far.
















TABLE OF CONTENTS
Page

A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF TABLES ...... ............. ......... .................... viii

LIST OF FIGURES ......... ......................... ...... ........ ............ ix

ABSTRACT .............. ..................... .......... .............. xii

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

O v e rv iew .................................................................................. 1
G o a ls ....................................................................................................... . 2
O u tlin e ............................................................................ . 3

2 BACKGROUND ON RAPID PROTOTYPING SYSTEMS ..................... ..........5

Overview of Rapid Prototyping Technologies ...................................... .... ...............5
Lam inated Object M manufacturing ...................................................................... ...... 6
Fused Deposition Modeling.................. ............................8
Stereo Lithography ............................ ...... ..........................................
Selective Laser Sintering ............................................. ........... ..... ...............10
Three D im ensional Printing .......... .. ....................... .................... ............... 11

3 BACKGROUND ON ELECTROPHOTOGRAPHY ...............................................13

Intro du action ..................................... .................. .................................... .. .. .. 13
Photoconductor M materials ........................................... .. .... .. .. ................. 14
D ark D ecay ................................................ ...... .............................. 14
Charge A acceptance ......... ................... ............... ................. 14
Image Formation Time .....................................................15
Im a g e S tab ility ............................................................................................... 1 5
R esidual Im age ................................... ........................ ..... ............ 15
M material S election ..................................................................................... 15
The Electrophotographic Process ....................................................... 16
C charging .............. .................................................. ..... ... ...... . .. 16
C o ro n a ................................ ........................................................ 17
C charging roller .................................. .......................................... 17


v









Im a g in g .......................................................................................................... 1 8
D evelopm ent ............................................. 18
Toner transport .................. .......................... ... ..... ................. 20
Toner charging ................................... .... ........ ............ 23
T ran sfer ...................................................................................................... 24
F u sin g ................................................................2 4
C lean in g ..................................... .........................................................2 5
Case Study: The Hewlett-Packard LaserJet 4.................................. ...............26

4 ELECTROPHOTOGRAPHIC SOLID FREEFORM FABRICATION.....................32

In tro du ctio n ............................ ............................ ............. ................ 3 2
Development of an ESFF tested system ....................................... ............... 32
M option C control ..............................................................33
P rin tin g ................................................................3 4
F u sin g ................................................................3 4
Softw are .............. ............... ...................................34
Development of a Charge Measurement Apparatus .................................................35

5 MODELING OF THE ESFF PROCESS................................. .. .........39

In tro d u ctio n ........................................... .. ............................................................ 3 9
Electrostatic Voltmeter Testing .................................................40
C o ro n a C h arg in g ................................................................................................... 4 2
T ransfer.... .............. ...... .......... .................................. 47
Agreement of Model with Experimental Data...................................... .................... 53
C o n c lu sio n s........................................................................................................... 5 6

6 PATTERN PRINTING..........................................59

Introduction .........................................................59
Theoretical Model ............................. ...................... ..... ......59
Experim mental R results ................. ............................................ 65
C o n clu sio n s...........................................................................................7 1
F u tu re W o rk .......................................................................................................... 7 2

7 DESIGN OF AN ELECTROPHOTOGRAPHIC DEVELOPER SYSTEM .............74

Introdu action ................................................................................. 74
D developer System Fundam entals ....................................................... 75
Pow der Storage................................................. 75
Powder Charging .......................................... .................. ... .......75
Corona charging ................................. .......................... .. ....... 75
Injection charging .... ................................................................. .... 76
Triboelectric charging ..................................... ....................76
P ow der T transport ......................................................... ............. .. ............. 76
M magnetic transport.................................................................................. 77









C ascade transport ............................................... ........ .. ...... ............77
Powder Transfer ...................... ................................. .. 78
Evolution of ESFF Developer Design................ .................................................79
Experimental Analysis of the Two-Roller Developer ..............................................85
C o n c lu sio n s........................................................................................................... 8 6

8 DESIGN OF A NEW ESFF TESTBED ...... ................ ............... 88

R eason s for N ew D design ................................................................. .....................88
Design Concept......................... ............. 89
T he P hotoconductor P late...................................................................... ... ..... 90
T he D ev eloper Sy stem ............................................................. .....................92
The Im aging System .................. ............................. .. .... ... ............ 94
Im aging Sy stem A naly sis ........................................ ...........................................95
Im aging Sy stem C control .................................................................. .....................99
F u tu re W o rk ........................................................................................................ 1 0 0

9 CONCLUSIONS AND FUTURE WORK ....................................... .................102

C o n c lu sio n s ......................................................................................................... 1 0 2
System M odeling .................. ............................. ........ .. ............ 102
Pattern Printing ........................................................ ................. 102
D developer D design ............................................................ .. .................. 103
N ew E SF F T estb ed ............ ... ..................................................... .. .... .. .... .. 103
F u tu re W o rk ........................................................................................................ 1 0 3
System M odeling .................. ............................. ........ .. ............ 103
Pattern Printing ........................................................ ................. 104
D ev eloper D design ............................................................ .................... 104
N ew E SF F T estb ed ............ ... ..................................................... .. .... .. .... .. 104
O v e rv ie w ............................................................................................................. 1 0 5

APPENDIX CODE FOR MATLAB EFFICIENCY SIMULATION.............................106

L IST O F R E F E R E N C E S ......... ................. ................................................................. 108

BIOGRAPHICAL SKETCH ...... ........ ................... ............................. 10
















LIST OF TABLES

Table p

5-1 Param eters for num erical sim ulation...................................... ......................... 54

6-1 Results of varying the discharged area width ............................. ..... ..........64

6-2 Results of varying the charged area width ............... .......................................64

6-3 Pattern printing experim ental results............................................... ........ ....... 66

6-4 P pattern printing rank table ........................................ .............................................67

8-1 D C controller connections chart...................................................................... .. .... 97
















LIST OF FIGURES

Figure pge

2-1 The rapid prototyping process ............................ ... .............. ............... ...............

2-2 Schem atic of a typical LOM system ........................................................................ 7

2-3 Schem atic of m etal foil LOM system ........................................................ ... ........... 8

2-4 Schem atic of a typical FDM system ..................................................... ............ 9

2-5 Schem atic of a typical SLA system ............................................................ ........... 10

2-6 Schem atic of a typical SL S system ........................................................................ 11

2-7 Schematic of a typical three-dimensional printing system ..........................................12

3-1 Schematic of a typical drum electrophotography system ..........................................17

3-2 A typical shielded corotron................................................. ............................. 18

3-3 The im aging process .................. ................................. ..... .. ........ .... 19

3-4 A typical develop ent system ......................................................................... ... ... 19

3-5 A cascade develop ent system ............................................................................21

3-6 A typical magnetic brush development system .................... ......................... 22

3-7 T h e tran sfer process............ ... .............................................................. ....... ............... 2 5

3-8 The LaserJet 4 printing system........................................................................ 26

3-9 Diagram of LaserJet 4 control architecture ......................................................27

3-10 L aserJet 4 im ager diagram ............................................... .............................. 29

3-11 LaserJet 4 developer schem atic .................................................. ..................31

4-1 The ESFF testbed................. ................ ..... ............. 33

4-2 Flow chart of the ESFF process ................ ........... ........................ ....................36









4-3 Schematic of the charge measurement apparatus.......................................................37

5-1 M odel of the voltage measurement stage .................... ..................... ............... .41

5-2 C orona charging schem atic .............................................................. .....................43

5-3 M odel of the corona charging stage ........................................ ........................ 44

5-4 M odel of the printing stage............................ .................. ................. ............... 48

5-5 Results of simulation of printing model ....... .. ...............................................55

5-6 Experim ental printing build rates ........................................ .......................... 56

6-1 Solid area printing m odel ................................................. ............................... 60

6-2 Solid area printing m odel results ............ .... ............................ ............ ... 61

6-3 P pattern printing m odel ........................................................................ ...................6 1

6-4 Pattern printing m odel results........... .................. ......... ............... ............... 62

6-5 P rint w ith no pattern ....................... .. .......................... .. ....... ............... 68

6-6 Print with a 1/72-inch black and white line pattern.............. .... ...............68

6-7 Print with a 4/72-inch black line and 1/72-inch white line pattern ...........................69

6-8 Print with a 4/72-inch black and white line pattern ............... ............. ...............69

6-9 Pattern printing parts, 250 prints ........................................ ........................... 70

6-10 Further pattern printing parts, 250 prints.......................... ...... ............... 71

6-11 Comparison image of parts from Figure 6-10 without pattern printing ....................71

7-1 D evelopm ent system schem atic........................................................ ............... 74

7-2 Cross-section of original developer design ...................................... ............... 80

7-3 Cross section of improved developer design..... ............................................... .........81

7-4 Cross-section of two-roller developer design.... .................... ................83

8-1 Conceptual schematic of the new ESFF testbed............................... ...............89

8-2 Conceptual schematic of new developer ..... ..................... ...............93

8-4 Im ager control diagram ....................................................................... ..................96



x









8-4 Im aging control architecture.............................................. .............................. 99















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

ELECTROSTATIC ANALYSIS OF AND IMPROVEMENTS TO
ELECTROPHOTOGRAPHIC SOLID FREEFORM FABRICATION
By

James Edward Fay Jr.

December 2003

Chair: Ashok V. Kumar
Major Department: Mechanical and Aerospace Engineering

Electrophotographic solid freeform fabrication (ESFF) is a method for rapid

prototyping under research at the University of Florida. This system uses laser printing

technology to build parts by depositing successive layers of a powdered material. The

material is deposited through the use of electrostatic charge, giving electrophotography

its name. There are four main areas of research in this thesis.

First, several stages of the ESFF process were modeled to help understand the

results of printing as they relate to controlled system parameters. This modeling provides

a basis for understanding and eliminating several part defects caused by uneven printing

across the layer. The reasons for the uneven printing are explored. Solutions are provided

where applicable, and limitations of the technology caused by these defects are discussed.

Second, a new method of printing line patterns in the cross section instead of a

solid area is discussed. The technique is intended to solve an issue of uneven printing

whereby the edges of a part grow faster than the center area. The process is examined









using finite element analysis to test the theoretical validity of the solution. Experimental

research is next presented to validate the results of the finite element analysis. The

advantages and problems presented by this method are discussed in relation to both the

finite element analysis and the experimental results.

Third, a novel design for a device called a developer is presented. This device is

used in electrophotography to charge powder so that it can be used to form an image. The

theory of developer design is reviewed. A history of the various versions of the device

designed in this research is presented. The practical issues with the device are discussed

in light of a new design for the overall ESFF process that will be more accommodative to

developer design.

Finally, a new design for the ESFF test apparatus is presented. The issues this new

design is intended to resolve are discussed. The conceptual design of several components

is presented. A control system for imaging that will remove many current technological

restrictions is presented and discussed.














CHAPTER 1
INTRODUCTION

Overview

Electrophotographic solid freeform fabrication (ESFF) is a new method for rapid

prototyping under development at the University of Florida. Like other rapid prototyping

technologies, ESFF adds material in layers to form parts in an arbitrary shape. This

allows the production of prototype-quality parts without the need for expensive, time-

consuming tooling operations. While slower than some traditional machining methods for

mass production, rapid prototyping technologies can produce parts with prohibitively

complex geometries and very fine features. The ESFF technique attempts to expand the

rapid prototyping field by allowing for the production of very fine tolerance parts in a

variety of materials.

Rapid prototyping technologies are currently limited in their ability to produce

parts with very small features, and are generally reliant on polymers as modeling

materials. There are a variety of methods currently used for the production of rapid

prototyping. ESFF introduces a new technology to the field, that of electrophotography.

This technology, which is the basis for laser printers, uses charge and field attraction to

move powder and special materials to create an image using a laser beam. The powder

transportation method holds the possibility of creating parts in a wider variety of

materials than previously available. The theoretical limits of the imaging system are also

much finer than current technologies, even finer than traditional machining.









To date, much progress has been made on realizing a working ESFF system. A

hardware testbed and a software control system have been developed. In early tests a

build height limitation of approximately 1 mm was found. This problem was analyzed by

physical modeling and solved by the addition of a surface charging system. The physical

characteristics of a number of powders have been studied and their relationship with the

ESFF process modeled. Detailed models of some stages of the ESFF process have been

constructed.

Several challenges have not been overcome, and some new problems have emerged

as the technology progressed. A poor understanding of some of the stages of the ESFF

process that had not been modeled created a difficulty in trying to solve problems and

improve performance. A problem in all electrophotography is the uniform imaging within

a solid area, due to changes in field strength. A solution to this problem had been

proposed but not tested. While powders had been examined, a system for using these

powders to create parts was still needed. Finally, a new design for the ESFF system was

needed to improve printing with alternative materials and remove the reliance on a

particular printing system.

