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Numerical Simulation of Wear for Bodies in Oscillatory Contact

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PAGE 1

1 NUMERICAL SIMULATION OF WEAR FOR BODIES IN OSCILLATORY CONTACT By SAAD M. MUKRAS A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2006

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2 Copyright 2006 by Saad M. Mukras

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3 To my parents, Professor Mohamed Mukras and Bauwa Mukras, and to my siblings, AbduRahman, Suleiman, and Mariam

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4 ACKNOWLEDGMENTS I express my humility and utmost gratitude to Allah for his blessings in my life. Verily no success would have been achieved without his gra ce and mercy. I would next like to thank my parents for their support in my e ducational pursuits. I owe them mu ch more than I can ever give back. I would like to acknowledge Dr Nam-Ho Kim, my adviser, for the support that he has provided. Because of his advice and challenges, I ha ve matured as a student and as a researcher. I would like to thank my colleagues, friends and me mbers of the university staff that have also aided me. Indeed, it would be negligent not mention the support that I have received from the members of the Masaajid in Gain esville who have enabled me to feel at home while away from home.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES................................................................................................................ .........8 ABSTRACT....................................................................................................................... ............10 CHAPTER 1 INTRODUCTION..................................................................................................................11 Background..................................................................................................................... ........11 Scope and Objective............................................................................................................ ...14 Thesis Organization............................................................................................................ ....15 2 WEAR-PREDICTION METHODOLOGY FOR BODIES IN OSCILATORY CONTACTS....................................................................................................................... ....16 Introduction................................................................................................................... ..........16 Wear Model..................................................................................................................... .......16 Simulation Procedure........................................................................................................... ...19 Pin-Pivot Finite Element Model......................................................................................21 Geometry Update Procedure...........................................................................................22 Conclusion..................................................................................................................... .........25 3 EXTRAPOLATION SCHEMES............................................................................................30 Introduction................................................................................................................... ..........30 Constant Extrapolation......................................................................................................... ..30 Adaptive Extrapolation Scheme.............................................................................................33 Conclusion..................................................................................................................... .........34 4 PARALLEL COMPUTATION IN WEAR SIMULATION FOR OSCILLATORY CONTACTS....................................................................................................................... ....36 Introduction................................................................................................................... ..........36 Cycleand Intermediate Cycle-Update..................................................................................36 Parallel Computation........................................................................................................... ...38 5 WEAR-SIMULATION PROGRAM......................................................................................43 Introduction................................................................................................................... ..........43 Wear-Simulation Program Format.........................................................................................43

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6 Ansys Input Code............................................................................................................43 Contact analysis........................................................................................................44 Output of results.......................................................................................................44 Simulation Managing Code.............................................................................................45 6 EXPERIMENTAL VALIDAT ION OF THE WEAR-SIMULATION PROCEDURE.........48 Introduction................................................................................................................... ..........48 Wear-Simulation Validation...................................................................................................48 Step-Update Simulation Test...........................................................................................49 Intermediate Cycle-Update : Parallel Computation.........................................................50 Conclusion..................................................................................................................... .........51 7 WEAR-SIMULATION EXAMPLE: ESTI MATION OF BACKHOE BUCKET TIP DISPLACEMENT..................................................................................................................58 Introduction................................................................................................................... ..........58 Estimation of Tip Displacement.............................................................................................58 Conclusion..................................................................................................................... .........60 8 CONCLUDING REMARKS..................................................................................................65 9 RECOMMENDATIONS FOR FUTURE WORK.................................................................67 LIST OF REFERENCES............................................................................................................. ..68 BIOGRAPHICAL SKETCH.........................................................................................................71

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7 LIST OF TABLES Table page 6-1 Wear test information fo r the pin and pivot assembly............................................................53 6-2 Simulation parameters for th e pin in pivot simulation test.....................................................53 6-3 Comparison of results form the simulation te sts and actual wear tests for the pin in pivot assembly....................................................................................................................... ..........53 7-1 List of loads and re lative rotation angles at th e joints of the backhoe....................................61 7-2 Summary of the wear depth at the joints after 20,000 cycles as we ll as the extrapolated wear depth at 90,000cycles.....................................................................................................61 7-3 Displacement of the boom comp onent parts from the center line..........................................61

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8 LIST OF FIGURES Figure page 2-1. Oscillatory contact for a pin-pivot assembly.........................................................................26 2-2. Wear simulation flow chart for the step update procedure.................................................27 2-3. Pin-pivot finite element model........................................................................................... ...28 2-4. A three-node contact element used to represent the contact surface.....................................28 2-5. Geometry updates process................................................................................................. ....29 2-6. Surface normal vector for the pin-pivot assembly prior to update........................................29 3-1. Contact pressure distribu tion on a pin-pivot assembly..........................................................35 3-2. Extrapolation history for a pin-pivot assembly.....................................................................35 4-1. Wear simulation flow chart for the cycle-update procedure...............................................40 4-2. Wear simulation flow chart for th e intermediate cycl e-update procedure..........................41 4-3. Wear simulation flow chart for the para llel implementation of the cycle-update procedure...................................................................................................................... .........42 5-1. Interaction between the C c ode and the Ansys input code....................................................46 5-2. Function of the Ansys input code......................................................................................... .46 5-3. Structure of the wear-simulation program.............................................................................47 6-1. Pin-pivot assembly for the wear test..................................................................................... .54 6-2. Cumulative maximum wear on pin and pivot.......................................................................54 6-3. Contact pressure dist ribution on the pin and pivot during wear analysis..............................55 6-4. Extrapolation history plot for the step updating simu lation procedure.................................56 6-5. Cumulative maximum wear on pin and pivot for the interm ediate cycle updating procedure and the parallel implementation...........................................................................56 6-6. Extrapolation history plot for the intermediate cycle upd ate procedure and its parallel implementation................................................................................................................. ....57 7-1. Pin-pivot assembly for the wear test..................................................................................... .62

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9 7-2. Joint consisting of a pin and pivot...................................................................................... ...62 7-3. Wear on the pin and pivot at the backhoe Joints...................................................................63 7-4. Backhoe component displacement from the vehicle centerline............................................64

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10 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science NUMERICAL SIMULATION OF WEAR FOR BODIES IN OSCILLATORY CONTACT By Saad M. Mukras December 2006 Chair: Nam-Ho Kim Major Department: Mechanic al and Aerospace Engineering When bodies are in contact and in relative mo tion, wear becomes an important aspect that should be considered during design. In mechanisms, wear is experi enced at connections such as joints. A particular type of c ontact condition, known as oscillat ory contact, exists at these connections and is partly respons ible for wear. The objective of th is study is to develop a wearprediction procedure for bodies that expe rience this type of contact condition. A prediction procedure for wear occurring in bo dies that experience oscillatory contact is proposed. The methodology builds upon a widely used iterative wear-predi ction procedure. Two techniques are incorporated into the methodology to minimize the simulation computational costs. In the first technique, an extrapolation scheme that optimizes the use of resources while maintaining simulation stability is implemente d. The second technique involves the parallel implementation of the wear-pre diction methodology. The methodol ogy is used to predict the wear on an oscillatory pin joint and the predicted results are validated against those from actual experiments.

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11 CHAPTER 1 INTRODUCTION Background Mechanical systems employ mechanisms that ar e used to convert one type of motion into another. These systems consist of connections such as joints where two components of the system establish contact a nd are in relative motion dur ing operation. Depending on the kinematics of the mechanism, either of severa l contact conditions may exist at the connection. One particular contact conditions that is widely encountered is the osc illatory contacts. This contact condition coupled with othe r factors give rise to wear wh ich could cause the system to fail. The importance of wear and the need for its consideration in de sign is dependant on a number of factors which may be either technical or economical or both. An example in which wear is of great concern is at th e joints of heavy equipments such as backhoes. The joints of such equipments experience considerab le amounts of wear while in ope ration. In order to minimize the wear occurring is such joints designers have implemented several tech niques such as select materials based on material ranking or using wear resistant coating on th e contacting surfaces. Although these procedures are widely used, they do not give sufficient in sight or quantitative information on how a system may fail due to wear. It would thus be adva ntageous for designers to have the ability of predicting the wear before hand. One way that has been used to achieve this has been the use of accelerated design verificatio n procedures on prototypes. The procedures are generally expensive and destruc tive in nature but provide an abundant amount of information regarding the wear as a mode of failure. An enormous amount of effort and resources has been placed into developing techniques that utilize computer simulati ons in the prediction of wear. Use of simulations for wear prediction has a number of benefits, one of whic h is its potential to re ducing or eliminating

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12 costly tests that may be required when cons idering wear in design. Simulations for wear predictions are also a versatile alternative, allowing for rapid changes in the simulation conditions with little effort. A number of papers have been written dea ling with the subject of wear prediction. A general trend that that has emerged is the use of numerical methods togeth er with variations of Archards wear model in predicting wear. Pdra and Andersson [1] used finite element method (FEM) in an iterative procedure to determine the wear on a pin placed over a moving disk. The simulation yielded results similar to those of an analogous experime nt. In a separate paper, Pdra and Anderson [2] discuss the use of finite elem ent analysis in wear simulation of a conical spinning contact. They compared simulation resu lts to analytical re sults which showed good agreement. Pdra and Andersson [3] also used the Winkler surface model, to compute contact pressure instead of the finite element method, to simulated wear. They reported results that showed close agreement with simulations in wh ich the finite element method was used. Yan et al. [4] predicted the wear resulting form a loaded pin contacting a rotating disc, by noting that the center of the disc wear track may be approximated as a plain strain region They showed that the prediction results were consistent with experime ntal measurements. Wear simulations for a pin on disk problem were performed by Gonzalez et al. [5] using finite element method in conjunction with an incremental wear-prediction technique. In their simulation procedure, the geometry was updated at the end of each itera tion. This was done to account for the worn out material. Telliskivi [6] preformed simulations to predict the wear on a disc-on-disc assembly using the Winkler mattress model. Good agreem ent between experiment and the simulation results were reported. Dickrell a nd Sawyer [7] developed a model to study the evolution of wear for a shaft and bushing assembly and ra n experiment to validate the model.

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13 A number of papers dealing with wear pred iction of more complicat ed geometries have also been written. Flodin and Andersson [8], simu lated the wear on spur gears using the Winkler model. They used an incremental wear-predicti on approach in which the geometry was allowed to evolve as the simulation progressed. Fl odin and Andersson [9] later extended their methodology to helical gears. They treated the helical wheel as several thin independent spur gear teeth. Brauer and Andersson [10] conducted wear simulations for gears using a combination of finite element method and an analytical ap proach based on Hertz theory. The FEM was used to determine the loads resulting form gear teeth in teraction which were in turn used to determine contact pressure using th e analytical expressions. In one paper Hugnell et al [11] simulated the wear resulting from a cam-follower contact and in another paper [12] they simulated the mild wear in a cam-follower contact with follower ro tation. They also used an incremental wearprediction procedure and allowed the geometry to change after every simulation step. Nayak et al [13] predicted the wear on a cam-follower and presented a guideline on designing cam followers for low wear. Fregly et al [14] performed wear analysis to simulate mild wear on a tibial insert model. They reported close agreem ent between the simulation results and damage observation on actual tibial insert. Wear predictions on total hip ar throplasty were performed by Maxian et al [15]. Bevill et al [16] also performed simulations to determine the damage on a total hip arthroplasty due to wear and creep. Depending on the complexity of wear mechan isms, wear predictions using computer simulations have yielded rela tively reasonable results [1, 17]. The simulations, however, have been found to be quite computationally expe nsive. Several ideas have been implemented in an attempt to reduce computational costs associat ed with the wear-simulat ion process. Pdra and Andersson [3] attempted to minimize the comput ational cost by using the Winkler model to

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14 determine the contact pressure di stribution. The Winkler model was us ed as an alte rnative to the more expensive but relatively accurate FE M. Although the method was found to be less expensive it can be argued that th e benefit of using more accurate results from the finite element technique outweigh the gains in computational efficiency when complicated geometries are considered. Pdra and Anderson [1] also employed a scaling approach to tackle the problem of computational costs. In this approach the incr emental wear at any particular cycle of the simulation was scaled based on a predefined ma ximum allowable wear increment. The scaling factor was obtained as a ratio between the ma ximum allowable wear increment and the current maximum wear increment (maximum wear incremen t of entire geometry). They found that this procedure was more computationall y effective. Kim, et al. [18] used a constant extrapolation technique to reduce the computati onal costs for the oscillatory w ear problem. In their technique one finite element analysis was made to represent a number of wear cycles. Through this extrapolation, they were able to reduce the total number of analyses needed to estimate the final wear profile. A similar procedure was done by McColl, et al. [19] as well as Dickrell et al. [20]. In another paper [4], the computational costs of simulating a pin on a rotating disc was reduced by approximating the state of strain on the center of the wear track as plain strain. A less costly two-dimensional idealization was then used in place of the more expensive three-dimensional problem. Scope and Objective As is apparent from the literature, a number of procedures have been proposed to simulate wear. In addition several procedures have been proposed to simulate wear in more specific assemblies such as gears and cam-follower systems. One type of assembly that is encountered in numerous applications is one in which the oscillatory contact is experienced. These types of assembly are commonly found at the connections of mechanisms. Due to the nature of relative

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15 motions at such assemblies, wear is inevitable. In this research, the obj ective is to develop a simulation framework for wear prediction in bodie s that experience oscillatory contact. In addition to developing the predic tion procedure, emphasis is ma de on incorporation techniques that minimize the overall computational costs and enable stable simulations. Thesis Organization In Chapter 2, the details of the wear model used in the prediction procedure are discussed. The simulation prediction procedure specific to b odies experiencing oscillatory contact will then be presented. A representative model to be used to demonstrate the proc edure is introduced and discussed in Chapter 2. Chapter 2 will close wi th a discussion of a geometry updating technique that minimizes the mesh distortion. Techniques to minimize computational costs will be presented in Chapter 3 and 4. Discussions in Chapter 3 will focus on the use of extrapolations to minimize costs. The issue of instability when extrapolations are used as well as a proposed so lution is included in Chapter 3. In Chapter 4, the implementation of parallel computation as a way to reduces computational costs is discussed. In order to implement the wear-prediction procedur e, a simulation program was written. The details of the program are discussed in Chapter 5. Validation of the wear-prediction procedur e is discussed in Chapter 6. Results from experiments are compared to results from the wear simulation. In Chapter 7, an example .that demonstrates how the wear-simulation program can be used to evaluate the effect of wear on the performance of a system is pres ented. Finally conclusions abou t the wear-prediction procedure will be drawn in Chapter 8 and suggestions for future research will be made in Chapter 9.

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16 CHAPTER 2 WEAR-PREDICTION METHODOLOGY FOR B ODIES IN OSCILATORY CONTACTS Introduction When two bodies are in contact and are in relative motion with respect to each other, wear is expected to develop on the regions of contact. The type of contact that the bodies experience is dependent on how the bodies move relative to each other. One type of cont act condition that is of interest is the osci llatory contact. This type of contact condition is char acterized by an oscillatory relative motion between the bodies th at are in contact. The contact between a pin and a pivot in a center-link pivot joint is an exam ple of this type contact. This example is shown in Figure 2-1 where the pin oscillates between two extreme angl es. In this Chapter a procedure to predict the wear occurring in this type of contact is discussed. In this wor k, the assembly shown in Figure 21 will be used as a representative case of the oscillatory contact to illustrate the wear-prediction procedure. Wear Model In developing the wear-prediction methodology it is assumed that all the wear cases to be predicted fall within the plastically dominated wear regime, where slide velocities are small and surface heating can be considered negligible. Arch ards wear law [21] would thus serve as the appropriate wear model to desc ribe the wear as discussed by Lim and Ashby [22] as well as Cantizano, et al [23]. In that model, first published by Holm [24], the worn out volume, during the process of wear, is consider ed to be proportional to the normal load. The model is express mathematically as follows: NF V K sH (2-1)

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17 where V is the volume lost, s the sliding distance, K the dimensionless wear coefficient, H the Brinell hardness of the softer material, and NF the normal force. Since the wear depth is the quantity of interest, as opposed to the volume lo st, Eq. 2-1 is usually written in the following form: NhA kF s (2-2) where h is the wear depth and A is the contact area such that VhA The non-dimensioned wear coefficient K and the hardness are bundled up into a single dimensioned wear coefficient k (Pa-1). It should be noted that the wear coefficient kis not an intrinsic material property but is also dependent on the operating condition. The value of k for a specific operating condition and given pair of materials may be obtained by experiments [25]. Also worth noting, is that measured values of wear coefficients usually have la rge scatter and may affect wear predictions significantly. Care should thus be taken in obt aining these values. Uncertainty analysis for measured values of wear coefficients, such as those presented by Schmitz et al. [26], may be of considerable benefit. Equation 2-2 can further be simplified by no ting that the contact pressure may be expressed with the relation N p FA so that the wear model is expressed as h kp s (2-3) The wear process is generally considered to be a dynamic process (ra te of change of the wear depth with respect to slidi ng distance) so that the first orde r differential form of Eq. 2-3 can be expressed as: ()dh kps ds, (2-4)

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18 where the sliding distance is considered as the time in the dynamic process, and the contact pressure is a function of the sliding distance. A numerical solution for the wear depth ma y be obtained by estimating the derivative in Eq. 2-4 with a finite divide differe nce to yield the depth as follows: 1 jjjjhhkps. (2-5) In Eq. 2-5, jh refers to the wear depth at the th j iteration while 1 jh represents the wear depth at the previous iteration. The last te rm of Eq. 2-5 is the incrementa l wear depth which is a function of the contact pressure and incremental sliding distance (js ) at the corresponding iteration. If information about the wear coefficientk, the contact pressure j p and the sliding distancejs is available at all iterations ( j ), the wear depth on a cont act interface fo r a specified sliding distance s can be estimated using Eq. 2-5. Here the sliding distance is an accumulation of the incremental sliding distance for all iterations (_niter) as is expressed in Eq. 2-6. 1 niter j jss. (2-6) The contact pressure ( p ) may be obtained through numeri cal methods. The finite element method appears to be the most widely used met hod. This is probably due to its accuracy. Several papers [3, 6, 27] have been written in whic h an elastic foundation m odel has been used in place of the finite element method. The wear coefficient can be obtained through experiments such as this explained by Kim et al. [18, 25] where as the increm ental sliding distance may be obtained from the finite element analysis or can be specified by the user.

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19 Simulation Procedure The most widely used procedure to simulate wear occurring at a c ontact interface is an iterative procedure describe by th e numerical integration in Eq. 25. A number of papers [1,2,17 19,25,29], that demonstrate the implementation of Eq 2-5 in predicting wear have been written. Although the details of the various procedures di ffer, three main steps are common to all of them. These include the following: Computation of the contact pressure resulting from the contact of bodies. Determination of the incremental w ear amount based on the wear model. Update of geometry to reflect the wear am ount and to provide the new geometry for the next iteration. The procedure developed for predicting wear on oscillatory contacts incorporates the aforementioned steps. As was mentioned earlier the pin-pivot assemb ly shown in Figure 2-1 will be used to illustrate the simulation procedure. In this assembly the pin is fixed so that it does not translate in any direction but is allowed to os cillate (in an axis perpendicular to the paper) from one extreme to another (bounded by specified amplitude). Contra ry to the conventional definition of a cycle, in this work a cycle is defined as a rotation of the pin from one extr eme angle to the other (e.g.0 ). The goal is to develop a procedure that can predict the wear over several thousand cycles. It is worth noting that most of the work present in the literatu re dealing with wear simulation does not address this type of motion but rather, that which is of a continuous nature such as in rotational contacts. The simulation of wear at the contact interf ace of the pin-pivot assembly is achieved by considering each cycle separately. The wear in any cycle can be obtained by discretizing the cycle into a number of steps and thereafter applying Eq. 2-5. The di scretization is such that each

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20 step corresponds to a specific pi n angle between the two extremes. In the application of Eq. 2-1, the wear coefficient kand the incremental sliding distancejs are taken to be constant where as the contact pressure j p is computes by the finite element me thod. The pin-pivot finite element model used to illustrate the simulation procedure will be described a later subsection. At each step a finite element analysis is perf ormed to determine the contact pressure over the contact region. The wear de pth during any cycle and at any point on the contact surface can then be determined by Eq. 2-7 which is a modification of Eq. 2-5. ,,,1,,nijnijinihhkps. (2-7) In Eq. 2-7, n refers to surface nodes number (of the finite element model) which may or may not establish contact with th e opposing surface. The subscript i and j indicate the current step and cycle, respectively. All other terms are as defined previously. The geometry is then updated to reflect the amount of wear and to prepare the model for the next step. Details of the geometry update procedure will be disc ussed in subsequent subsection. At this point the simulation progres ses to the next step and the oscillating pin assumes a new position. This involves a rota tion through an angle corresponding to the incremental angle. The previously described proc esses are repeated up until all steps in a cycle are completed. The direction of pin rotation is reversed and the simula tion of the next cycle commences. The term step update is adopted for this procedure since the geometry is updated after every step. The simulation process for the step update procedure is summarized in the flowchart shown in Figure 2-2.