Goals

The goal of this study was to find solutions wherever possible to the outstanding

issues in the ESFF process. This goal involved a number of specific objectives, namely:

* Modeling of poorly understood stages of the ESFF process and construction of
more detailed models in some areas.

* Testing and evaluation of the pattern printing system to solve the problem of solid-
area development.

* Design, testing, and evaluation of a development system to print new powder
materials.









* Overall design of a new ESFF hardware system, with study of an imaging system
for use in the new design.

Outline

Chapter 1 is a short introduction to the overall work. This contains a brief

description of the place of ESFF in the manufacturing field. It also provides a description

of the current state of ESFF research and the problems yet to be overcome.

Chapter 2 is an overview of the history of the rapid prototyping field. Issues related

to the field are discussed. Several prototyping technologies are described and their

relative merits and drawbacks presented.

Chapter 3 is a description of electrophotography technology. This technology is

covered in some detail in order to lay the groundwork for later. An example of the

technology, the LaserJet 4 printer used in the ESFF system, is described in detail.

Chapter 4 deals with work to date on the ESFF system. This chapter describes

ESFF technology in detail in preparation for later chapters. This chapter also serves to

document the work done to date to some extent for other projects. Problems in the

technology are described to show the importance of the work presented here.

Chapter 5 presents the modeling work done for this thesis. Three main stages of the

process were modeled: voltage measurement, corona surface charging, and powder

transfer. The first two stages mentioned had not been previously modeled, which led to

many difficulties in understanding experimental results and attempting to solve problems.

The third stage was modeled in more detail than in previous works to account for areas of

interest not studied in those models. The agreement of the models with observed behavior

is discussed.









Chapter 6 discusses the experimental results of a study of pattern printing.

Sivakumar Bhaskarapanditha (2003) first proposed the basis of this process. His work is

reviewed, along with the theoretical background. Experimental testing of the system is

presented, along with further modeling of the process. The advantages and problems this

system entails are discussed.

Chapter 7 is a discussion of the design of a new developer system to be used for

printing new powders. The iterations of system design are discussed to show the reasons

for the aspects of the final design. A theoretical model of the final design is shown. The

problems associated with this system are discussed.

Chapter 8 describes the new ESFF testbed design. The reasons this design is

necessary are enumerated. An overview of the design is presented. The results of system

modeling of the imager system from the current testbed are shown, along with the control

architecture used to use this system alone without the need for the complete printer.

Finally, Chapter 9 will provide conclusions to the research and describe future

work to be done. The conclusions presented in Chapters 5 through 8 will be summarized

to provide an overview of the research as a whole.














CHAPTER 2
BACKGROUND ON RAPID PROTOTYPING SYSTEMS

Overview of Rapid Prototyping Technologies

Rapid prototyping, also known as solid freeform fabrication or layered

manufacturing, is a new but well-established tool in the manufacturing field. The

technology allows for the creation of individual prototype-quality items in little time

without the need for expensive tooling. In some applications the technology can also be

used to quickly produce specialized tools or casts for traditional manufacture.

The parts are first generated as computer models, then sent to the prototyping

machine of choice. The generation of tool paths is performed automatically. The

prototyping machine builds the part, which may then require post-processing treatments

such as curing or support material removal. A flowchart of this process is shown in

Figure 2-1.

There are several important characteristics of a rapid prototyping technique. The

speed at which a given technique is able to build parts is of course important, as is the

accuracy with which those parts can be produced. Another important factor is the

material used to produce the parts. Some technologies require the use of a special

material that may be expensive or may have undesirable mechanical properties, other

technologies can use multiple materials. To date most rapid prototyping technologies

have used polymers of some variety as their build materials, and there is much research

underway to produce technologies that can build with metals or ceramics.



































Figure 2-1. The rapid prototyping process

There are many rapid prototyping technologies currently available commercially.

There are also several experimental technologies that offer promise for the future. This

chapter will give a brief overview of some of these technologies.

Laminated Object Manufacturing

Laminated object manufacturing (LOM) is a straightforward technology that

produces a part by cutting cross sections out of a film using a laser and joining them.

Both the part cross section and the surrounding paper are left in place after division, with

the end result being a cube that can easily be separated into the part and waste material.

This provides the support material needed for overhanging sections. The production rate

is very quick for parts with large cross sections, because the system only needs to trace

the edge of the cross section with a laser rather than place material or fill in the area










(Cooper 2001). The finished part has mechanical properties similar to pressed wood. A

schematic of a typical LOM system is shown in Figure 2-2.





moving aw-l iA*



n ilt JV- a Wier
LiXt ,, ,,








lakr-up Mll O O Y- nrl



Figure 2-2. Schematic of a typical LOM system (Kochan 1993)

Unfortunately, the LOM system requires a material that can be formed into a film,

which is not always desirable. There is also a large amount of material waste in the

system, since not only the part but also the surrounding area must be removed, and the

resulting webbing is not reusable. Because paper is a common choice for the LOM

process the costs associated with material waste are not generally great, but there is a

certain amount of smoke produced in the laser cutting operation that must also be carried

away when paper is used (Cooper 2001).

A similar technology is currently under research that uses sheets of metal foil as the

material (Doumanidis and Gao 2002). The material is compressed onto previous layers

using a magnetic field, then the cross section shapes are cut with a diamond bit and

joined by ultrasonic spot welding. This technology has some of the same drawbacks seen

in traditional LOM, but offers the ability to quickly prototype metal parts with large cross









sections, which would be a significant advance. A schematic of the system is shown in

Figure 2-3.



ZM compression to

i.onotrode uni


roll roll
tip


retracuble
fixture &

table' V y-sage

Fig. 2 Schematic arrangement of ultrasonic rapid prototyping


Figure 2-3. Schematic of metal foil LOM system (Doumanidis and Gao 2002)

Fused Deposition Modeling

Fused deposition modeling (FDM) is a very popular commercial rapid prototyping

technology. An actuated head moves in two axes to build a planar cross section on a build

platform, which is capable of translating in a third direction to give the part height. The

part is built using material extruded from a nozzle on the head, which traces the outline of

the part then fills in the solid area with cross-hatching. A typical FDM build head has two

nozzles, one for the part material and one for a support material. The material is stored as

a spooled filament, extruded into the heated nozzle and then cools and solidifies once

placed. A large number of materials can be extruded in this manner, although to date

almost all FDM technology is based on plastics and waxes because the heat required to

melt and extrude metal is prohibitive from both safety and energy perspectives. Even so,








this grants a fairly broad amount of freedom in the type of material used. A typical FDM

system is depicted in Figure 2-4.



6- A nlwEMTI STEM

LL 4rfAD

__l__ _I AM.FME C M I_ L
CREAIIN
1 AI fitoAiWE 3tRE MIi1ES







Figure 2-4. Schematic of a typical FDM system (Kochan 1993)
FDM technologies are not as fast as LOM systems, because they must trace the

cross-hatching for each section, and because they require the movement of a physical

head to build the part rather than laser cutting. However, FDM systems can use a variety

of plastics, as well as waxes that can be used to make molds for casting. Furthermore,

FDM systems have far less material waste, because they build support structures only

where needed.

Stereo Lithography
Stereo lithography (SLA) systems are the oldest rapid prototyping technology. The

system features a build platform immersed in a liquid polymer bath. The part is built by

tracing a cross section with a laser in the thin layer of liquid polymer on top of the build

platform, which solidifies the special polymer used. This technique requires cross-

hatching of the section, and the construction of supports is problematic. These supports

are usually constructed by building a network of fine mesh in the desired areas that









require a significant amount of post-processing to remove. A typical SLA system is

shown in Figure 2-5.


Laser




Part

P ---- Build
Platform



Liquid
Polymer


Figure 2-5. Schematic of a typical SLA system

The main drawback of this technology is the special polymer material used. The

material is a proprietary polymer, and is much more expensive than the materials used in

other technologies. Earlier technologies also used a material that was somewhat

hazardous, though there are now build materials that are much safer (Cooper 2001).

Selective Laser Sintering

Selective laser sintering (SLS) is another popular commercial technology. In this

system, a thin layer of powder is spread uniformly over the build platform. A laser then

fuses the powder into a solid by heating it to just below the melting point. This

technology is able to create parts form a large number of materials, mostly polymers and

waxes. However, recently the technology has been used to build parts from metal

powders in which the particles have been coated with polymer. This produces a metal

part with green strength sufficient to be processed in a furnace. If a fully dense metal part









were desired a post-processing step is needed to infiltrate the metal part with copper to

fill the gaps between sintered particles. Another way to achieve fully dense metal parts is

to use the system to make a blank for a mold, then cast the part.

The powder bed is full, so there is no need for support material, much like LOM.

However, once the part is finished the excess powder can be recovered and reused,

significantly reducing waste costs. A typical SLS system is shown in Figure 2-6.



---Laser




/ Part

Levelling
Roller
Build
Powder Platform




Figure 2-6. Schematic of a typical SLS system

Three Dimensional Printing

Three-dimensional printing is very similar to SLS. Thin layers of powder are

spread over the build area, then joined into a cross section. In this case, however, the

cross section is joined using an inkjet head that disperses a resin onto the powder. This

allows the technology to build parts from virtually any material that can be powdered.

However, the building speed is slower than SLS, since a print head must be moved to

create the cross section rather than tracing it with a laser. The parts may need additional

post-processing as well, as the resin may not provide the part with as much mechanical










strength as in the sintering process. A depiction of a three-dimensional printing system is

shown in Figure 2-7.


InLerrnedate 8tag t L~s ayr Printed Finished Part


Figure 2-7. Schematic of a typical three-dimensional printing system (Kochan 1993)














CHAPTER 3
BACKGROUND ON ELECTROPHOTOGRAPHY

Introduction

Electrophotography, sometimes called xerography because of its early development

by the Xerox Corporation, is a widespread method for the creation of printed documents.

Laser printers and copiers are based on the technology, as are some types of imaging

systems used to digitally capture x-ray scans. The technology was first developed by

Chester Carlson (Carlson 1942). The first experiments in electrophotography involved a

charge image created in a glass slide, which was used to pick up powder and transfer it to

wax paper. Such permanent slide methods are still sometimes used, as in mass printing of

journals and the like, in a manner analogous to typeset printing.

Modem electrophotography uses a much different technique. A uniform charge is

deposited on a photoconductive surface with a grounded backing. This surface is then

selectively exposed to light of a specific wavelength, turning the substrate conductive and

thus discharging the surface at specified points. Depending on the printing technique, a

powder called toner is picked up either in the charged or discharged area. This allows for

the creation of a temporary image and the reuse of the imaging medium. The toner itself

is charged in a device called a developer, which also brings the toner near the imaging

surface to create a toner image using the latent charged image. The toner image is then

transferred to an external medium, usually paper. The toner powder is then fused to the

paper, making the image permanent. Finally, any excess toner that was not transferred is

cleaned from the imaging surface.









Photoconductor Materials

There are a number of materials used in photoconductive imaging. The two most

common materials are amorphous selenium, which was used in many early imaging

systems, and organic photoreceptors, used in most printers today. The common property

they share, photoconductivity, denotes that a certain wavelength of incident radiation

causes a large decrease in their resistivity. The exact chemical mechanism by which this

occurs is not within the scope of this thesis. The major characteristics of a

photoconductor that are of interest here are dark decay, charge acceptance, image

formation time, image stability, and residual image.

Dark Decay

Dark decay is essentially the permanence of an charge image on the

photoconductor. Even in the absence of light, the photoconductor is not a perfect

insulator and will slowly shed its charge. The time needed for the photoconductor to shed

half its charge is referred to as the depletion time. Organic photoreceptors typically have

much shorter depletion times than amorphous selenium (Diamond 1991).

Charge Acceptance

The surface charge density that can be deposited on the photoconductor by a given

voltage is the charge acceptance. This characteristic is determined primarily by the

dielectric properties of the photoconductor. So long as the charge acceptance is high

enough to sustain a charge that will allow transfer of toner from the developer to the

charge image, the photoconductor material is adequate. A charge acceptance much higher

than this necessary minimum will lead to a large force holding the toner to the imaging

surface, thus making the transfer to paper problematic.









Image Formation Time

The image formation time is the amount of time necessary for the imaging light

source to discharge the photoconductor. In point of fact, a more proper term would be the

image formation energy, but since the intensity of light is considered a given in a specific

electrophotography application, it is the time that is considered the variable. This time is

critical to the speed of the printing system, and thus is one of the more important

characteristics of the photoconductor.