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21 Pin-Pivot Finite Element Model Two methods that have been used in the litera ture to calculate the c ontact pressure at the contact surface were mentioned as the elastic fou ndation and the finite element method. The least expensive of the two methods, in terms of comput ational costs, is the el astic foundation method. This method is, however, the least preferred due to its level of accu racy especially for complicated geometries. To illustrate the simula tion procedure the finite element method has be selected. The diagram of the 2D finite element model fo r the pin-pivot assembly is shown in Figure 2-3. As can be seen from the diagram, three ki nds of elements have been used. The eight-node quadrilateral elements were used to model the pin and the pivot. Threenode contact elements were used to represent the contact surface. It is worth noting that the contact elements coat the outer and inner surface of the pin and pivot, respectiv ely. It should also be noted that the contact element do not add any new nodes to the model. In stead, the nodes of the quadrilateral elements that appear on the surface make up contact elements. The third type of element that was used is the link (truss) elements. This element was us ed to prevent rigid body motion (RBM). It was mentioned earlier that the pin is fixed from translating but allo wed to rotate in a controlled manner. Specifically the rotation is allowed onl y once the finite element analysis has been completed. This means that the pin will not ex perience RBM. The pivot, however, is fixed along its lower edge to prevent any horizontal translations as well as rotation in any axis but is allowed to translate in the vertical direction. This is al so the direction of loading as is shown in Figure 21. There is thus a potential for RBM to occur. The link element is used to eliminate this possibility. The effect of the link element is re duced by assigning it a very small elastic modulus.

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22 Geometry Update Procedure The process of geometry update is necessary in order to correctly simulate and predict the wear occurring at the contact in terface. Indeed material remova l changes the contact surface and causes a redistribution of the cont act pressure resulting from the contact. These changes can only be captured if the surf ace is altered through a geometry upda te. Estimation of wear through an extrapolation which is based on the original surface has been shown to produce erroneous predictions [30]. It is therefor e becoming as standard, as is evident in the literature [1, 17, 25, 29, and 31], that geometry updates are incl uded in the process of wear simulation. The procedure proposed to update the geometry in this research involves two steps. These steps are outlined below: Determine the normal direction (vector) of th e contact surface at the location of each surface node (contact node). Shift the position of the surface nodes in the direction of the normal vector by an amount equal to the wear increment. The normal direction of the surface nodes at the location of the contact nodes can be obtained by considering the locations of the c ontact elements. The contact elements at the surface have three nodes each. This element is illustrated in Figure 2-4. The corresponding shape functions for this element may be written as follows: 1 2 31 1 2 11 1 1 2Ntt Ntt Ntt (2-8) where t is the local coordinate parameter. The surf ace of an element can then be described in terms of the nodal coordinates and as a function of the local coordinate. The expression for the surface is given in Eq. 2-9.

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23 1 1 1232 1232 3 3000 000 x y NNNx x NNNy y x y (2-9) where k x and k y are the coordinates of node k (1,2,3 k )for the element of interest. If the vector tangent to the surface (conta ct element surface) is denoted as tv then its value for the element can be obtained as follows: 0xy tt tvi j k (2-10) where the partial differentials is given in Eq. 2-11 or 2-12. 1 1 3 12 2 2 3 12 3 3000 000 x y N NN x x tttt y yN NN t ttt x y (2-11) or 3 1 3 1 r r r r r rN x x tt N y y tt (2-12) The vector normal (nv ) to the surface (depicted in Figure 2-4) can be expressed as a cross product of the tangent vector (tv ) and the vector perpendicular to the plane of the surface ( 0,0,1 pv). This cross product is e xpressed in Eq. 2-13.where n denotes the node number.

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24 , n n n tp n tpvv v vv (2-13) The resulting unit normal vector then appears as follows: 22 nyx tt x y tt ni j v (2-14) or, ,_,_, nnormxnnormynvv nvi j (2-15) where _normxv and_normyv are the components of the vector normal to the surface. Once the contact pressure distribution and normal vect ors at all the nodes on the surface have been determined, the geometry can then be updated. The update is done by moving the surface nodes in the direction of the unit normal vector. The co ordinate of the new node position at any step of any cycle can be written as follows: ,,,1,_, ,,,1,_, nijnijnormxn ni nijnijnormxnxxv kps yyv (2-16) The process of the geometry upda te is shown in Figure 2-5. In this diagram the wear depth is grossly exaggerated to illustrate the concept. The procedure for the geometry update has been used successfully in the wear-sim ulation process. A possible probl em that could be encountered during model updates is mesh distortion. In the pin-pivot model, mesh distortion during model update is minimized through a carefully created fin ite element model. The FE model is initially created in such a way that all normal vectors at surface nodes, before any update is performed, will be in a direction parallel to the element e dge. This idea is illustrated in Figure 2-6. After

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25 several geometry updates it can be expected that th e vector will no longer be parallel to the edge. The deviation is however small to be of any major consequence. Conclusion The procedure discussed was used to predic t the wear occurring at the interface of the pin-pivot assembly. Although this was a specific problem, the general framework outlined can be extended and used to predict wear in ot her 2D oscillatory contact problems.

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26 Figure 2-1. Oscillatory cont act for a pin-pivot assembly.

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27 Figure 2-2. Wear simulation flow ch art for the step update procedure. In p ut Model Solve Contact problem (Contact Pressure) Application of Wear Rule 1) Determine wear amount 2) Determine new surface loc. U p date Model Total Cycles? End of Simulation C y cle Coun t Ste p coun t Total Steps/cycle ?

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28 Figure 2-3. Pin-pivot finite element model. Figure 2-4. A three-node contact element used to represent the contact surface.

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29 Figure 2-5. Geometry updates process. Figure 2-6. Surface normal vector for th e pin-pivot assembly prior to update

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30 CHAPTER 3 EXTRAPOLATION SCHEMES Introduction The procedure discussed in Chapter 2 provides a way to simulate the wear resulting from oscillatory contacts. However, the process can be quite expensive. For instance, if one desires to simulate 100,000 oscillatory cycles for a case in which each cycle is discretized into 10 steps then 1,000,000 finite element analyses (nonlin ear) as well as geometry updates would be required. Clearly this may not be practical and the need for techniques to combat the computational cost becomes immediately appare nt. Techniques to tackle the problem of computational costs will be discussed in the current and following Chapters. Constant Extrapolation Extrapolations have been used in various forms with the goal of reducing computational costs. In this work an extrapolation factor (A) is used to project the w ear depth at a particular cycle to that of several hundreds of cycles. Essentially, the extrapolation is the total number of cycles for which extrapolation is desired. Thus according to this defini tion, the extrapolation factor can only take on positive integers values. The equation used to determine the amount of we ar at a particular node during any step in a cycle was expressed in Chapter 2 as; ,,,1,, nijnijinihhkps. (3-1) Equation 3-1 can be modified slightly in order to incorporate an extra polation factor. It is first noted that the first term on the right hand side (R.H.S.) of Eq. 3-1 refers to the cumulative wear depth from previous cycles whereas the last term refers to the incremental wear depth at the current step and cycle. As way to minimize com putational costs, it is assumed that the next A cycles (as many cycles as the value of the extr apolation) will have th e same amount of wear

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31 depth as that of the current st ep and cycle. The total incremental wear depth for those many cycles may then be obtained by multiplying last te rm of Eq. 3-1 with the extrapolation factor. The resulting expression is show n in the following equation: ,,,1,, nijAnijinihhkAps. (3-2) Utilizing the same concept, a new expression can be written to describe the position of the contact nodes during the wear-simulation process. This expression is as follows: ,,,1,_, ,,,1,_, nijAnijnormxn ni nijAnijnormxnxxv kAps yyv (3-3) Extrapolation and stability. As may be expected, the leve l of accuracy of the wear simulation is reduced when extrapolations are used. This is directly related to the assumption that the same value of incremental wear depth is maintained for several cycles. This is, however, not the case since in reality the geometry would cons tantly evolve which in turn would lead to a continuous redistribution of the c ontact pressure and thus a change in the incremental wear depth at each cycle. However the difference is small en ough that it may be neglected as is evident from the overall error of simulation results. Use of extrapolations may also cause problems in simulation stability. Here stability is defined with regard to the cont act pressure distribution and hen ce the wear profile. An ideally stable wear simulation would be defined as one in which the contact pressure distribution remained smooth (with no sharp or sudden changes in the distribution) for the entire duration of the simulation. It is however unlikely to ha ve smooth pressure di stribution throughout the simulation process. As a result a more relaxed definition of stability is adopted where by sudden changes in the pressure distributi on are allowed to occur. In Figur e 3-1A, the contact pressure is seen to vary smoothly over the contact region exce pt for small peaks at the contact edges. The

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32 peaks are attributed to the transition form a re gion of contact to a region of no contact. This transition occurs at a point whic h can not be represented by a disc rete model. The result is that there is an abrupt change in the surface curvature which causes high pressure. If such contact pressure distribution is maintain ed through out the simulation, th e simulation can be referred to as stable. On the contrary, the diagram in Figur e 3-1B is representative of contact pressure distribution that would constitute an unstable wear simulation. The two diagrams show the contact pressure distribution for a stable and unstable wear simulation consistent with the adopted definition of stability. When very large extrapolation sizes are used wavy pressure distri butions (Figure 3-1B) are observed and the simulation becomes unstable. The shift to instability due to the use of large extrapolation sizes can be explained as follows. The contact pressure dist ribution (obtained from the finite element analysis) is generally not perfectly smooth. This may be due to the discretization error stemming form the finite elemen t analysis. The use of an extrapolation factor magnifies these imperfections so that when the geometry is update d the contact surface smoothness is reduced. If large extrapolation sizes are used, the regions that experience high contact pressure in a particular step of the simulation are worn out excessively so that in the following step these regions experi ence little or no contact. On the other hand, the regions that did not experience high contact pressure will be worn out less and thus will experience greater contact pressure in the next step. This behavi or will repeat in subsequent steps causing the surface to become increasingly unsmooth. The simulation will then become unstable. If, however, smaller extrapolation si zes are used the wearing proce ss acts as an optimizer to smoothen the surface.

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33 A smooth contact surface is cr itical for two reasons. The first reason is that a smooth contact surface is consistent with the actual case that is being simula ted, and the second is that a non-smooth surface would affect th e solution of the finite element problem. Due to these reasons, a condition is placed on the selection of the extrapolation si ze such that the selected size would not severely affect the smoothne ss of the pressure distribution. Extrapolations provide a solution to the co mputational cost problem but as has been discussed its use may introduce other problems. Th e accuracy and stability of the simulation may be jeopardized by using extrapolat ion sizes that are too large. Using small extrapolation sizes will produce more reliable solutions but will result in a less than optimum use of resources. It may also be argued that even if an appropriate extrapolation size was selected at the beginning of the simulation it may be that at a different stage of the simulation a differe nt extrapolation size would be required to provide opt imum use of the available res ources. In the next subsection a procedure is described that seeks for the larges t extrapolation sized while maintaining stability during the entire simulation process. Adaptive Extrapolation Scheme The adaptive extrapolation tec hnique is an idea proposed as an alternative to the constant extrapolation scheme. The idea behind it is to se ek for the largest extrapolation size while maintaining a state of stability (smooth pressure distribution) throughout the simulation process. The scheme is a three-step process. In th e first part an initial extrapolation size (0A) is selected. The selection is based on experience. In the second part of the adaptive extrapola tion scheme, a stability check is performed. A single check, preferably at the cen ter step of the cycle, is sufficient for an entire cycle. The stability check involves monitori ng the contact pressure distribu tion within an element for all

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34 elements on the contact surface. This essentiall y translates to monito ring the local pressure variation. If the contact pressure difference within an element is found to exceed a stated critical pressure difference crit p then a state of instability is noted a nd vice versa. In the final step of the adaptive scheme, the extrapolation size is altered based on the result of the stability check. That is, the extrapolation size is increased for the stab le case and a decrease for the unstable case. This process can be summarized as follows: 1incelecrit 1decelecrit if if j j jAApp A AApp. (3-4) It must be mentioned that in order to main tain consistency in the geometry update as well as in the bookkeeping of the number of simulated cycles, a si ngle extrapolation size must be maintained through out a cycle. That is, every st ep in a cycle will have the same extrapolation size while different cycles may have different extrapolation si zes. Figure 3-2 shows a graph of the extrapolation history for the oscillating pin-pivot assembly. Fr om the graph, it can be seen that the extrapolation took on a conservative initial value of about 3900 and increased steadily up to the 12th cycle (actual computer cycles not consider ing the extrapolations). Thereafter the extrapolation size oscillated about a mean of about 6000. Conclusion The use of extrapolations is an efficient way to cut down on computational costs. Even though no way of accounting for the error involved has been developed, the results observed from simulation runs have shown acceptable error ranges. An adaptive extrapolation scheme was proposed to govern the selection of the extra polation size during the simulation. The scheme ensures that the largest allowabl e extrapolation size is used during the simulation. The scheme thus provides for a way to minimize computational costs while maintaining a stable simulation.

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35 A B Figure 3-1. Contact pressure di stribution on a pin-pivot assembly. A) The case of a stable wear simulation. B) The case of an unstable wear simulation. Figure 3-2. Extrapolation hist ory for a pin-pivot assembly. 0 5 10 15 20 25 30 35 40 0 1000 2000 3000 4000 5000 6000 7000 CyclesExtrapolationExtrapolation Vs Cycles (E=207Gpa & Pivot thikness t=19mm)

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36 CHAPTER 4 PARALLEL COMPUTATION IN WEAR SIMULATION FOR OSCILLATORY CONTACTS Introduction Although the use of extrapolat ions is probably the most effective way to reduce the computational costs, other ways are also availa ble. A parallel processing implementation of the simulation procedure is proposed as an additional way to remedy the problem of computational costs. This technique may be us ed in conjunction with the extra polation scheme to further reduce computational costs. The discussion of parallel computation will be preceded by an introduction to the concept of cycle-update and intermedia te cycle-update which ar e central ideas in the parallel computation procedure. Cycleand Intermediate Cycle-Update The wear-simulation procedure th at was discussed earlier was te rmed as the step-updated for the reason that geometry updates were preforme d after every step. An a lternative to the step update procedure would be to exclude all geomet ry updates during the entir e cycle and perform a single update at the end of the cycle. We term this procedur e as the cycle-update. The cycleupdate is a modification of the step-update wh ere updates are performe d at the end of each step/analysis. For the cycle-update, information from each analysis performed at each step is stored and later used to update the model at the end of the cycle. The equation for the wear depth at the contact interface for the cycleupdate is expressed as follows; ,,1, 1 nstep njAnjjini ihhkAps (4-1) where _nstep is the total number of steps in a cycle. All other terms are as defined previously. The cycle-update procedure can be summarized in the flowchart shown in Figure 4-1.

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37 It should be noted that in both the cycleand step-update tech niques, the material removal is discrete which is at variance with the actual process of wear in which the material removal is continuous. The situation is, however, worse for the cycle-update since the frequency of material removal is much less than in the st ep-update procedure. The step-update therefore has a closer resemblance to the to th e actual wear process. It would th erefore be expected that the use of the cycle-update procedure in wear simulations would yield less reliable results in comparison to the step-update counterpart. Indeed this is what is observed when th e procedure is tested. More specifically the smoothne ss of contact pressure distri bution during the simulation is severely affected by the cycle-upda te than is by the step-update. A simplified explanation for this phenomenon is that the step-update, performed at each step, closely captures intermediate geometry changes within a cycle and hen ce the contact between two mating surface is approximately conforming throughout the simulation. The result is that th e pressure distribution remains reasonably smooth. In the case of the cy cle-update, the geometry is updated once in an entire cycle. This dose not allow for the cont acting surface to evolve smoothly throughout the cycle and hence resulting in a less conforming c ontact between the mating surfaces. In this case the pressure distribution would be less smooth, putting the accuracy of the results to question. Although the cycle-update techni que may yield less than accu rate results, the technique may still be used with caution. A general observation can be made regarding the accuracy when using the cycle-update procedure. It has been obser ved that for a fixed extrapolation size, as the total sliding distance covered th rough a complete cycle increases the smoothness of the pressure distribution is affected and he nce the stability and accuracy of the simulation. Based on the observation, a critical sliding distance crits is defined which if exceed during sliding, geometry update must be performed. Determination of th e critical sliding distance is unnecessary since

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38 short simulation runs can determine if the cycl e-update is the appropriate produce. Thus the mention of the critical sliding distance is purel y for academic reasons rath er than for practical reasons. It is concluded that the cycle-update is best suited for cas es in which the total oscillation angle is small so that the sliding distance in a single cycle is less thancrits. In the event that the total sliding dist ance for a complete cycle is larger thancrits, we may still take advantage of the idea behind cycleupdate procedure. Instea d of performing a single update at the end of the cycle we may perform several equally spaced upda tes within the cycle. This can be considered to be a hybrid of th e stepand cycle-update procedure and the name intermediate cycle-update is used for the procedure. The advantage of this idea is that the number of updates in a cycle is reduced without affecting the stability of the simu lation. The intermediate cycle-update procedure can be summari zed as is shown in Figure 4-2. Parallel Computation Computers may be configured to operate in parallel mode with the advantage that results can be produced at a quicker rate. The idea proposed as a cost cutting means is a direct parallel implementation of the cycle-upd ate and the intermediate cycl e-update procedures. Since the implementation of the two procedures is simila r, only the parallel impl ementation of the cycleupdate is discussed. The cycle-update procedure is centered on the idea that no update is performed on the geometry during the entire cycle. This means that a ll the analysis performed at each step within a cycle is done on same geometry. The difference be tween any two analyses within a cycle is the angle at with the two bodies co ntact during the analysis. This in formation may be exploited to construct the parallel comput ation equivalent of the w ear-simulation procedure.

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39 The parallel implementation works as follows Several processors are dedicated to the wear analysis simulation. One of these processo rs is assigned the duty of a master processor. This will be the processor responsible for distributing tasks to other processors as well as consolidating the results from other process. The remaining processors will be the slave processors. Each of the processo rs, both slave and master processo rs, will represent a particular step within a cycle. In the begi nning of any cycle, the appropriate model of the assembly to be analyzed for wear is fed into the master proce ssor. The master processor then distributes the same model to the remaining processors. The ma ster processor also allocates contact angles (each slave will have a different contact angle corresponds to a sp ecific step in the cycle) and corresponding analysis conditions to each of the slave processors. At this point the master processor instructs the slave processor to solve their co rresponding contact problem. Once the analysis in the different slave processors is done the master node collects the results and computes the wear amount for that cycle. The model geometry is then undated and thereafter a new cycle commences. The parallel implemen tation of the cycle-update procedure is summarized in the flowchart shown in Figure 4-3. From the flowchart it can be seen that c onsiderable amount of time is saved by using the parallel computational in co mparison to the cycle-updating pr ocedures. If the number of processors available is equivalent to the numbe r of steps selected for a cycle, then the time required to complete a single cycle while using th e parallel procedure is approximately equal to the time required to complete a single step in the step and cycl e updating procedures.

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40 Figure 4-1. Wear simulation flow char t for the cycle-upd ate procedure. Input Model Solve Contact problem ( Obtain Contact Pressure ) Save Analysis Info. Update Model Total Cycles? End of Simulation Cycle Count Step count Total Steps/cycle ? Wear Rule Determine wear amount

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41 Figure 4-2. Wear simulation flow chart for the intermedi ate cycle-update procedure. Input Model Solve Contact problem ( Obtain Contact Save Analysis Info. Update Model End of Simulation Cycle Count Update step coun t Total ste p s / c y cle? Determine wear amoun t Steps before update Total cycles? Ste p coun t

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42 Figure 4-3. Wear simulation flow chart for th e parallel implementation of the cycle-update procedure. Input Model Collect Pressure Info. Update Model Total Cycles? End of Simulation Cycle Count Wear Rule Determine wear Step 1 Step 2 Step 3 Step n Solve Contact problem (ObtainContactPressure)

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43 CHAPTER 5 WEAR-SIMULATION PROGRAM Introduction A simulation program was written in order to execute the wear-simulation procedure that has been discussed in Chapters 2. The progr amming language used was C and the Finite Element Analysis software us ed was Ansys. Ansys Parametric Design Language (APDL) was used to write the commands necessary for the anal ysis. It should be men tioned that the choice of language and software for this task, was base d on convenience rather than limitation. Other languages and analysis software may be used. In this Chapter the basic structure of the program will be discussed. Wear-Simulation Program Format The wear-simulation program is composed of two parts. The fi rst part of the program is a C-program responsible for managing the simulati on process and the second part is an Ansys analysis input file, written in APDL, consisting of a set of commands related to the finite element analysis. There exists an interaction between the two programs in which information is exchanged. The interaction is managed by the Cprogram. A representation of the interaction is shown in Figure 5-1. These two parts will be discussed in the following subsections. Ansys Input Code The Ansys input code is composed of a set of commands necessary to perform an analysis on the finite element model and output analysis results. The input code has two main functions which include performing contact analysis and extr acting results from the analysis. These will be discussed in the following subsections.