Image Stability

Image stability refers to the tendency of the charge image to migrate and spread

across the imaging surface. Some image instability is due to the inability of the

photoconductor medium to sustain a highly localized area of discharge. Surface

contamination also plays a role, allowing charge to move or dissipate on the surface

itself.

Residual Image

Residual image is due to residual charge on the imaging surface that is not

discharged in the printing process. There are a number of reasons this can occur, and the

effect is especially noticeable after many prints, when ghost images can begin to appear.

Printers typically feature a discharging cycle after each print to alleviate the problem, but

with high rates of printing it can be problematic to completely eliminate latent charge.

Material Selection

As mentioned above, the tendency in commercial electrophotography systems has

been moving from amorphous selenium photoconductors towards organic photoreceptors.

At first this would seem counterintuitive. Organic photoreceptors are softer and thus

more prone to wear. They also do not hold an image for as long as amorphous selenium,









and suffer gradual breakdown from environmental exposure. However, organic

photoreceptors are significantly less expensive, even considering the need for frequent

replacement. Printer design has minimized the impact, since the imaging drum in most

printers is now part of the toner cartridge, which is sent for recycling periodically as the

toner is depleted. During the recycling of the cartridge the drum can be inspected and, if

necessary, re-coated. The issue of image duration is not of major significance in current

printers, because printing speed has now reached the point where even the shorter image

duration seen in organic photoreceptors is more than sufficient. Amorphous selenium has

a fairly broad range of acceptable wavelengths, making it suitable for many applications

but meaning it must be protected from light, while organic photoreceptors function only

with light in the ultraviolet spectrum, meaning that these materials do not require as much

shielding.

The Electrophotographic Process

As described earlier, there are six main steps in the electrophotographic cycle:

charging, imaging, development, transfer, fusing, and cleaning. In most printers this

process is carried out on a drum, which minimizes space, allowing for the current

generation of small laser printers for desktops. A depiction of a drum electrophotography

system is shown in Figure 3-1.

Charging

The first stage of the electrophotography process is to charge the surface of the

imaging system. It is of the utmost importance to the picture quality that this charge be

uniform across the surface. There are two main methods to accomplish charging, a

corona and a charging roller.











-------- Laser


Developer Charging Roller
Developer

Cleaning Blade


Toner
Receptacle
Photoconductor
Drum








Charging Roller Heated Fusing
Rollers


Figure 3-1. Schematic of a typical drum electrophotography system

Corona

A corona charging system is essentially an ion jet. Most current printers use a

shielded corotron charger. In this arrangement, a wire at high voltage is surrounded by a

metal shield at the same voltage, generally around 7000 volts (Schaffert 1975). The wire

produces ions by dielectric breakdown of air. The ions with the same sign as the wire are

repelled away in all directions. The shield serves to deflect these ions in one specific

direction. This produces a steady stream of ions and a regular charge. However, the high

voltage required by the corotron, as well as its somewhat bulky size, has caused these

systems to fall out of favor. A typical shielded corotron is shown in Figure 3-2.

Charging roller

Roller charging is the preferred method for charging the photoconductor drum in

current printers. The system is more compact than a corotron, and requires a much lower









voltage. The charge roller is made up of a metal axis surrounded by a layer of relatively

conductive polymer foam. The shaft is subjected to a DC-biased AC voltage. This causes

an intense electric field, leading to small discharges between the irregular polymer

surface and the photoconductor drum (Hirakawa and Murata 1995).












Figure 3-2. A typical shielded corotron

Imaging

Once the photoconductor surface is charged, the next step is to selectively

discharge areas to produce an image. A polygonal mirror, where each face is one scan

line, reflects a laser of the appropriate wavelength onto the photoconductor surface. The

laser is switched on and off at high speeds to discharge specific dots. The resolution of

the image is determined by the wavelength of the beam and the switching speed. A

depiction of the process is shown in Figure 3-3.

Development

Development is the process of charging the toner powder and transferring it to the

latent charge image. This is by far the most complex part of the electrophotography

process. The toner powder is metered by a doctor blade to ensure a thin, uniform layer of

toner is constantly brought out. The toner is charged, and brought near the

photoconductor drum so that electrostatic force may draw the toner off onto the latent






19

charge image. The topic of development is explored in greater detail in Chapter 7. A

schematic of a typical developer is shown in Figure 3-4.

Laser Beam


+ + + + +


+ + + +


Photoconductor Layer

Conductive Layer


Discharged
Area


Figure 3-3. The imaging process


Developer Roller


Figure 3-4. A typical development system


I I~









Toner transport

One of the most difficult parts of development is constantly providing a thin,

uniform layer of toner for the photoconductor drum. To accomplish this goal,

development systems progressed from cascade development, to insulative magnetic brush

development, to conductive magnetic brush development (Schein 1988). All of these

systems used a two-component toner, composed of carrier particles crucial to transport

and charging as well as the toner particles that were ultimately transferred.

Cascade development was a very simplistic mechanism whereby charged powder

was brought across the photoconductor surface by mechanical force. In the earliest days

of electrophotography the photoconductor was a plate, and a powder of carrier particles

coated with toner was simply poured or "cascaded" across its face, giving the

development system its name. Because toner was attracted by field force rather than by

charge itself, solid area development was problematic (Schein 1988). Large charged areas

have no field in the center, and thus toner was only attracted to the edge of an image.

Another problem with this development system was the number of forces acting on free-

flowing powder. Charge force was only one of many forces that may attract or repel toner

from the photoconductor surface, and as such it was difficult if not impossible to control

powder behavior. Cascade development also tended to have a great deal of powder loss

and spillage. For these reasons, cascade development was largely abandoned when

magnetic development systems were invented. A depiction of an early cascade system is

shown in Figure 3-5.

Insulative magnetic brush development was a significant step forward. In an

insulative brush system, a stationary magnet inside the developer roller attracted iron in

the carrier particles, which were coated in toner particles. This provided a counter-force









to the charge force, and served to nullify a number of minor forces that disrupt control in

cascade development. A roller rotated around this stationary magnet, carrying the toner

by friction. The carrier particles formed chains in the magnetic field, such that the roller

appeared to be a brush. Charged toner was carried across to the photoconductor drum

when the electric field force was greater than the friction force holding the toner onto the

carrier. The carrier beads were spherical, and the transfer of toner was limited by a

balance of charge between the photoconductor surface and the carrier particles (Schein

1988). A depiction of a magnetic brush development system is shown in Figure 3-6.


















Figure 3-5. A cascade development system

Conductive magnetic brush development was the most successful form of two-

component development. The major change was that the carrier was now composed of

irregular particles that were more capable of transmitting current across the development

gap. This meant that there was not a balancing charge buildup in the carrier particles, and

thus that much more powder could be transferred (Kasper and May 1978). This lead to

darker lines and text, and more regular solid area development. The need for two-









component toner, however, was undesirable, as this lead to larger toner cartridges that

had to be refilled more frequently.


/ Carrier
Photoconductor Particles
Drum


Figure 3-6. A typical magnetic brush development system

Most printers currently use a mono-component toner that is insulative and

magnetic. In this system, the toner, usually a polystyrene powder, is doped with iron

compounds to make it magnetic. Thus the same advantages of force cancellation and

control are present as in two-component magnetic development. The toner particles on

the developer roller are charged, and thus may be stripped off the roller by the force of

attraction with the image field. To aid in this process, an alternating current is applied to

the developer roller, causing the charged toner particles to bounce back and forth from

the roller surface, forming a cloud. An exception to this trend is in color printing where









cascade development is still used, because the iron compounds that provide magnetic

force would prevent proper coloration.

Toner charging

There are several methods for charging toner. The method used depends on the

nature of the toner itself. Some methods use the characteristics of the toner itself to

charge, while others create the charge externally.

The toner may self-charge due to either triboelectric effects or chemical effects.

Two-component toners often charge triboelectrically, with the contact friction between

the carrier and toner particles causing an opposing charge on each particle. Liquid toners,

used for applications involving extremely fine resolution prints due to the difficulty of

handling very fine powders, are charged chemically, with charge transfer occurring

between the toner and the liquid in which it is suspended. Chemical charging is also used

to some degree in monocomponent toners, which are doped with charge control agents

that have a similar effect, but these agents can only induce a part of the charge needed to

print. The main purpose of the charge control agents is to render the toner susceptible to

external charging.

There are also several charging methods that allow charge to be applied to the toner

by the developer. The most direct system of this kind is corona charging, identical to

corona charging of the photoconductor. In addition to the normal problems of corona

charging, the corona wire may become coated with toner particles, rendering it

inoperable. The toner can be charged by triboelectric effects from rubbing with parts of

the developer. This method is now very popular because the charge control agents in

mono-component toners can make the toner particles triboelectrically active (Schein

1988). If the toner is conductive it can induce charge by passing through an electric field.









Finally, insulating toner particles can be injected with charge by moving it rapidly around

the developer roller through an electric field, though the exact mechanics of this process

are poorly understood (Nelson 1978).

If the charge per unit mass on the toner is too low, there will be insufficient

electrostatic force to strip the toner from the magnetic roller. If the charge per unit mass

is too high, a very thin layer of toner will cancel the image charge and make a light

image. Thus the optimum design is to charge toner to the critical threshold value, which

will depend on the magnetic field strength of the developer roller.

Transfer

Once the image is developed in toner powder, the next step is to transfer the toner

to the paper. This transfer is accomplished by a mix of electrostatic and mechanical

transfer force. An elastic charge roller presses the paper against the photoconductor drum,

while depositing a charge opposite to that of the toner on the back face of the paper. The

paper is sufficiently insulative for this charge to form a field across the paper width with

the toner, helping to hold the toner onto the paper as it is pressed against the

photoconductor drum. A schematic of the transfer stage is shown in Figure 3-7.

Fusing

The image on the paper is not yet in a permanent form. The charge force is

sufficient to hold the toner to the paper lightly, but it must be fixed permanently so that it

will not wipe off as soon as the paper is handled. In early electrophotography the toner

powders were specialized powders, and wax paper was used as the fixing mechanism. In

current printers toner technology has advanced significantly, and the toner has been

adapted to the role of fixing agent so that ordinary paper may be used. The toner is

mostly composed of polystyrene, which has a low melting point. The paper with the toner









image is heated, causing the toner to melt. Some printers use a radiant heater, but many

now opt for a heating roller that can both melt the toner and press it into the paper for

better image fixing. The disadvantage of a heating roller is that it may pick up some

toner, which will then smudge later pages. Nonstick coatings such as teflon are used on

the heating rollers for this reason.







Photoconductor Drum












Developer Roller


Figure 3-7. The transfer process

Cleaning

The final step in the cycle is to clean the photoconductor drum for later prints. In

current desktop printers cleaning actually occurs within the cycle, as the photoconductor

drum goes through several rotations for each page. The toner is scraped from the drum by

a flexible blade and captured in a receptacle. This receptacle must be emptied

periodically, but is usually designed to be large enough that it needs to be emptied less

frequently than the toner must be replenished, so that the end user does not need to take

the cartridge apart themselves.










Case Study: The Hewlett-Packard LaserJet 4

The LaserJet 4 printer used in the Electrophotographic Solid Freeform Fabrication

system is a typical example of the current generation of desktop laser printers. The

LaserJet 4 uses an organic photoreceptor drum charged by roller. The imaging system is

based on an ultraviolet laser and produces an image with a maximum resolution of 600

dots per inch (dpi). The developer is a mono-component magnetic insulative system.

Fusing occurs by heating rollers. A diagram of the LaserJet 4 printing system is shown in

Figure 3-8.






Cartridge
Laser beam -

Primary charging roller
Blade /
Developing cylinder
Cleaning blade _
Upper fusing roller hg r Pick-up
sensive roller
drum

Static charge\
eliminator
Low e r fus ing ro lle r 0 '
Transfer
charging roller Cassette pick-up roller





Figure 3-8. The LaserJet 4 printing system (Hewlett-Packard 1996)

The print is sent to the LaserJet 4 via a normal print cable and arrives at a computer

board called the formatter. The formatter reads in the data and communicates the

necessary information to other printer components. The formatter is also responsible for

taking in settings from the printer control panel. The electromechanical control aspects of









printing are then handled by another computer board, the DC controller. As well as

sending control signals to the imaging system, the motor, the fuser, and the paper control

system, this board reads in signals from a variety of sensors and sends messages back to

the formatter as needed, such as when a paper jam is detected. The DC controller is also

responsible for breaking the data stream from the formatter into a series of pulses that are

transmitted to the imaging system, turning the laser on and off. A diagram of the printer

control architecture is shown in Figure 3-9.