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44 Contact analysis When the simulation program is launched, the Cprogram invokes Ansys and the Ansys input code is read. This will be the beginning of a step within the current cycle. The C-program also sends information to Ansys which will be read-in by the input file. This information may include the orientation of th e oscillating body, the current step and cycle. Based on the information from the C-program, the input file instructs Ansys to r ead-in the corresponding model (the model is in a file format with ex tension CDB) and prepare it for analysis. The preparation includes reorienting th e oscillating body into a positi on consistent with the current step. Any gaps occurring due to wear in the previ ous step are also closed. This essentially means that contact is established between the bodies before the analysis be gins. This is a necessary step since any gap may result in ri gid body motion (RBM). At this point, the input code instructs Ansys to solve the contact problem. Output of results The solution of the contact problem yield an enormous amount of information, most of which is not of interest in the wear problem. The second task of the input code is to extract the necessary information for the wear analysis. Spec ifically, the contact pr essure at each node is extracted from the contact analysis results. The in put code also extracts the coordinates of the contact node and computes the normal vector at each contact node. This information is required for the model update. The data extracted from the analysis as well as the model is written onto a text file in a predefined format that is readable by the C-progr am. Creating the text output file serves as the end of the step. Ansys software then shut s down and the C-program resumes command. A summary of the work done by the in put code is shown in Figure 2-2.

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45 Simulation Managing Code The other part of the wear-simulation program, written in C, act as the simulation manager. The codes main functions are to coordinating all the analysis performed by Ansys as well as performing the wear calculations. Once the simulation program is launched the Cprogram reads in a set of user defined parameters that describe the desired simulation. These parameters include information such as the value of the wear coefficient, the number of steps per cycle, the total cycles to be simulated and the oscillation amplitude. The C-program then invokes Ansys, as describe in the previous section, and stays dormant until the contact analysis is done. Re sults from the contact analysis stored in the text output file are then read in by the C-program. Stability check and extrapolation modifications are then performed as was outlined in Chapter 2. The wear rule is then applied. This determines the amount of wear increment at each node consistent with the contact pressure form the analysis and the wear coefficient. Ba se on the incremental wear depth geometry update is updated and a data file in text format is cr eated. Information such as the contact node number and the corresponding contact pressure and wear de pth are appended to the file as the simulation progresses. At this stage a cycle is completed and a new cycle commences. The structure of the simulation program is depi cted in Figure 5-3.

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46 Figure 5-1. Interaction between th e C code and the Ansys input code. Figure 5-2. Function of the Ansys input code.

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47 Figure 5-3. Structure of the wear-simulation program.

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48 CHAPTER 6 EXPERIMENTAL VALIDATION OF THE WEAR-SIMULATION PROCEDURE Introduction Probably the most convincing wa y to validate the results of a simulation is to compare them against those from an actual experiment. In this work the simulation procedure is validated by comparing simulation results to results from a wear tests performed on an oscillating pin in pivot assembly. The simulation proc edure is then used to simulate the wear occurring at the pin joints of a backhoe (construc tion equipment). The effect of wear on the performance of the backhoe is then demonstrated. Wear-Simulation Validation The wear simulation is validated through a co mparison of simulation and test results. The wear test consisted of a fixed st eel pin inside an un-lubricated oscillating steel pivot. The pivot was set to oscillate with amplitude of 30 and was loaded in the directi on of its shoulder as shown in Figure 6-1. The resulting pressure at the cr oss-sectional of the pivot was 60MPa. The pressure was kept approximately constant through out th e test. A total number of 408,000 cycles were completed during the test to yield a maximum wear depth of about 2mm. It should be noted, for the sake of comparison, that the definition of th e test cycles is differe nt from that of the simulation cycles. Here a test cycle is defined as a complete rotation from one extreme to the other and then back to the st arting position (in this case -30 to 30 and back to -30). The test information is summarized in Table 6-1 for convenience. Three simulation experiments were performed to mimic the actual tests performed on the pin and pivot assembly. The three simula tions experiments were as follows: step-updating procedure intermediate cycle-update procedure

PAGE 49

49 parallel implementation of the in termediate cycle-update procedure All three simulation tests were performed w ith the model shown in Figure 6-1. A wear coefficient of 51.010mm3/Nm (typical on un-lubricated steel on steel contact) was used. This value is obtained from pin-on-disk tests results reported by Kim et al. [18]. In all three cases the cycles were discretized into 10 steps. Both the stepand intermediate cycle-updating simulation tests were performed on the same computer (for time comparison), however, the parallel implementation was performed on a parallel cluster. The following is a brief discussion of these simulation test and the corresponding results. Step-Update Simulation Test The step updating simulation test was perfor med with oscillation am plitude and loading identical to that of the actual wear test The simulation test was run for 100,000 cycles (considering the extrapolation). The simulation te st parameters are summarized in Table 6-2 below. In Figure 6-2, the history of wear for the pin and pivot nodes that experienced the most wear is shown. From the figure, a transient and steady state wear regime can be identified as discussed by Yang et al. [32]. The transient wear regime corresponds to the beginning of the simulation until the contact between the pin and the pi vot is conforming. Th ereafter the wear transitions to the steady state wear regime. The steady state wear regime in marked by an interesting phenomenon where by the contact pressure distribution is observed to be approximately constant over the region of contact. This is in contrast to the transient we ar regime during which a range of contact pressure values is observed over the cont act region. This concept is illustrated in Figure 6-3. Within the steady state wear regime, the wear is approximately linear with respect to the cycles as can be seen in Figure 6-2. This information may be exploited to determine the wear on

PAGE 50

50 the maximum wear nodes after 408,000 cycles. Noting that one test cycle has twice the sliding distance in comparison to that of the simulation te st, an extrapolation within the steady state can be made to predict the wear depth at the 408,000th cycle. The expression for the predicted wear depth is a follows; 1 211 21test2()sim FEMFEMFEM simsimnn hhhh nn (6-1) where, h is the predicted wear depth, 1 s imn and 2 s imn are the total simulated cycles at two points within the steady state regime whereas 1FEMhand 2FEMh are the corresponding simulate wear depths at these cycles. In this equation the experiment test cycles is denoted bytestn. A value of 1.867mm was predicted as the maximum wear depth on the pin. Although this value underestimates the wear de pth it is a reasonable predicti on considering th at the wear phenomenon is a complex process. The variation of the ex trapolation size is depicted in Figure 64. The simulation took approximately 206 minutes. Intermediate Cycle-Update: Parallel Computation The Intermediate cycle-update procedure and its parallel implementation were performed with the same parameter values as were used in the step-updating procedure (see Table 6-2). However, in this procedure, th e update was performed after every 3 steps so that 3 updates were performed in each cycle. This is in contrast to the step-update procedure where 10 updates were performed, one at the end of every step. The result for the intermediate cycle-update and the corresponding parallel implementa tion are identical. The plot of the wear on the pin and pivot nodes that experience the most w ear is shown in Figure 6-5. A maximum wear depth (on th e pin) of 1.854mm was obtained from the intermediate cycle-update procedure and its parallel implementa tion. A plot of the extrapolation during the

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51 analysis is shown in Figure 6-6. A simulation tim e of 450 minutes was noted for the intermediate cycle update procedure. This is slightly more than twice the ti me it took to complete the stepupdate simulation test. This time difference can be explained by examin ing the extrapolation history plots (Figure 64 and Figure 6-6) for the two proce dures. The average extrapolation for the step update is slightly greater than twice that of the intermediate cycle update procedure. This is because the step update is a more stable procedure than the inte rmediate cycle updating procedure. The stable characterist ic of the step update allows fo r the use of larger extrapolation and thus few simulations cycles are required to predict the wear depth. In the present case, only 19 cycles were required to complete the stepupdate simulation test whereas 49 cycles were required to complete the intermediate cycle upda te simulation test. The parallel implementation of the intermediate update procedure only took approximately 135 minutes to complete. Clearly this procedure provides a time advantage. A comp arison of the results form the simulation tests and the actual tests ar e shown in Table 6-3. Conclusion The discussion in this Chapter focused on va lidating the wear-simulation procedure that was presented previously. The validation is done by comparing the results from the simulation to that of an experimental counter part. The wear occurring at the contact interface of an oscillation pin-pivot assembly was simulated. The pred icted wear depth devi ated from the actual experimental wear depth by approximately 7%. Ev en though this deviation appears to be large the predicted results is able to give a good insi ght into the wear occu rring at the interface. Indeed like any other approxima tion technique, errors are in herent. A number of factors contribute to this discrepancy in cluding the wear model, which is not an exact representation of wear and the finite element analysis, which is an approximation technique.

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52 Another contributor is the wear coeffici ent. The wear coefficient is obtained experimentally and as was mentioned has a larg e scatter. Errors in the wear coefficient considerably affect the results of the simulation. For instance, if instead a wear coefficient of 51.210mm3/Nm was used the new predicted wear depth would be 2.028mm. The new wear coefficient, which is still within the range of scatter according to Kim et al. [18], has a deviation of about 1.4% from the experimental value. This is indeed a large improvement from the previous predictions. It is thus concluded th at even though the proced ure does not accurately predict the wear the results obtai ned are of the correct order of magnitude and can be used for preliminary design.

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53 Table 6-1. Wear test informati on for the pin and pivot assembly. Test Parameters Values Oscillation amplitude 0 Load (cross-sectional pressure) 60MPa Test condition Un-lubricated steel on steel Total cycles 408,000 Max wear depth on pin ~2.00mm Table 6-2. Simulation parameters fo r the pin in pivot simulation test. Simulation Parameters Value Oscillation amplitude 0 Load (cross-sectional pressure) 60MPa Wear coefficient (k) 51.010 mm3/Nm Total cycles 100,000 Steps per cycle 10 Table 6-3. Comparison of results form the simu lation tests and actual wear tests for the pin in pivot assembly Max. wear depth (pin) (mm) Simulation time (min.) Actual test 2.000-Step update 1.867206 Inter. cycle update 1.854450 Parallel 1.854135

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54 Figure 6-1. Pinpivot assembly for the wear test. 0 1 2 3 4 5 6 7 8 9 10 x 104 0 0.05 0.1 0.15 0.2 0.25 cycleswear amountWear on pin & pivot (Step Update) pin pivot Figure 6-2. Cumulative maxi mum wear on pin and pivot.

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55 A B Figure 6-3. Contact pressure di stribution on the pin and pivot dur ing wear analysis. A) Contact pressure distribution in the transient wear regime. A range of pressure values is observed. B) Contact pressure distribu tion within the steady wear regime. The pressure distribution is a pproximately constant over the region of contact.