Figure 3-9. Diagram of LaserJet 4 control architecture (Hewlett-Packard 1996)









A single motor provides the drive to the paper handling system, the photoconductor

drum, and the developer through a system of gears. This motor is equipped with its own

dedicated control circuit for managing speed and acceleration, and requires only power

and an on/off signal from the DC controller. The paper handling system uses a number of

rollers to feed paper through the printer from the paper tray. A series of photosensors

make sure that paper is feeding through properly and send paper jam warnings to the DC

controller.

There are two power units, one that takes in the voltage from the power socket of

the printer, and another that breaks this voltage down into a number of high voltages for

the various printing components. There are several components such as the charge rollers

and heating system that use voltages so high that they must be isolated from the printer

circuitry to prevent damage. There is a feedback system that ensures that voltage is being

applied to the photoconductor drum, developer, and heating roller by resistance

measurement. This signal is returned to the DC controller.

The imaging system of the LaserJet 4 was designed to produce high-resolution

images in a compact environment. At the time of the design the 600-dpi resolution was

considered high for laser printers, though today there are higher resolution systems. The

laser is a standard ultraviolet source with its own control board. This board takes in the

laser pulse signal and status signals and outputs an error signal if necessary. The laser

beam makes its way to the photoconductor drum by way of a rotating polygonal mirror

that turns the laser stream into a scanning beam moving along the length of the

photoconductor drum. The beam passes through two lenses to be focused and is then

reflected by an angled mirror because the imager is at an angle to the drum. The









polygonal mirror motor has its own control system and is turned on and off by the DC

controller. The final part of the imager system is a photosensor that detects the start of

each scan line, analogous to a homing sensor on a motor control system. A diagram of the

LaserJet 4 imager is shown in Figure 3-10.


Laser Diode Beam Detect PCA

Focus Lens E @m.^

Exit Mirror







Correction Lens

Scan Motor \ -i` a ss^

BD Mirror


Figure 3-10. LaserJet 4 imager diagram (Hewlett-Packard 1996)

The developer system is based on insulative magnetic mono-component toner

technology. The toner itself is a polystyrene powder base doped with charge control

agents, iron compounds for magnetism, and carbon black for color. A stirring rod is

present to keep the powder moving in a pseudo-fluid flow. The toner is primarily charged

triboelectrically by rubbing with the material on the doctor blade. A DC-biased AC signal

on the developer roller forms a powder cloud. The LaserJet 4 developer system is shown

in Figure 3-11.

The toner image is transferred to the paper using the elastic roller method described

earlier. Once the image has been transferred the reverse side of the paper is discharged to






30


prevent the paper form picking up any loose toner that may be present in the paper

handling system. The paper is then fed through a pair of heating rollers for fusing before

being sent out of the printer. A cleaning blade removes excess toner from the

photoconductor drum.

































Figure 3-11. LaserJet 4 developer schematic (Hewlett-Packard 1996)














CHAPTER 4
ELECTROPHOTOGRAPHIC SOLID FREEFORM FABRICATION

Introduction

Electrophotographic solid freeform fabrication (ESFF) is a recent innovation in the

field of rapid prototyping developed at the University of Florida (Kumar 2000). The

concept is to use the technology of electrophotography to deposit layers of powder

imaged to form the cross sections of a part, then fuse them together.

This combines the advantages of many existing freeform fabrication technologies.

Using the speed of laser imaging and a rotating drum, the technology can deposit a layer

of powder in seconds. The build material is also flexible, as any powder that can be

charged and fused is usable. Powders which cannot be fused could still be used, but

would require an additional binder layer. The resolution is very fine, as there are

commercially-available printing systems which can image at resolutions well above 1000

dots per inch, and if the technology were to be applied specifically to this application

there is no reason why imaging could not be performed at even finer resolutions. The

main drawback ESFF is that the process is very complex and difficult to control.

Development of an ESFF testbed system

The first stage of ESFF research was the creation of a system that would allow for

experimentation with ESFF technology. The system required a two-axis movement

platform, a printing system, and some mechanism for fusing the imaged powder (Zhang

2001). A model of the ESFF testbed is shown in Figure 4-1.










C *ipactig Systtm


Figure 4-1. The ESFF testbed (Dutta 2002)

Motion Control

A Parker automation system was used to provide the motion and control. This

system provides translation in two axes and a frame to mount the components of the

ESFF apparatus. A Galil control system actuates the motors, as well as serving as an

input/output junction between the computer and the various controls and sensors. The

system includes a software control mechanism and an interface that allows the system to

be controlled from within C++ programs.

The build platform this system actuates is a spring-mounted plate with flanges to

clip on the paper for printing. The springs allow the platform to be pushed against the

photoconductor drum for better transfer without damage, and alleviate any issues related

to the platform mounting not being perfectly horizontal. Finally, the platform allows

control of the pressure of fusing during compaction by compressing the springs to a









selected distance. A position sensor measures when this compression is reached and

sends a signal to the Galil controller. There is also a connection to the voltage source so

that the platform can be electrified in order to attract charged powder during printing.

Printing

The printer selected was a Hewlett-Packard LaserJet 4. This printer has a resolution

of 600 dots per inch. To work within the ESFF testbed the printer required significant

modification. Much of the printer had to be stripped apart so that the build platform

would have access to the photoconductor drum. The internal sensors that detected the

mechanical status of the printer had to be bypassed or controlled in order to simulate

operation under normal conditions. Several communication signals within the printer also

had to be intercepted so that the build platform and the printer could work together

seamlessly. A schematic of the Hewlett-Packard LaserJet 4 was shown in Figure 3-8.

Fusing

The original fusing system used a radiant heater to melt the plastic toner powder.

However, there are always slight variations in the amount of powder deposited across an

image, so a compaction system was desired to level the powder during fusion. The

heating system was thus changed to a compaction plate warmed by a mica strip heater.

Recently a teflon-coated plate was added to the compaction and fusing system in order to

prevent part damage due to sticking.

Software

To control this hardware, a software system was developed that would automate the

process of building a part. A flowchart of the system and its controls is shown in Figure

4-2. There are several levels of programming in the software. There is a specific

programming language of commands for the Parker automation system. Scripts









programmed in this language may be called from C++ programs, which are stored in a

dynamic link library. Finally, the SolidSlicer program developed in Java for the ESFF

testbed reads in model files created in CAD software, divides them into cross sections,

allows for positioning of the parts on the build platform, automates the process of

building the part, and stores a log of each build (Bhaskarapanditha 2003).

This ESFF apparatus provides a suitable mechanism for basic testing. A variety of

parameters within the printing process can be varied. The qualities of the printed image

can be manipulated through software, which will be touched on in a later chapter.

Furthermore, a variety of analysis and sensor equipment can be installed within the

testbed to evaluate different stages of the process and the effects of manipulating those

stages. However, there are areas within the process that are essentially "black box"

technology. The printer in particular has issues with process stages that are not

transparent to an outside observer. For this reason, further test equipment and modeling is

needed.

Development of a Charge Measurement Apparatus

One of the most important parts of the printing process is the charging of toner

powder. The powder must be charged effectively enough that it can transfer an even layer

onto the latent charged image, but not so charged that a tiny amount of powder can cancel

the charge of the latent image. This testing would be very difficult, if not impossible, on

the ESFF testbed because of the difficulty of testing charge within the framework of that

system, as well as problems of recovering the powder. For this reason, a separate system

was created which could test the charge and mass of printed powder. This system is

shown in Figure 4-3.













Implemented in DMC and


Implemented in JAVA and
running on WINDOWS NT PC


Figure 4-2. Flowchart of the ESFF process (Dutta 2002)











Magnetic Powder
Deueloper Cartridge-. '





Photoconductor

DC biased AC
development voltage


O Electrometer






Figure 4-3. Schematic of the charge measurement apparatus (Gokhale 2001)

The charge measurement apparatus replaces the printer drive mechanism and

photoconductor drum, and provides an attachment point for a developer. The developer

cartridge is attached to a fabricated stand and attached to a voltage source. A

photoconductor drum is attached and grounded through an Keithley electrometer that has

the ability to integrate current over time, thus measuring the amount of charge flowing to

the ground (Keithley Instruments 1995). When toner is deposited on the surface of the

drum, the grounded metal on the opposite side of the insulator induces an equal and

opposite charge that flows out through this ground. The photoconductor drum is removed

and its mass measured before and after printing in order to determine the mass of powder

deposited. Printing area may be normalized by controlling the time of operation through

computer control of the drive motor.









This system was initially used to optimize printing using the standard LaserJet 4

developer cartridge. It has also been used to test development systems created for

research of the charging characteristics of other powders. The function of the system is

the same in all cases. The design of such development systems is discussed in detail in a

Chapter 7.

The main problem with this measurement system is the measurement of powder

mass. Removing the photoconductor drum mechanically causes powder to be lost,

making the readings less accurate. A more accurate system would be possible if the

measurement could be made in place, but this is problematic in practice. Another

alternative currently being explored is to include a system for cleaning the powder from

the photoconductor drum into a container, which could be removed and tested without

loss of powder.














CHAPTER 5
MODELING OF THE ESFF PROCESS

Introduction

The electrophotographic printing process used in ESFF is an extremely complex

transfer method. In order to understand and optimize the process it is necessary to

construct a detailed model of each step, as what seems intuitive will often prove wrong

when analyzed further. It is also important to take into account the ways in which

different stages of the ESFF process are interconnected.

There were several areas in which it was desirable to perform a detailed analysis of

the process. The first was the relationship between the surface voltage of a part measured

by an electrostatic voltmeter and the charge state of the part. This is important because an

electrostatic voltmeter is used experimentally to gauge both surface charge and

volumetric charge, and it was necessary to understand what its readings indicated in

regards to both values.

The second stage of interest for modeling was the characteristics of corona

charging. As a part builds, it is necessary to charge the surface in order to continue

attracting charged powder. This is done in the ESFF platform using a corona charger. It

was desirable to understand how the various characteristics of a building part such as

thickness and charge state would effect the level of surface charge as the part builds,

since this will determine both how well a part can be built and how consistently new

layers will be deposited.









The final stage to be modeled was the transfer of powder from the photoconductor

drum onto the part. The results of the corona charging model were relevant here, because

the surface charge deposited by the corona serves to enhance transfer. It was important to

see what system parameters would alter both the consistency of a print within a layer and

the amount of powder being transferred overall.

Electrostatic Voltmeter Testing

An electrostatic voltmeter is the best tool for measuring the surface voltages that

are the basis of electrostatic transfer. The voltmeter determines the surface voltage by

altering the voltage applied to a vibrating reed until the induced current is negated,

showing that there is no field and thus that the reed and surface voltages are equal. The

probe is calibrated to be held in air a specified distance from the surface being tested,

which allows this field to be converted to a voltage on the surface.

When the measurement involves a simple charged surface as the probe is designed

for, the meaning of the measured voltage is clear. When used in a more complex

measurement such as measuring the charge on the surface of a part that may contain a

volumetric charge, it is necessary to do some analysis to ascertain what the reading given

by the voltmeter indicates in regards to the contributing charges. First a model must be

constructed to approximate the system, and then the field that the voltmeter probe detects

must be derived as a function of the parameters of interest.

In order to construct a model of the situation in probe testing on the ESFF system,

several assumptions and simplifications had to be introduced. The system was modeled

as a Gaussian series of parallel planes, with each plane representing a material layer in

the system. The layers are the part itself, the paper substrate the system builds on, an air

gap introduced to assess the effects of irregularities below the substrate, and the grounded









metal plate on the build platform. Because the cross sectional area of a typical printed

part is many orders of magnitude larger than the thickness, it was assumed that the

various layers were infinite. Along with the material properties of the various layers, a

surface charge ot and volumetric charge pt were assumed to be present on the part. This

simulates a part wherein the surface charge has not been totally nullified by charged

powder deposition and the volumetric charge has not been totally dissipated, both of

which are common situations in the part building process. The field above the part was

taken as zero, as would be the case if the voltmeter probe is behaving properly. The

system model is shown in Figure 5-1.


Electrostatic Voltmeter,: f o
Probe dx: Thickness of layer
4
SKx: Relative permissivity of layer material

Toner (dt, Kt, t, Pt) 3 ox: Surface charge density on layer

Air (da, Ka) px: Volumetric charge density in layer
Plate 0

Ground


Figure 5-1. Model of the voltage measurement stage

First, boundary conditions must be defined. The voltage on the metal plate is

known to be ground as shown in Equation 5.1.

VO =0 (5.1)

The surface voltage is the total potential drop across all the layers, shown in

Equation 5.2.