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56 0 2 4 6 8 10 12 14 16 18 20 0 1000 2000 3000 4000 5000 6000 CyclesExtrapolationExtrapolation History (Step Update) Figure 6-4. Extrapolation history plot for the step updating simulation procedure. 0 1 2 3 4 5 6 7 8 9 10 x 104 0 0.05 0.1 0.15 0.2 0.25 cycleswear amountWear on pin & pivot (Inter. Cycle Update) pin pivot Figure 6-5. Cumulative maximu m wear on pin and pivot for th e intermediate cycle updating procedure and the parallel implementation.

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57 0 5 10 15 20 25 30 35 40 45 50 0 500 1000 1500 2000 2500 3000 3500 CyclesExtrapolationExtrapolation History (Intermediate Cycle Update) Figure 6-6. Extrapolation hist ory plot for the intermediate cycle update procedure and its parallel implementation.

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58 CHAPTER 7 WEAR-SIMULATION EXAMPLE: ESTI MATION OF BACKHOE BUCKET TIP DISPLACEMENT Introduction In Chapter 6, the wear-simulation procedure for oscillatory contact was validated through experiments. It was found that the method can reasonably predict we ar occurring at such interfaces as long as accurate wear coefficients are obtained. In this Chapter, the usefulness of the procedure will be demonstrated through an example. The example involves determining the erroneous displacement at the tip of constructio n equipment due to wear at various joints. Estimation of Tip Displacement A backhoe system will be used to demonstrate how the simulation procedure can aid in determining the effect of wear on the performance of a system. The system is a part of a construction vehicle used in excavation work. The pa rticular backhoe system to be used in this example consists of three major parts (boom, di pper and bucket) as shown in Figure 7-1. The system consists of three joints; two connect the three parts together while the third one connects the backhoe system to the vehicle (not shown in Figure 7-1). Each jo int consists of two components that are in contact and experience relative oscill atory motion when the backhoe undergoes a cycle of digging and loading. The co ntact at these joints can be considered as oscillatory and as may be expected, large amounts of wear occur at these joints. The goal in this example is to estimate the amount of control of the bucket tip that is lost due to wear at these joints. The loss in control is quantified as the magnitude of the unwanted bucket tip displacement that occurs when the backhoe is rotated about the rotation axis. The tip displacement is shown in Figure 7-1. The diagram in Figure 7-2 shows a pivot join t before and after wear has occurred. In Figure 7-2A diagram no wear has occurred and the pin sits snugly in the pivot hole. In such a

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59 case the tip displacement is negligible. However, on ce wear has occurred at the joints, the pin is able to rotate through an angle as shown in Figure 7-2B. This ki nd of rotation propagates through all three joint and eventually causes a bucke t tip displacement. The magnitude of the tip displacement is dependent on the amount of wear. In this example the tip displ acement will be obtained assuming that the backhoe has been in operation for a period of one y ear. This corresponds to a total of 90,000 cycles of digging and loading dirt. This is obtained by assuming that the backhoe executed 60 cycles an hour, 5 hours a day for 300 days in a year. The tip displacement is obtained by first determining the amount of wear at each of the joints. In this case the jo ints are represented by a pin and pivot assembly similar to that used in the previous Chapters. Th e loading at each joint is taken to be constant throughout the entire cycle. A list of the loads app lied at each pivot is show n in Table 7-1. Also listed in Table 7-1, are the oscillation amplit udes of the each pin at each their corresponding joint. It is worth noting that an assumption is made that no other factor s contribute to the tip displacement and that the initial tip displacement is zero. The three joint are assumed to be made of steel and that no lubricant is used. A wear coefficient with a value of 51.010mm3/Nm is thus used in the analysis. This choice is consistent with experiments performed by Kim et al. [18]. A wear analysis is performed on all the joints for the specified parameters. Only 52440 cycles are simulated and the final results are linearly extrapolated. The wear de pth at the joints obtained from the simulation is shown as a function of the cycles in Figure 73. It can be seen from Table 7-2 that the wear on joint 3 is greatest. This is consistent with the fact the osci llation amplitude for the th ird joint is the largest. The maximum wear depth on the pin and pivot at 20,000 cycles and the extrapolated wear depths at 90,000 cycles for the three joints are reported in Tabl e 7-2. The wear depth at 90,000 cycles is

PAGE 60

60 used to determine the bucket tip displacements of all the component parts from the centerline. The component displacements as well as the overall backhoe tip displacement are listed in Table 7-3 and are depicted in Figure 7-4. A maximum bucket tip displacement of 149mm is estimated. This can be interpreted as the additional distance, from the desi red position, that the bucket tip wi ll travel be for coming to a halt when the backhoe is rotated. Conclusion The value of the simulation procedure was de monstrated through an example in which the erroneous bucket tip displacement, attributed to wear, for a backhoe system was estimated. Although the input values for the ba ckhoe system and thus the tip displacements are not from an existing case, the example demonstrates how the performance of a system can be affected by wear and how the simulation procedure can ai d in quantifying the lo ss in performance.

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61 Table 7-1. List of loads and relative rota tion angles at the joints of the backhoe. Load (MPa) Oscillation amplitude Joint 1 10.75 -150 to 150 Joint 2 10.40 -22.50 to 22.50Joint 3 12.15 -350 to 350 Table 7-2. Summary of the w ear depth at the joints afte r 20,000 cycles as well as the extrapolated wear depth at 90,000cycles Initial diameter (mm) Wear depth at 20000 cycles (mm) Wear depth at 90000 cycles (mm) Pin Pivot Pin Pivot Pin Pivot Joint 1 74.47 75.44 0.1140.1280.5160.576 Joint 2 75.13 76.11 0.1390.1680.6260.758 Joint 3 54.48 55.19 0.1610.2160.7240.974 Table 7-3. Displacement of the boom component parts from the center line. Part Angle deflection Distance from center (mm) Boom BM 1.6880LBM 73.64 Dipper D 0.4260LD 55.34 Bucket BU 0.4320LBU 20.00 Tip displacement 148.98mm

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62 Figure 7-1. Pinpivot assembly for the wear test. A B Figure 7-2. Joint consisting of a pin and pivot: A) Joint befo re wear has occurred on both components. B) Joint after wear has occurred on both components.

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63 Figure 7-3. Wear on the pin and pi vot at the backhoe Joints. A) Wear at joint 1. B) Wear at joint 2. C) Wear at joint 3. A B C

PAGE 64

64 Figure 7-4. Backhoe component displ acement from the vehicle centerline.

PAGE 65

65 CHAPTER 8 CONCLUDING REMARKS The objectives in this work were two fold. One goal was to develop a wear-simulation procedure to predict wear occurring on bodies experiencing oscillatory contact. The second goal was to incorporate into the wear procedure, techniques that would minimize the associated computational costs of the simulation process wh ile ensuring stability through out the simulation process. The wear-prediction procedure was developed based on a modifi ed form of Archards wear law. It involves determining wear at incrementa l steps within a cycle for the total number of cycles to be simulated. At the end of every step the geometry is updated to reflect the evolution of the surface and thus account for changing cont act conditions. This update procedure, termed as step update, is a more stable procedure than the cycle and inte rmediate cycle update procedures in which updates are de layed to the end of the cycle or after several steps have been simulated. Two techniques were proposed to minimize th e computational costs of the simulation. The first technique was an incorporation of an adapti ve extrapolation scheme into the wear-prediction procedure. The purpose of scheme was to optimize the selection of the extrapolation factor for the best use of the available resources wh ile ensuring stability in the simulation. The second technique is a parallel implementa tion of the cycle and intermediate update procedures. With no parallel impl ementation, step update approach is computationally cheaper than the intermediate cy cle update procedure. The reason for th is is that the intermediate cycleupdate procedure is a less stable procedure (due to the reduced number of geometry updates in a cycle) and thus requiring the use of smaller ex trapolation sizes. This results in a longer simulation time. When parallel computation is us ed, the intermediate cycl e update procedure is a

PAGE 66

66 cheaper alternative in term s of computational cost. It is deduced that in the absence of parallel computing resources, the most reasonable simula tion procedure to use is the step-updating procedure where as the intermedia te cycle updating procedure is be st when parallel computing is available. In the simulation validation process, it was f ound that the wear dept h on the pin predicted by the simulation procedure was under predicte d but within a reasonable range. This under prediction is largely attributed to the wear coefficient used The wear model used is a phenomenological model in which the wear coe fficient is determined through experiments. Hence an inaccuracy in this coefficient has a gr eat effect on the prediction process as was shown in Chapter 6. Based on the results it is concl uded that the procedure is a reasonable way to predict wear on bodies experi encing oscillatory contact

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67 CHAPTER 9 RECOMMENDATIONS FOR FUTURE WORK The wear-prediction procedure presented in this work provides a way to determine the wear occurring on bodies that ex perience oscillatory contacts. In the procedure, the changing contact condition or evolving surface was accounted for by updating the surface as the simulation progressed. This ensured for a more realistic simulation of the wear process. The prediction process can be made even mo re realistic by considering how the wear affects the kinematics and dynamics of a system and in turn how the kinematics and dynamics of the system affects the wear proc ess. In mechanisms, once wear ha s occurred at connection, the initial paths through with components of the me chanism travel are no longer preserved. The loads involved may also be affected. These change s occur due to the gap or change in geometry that is introduced at the connectio ns as wear occurs. It should al so be noted that the changes in the motion of the components, as well as the loading, will affect the wear process. The procedure that has been presented is an idealized case in which the changing system does not affect the wear process and vice versa. Essentially wear pred icted by isolating the region in which the wear occurs and thus negl ecting any changes that the wear would have on the overall system. A recommendation for future wo rk is to study the effect of a continuously changing system (changing due to w ear) on the wear process itself.

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68 LIST OF REFERENCES [1] P. Pdra, S. Andersson, Simulating sliding wear with finite element method, Tribology International, Vol. 32 (1999) 71. [2] P. Pdra, and S.Andersson, Finite element an alysis wear simulation of a conical spinning contact considering surface topogr aphy, Wear Vol. 224 (1999) 13. [3] P. Pdra and S. Andersson, Wear simulation with the Winkler surface model, Wear Vol. 207 (1997) 79. [4] W. Yan, N.P. ODowd, E.P. Busso, Numerical study of slide wear caused by a loaded pin on a rotating disc, Journal of mechanics and physics of solids Vol. 50 (2002) 449. [5] C. Gonzalez, A. Martin, J. Llorca, M.A. Ga rrido, M.T. Gomez, A. Rico, J. Rodriguez, Numerical analysis of pin-ondisk test on Al-Li/SiC compos ites, Wear Vol. 259 (2005) 609. [6] T. Telliskivi, Simulation of wear in a rolling-sliding contact by a semi-Winkler model and the Archards wear law, Wear Vol. 256 (2004) 817. [7] D. J. Dickrell, III and W. G. Sawyer, Evol ution of wear in a two-dimensional bushing, Tribology Transactions, Vol. 47 (2004) 257. [8] A. Flodin and S. Andersson, Simulation of mild wear in spur gears, Wear Vol. 207 (1997) 16. [9] A. Flodin and S Andersson, A simplified model for wear prediction in helical gears, Wear Vol. 249 (2001) 285. [10] J. Brauer and S. Andersson, Simulation of wear in gears with flank interference-a mixed FE and analytical approach, Wear Vol. 254 (2003) 1216. [11] A. B.-J. Hugnell, and S. Andersson, Simulating follower wear in a cam-follower contact, Wear Vol. 179 (1994) 101. [12] A. B.-J. Hugnell, S.Bjorklund and S. Anderss on, Simulation of the mild wear in a camfollower contact with follower ro tation, Wear Vol. 199 (1996) 202.