V, = V3 = V (5.2)









By integrating the fields as shown in Equations 5.3 through 5.5 and summing the

potential differences as shown in Equation 5.6, the surface voltage Vs was found, and is

presented in Equation 5.7.

dt 2
S-J=- ptddx + 2 (5.3)
0 K-to \Kt o 2Kcto )


d p t + Atd, td + ptdtd
VI V2 dxf (5.4)
0 CpEO [CK C KPE


o-V at + ptd, ,d, ptdd, (5.5)
f Klaa0 K'a0


-(V2-V3 +V -V2 +V,-V=V3-V, =V (5.6)


1 dt + da d' d did (5.7)
V, = I t I t + +I + pd, 2 + + I(5.7)
0 Kt Kp Ka2 2, Kp Ka

Most of these parameter values are either documented or can be determined

experimentally. This equation shows that in order to use the voltmeter to measure surface

charge it is necessary to first test the part before charging to find the portion of the

voltage contributed by volumetric charge. Measuring this value and knowing the system

parameters allows the surface charge yt to be found using the voltmeter probe, which is

very valuable in areas such as corona charging optimization experiments.

Corona Charging

The voltmeter probe simulation allowed for better understanding of experimental

measurements of the corona charging process, among other things. It was also desirable

to have a more detailed understanding of the charging process itself.

The corona produces a stream of ions of both charge signs due to field breakdown

of air around a high voltage wire. These ions are either attracted or repelled to the corona









wire due to their sign and the sign of the wire voltage. The wire itself repels opposite

charged ions in all directions, however in a corona charging device there is a metal shield

around the wire at the same voltage, which subsequently repels the ions deflected in its

direction. This shield has an opening at one side, and the ions are thus deflected out

through this opening. Many corona charging systems also use a metal grid or a number of

wires across the opening held at the same voltage as the corona wire, which serve to

nullify velocities in all directions except that normal to the plane of the grid surface. The

corona may thus be deemed for purposes of modeling a plane with a fixed flux of charge.

A corona charge system is shown in Figure 5-2.

Corona wire, shield, and
grid wires held at same
voltage








,le'ele






Figure 5-2. Corona charging schematic

The charge will deposit onto another surface until that surface becomes saturated.

The saturation takes place due to the fact that eventually the surface has so much charge

that it becomes repulsive to new particles. If the charge particles are depositing onto a

conductive surface that has been grounded, the charging can go on more or less

indefinitely. If the ions are depositing onto an insulative surface, there is a finite limit.









Placing a grounded plate behind the insulative surface has the effect of suppressing the

field the ions create and thus extends the charge capacity of the surface.

The model used for the corona charging simulation is very similar to the one used

in the voltmeter simulation. A new layer has been introduced, which models the air gap

above the part filled with ions of a constant charge density pc. The corona itself is seen as

a plane at a fixed voltage. The model is taken at equilibrium once charging has stopped,

which was assumed to occur when field in the corona gap dropped to a critical

magnitude. The charging causes an induced field in the build platform, modeled by a

surface charge Gb. The corona voltage is a known value. The model of the charging

process is shown in Figure 5-3.



/ Vorona
S'4
Corona
Gap
(do, Ka,
Pc)
Toner (dt, Kt, ot, Pt) 3
2
1
Air (da, Ka) 0
Plate (Gb
Ground

Figure 5-3. Model of the corona charging stage

First, boundary conditions were defined. The conditions in this case were the

ground voltage on the bottom plate and the applied voltage on the corona, Vcorona. The

boundary conditions are shown in Equations 5.8 and 5.9.

Vo =0 (5.8)









V4 =V ..... (5.9)
4 corona

As before, the field in each layer was integrated to find the potential difference

across the layer. This process is shown in Equations 5.10 through 5.13.

da
V V= dx a= (5.10)
0 K'a0 K'a0


VI -V = dx .dx.b (5.11)
opE, K S0



0 Ktso Ktso Ktso 2tE (5.1

d Ut + td, +Cb + P bCAd" Ad dd eA Pcd 5
SV3 -V + dx= + c + + (5.13)
K a e Kap S KaS 2KeaEo

The next step was to sum the potential differences as shown in Equation 5.14. This

equation was then expanded with the calculated potential differences to yield Equation

5.15.

V-V4- = ,,,,, = -(V3 V4 )-(V2 -V3)-(V -V2 )-(Va -VI) (5.14)


1 da+d d d, d, d, d P (5pd2
VCorom -- +- +- + -t + Ptd,-- +-- (5.15)
6 p t t 2) 2, K) 2K I

To determine the field in the corona gap, it was necessary to solve for the induced

charge in the platform in terms of the system parameters, as shown in Equation 5.16.

Kd, d. d, d 2KP
EO corona C + d -Pd, --- + d ) -----
Ub = I 2 (5.16)
da +d, d, dt
a pK Kt

Finally, the field at the top surface of the part was computed using this charge. The

result is shown in Equation 5.17.










-d0 d d2 dp de Pcdid
E orona + +d' + dp + p,d,
ab + t + ptd, a p a / p 21, 2
lcaE C CEE

(5.17)

Using the equilibrium assumption of a zero field at this surface and simplifying the

equation for the surface charge density ot results in a solution for the maximum charge

density on the surface, ot,max, shown in Equation 5.18.


pd + soVorona ptd + +
Otmax c d d (5.18)



It is desirable that this value be large and positive. Although the charge density in

the corona gap was assumed to be constant, it is in fact a function of the corona voltage,

with an optimum value determined by the mechanics of the corona itself. This

relationship was not known precisely, so the constant value was used. Equation 5.4

demonstrates that it would be ideal to use either the optimum voltage, or if this was not

attainable, the maximum voltage that could be provided. At first glance it would appear

that the volumetric charge should be minimized, but the sign of this charge density will

be opposite that of the charge being deposited. Thus the negatively charged part in fact

enhances positive corona charging. As the part grows and dt becomes larger, the

volumetric charge density of the part will dominate the equation.

With the mechanics of corona charging determined, it became possible to examine

the mechanics of the printing process itself in a very detailed manner.









Transfer

The transfer stage of the ESFF system is both the most critical and most complex

stage of the entire process. It is necessary to model this system in order to find the

parameters that will insure that the amount of powder transferred is maximized, and that

the printing of each layer remains consistent. This will create a better build rate, and

improve part quality.

The system model was again a Gaussian series of infinite planes. This is more of an

approximation in this case than previously, because the photoconductor drum and the

model layers that are attached to it are in fact cylindrical. However, the radius of

curvature of these layers is orders of magnitude larger than the thickness of the layers, so

the approximation is a reasonable one. Furthermore, this model is too complex to be a

realistic numerical simulation, because too many parameters involved are either not

known with any useful precision or vary too widely over time for a realistic numerical

snapshot to be constructed. For this reason, the error introduced by the parallel planes

approximation is of little importance given the overall numerical uncertainty of the

simulation. This is not to say, however, that the model itself is not useful. It is enough to

know that the optimum system performance can be obtained by maximizing or

minimizing certain variables without necessarily finding numerical values for those

parameters.

This model again sought to simulate a system at equilibrium. It was assumed there

was an initial layer of powder on the photoconductor drum of thickness di, which was

transferred with efficiency r. An air gap was introduced between the photoconductor

drum and the part to simulate irregularities in the part surface. Two layers of toner are









now present on the build platform, the fused powder which has both a surface charge and

residual volumetric charge, and the fresh toner transferred during printing which has only

a volumetric charge of density pi. The model of the system is shown Figure 5-4.

Ground

Metal Drum (yd)
-7
Toner ((1-r di, Kt, p1) 6
5
Toner (rdl, Kt) 4
Toner (df, Kt, Pt)
2
Air (da, Ka)
Plate

Platform

Figure 5-4. Model of the printing stage

The boundary conditions here are the voltages on the platform and photoconductor

drum backing, shown in Equations 5.19 and 5.20.

V = pla~orm (5.19)

V7 =0 (5.20)

Again, the voltage drop across the model was found by integrating the fields as

shown in Equations 5.21 through 5.27 then summing as in Equation 5.28.


V -V6 d (5.21)
0 KIC0 KCI0


V6 V =- 'i Cd + plx dx =- Cd(1 ~)dpl pldl (I2l + d (5.22)
0 K Ktto 2Ko )


V4 -V5 fd IC-' "'0dx IdC 'ICA ll (5.23)
0 Kg Ka80 Ka8O )










v d Cd +P (1 -)d, +
V3 -V 4 =-f

o K t d

V2 3 d + Pld+ +o, + pt, X
0 K', 0

dp
V2 3 fV3

0 t 60
Vd -V d7dPId +a,+ pd, d

d

Vo V JUd+PId +, + pd,
0 ,a0


6 0a 1i


x =-dqdl 2 2-2
It + 22P J2 0
StKo 2K,so

_( ddf plddf +o,df p,d 2
KIto Kto K o60 2KtO


apdd, p + ldp + ,dp
+ +P 0 p0
Kp80 Kp80 Kp80


a Udd,
Sae0


+ Adid + ud
a60 a60


p d, d
+
Kp0
,~G PJ~p


d, +d dg+da dp
t a +
Kt Ka Kp K


1- 2 + 2d + 2d (1- 7)dg +C d d


+ df


Kp d~
IC p KIa


2 p d d,P+lK
\+p <,d \-- +


d1a
Ica


(5.28)


The next step was to solve for the induced charge od, shown in Equation 5.29.


1-2+2dl +2df (1-r7)dg +d d
-p Id, 2 f +
2K, ra Kp


d 0 platform
+L


d d+ da a df dp d
-a\ /-+--+--\-p,dl--- +--+--/
Ict ICP Ic Ic C Ica

(5.29)

To manage this complex equation, coefficients are defined as shown in Equation


5.30.


Np,df


SoVplaom Lpld M ,


(5.30)


(5.24)



(5.25)



(5.26)



(5.27)


d + d, +d d +d
+ +









The next step was to solve for the field in the printing gap, Ec, in terms of the

defined system. This field equation is shown in Equation 5.31.

E a+pd I, cVprm + (Pr L)p -M, -Np,df (5.31)
E = (5.31)
KaS0 PKa80

Only the pi coefficient contains rl, so expanding P 1-L will allow for solution in

terms of l. First, the field equation is solved in terms of this quantity, shown in Equation

5.32.

S PKrCoEc + EoVpzParm + M-c + Np,df
Pr- L= (5.32)
p, d

Next, the quantity Pq-L is expanded. Because the L term contains q, the equation is

separated to isolate the efficiency term. The result is shown in Equation 5.33.


P1-L= d- +df d, +da d, Ia-Cdg,
^ Kt Ka Kp KaKt
S(5.33)
1+ 2d + 2d, d +da dp
-+ +
2Kct IcK

Substituting Equation 5.33 into Equation 5.32 yields a solution for q, shown in

Equation 5.34.

l1+2d, +2d d +d d P
PKI8CE, + ,oVP jarm +MOt + Nptdf, + p+1,
2KcIa KIC
2 =
7(d, d, +d, d +da dp Ia Kd
I K" t Ia K'p Ica )t

(5.34)

Substituting the value for ot found in Equation 5.18, an equation for the efficiency

in terms of both printing and corona-charging parameters is obtained. This result is

shown in Equation 5.35.










q = { oVplatform
d = di,+ddf dg +da d a-dg O laKf-oKrr

d,+2d+ d, f + dg + d
SKt Ka Kp KaKtP

df d, da
K, Kp Ka d di +df d, +da dp
OVCorona + + + + aoE,

da d a p
+



1+ 2d, + 2df d, + da dp r r, r /C 'a dc

S 2d + d +d o + 2



K a Kp d
df d d a



(5.35)

In order to make this equation more manageable, constants are defined. This is

shown in Equation 5.36.

EoVplatform CV+C rna+C2E +C3p1 +C4p, +C5pt
77= (5.36)
C6p,

Now that the model solution for printing is solved, the next phase is to analyze this

result and learn what it means. The constant thicknesses and material properties may be

ignored, since they are unalterable.

The platform voltage, corona voltage, and critical transfer field Ec are all multiplied

by the permissivity of free space, so. Because this constant has a value of 8.85x10-1s C2

V2 / mm2, the magnitude of these three contributions will be orders of magnitude less

significant than other factors. For this reason the impact of these three variables can

reasonably be assumed to be negligible.









The contribution of the volumetric charge density in fresh toner, pi, is complex,

especially in that it has a contribution both to the numerator and the denominator. The

numerator contribution will grow with di, the initial toner layer thickness brought out by

the photoconductor drum. It will also grow with the fused part thickness df. Finally, the

numerator contribution will grow proportionally with the transfer gap dg and the substrate

irregularity gap da. The contribution of the denominator term will follow these trends as

well. The multiplier of the denominator term should be larger in general, so the

magnitude of the charge density in fresh toner should be small to increase the amount of

toner transferred. This is reasonable, since a more highly charged toner will require less

transferred mass to cancel the field.

The corona gap charge density p, is more straightforward. This term exists only in

the numerator, so it should be as large as possible. The multiplier of this term will grow

with fused toner thickness, because as seen earlier the charge in the fused part can attract

more charge from the corona. There is also a dependency on the air gap thickness, but

this term exists in both the numerator and denominator of the multiplier term. As such the

impact of the air gap in this term will be mitigated to a degree.

The final term to be considered is the volumetric charge in the fused toner. The

charge density pt has a negative sign, and its multiplier is positive. This means the overall

contribution of the fused toner charge will be negative, despite its effects in the corona

charging process. The contribution of this charge density grows very quickly with part

height, and shows variation with substrate adhesion.









Agreement of Model with Experimental Data

In order to evaluate the model of the printing stage, a computer simulation was

constructed based on the model. The print cycle was then simulated over a range of

volumetric charge densities in the fused toner to study the impact of discharging the fused

powder on the part build rate. The values for the variables were the known values were

applicable. Many values are unknown, however, or vary greatly. For these variables,

values were selected that were deemed realistic. As such, the simulation is not an

accurate numeric depiction of expected results, but such a depiction was not expected.

The value in the simulation lies in showing the trends that occur as certain parameters

vary. The values used in the simulation are provided in Table 5-1.

The computational method used in the simulation was fairly simple. The part height

began at zero. For the parameters used, the transfer efficiency was calculated, then an

assumed value for the amount of toner brought out by the photoconductor drum was used

to calculate the amount of toner transferred. This process was repeated over 500 prints.

The charge density in fused toner was varied to analyze the changes in the system due to

the efficiency of discharge. The other parameters were held constant. This is an

unrealistic assumption, but provides an understanding of the impact of a specific variable.

The results of the simulation are shown in Figure 5-5. The part height is given in inches

for comparison with experimental data below. The code for the program is provided in

the Appendix.









Table 5-1. Parameters for numerical simulation
Symbol Meaning Value Source
da Mean substrate irregularity thickness 0.1 mm Estimated
d, Corona gap thickness 10.16 mm Measured
df Fused toner layer thickness Variable
d Mean printing gap thickness due to 0.05 mm Estimated
surface irregularity
di Insulation layer thickness 0.01 mm Measured
di Initial drum toner layer thickness 0.02 mm Estimated
dp Paper Thickness 0.25 mm Measured
Electric field in printing gap at which
Ec adhesion and electrostatic forces are 50 V / mm Estimated
equal
Vcorona Voltage applied to corona 5000 V Controlled
Platform Voltage applied to platform during 1000 V Controlled
Vplatformn 1000 V Controlled
printing
8.85x10-18 C2 V2 Scientific
so Permissivity of free space mm2 Constant

Ka Relative permissivity of air 1 Estimated
K, Relative permissivity of insulation 3 Estimated
K, Relative permissivity of paper 2 Estimated
Kt Relative permissivity of toner 3.42 Measured
L Transfer efficiency over printing gap Variable
pC Charge density in corona gap 2x10-6 C mm-3 Estimated
-7.28x10-9 C
pi Charge density in fresh toner .3 Esitmated
mm3
Charge density in fused toner Var
Pt Variable
t on platform
Charge density on fused toner on Var
t latfoVariable
platform












Part height as a function of number of prints and charge density in fused toner




0 06

005

0 04

003

002

001

0-
500
400 I
300 -2
200 4
100 7 x10
0 -9
Print number
Charge density magnitude in fused toner (C mm 3)



Figure 5-5. Results of simulation of printing model


For all charge states the build rate was quicker for the first few layers, where the


field generated by the platform voltage still had a major impact. The build rate then


experienced a falloff. For full discharge this falloff was very minor, but if the discharge


was less efficient the falloff was significant, almost creating a plateau.


This result was consistent with observed behavior over a very large number of


samples in ESFF testing. The number of prints is obviously simple to control, but the


charge density is problematic to vary, or even to measure after the discharge during


printing. However, many of the parameters such as the relative permittivity of the


materials can be reasonably assumed to vary only slightly. Discharge would vary over a


greater range, so its impact should be more noticeable. The experimental data are shown


in Figure 5-6.











Part Height vs. Number of Prints


1.20E-02
*
1.00E-02 A

o- 8.00E-03 A



a 4.00E-03
0l


2 .00E -03 `

0.00E+00
0 5 10 15 20 25

Number of Prints

Build A Build 2 x Build 3 o Build 4 Build 5 -Average


Figure 5-6. Experimental printing build rates

The experimental data shows that the prints began with a similar build rate, which

then decreases over time. They also show that the variance in the different part models

becomes greater as the number of prints increases. This data is consistent with the above

simulation results for variations in build rate due to differences in discharge.

Undoubtedly there were variations in many of the parameters taken as constants in the

simulation, but it is reasonable to assume that the charge state varied more significantly,

since the dielectric properties of materials are regular, and the variations in thickness of

the layers would be randomized across the area of the print.

Conclusions

Overall, it would appear that the part would continue to build indefinitely with

adequate corona charging, but that the average build rate would decrease drastically after









several prints. This is in line with many observations over long printing times. These

results indicate the need for consistent discharge of the part in the current transfer model.

Inconsistencies in the adhesion of the substrate to the build platform will yield a

warped part surface. This is, of course, undesirable. This effect has been observed in part

builds in the past. It is difficult to overcome this problem in the current system, because

the paper substrate is merely clipped onto the build platform. For the moment this effect

seems to be beyond solution for the project. Ultimately, it would be desirable to have a

build platform machined that would have a much smaller tolerance for surface

irregularities. Adhesion of the paper substrate more tightly to the platform is also

difficult. An adhesive backed paper would mar the build platform and be difficult to

remove. A vacuum system would solve these problems, but would be expensive, difficult

to install, and might leave vent holes behind the paper which would exacerbate the

problem.

Another troublesome result of the analysis was the problem presented by

irregularities in the printed part surface. Not only are such irregularities undesirable in the

first place, they appear to have a self-propagating nature. There are finite limitations on

the ability to print a part regularly no matter how well the process is managed, and this

result shows that over a large number of prints the quality of the part will decrease.

The solution to this issue is to create a planar surface on the top of the part after

every print. This is in fact the purpose of the compaction during the fusing stage.

However, the compaction pressure needed to reduce irregularities in the part surface is

also sufficient to deform the part under heating. To allow proper compaction, it would be

necessary to surround the part with another powder to provide the needed support during









fusing and compaction. Printing the background of each layer in another powder would

accomplish this. The building part would then be encased in a block of secondary

powder, which would provide a support structure as well as allow proper compaction.

The secondary powder could be selected to allow easy removal during post-processing.

It is also necessary to read between the lines of the analysis. The charge densities

were assumed to be constant. However, in real life these densities will vary both between

prints and across the cross section of the part. Variations in powder charge across a cross

section could easily have the same self-propagating impact mentioned above, as not only

the amount of powder developed at a given location for a given print but also the residual

charge at that spot in subsequent prints would be impacted. Corona charge density would

not have as much of a long-term impact, but would impact a given layer, which is a self-

propagating situation in and of itself














CHAPTER 6
PATTERN PRINTING

Introduction

One of the major problems in electrophotographic printing is the phenomenon of

edge printing, where the edges of a solid print area are dark but the center appears faded.

This effect is due to the fact that the electric field gradient at the edge of the image is of

much higher magnitude than that in the center. This effect is not seen in the printing of

thin lines because the entire print area is within the range of the strong field gradient.

For electrophotographic solid freeform fabrication, this is a subject of special

importance. If the edges of a solid area consistently build faster than the center, soon

there will be a gap between the center of the print area and the photoconductor drum,

causing even less toner to transfer in successive images until only the edges build at all.

For this reason, it is desirable to use thin lines for ESFF in order to assure a more

consistent print across the cross section.

However, it is unrealistic to develop a rapid prototyping technology around a

specific type of cross section, as this would severely limit the number of applications.

Therefore it was decided to create a pattern of thin lines within the cross section in order

to break up the solid area and hopefully take advantage of the properties of thin line

printing.

Theoretical Model

The effect behind edge printing is well documented. The exact characteristics, like

many things in electrophotography, are very dependent on the individual characteristics






60


of the system. For this reason the simplest way to study the problem is finite element

analysis. The effect in this electrophotography system was first modeled by Sivakumar

Bhaskarapanditha, and it was found that a dramatic peak in field did indeed occur at the

very edge of a solid area image, with the center of the area having only a very slight field

(Bhaskarapanditha 2003). The physical model of the system is shown in Figure 6-1, with

the simulation results shown in Figure 6-2. The left half of the figure is the image area.

Although the field in the middle of the image here appears to be zero, it is in fact roughly

3.6x107 N/C, several orders of magnitude smaller than the value at the edge but still

positive. This large difference in electric field will lead to much faster growth at the

edges.

This was followed by a study of an alternating line pattern with lines of width 0.2

mm. A unit of the repeating pattern was modeled with several elements along the length

of both the charged and discharged areas. The model used by Mr. Bhaskarapanditha in

this simulation is shown in Figure 6-3, with the simulation results in Figure 6-4. The

charged area is in the center, with the discharged image areas on either side.




Charge per unit volume Development Roller (at V t! )
. .. . .
SNo Charge ** .'.. '. ...'.



STon .r Plihotoconducitor Drum (G rounded)
1 1 [fonerl
'iii Insulation


Figure 6-1. Solid area printing model (Bhaskarapanditha 2003)






61


Edge Growth


Figure 6-2. Solid area printing model results (Bhaskarapanditha 2003)


x


Chad Rgi
Charged Region


Figure 6-3. Pattern printing model (Bhaskarapanditha 2003)







62



Pattern Model (zoomed in)

6.OE+10I



2-00E+10--
X OAxis Ditatce of nods flon origin Imk
OOE+O0 .. ,, .. .
I _L L ?_
I~~~~~~l~ ', i : i 6 .


wI


-.UUOE+IU

d0.fE+10
J _OOE+ 10------------ -----------------I


-1 DlO E+I1 L--------------------------------------------

-IAOE+I

-1.40E+11-----


Figure 6-4. Pattern printing model results (Bhaskarapanditha 2003)

This simulation shows much preferable field effects. The edge effect is much less

noticeable, and there is a near-uniform field across the image area, meaning a more

consistent transfer of toner in regards to image field.

Thus pattern printing offers at least the possibility of an end to the edge effect. The

next step would be optimizing the pattern print in terms of both hardware and software

for the actual system and testing how it worked when applied.

Due to the programming language used to create the cross section images from

solid areas, the line widths have a set resolution of 1/72 inches (roughly 0.35 mm), and

all line patterns must be based on increments of that resolution. The patterns are created

by first creating an image using the part files as usual. The image is then overwritten with

a series of white lines. Finally, the outline of the part cross section is traced again in order

to maintain part cohesion.









A new analysis was necessary to find the ideal width of both the black lines in the

print and the white lines dividing them in order to maximize field and prevent any areas

of low field within the solid area. The new finite element analyses followed those

previously performed as closely as possible. The insulation layer was modeled with a

thickness of 10 micrometers, with a permissivity of2.6553x10-11 F/m. The toner layer

was specified to have a thickness of 30 micrometers, a permissivity of 3.09785x1011

F/m, and a volumetric charge density of-7.058 C/m3. The charge deposited on the

insulation was specified as 1x10-4 C/m2. The bottom of the insulation was specified as a

ground, and the top of the toner layer was specified as the developer roller mean voltage

of -500 V. These values were all taken from Mr. Bhaskarapanditha's thesis.

Two sets of analysis were performed, one holding the thickness of the charged area

constant and varying the thickness of the discharged area, the other holding the thickness

of the discharged area constant and varying the thickness of the charged area. This

models altering the white and black line widths in the printed pattern. Presenting the

entirety of the resulting data would be tedious and unnecessary. For the purposes of this

evaluation, the values of importance were the median field in the charged and discharged

regions, which govern powder transfer and image clarity. The strength of the peak values

near the edge of the pattern was also of interest, as these would govern the uniformity of

the print. The results of the two analyses are shown in Tables 6-1 and 6-2, respectively.