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69 [13] N. Nayak, P.A. Lakshminarayanan, M.K. Ga jendra Babu and A.D. Dani, Predictions of cam follower wear in diesel engi nes, Wear Vol. 260 (2006) 181. [14] B. J. Fregly, W. G. Sawyer, M. K. Harm an and S. A. Banks, Computational wear prediction of a total knee replacement from in vivo kinematics, Journal of Biomechanics Vol. 38 (2005) 305. [15] T. A. Maxian, T. D. Brown, D. R. Pedersen and J. J. Callaghan, A sliding-distance-coupled finite element formulation for polyethylene wear in total hip arthroplasty, Journal of Biomechanics Vol. 29 (1996) 687. [16] S. L. Bevill, G. R. Bevill, J. R. Penmetsa, A. J. Petrella and P.l J. Rullkoetter, Finite element simulation of early creep and wear in total hip arthroplasty, Journal of Biomechanics, Vol. 38 (2005) 2365. [17] M. qvist, Numerical simulations of mild wear using updated ge ometry with different step size approaches, Wear Vol. 249 (2001) 6. [18] N. Kim, D. Won, D. Burris, B. Holtkamp, G.R. Gessel, P. Swanson, W.G. Sawyer, Finite element analysis and experiments of metal/metal wear in oscillatory contacts, Wear Vol. 258 (2005) 1787. [19] I.R. McColl, J.Ding, S.B. Leen, Finite elem ent simulation and experi mental validation of fretting wear, Wear Vol. 256 (2004) 1114. [20] D. J. Dickrell III, D. B. Dooner, and W. G. Sawyer, The evolution of geometry for a wearing circular cam: analyti cal and computer simulation wi th comparison to experiment, ASME Journal of Tribology, Vol. 125 (2003) 187. [21] J.F. Archard, Contact and rubbing of flat surfaces, J Appl. Phys. Vol. 24 (1953) 981. [22] S.C. Lim and M.F. Ashby, Wear-mechanism maps, Acta metall, Vol. 35 (1987) 1. [23] A. Cantizano, A. Carnicero, G. Zavarise, Numerical simulation of wear-mechanism maps, Computational Materials Science Vol. 25 (2002) 54. [24] R. Holm, Electric Contacts, Almqvist & Wiksells Boktryckeri, Uppsala, (1946).

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70 [25] G.K. Sfantos, M.H. Aliabadi, Wear simu lation using an incremental sliding boundary element method, Wear Vol. 260 (2006) 1119. [26] L. Schmitz, J. E. Action, D. L. Burris, J. C. Ziegert, & W. G. Sawyer, Wear-Rate Uncertainty Analysis, ASME Journal of Tribology, Vol. 126 (2004) 802. [27] V. Hegadekatte, N. Huber, O. Kraft, Finite element based simulation of dry sliding wear, IOP Publishing, Vol. 13 (2005) 57. [28] Y. Bei, B.J. Fregly, W.G. Sawyer, S.A. Banks & N.H. Kim, The Relationship between Contact Pressure, Insert Thickness, and Mild Wear in Total Knee Replacements, Computer Modeling in Engineering & Sc iences, Vol. 6 (2004) 145. [29] W. G. Sawyer, Surface shape and contact pre ssure evolution in two component surfaces: application to copper chemical-mechanicalpolishing, Tribology Letters, Vol. 17 (2004) 139. [30] W.G. Sawyer, Wear Predictions for a Simple -Cam Including the C oupled Evolution of Wear and Load, Lubricati on Engineering (2001) 31. [31] L.-J. Xie, J. Schmidt, C. Schmidt and F. Bi esinger, 2D FEM estimate of tool wear in turning operation, Wear Vol. 258 (2005) 1479. [32] L.J Yang, A test methodology for determination of wear coefficient, Elsevier Science Vol. 259 (2005) 1453.

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71 BIOGRAPHICAL SKETCH Saad Mukras was born in Nairobi, Kenya. He was raised in Nairobi and partially in Gaborone, Botswana, where he completed his secondary education. He then joined University of Botswana and then transferred to Embry Riddl e Aeronautical University in Daytona Beach, Florida. There, he studied airc raft engineering technology and rece ived his bachelors degree in 2003. He then joined the Univer sity of Florida to pursue a ma sters degree in mechanical engineering in 2004. He worked under the superv ision of Dr. Nam-Ho Kim, completing several research projects, earning his masters degree in 2006.


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Title: Numerical Simulation of Wear for Bodies in Oscillatory Contact
Physical Description: Mixed Material
Copyright Date: 2008

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Source Institution: University of Florida
Holding Location: University of Florida
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NUMERICAL SIMULATION OF WEAR FOR BODIES INT OSCILLATORY CONTACT


By

SAAD M. MUKRAS













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

2006

































Copyright 2006

by

Saad M. Mukras



































To my parents, Professor Mohamed Mukras and Bauwa Mukras, and to my siblings,
AbduRahman, Suleiman, and Mariam










ACKNOWLEDGMENTS

I express my humility and utmost gratitude to Allah for his blessings in my life. Verily no

success would have been achieved without his grace and mercy. I would next like to thank my

parents for their support in my educational pursuits. I owe them much more than I can ever give

back.

I would like to acknowledge Dr Nam-Ho Kim, my adviser, for the support that he has

provided. Because of his advice and challenges, I have matured as a student and as a researcher. I

would like to thank my colleagues, friends and members of the university staff that have also

aided me.

Indeed, it would be negligent not mention the support that I have received from the

members of the Masaajid in Gainesville who have enabled me to feel at home while away from

home.












TABLE OF CONTENTS


page

ACKNOWLEDGMENTS .............. ...............4.....


LIST OF TABLES ................ ...............7............ ....


LIST OF FIGURES .............. ...............8.....


AB S TRAC T ............._. .......... ..............._ 10...


CHAPTER


1 INTRODUCTION ................. ...............11.......... ......


Background ................. ...............11.................
Scope and Objective ................. ...............14................
Thesis Organization ................. ...............15.................


2 WEAR-PREDICTION METHODOLOGY FOR BODIES INT OSCULATORY
CONT ACT S .............. ...............16....


Introducti on ........._... .. ....... ...............16...
W ear M odel .............. ...............16....
Simulation Procedure........................ ...........1
Pin-Pivot Finite Element Model ........._. ........_. ...............21...

Geometry Update Procedure .............. ...............22....
Conclusion ........._ ........_. ...............25....


3 EXTRAPOLATION SCHEME S............... ...............30


Introducti on ................. ...............30.................
Constant Extrapolation .............. ...............3 0....
Adaptive Extrapolation Scheme .............. ...............33....
Conclusion ............ ...... ._ ...............34....


4 PARALLEL COMPUTATION INT WEAR SIMULATION FOR OSCILLATORY
CONT ACT S .............. ...............36....


Introducti on ................... .. ................ ...............36.......

Cycle- and Intermediate Cycle-Update .............. ...............36....
Parallel Computation .............. ...............38....


5 WEAR-SIMULATION PROGRAM............... ...............43


Introducti on ................. ........... ...............43 .....
Wear-Simulation Program Format .............. ...............43....












Ansys Input Code .............. ...............43....
Contact analysis............... ...............44
Output of results ..........__._ .... .___ ...............44....
Simulation Managing Code ........._.___..... .___ ...............45....


6 EXPERIMENTAL VALIDATION OF THE WEAR-SIMULATION PROCEDURE......... 48


Introducti on ............... ......._ ...............48....
Wear-Simulation Validation............... ...............4

Step-Update Simulation Test............... ........ ............4
Intermediate Cycle-Update: Parallel Computation .............. ...............50....
Conclusion ............ _...... ._ ...............51....


7 WEAR-SIMULATION EXAMPLE: ESTIMATION OF BACKHOE BUCKET TIP
DI SPLACEMENT ............_ ..... ..__ ...............58...


Introducti on ............... ... ..__ ...............58...
Estimation of Tip Displacement ............_ ..... ..__ ...............58..
Conclusion ............ _...... ._ ...............60....


8 CONCLUDING REMARK S............_ ..... ..__ ...............65..


9 RECOMMENDATIONS FOR FUTURE WORK .............. ...............67....


LIST OF REFERENCES ............_ ..... ..__ ...............68...


BIOGRAPHICAL SKETCH .............. ...............71....










LIST OF TABLES


Table page

6-1 Wear test information for the pin and pivot assembly............... ...............53

6-2 Simulation parameters for the pin in pivot simulation test. .....__._.. ........_._ ...............53

6-3 Comparison of results form the simulation tests and actual wear tests for the pin in pivot
assem bly .............. ...............53....

7-1 List of loads and relative rotation angles at the j points of the backhoe ................. ................61

7-2 Summary of the wear depth at the j points after 20,000 cycles as well as the extrapolated
wear depth at 90,000cycles............... ..............6

7-3 Displacement of the boom component parts from the center line ................. ................ ...61











LIST OF FIGURES


Figure page

2-1. Oscillatory contact for a pin-pivot assembly. .............. ...............26....

2-2. Wear simulation flow chart for the 'step update' procedure. ................ .......................27

2-3. Pin-pivot finite element model. ................ ................ ........ ......... ....__ .28

2-4. A three-node contact element used to represent the contact surface .................. ...............28

2-5. Geometry updates process. .............. ...............29....

2-6. Surface normal vector for the pin-pivot assembly prior to update ............... ............._..29

3-1. Contact pressure distribution on a pin-pivot assembly............... ...............35

3-2. Extrapolation history for a pin-pivot assembly. ............. ...............35.....

4-1. Wear simulation flow chart for the 'cycle-update' procedure ................. ......................40

4-2. Wear simulation flow chart for the 'intermediate cycle-update' procedure. ......................41

4-3. Wear simulation flow chart for the parallel implementation of the 'cycle-update'
proce dure ................. ...............42....... ......