Table 6-1. Results of varying the discharged area width


1 1 1.272E+09 1.276E+09 -2.557E+09 -2.557E+09
2 1 1.260E+09 1.260E+09 -2.466E+09 -2.473E+09
3 1 1.224E+09 1.224E+09 -2.542E+09 -2.542E+09
4 1 1.295E+09 1.295E+09 -2.473E+09 -2.473E+09


Table 6-2. Results


of varying the charged area width


4 1 1.295E+09 1.295E+09 -2.473E+09 -2.473E+09
4 2 1.229E+09 1.229E+09 -2.538E+09 -2.547E+09
4 3 1.229E+09 1.231E+09 -2.530E+09 -2.616E+09
4 4 1.229E+09 1.375E+09 -2.530E+09 -2.681E+09

The discharged field strength in the center of the line seemed to vary only slightly

with changes in the discharged area, with less than a 6% change overall. No change was

observed in this value due to varying the charged area. This would indicate that in the

range evaluated in the test, this field strength is more or less constant. Under the

circumstances, it is always desirable to maximize the amount of the part cross section

being printed, so the thickest line would be the best choice.









The peak of the discharged field strength also had little variation in relation to the

discharged line width. There was a very slight peak in the thinnest line width, but its

strength was negligible. In varying the charged area widths, however, the peaks quickly

became noticeable as the white line width increased. This indicates that as the black lines

are separated, they act more and more like large solid areas. This would indicate the best

prints would come from having thin white lines breaking up the solid area.

As for the charged area field strength and its peaks, they were of lesser concern.

Had there been a large reduction in this field strength it could have meant that under

certain conditions the white area of the print would lose its field strength, possibly

resulting in significant background development. This did not occur, but there was a

slight increase in field strength magnitude and a significant increase in peak strength

when increasing the white line width. This would mean that in printing a larger white line

in the pattern would yield sharper, more differentiated lines. This would offset the above

disadvantage due to discharged peak magnitude.

Experimental Results

In order to verify the results of the finite element analysis, an experiment was

conducted to test the various characteristics of pattern printing. A particular set of parts

was printed multiple times with different patterns as well as with normal solid area

printing. The height and mass of the part were measured, and the various prints were

ranked in terms of print quality. The print quality rankings were by necessity a subjective

measure, but unfortunately there was not a readily measurable metric available to

compare the various prints in terms of how well the pattern overcame the solid area

printing issue. The subjective quality of the prints was based predominantly on whether

and to what degree they overcame the very noticeable gaps caused by the edge effect,










however, so the assessment was based on readily visible and discernable characteristics.

In the end, these quality rankings did not diverge greatly from the other metrics

regardless.

It was decided that the testing pattern would be to vary the black line width

between 1/72 and 4/72 inches in order to keep the test space to reasonable bounds. The

width of white lines would be varied between 1/72 and the width of a given black line,

because it was not desired to depart significantly from a fully dense part. The part was

then printed for roughly 15 layers to allow the results of the pattern to sufficiently emerge

while minimizing test time. The experimental results are presented in Table 6-3.

Table 6-3. Pattern printing experimental results

Black line width White line width Average layer Average layer mass
height
(1/72 inch) (1/72 inch) hegh(g/print)
(inch/print)
1 1 5.5E-04 5.53E-02
2 1 5.9E-04 5.14E-02
2 2 5.7E-04 5.30E-02
3 1 5.7E-04 5.50E-02
3 2 6.2E-04 5.22E-02
3 3 6.0E-04 5.19E-02
4 1 5.6E-04 5.12E-02
4 2 5.8E-04 6.55E-02
4 3 6.4E-04 5.72E-02
4 4 6.5E-04 6.60E-02
Solid N/A 5.7E-04 5.63E-02
Average: 5.9E-04 5.59E-02
Deviation: 3.3E-05 5.27E-03

This amount of data is difficult to analyze simply by looking at it. The best print in

terms of the two quantitative metrics was roughly two standard deviations above the

average in both measurements, indicating a significant improvement in print quality.

Traditional solid area printing was near the average in both metrics, implying that many

patterns were improving the printing process. To find the optimal pattern a ranking table

was constructed, with a subjective metric added based on visual print quality. An average










of the height, mass, and quality rankings was used to compare the various patterns. The

ranking table is presented in Table 6-4.

Table 6-4. Pattern printing rank table

Black line width White line width t Rk Ms R Quality Average
Height Rank Mass Rank
(1/72 inch) (1/72 inch) rank Rank

1 1 11 5 9 8
2 1 5 10 5 7
2 2 9 7 7 8
3 1 7 6 10 8
3 2 3 8 3 5
3 3 4 9 1 5
4 1 10 11 8 10
4 2 6 2 6 5
4 3 2 3 4 3
4 4 1 1 2 1
Solid N/A 8 4 11 8

For demonstration purposes, some of the resulting pattern prints are shown below.

Some digital editing was done to the images to reduce background print density for better

visibility. A print with no pattern is shown in Figure 6-5. A print with a white and black

line width of 1/72 inches is shown in Figure 6-6. A print with a black line width of 4/72

inches and a white line width of 1/72 inches is shown in Figure 6-7. Finally, a print with a

white and black line width of 4/72 inches is shown in Figure 6-8. The solid circular part

is 0.75 inches in diameter.

As can be seen in Table 6-4, there are several patterns that produce prints superior

to the solid area print. It can also be seen that the very fine patterns did not perform as

well as the solid area. From what was seen in the resulting parts it would appear that the

fine patterns do not have sufficient gaps between the lines to overcome the solid area

effect, and thus suffer the same setbacks, along with an additional disadvantage of only

part of the cross section being filled. It is also likely these parts suffered from mechanical

failure during fusing, since very thin lines would have difficulty tolerating compaction.







The prints with broader white lines seemed to overcome the solid area issue and print
more like lines. This is advantageous in terms of both print quality and mass. In terms of
height, it has been known from previous efforts that fine lines tend to collapse during
compaction as part height increases. Thus a wider black line yields a superior part in the
long run.


Figure 6-5. Print with no pattern


Figure 6-6. Print with a 1/72-inch black and white line pattern


~s~c~P~
































Figure 6-7. Print with a 4/72-inch black line and 1/72-inch white line pattern


Figure 6-8. Print with a 4/72-inch black and white line pattern









There are boundaries to these trends, however. At some point, a sufficiently broad

black line will become subject to the solid area problem itself. The benefits of a white

line will suffer diminishing value once the black lines are sufficiently isolated to prevent

solid area printing issues, and further white line width will merely serve to decrease the

amount of printed material.

To study the effects of pattern printing over a larger number of prints, as occurs in

part building, a group of parts were studied over a printing range of 250 prints. Based on

the earlier findings, a pattern of 4/72-inch white and black lines was selected. This

included some large solid parts to study the efficacy of pattern printing at overcoming the

solid area printing issue. Also included were some parts with small details, a critical test

of the pattern printing method as it applies to rapid prototyping applications. The printed

parts are shown in Figures 6-9 and 6-10. For comparison purposes, an image of the parts

in Figure 6-10 printed without patterns is shown in Figure 6-11. Background printing has

again been digitally removed for visibility.


Figure 6-9. Pattern printing parts, 250 prints







71






.. ,, "" .







Figure 6-10. Further pattern printing parts, 250 prints

















Figure 6-11. Comparison image of parts from Figure 6-10 without pattern printing (Dutta
2002)

The results of this test were mixed. Solid area parts continued to build consistently,

with no appearance of edge effect. This verified the purpose of pattern printing. Parts

with fine detail, however, have significant problems in print quality when the pattern

printing method was used. The pattern broke up the fine details, either eliminating them

entirely or preventing the parts from surviving the fusing and compaction process. This

would indicate that pattern printing should only be used for parts with large solid areas.

Conclusions

The experimental results indicate that pattern printing can indeed provide a superior

part to solid area printing, both qualitatively and quantitatively. From the results it would









appear that a broad black line with a broad white line seems to be the best pattern. It is

probable that the current set of experiments did not find the optimum pattern, given that

the best results were found at the limits of the test space. However, these results will

serve to improve the quality of printing, so they are useful.

The experimental results did not entirely agree with the finite element modeling.

Increasing the black line width within the test range did result in superior printing.

However, increasing the white line width did not appear to cause any edge development.

It is possible that the variance in field change predicted by the finite element analysis was

so small that its effects were not noticeable, and that the positive effects of stronger

charged area field differentiating the black lines in this case was more significant.

The printing of finely detailed parts showed a significant problem with pattern

printing. The pattern method proved more problematic than useful in this application. To

be used with finely detailed parts, as would be necessary in rapid prototyping, the

patterns would either have to be made finer depending on the part detail, or they would

have to only be applied to parts with large solid cross sections. This would prove difficult

in the current software arrangement, but would not be infeasible.

Future Work

A larger test space would obviously be advantageous. Also, refining the control

program in order to allow for finer resolution could allow a better result to be found. Both

of these would be too time-consuming for current project goals, however.

Another line of research that could prove fruitful would be to study the effects of

patterns other than a simple alternating line pattern. A grayscale could be used to

counteract the edge effect and yield a uniform part, or a dot pattern might allow sufficient

isolation of black areas with a printed area percentage. However, there are any number of









possible patterns, and a better theoretical understanding of the process would be desirable

rather than randomly testing patterns to see which work.

Also, it would be useful if a fully dense part could be created by printing the

normal pattern on one print, and filling in the white spaces on the next print. This was

originally planned as part of the pattern printing system, but unfortunately hardware

problems with the current system prevented it. There was an issue with the imaging

system not returning to precisely the same origin after each print. Thus a subsequent print

would be offset by a fraction of the software resolution. After several prints of this the

portion of the part where several prints had overlapped would be much thicker than

surrounding areas, leading to the same issues as with edge printing. A better-controlled

printing system would solve this issue, but would require more time and money than is

devoted to this project. This alternating printing arrangement could offset the problems

associated with finely detailed parts.















CHAPTER 7
DESIGN OF AN ELECTROPHOTOGRAPHIC DEVELOPER SYSTEM

Introduction

The developer system in a printer is the system responsible for transferring

powder to the proper areas of the photoconductor drum. A typical development system

stores the powder, charges the powder, transports the powder, and transfers the powder to

the photoconductor drum. A simplified schematic of a development system is shown in

Figure 7-1.

Doctor Blade

Powder
I Hopper



Transfer
Photoconductor Roller
Drum



Figure 7-1. Development system schematic

The main components of a developer system are labeled in Figure 7-1. The powder

hopper is a receptacle filled with toner powder. The doctor blade is a metering device

used to control the thickness of the powder layer being brought out of the hopper, and is

often a part of the charging system. The transfer roller serves to move the powder and

bring it near the photoconductor drum.









Developer System Fundamentals

Powder Storage

The storage of powder is a very straightforward part of the development process. In

general, developers will have a hopper of some variety filled with toner powder. Some

contain a stirring apparatus to prevent the very fine toner powder from agglomerating

into a solid mass. Many commercial systems will also have specially designed access

points to allow for refilling of the cartridge during recycling, and some new developers

contain electronic safeguards to prevent unauthorized recyclers from tampering with the

cartridge. The main concerns in this stage are that powder be prevented from leaking, and

that it be possible to replenish the powder supply when necessary.

Powder Charging

The proper charging of powder is critical to the electrophotographic imaging

process. If powder is not adequately charged, it will not transfer to the image areas. If it is

too highly charged, a very thin layer of powder on the image will be sufficient for charge

cancellation and the image will be very faint. If the powder is not charged consistently

there will be noticeable variations in imaging between prints or even within an image. If

powder charges to the wrong sign, there will be background printing in the final result.

There are currently three main methods used for powder charging: corona charging,

injection charging, and triboelectric charging.

Corona charging

Corona charging of powder works on the simple principle of subjecting a powder

layer to a stream of ions. The physics of corona charging have been covered at length

elsewhere in this paper, so they will not be discussed in detail here. The fundamental









problem with corona charging of toner is that powder particles may be airborne in the

developer and may then coat the corona wire, preventing it from being effective.

Injection charging

Injection charging is a very straightforward method for charging a wide variety of

powders. The powder particles are exposed to a significant voltage. This is often

accomplished by applying a voltage to a metallic foil attached to the doctor blade, which

powder must rub against as it passes by. The outer surface of the insulative toner material

will take on charge as it rubs against the surface. This is a very effective and popular

means for powder charging, with the minor issue of requiring the use of a high voltage

power source.

Triboelectric charging

Triboelectric charging is used in most current-generation printers, often in

conjunction with injection charging. In this charging method, electrons jump from one

material to another, causing a resultant positive and negative charge on the two bodies.

The triboelectric effect occurs between specific materials, so when used in development

the toner and triboelectric surface must be chosen carefully. This surface is usually a film

on the doctor blade, where it is known the toner particles will rub against the surface. The

excess charge on the film can be dissipated by means of a connection to ground. Special

charge control agents added to the toner powder cause it to charge triboelectrically.

Powder Transport

The movement of powder from the hopper to the photoconductor drum is a very

important and very difficult step in the development process. For proper imaging, a

consistent layer of powder must be moved to the photoconductor drum without spilling.

The doctor blade helps to maintain a consistent layer thickness so long as the transfer









roller is initially bringing out a layer thicker than the doctor blade is designed to meter

out. There are two main methods currently used for powder transport: magnetic and

cascade transport.

Magnetic transport

Magnetic transport is by far the most popular method for transporting powder. In

this method, the toner particles are doped with a magnetic substance, usually an iron

oxide compound, and the transport roller has a magnetic core that provides an attractive

force for the particles. Either the magnetic core itself or an outer frictional roller revolves,

circulating the powder with it. This method of transport virtually eliminates spilling,

keeps powder flow consistent, and makes it fairly easy to predict the amount of powder

the roller will draw out.

There is the added advantage that in the transfer stage, the particles must overcome

the magnetic force by electric field force, which greatly reduces the transfer of wrong-

sign charged toner. However, there is one notable disadvantage to this method, and that is

the requirement of a magnetic material. In printing this means the method is only useful

for black toners, and the method is not favorable for ESFF because it introduces

significant restrictions on the toner material.

Cascade transport

Cascade transport is so named because in the very early days of

electrophotography, images would be developed by pouring or "cascading" charged toner

down a plate with a latent charge image. Toner would stick to the image areas due to

electrostatic force, forming an image that could be transferred for permanent printing. In

a modem system this process is a bit more complex. Toner is brought out of the hopper

by mechanical force, usually friction, by a roller. A layer of the toner on the transfer









roller then passes near the photoconductor drum, where particles are attracted to the

properly charged areas. Because there is no adhesive force between the transfer roller and

the toner, the doctor blade can knock off more powder than it is meant to meter, causing

uneven prints. There are also unavoidable spilling problems.

This development method is necessary for color printing with electrophotography,

but with ink-jet printers becoming comparably fast to laser printers the drawbacks of the

system are preventing it from being used. This system is needed for ESFF using a

traditional drum printer, however, because it can develop arbitrary powders.

Powder Transfer

The final step of the development process is to transfer powder to the image on the

photoconductor drum. The quality of this process in a given system is fundamentally a

balance of forces. There is the electrostatic force pulling the charged particles towards the

image, the attractive forces which draw the particles towards the surface to which they

are most closely adhered, and the attractive forces between particles. Ideally, there would

be a strong tendency for particles to stay on the transfer roller due to attractive forces

except where drawn off by electrostatic effects. This produces a clear image with

minimal transfer in the background areas.

This is easily accomplished in magnetic powder transport because of the strong

magnetic attractive force. The charged powder is caused to jump on and off the roller by

an AC field, creating a cloud of powder around the roller. The magnetic strength of the

roller and the AC voltage can be varied to optimize printing.

Cascade transport suffers more difficulties in this area. Because of the high surface

area to density ratio of most toners, especially polymer toners, the electrostatic and van

der Waals forces are orders of magnitude larger than forces pertaining to mass. This









means that these powders will not be firmly adhered to the transfer roller, and that

interparticular attraction will be very significant. For this reason, cascade systems will

have significant background printing. Also, if the toner from previous prints is not

adequately cleaned from the photoconductor drum, it can act as a "seed" to attract

powder in subsequent prints due to the interparticular attraction.

Evolution of ESFF Developer Design

In past work with the ESFF testbed, it has been necessary to use standard printer

toner to build parts because of the lack of a system to print other powders. This is

disadvantageous, in that the toner powder used in laser printing produces brittle parts, and

that simply printing small plastic parts would not be a significant advancement in the

field of rapid prototyping. For reasons of construction simplicity and flexibility in terms

of which powders would be printed, it was decided to use a design based on cascade

transport and injection charging. This combination allows for development of nearly any

insulative powder.

The first developer design is shown in Figure 7-2. The first design for this

developer was a very simplistic device involving a powder hopper, a developer roller,

and a cantilevered doctor blade actuated by a screw plate. Plastic pieces were built to

encase the transfer roller on the sides and bottom. A press fit piece in one side allowed

the roller to be removed laterally through a large opening. The roller itself pressed against

the photoconductor drum directly. It was believed this would balance forces causing

powder to adhere to the surfaces, leading to better development. The LaserJet 4

photoconductor drum is roughly 1.2 inches in diameter.











L I
Doctor Blade

Powder Hopper



Screw Plate

Dex elopei Roller






Photoconductor
Drum

Figure 7-2. Cross-section of original developer design

This design suffered from a number of shortcomings. The plastic casing was not

adequate to prevent leaks. The doctor blade was not rigid enough to maintain a consistent

powder flow across its length. Finally, the direct contact between the transfer roller and

the photoconductor drum led to powder being sheared off at the intersection of the

rollers, causing an unacceptable spillage rate. The bottom lip of the developer was also

insufficient, because it sat too high and too close to the transfer roller to catch any

powder which spilled off the bottom side of the roller due to gravity. The distance

between the roller and the mouth of the powder hopper often caused powder flow to cut

off, but was necessary for the cantilevered doctor blade.

Measures were taken to try and correct these problems within the context of the

same basic design. The second design of the developer is shown in Figure 7-3. The

plastic casing had foam gaskets added to reduce leaking. The roller was assembled by










sliding it into narrow, baffled fittings. The bottom lip was brought as close as possible to

the photoconductor drum to catch any falling powder. Offset rollers were added to

provide a small gap between the transfer roller and the photoconductor drum, thus

preventing spilling due to powder shear. The doctor blade was changed to a leaf-spring

actuated design wherein powder would have to slide past the blade over a longer

distance, leading to more consistency regardless of particle size. Also, small protrusions

were added to the side of the casing which were meant to keep powder from reaching the

side connections, further reducing leaking.


Powder Hopper


Leaf Spring


Doctor Blade


Photoconductol
Drum Developer Roller


Figure 7-3. Cross section of improved developer design









This design suffered from some of the same problems as the previous design, but

showed improvement in many areas. Powder leaking from the casing itself was greatly

reduced, almost to the point of being eliminated. The offset rollers used were not

consistent enough in providing a gap and allowing proper rotation of the roller, and had

to be abandoned. This reintroduced the shearing problem seen before. The extended

bottom lip was still not able to catch all falling powder. The doctor blade had improved

consistency, but was more difficult to actuate if a different flow rate was desired. The

side protrusions added a great deal of friction, making the developer difficult to drive.

It was clear at this point that a different design path was needed. This resulted in

another design, shown in Figure 7-4. Successful ideas like gaskets and baffled fittings

were kept and expanded, with almost all fittings now being baffled and gaskets added

wherever desirable. A printing gap was included to prevent spilling due to shearing of

powder in the printing interface. Instead of offset rollers, the gap in this system would be

provided by tapes on a metal developer roller, providing a very thin and very consistent

gap. A two-roller design was introduced, in hopes that by including an initial electrostatic

transfer across a gap, the amount of powder brought out by the system could be reduced,

and that the powder could then be effectively recirculated. It was also hoped this would

give greater control over the charge density on the powder that would form the toner

image.

This final design greatly increased the complexity of the process. The doctor blade

opening, the gaps between the two rollers and between the second roller and the

photoconductor drum, and the charge voltage can all be varied. This is advantageous, in

that it gives a great deal of control over the transfer process. However, there is a










significant drawback in that these variables must be controlled precisely and consistently

in order to maintain proper development.


Powder Hopper


i ) I lade


Photoconductor
Drum


Second
Developer
Roller


First
Developer
Roller


Figure 7-4. Cross-section of two-roller developer design

The doctor blade gap is on the surface a straightforward control system. The wider

the gap, the more powder is brought out. However, there are complications in controlling

this aspect of the developer. Because this developer system has two transfer stages, it will

be inherently less efficient than a single-transfer developer design. Therefore, enough

powder must be brought out to compensate for the loss in the process. If too much









powder is brought out, however, it will not be possible to recirculate all the excess

powder, and the device will clog. Furthermore, it is critical that the amount of powder

brought out be uniform. To achieve uniformity, precise control of the gap is necessary, as

are rigidity in the doctor blade and manufacturing tolerances.

The transfer gap between the two developer rollers serves as a control over the

charge density in the powder presented for final development. Powder will be attracted

across this gap by induced field on the second metal roller, caused by the field between

the developer voltage source and the grounded photoconductor drum. This field will

cause the metal roller to take a median charge state between the two rollers, attracting

powder from the first roller but being less attractive than the photoconductor drum. The

larger the gap between the developer rollers, the higher the charge in the transferred

powder must be to be attracted across the gap. Thus a small gap will serve to screen out

particles with the wrong charge sign, or with insufficient charge. If the gap is made too

large, only highly charged particles will be transferred, which will decrease the transfer

mass both as a matter of charging statistics and because a small mass of highly charged

particles can cancel out a large field. If the gap is too small, a larger mass of particles will

be transferred, and the layers of powder on the two developer rollers may contact each

other. Both of these trends could result in clogging of the developer.

The transfer gap between the second roller and the photoconductor drum is also of

critical importance. This gap will control the amount of powder transferred to the toner

image. The larger this gap is, the less powder will be transferred. If the gap is too small,

however, there may be shearing of powder between the two rollers. Furthermore, the

amount of powdered carried over from the first transfer is also important, since the









thicker the layer of powder on the second developer roller the larger the final gap must be

to prevent shearing.

The final control characteristic is the charging voltage. This voltage has two effects,

first in controlling the amount of powder charge, and second in determining the field

present between the photoconductor drum and the developer. As far as powder charging,

a higher voltage will result in a higher average charge density in the toner. As mentioned

earlier, to maximize the transfer mass it is necessary to charge the powder to a critical

threshold value, as too little charging will result in an inability to transfer, and too much

charging will result in a small powder mass being adequate to cancel the field. Thus from

the charging perspective, there is an optimal voltage. In establishing the overall field

across the entire development process, it would be ideal to have an arbitrarily high

voltage, since this will maximize the field and with it the mass of toner transferred.

Experimental Analysis of the Two-Roller Developer

Once the system was built, the next step was to analyze the performance of the

developer. The system would first be tested on the charge-measuring unit (Gokhale

2001). The unit allows the testing of charge and mass, such that the performance of a

particular toner powder or developer system could be measured and optimized. If this

testing was successful, the developer would then be used in the ESFF testbed itself,

where it could be used to actually deposit imaged layers.

Some success was seen in charging and transferring powder. Preliminary testing

with nylon powder showed that the device could transfer a powder layer across the

printing gap onto a grounded drum after charging. This showed the capacity for

electrophotographic development of an arbitrary insulative powder in its most basic form.









There were several major problems with the design, however. The complex design

was difficult to manufacture and assemble properly, making for improper fits and uneven

gaps. There was significant friction in the system, which made driving the developer

difficult and caused some jumping during motion. The powder flow was uneven across

the length of the developer, meaning that any toner images produced by the developer

would be badly uneven across their area, leading to deformation of cross sections as well

as significant difficulties in the printing of multiple layers. The gap between the rollers

proved difficult to control to sufficient resolution. When the gap was too small, there

would be additional friction from the rollers touching and the powder between them

getting compacted, as well as an overabundance of powder being brought out. When the

gap was too large, powder would not transfer to the second roller, preventing printing.

All in all, even after many enhancements the design of an effective cascade developer

proved unmanageable. The underlying difficulties of cascade developer design, which

plague even professionally manufactured systems, could not be overcome in the lab.

Conclusions

While no cascade developer proved useful for placement in the ESFF testbed for

part building, the developers did yield many insights into the printing process. Powder

leakage could be ignored in charge measurement tests, and the final generation of single

roller developer found use in a new charge measurement apparatus designed by Ajay

Das. Early testing also disproved a notion of field transfer to the grounded

photoconductor drum. It was demonstrated that surface charging of the drum was needed

for transfer, not just a grounded backing. This led to a reworking of the charge

measurement system to accommodate surface charging.









Although the developers performed poorly, this is not completely attributable to

their designs. These developers were manufactured on a fused deposition modeler in

order to produce a test part faster and to reduce costs. As such, the manufacturing

tolerances were not as rigidly controlled as they would have been if the parts had been

machined. Most parts were also plastic, which greatly reduced strength and rigidity.

In the long run, a method for developing new powders is critical to the project.

Once it was seen that conventional cascade development would not be capable of

achieving satisfactory development, it was decided to fundamentally alter the ESFF

testbed to accommodate a new development system that would seek to overcome these

new challenges. This design is discussed in Chapter 8.