5-1. Interaction between the C code and the Ansys input code .................... ............... 4

5-2. Function of the Ansys input code. ................. ....__ ....__ ....__ ..............46

5-3. Structure of the wear-simulation program ................. ...............47...............

6-1. Pin-pivot assembly for the wear test ................. ...............54........... .

6-2. Cumulative maximum wear on pin and pivot. ............. ...............54.....

6-3. Contact pressure distribution on the pin and pivot during wear analysis.. .................. ..........55

6-4. Extrapolation history plot for the step updating simulation procedure. ............. .................56

6-5. Cumulative maximum wear on pin and pivot for the intermediate cycle updating
procedure and the parallel implementation ................. ...............56........... ...

6-6. Extrapolation history plot for the intermediate cycle update procedure and its parallel
implementation. ............. ...............57.....

7-1. Pin-pivot assembly for the wear test ................. ...............62........... .











7-2. Joint consisting of a pin and pivot. .............. ...............62....

7-3. Wear on the pin and pivot at the backhoe Joints ................ ........... .....................63

7-4. Backhoe component displacement from the vehicle centerline. ............. .....................6









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

NUMERICAL SIMULATION OF WEAR FOR BODIES INT OSCILLATORY CONTACT

By

Saad M. Mukras

December 2006

Chair: Nam-Ho Kim
Major Department: Mechanical and Aerospace Engineering

When bodies are in contact and in relative motion, wear becomes an important aspect that

should be considered during design. In mechanisms, wear is experienced at connections such as

joints. A particular type of contact condition, known as oscillatory contact, exists at these

connections and is partly responsible for wear. The obj ective of this study is to develop a wear-

prediction procedure for bodies that experience this type of contact condition.

A prediction procedure for wear occurring in bodies that experience oscillatory contact is

proposed. The methodology builds upon a widely used iterative wear-prediction procedure. Two

techniques are incorporated into the methodology to minimize the simulation computational

costs. In the first technique, an extrapolation scheme that optimizes the use of resources while

maintaining simulation stability is implemented. The second technique involves the parallel

implementation of the wear-prediction methodology. The methodology is used to predict the

wear on an oscillatory pin joint and the predicted results are validated against those from actual

experiments.









CHAPTER 1
INTTRODUCTION

Background

Mechanical systems employ mechanisms that are used to convert one type of motion into

another. These systems consist of connections such as j points where two components of the

system establish contact and are in relative motion during operation. Depending on the

kinematics of the mechanism, either of several contact conditions may exist at the connection.

One particular contact conditions that is widely encountered is the oscillatory contacts. This

contact condition coupled with other factors give rise to wear which could cause the system to

fail. The importance of wear and the need for its consideration in design is dependant on a

number of factors which may be either technical or economical or both. An example in which

wear is of great concern is at the j points of heavy equipment such as backhoes. The j points of such

equipment experience considerable amounts of wear while in operation. In order to minimize

the wear occurring is such joints designers have implemented several techniques such as select

materials based on material ranking or using wear resistant coating on the contacting surfaces.

Although these procedures are widely used, they do not give sufficient insight or quantitative

information on how a system may fail due to wear. It would thus be advantageous for designers

to have the ability of predicting the wear beforehand. One way that has been used to achieve this

has been the use of accelerated design verification procedures on prototypes. The procedures are

generally expensive and destructive in nature but provide an abundant amount of information

regarding the wear as a mode of failure.

An enormous amount of effort and resources has been placed into developing techniques

that utilize computer simulations in the prediction of wear. Use of simulations for wear

prediction has a number of benefits, one of which is its potential to reducing or eliminating









costly tests that may be required when considering wear in design. Simulations for wear

predictions are also a versatile alternative, allowing for rapid changes in the simulation

conditions with little effort.

A number of papers have been written dealing with the subj ect of wear prediction. A

general trend that that has emerged is the use of numerical methods together with variations of

Archard's wear model in predicting wear. Padra and Andersson [1] used finite element method

(FEM) in an iterative procedure to determine the wear on a pin placed over a moving disk. The

simulation yielded results similar to those of an analogous experiment. In a separate paper, Padra

and Anderson [2] discuss the use of finite element analysis in wear simulation of a conical

spinning contact. They compared simulation results to analytical results which showed good

agreement. Padra and Andersson [3] also used the Winkler surface model, to compute contact

pressure instead of the finite element method, to simulated wear. They reported results that

showed close agreement with simulations in which the finite element method was used. Yan et

al. [4] predicted the wear resulting form a loaded pin contacting a rotating disc, by noting that the

center of the disc wear track may be approximated as a plain strain region. They showed that the

prediction results were consistent with experimental measurements. Wear simulations for a pin

on disk problem were performed by Gonzalez et al. [5] using finite element method in

conjunction with an incremental wear-prediction technique. In their simulation procedure, the

geometry was updated at the end of each iteration. This was done to account for the worn out

material. Telliskivi [6] preformed simulations to predict the wear on a disc-on-disc assembly

using the Winkler mattress model. Good agreement between experiment and the simulation

results were reported. Dickrell and Sawyer [7] developed a model to study the evolution of wear

for a shaft and bushing assembly and ran experiment to validate the model.









A number of papers dealing with wear prediction of more complicated geometries have

also been written. Flodin and Andersson [8], simulated the wear on spur gears using the Winkler

model. They used an incremental wear-prediction approach in which the geometry was allowed

to evolve as the simulation progressed. Flodin and Andersson [9] later extended their

methodology to helical gears. They treated the helical wheel as several thin independent spur

gear teeth. Brauer and Andersson [10] conducted wear simulations for gears using a combination

of finite element method and an analytical approach based on Hertz theory. The FEM was used

to determine the loads resulting form gear teeth interaction which were in turn used to determine

contact pressure using the analytical expressions. In one paper Hugnell et al. [l l] simulated the

wear resulting from a cam-follower contact and in another paper [12] they simulated the mild

wear in a cam-follower contact with follower rotation. They also used an incremental wear-

prediction procedure and allowed the geometry to change after every simulation step. Nayak et

al. [13] predicted the wear on a cam-follower and presented a guideline on designing cam

followers for low wear. Fregly et al. [14] performed wear analysis to simulate mild wear on a

tibial insert model. They reported close agreement between the simulation results and damage

observation on actual tibial insert. Wear predictions on total hip arthroplasty were performed by

Maxian et al. [15]. Bevill et al. [16] also performed simulations to determine the damage on a

total hip arthroplasty due to wear and creep.

Depending on the complexity of wear mechanisms, wear predictions using computer

simulations have yielded relatively reasonable results [1-3, 17-18]. The simulations, however,

have been found to be quite computationally expensive. Several ideas have been implemented in

an attempt to reduce computational costs associated with the wear-simulation process. Padra and

Andersson [3] attempted to minimize the computational cost by using the Winkler model to










determine the contact pressure distribution. The Winkler model was used as an alternative to the

more expensive but relatively accurate FEM. Although the method was found to be less

expensive it can be argued that the benefit of using more accurate results from the finite element

technique outweigh the gains in computational efficiency when complicated geometries are

considered. Padra and Anderson [1] also employed a scaling approach to tackle the problem of

computational costs. In this approach the incremental wear at any particular cycle of the

simulation was scaled based on a predefined maximum allowable wear increment. The scaling

factor was obtained as a ratio between the maximum allowable wear increment and the current

maximum wear increment (maximum wear increment of entire geometry). They found that this

procedure was more computationally effective. Kim, et al. [18] used a constant extrapolation

technique to reduce the computational costs for the oscillatory wear problem. In their technique

one finite element analysis was made to represent a number of wear cycles. Through this

extrapolation, they were able to reduce the total number of analyses needed to estimate the final

wear profile. A similar procedure was done by McColl, et al. [19] as well as Dickrell et al. [20].

In another paper [4], the computational costs of simulating a pin on a rotating disc was reduced

by approximating the state of strain on the center of the wear track as plain strain. A less costly

two-dimensional idealization was then used in place of the more expensive three-dimensional

problem.

Scope and Objective

As is apparent from the literature, a number of procedures have been proposed to simulate

wear. In addition several procedures have been proposed to simulate wear in more specific

assemblies such as gears and cam-follower systems. One type of assembly that is encountered in

numerous applications is one in which the oscillatory contact is experienced. These types of

assembly are commonly found at the connections of mechanisms. Due to the nature of relative









motions at such assemblies, wear is inevitable. In this research, the obj ective is to develop a

simulation framework for wear prediction in bodies that experience oscillatory contact. In

addition to developing the prediction procedure, emphasis is made on incorporation techniques

that minimize the overall computational costs and enable stable simulations.

Thesis Organization

In Chapter 2, the details of the wear model used in the prediction procedure are discussed.

The simulation prediction procedure specific to bodies experiencing oscillatory contact will then

be presented. A representative model to be used to demonstrate the procedure is introduced and

discussed in Chapter 2. Chapter 2 will close with a discussion of a geometry updating technique

that minimizes the mesh distortion.

Techniques to minimize computational costs will be presented in Chapter 3 and 4.

Discussions in Chapter 3 will focus on the use of extrapolations to minimize costs. The issue of

instability when extrapolations are used as well as a proposed solution is included in Chapter 3.

In Chapter 4, the implementation of parallel computation as a way to reduces computational

costs is discussed. In order to implement the wear-prediction procedure, a simulation program

was written. The details of the program are discussed in Chapter 5.

Validation of the wear-prediction procedure is discussed in Chapter 6. Results from

experiments are compared to results from the wear simulation. In Chapter 7, an example .that

demonstrates how the wear-simulation program can be used to evaluate the effect of wear on the

performance of a system is presented. Finally conclusions about the wear-prediction procedure

will be drawn in Chapter 8 and suggestions for future research will be made in Chapter 9.









CHAPTER 2
WEAR-PREDICTION METHODOLOGY FOR BODIES INT OSCILATORY CONTACTS

Introduction

When two bodies are in contact and are in relative motion with respect to each other, wear

is expected to develop on the regions of contact. The type of contact that the bodies experience is

dependent on how the bodies move relative to each other. One type of contact condition that is of

interest is the oscillatory contact. This type of contact condition is characterized by an oscillatory

relative motion between the bodies that are in contact. The contact between a pin and a pivot in a

center-link pivot joint is an example of this type contact. This example is shown in Figure 2-1

where the pin oscillates between two extreme angles. In this Chapter a procedure to predict the

wear occurring in this type of contact is discussed. In this work, the assembly shown in Figure 2-

1 will be used as a representative case of the oscillatory contact to illustrate the wear-prediction

procedure.

Wear Model

In developing the wear-prediction methodology it is assumed that all the wear cases to be

predicted fall within the plastically dominated wear regime, where slide velocities are small and

surface heating can be considered negligible. Archard's wear law [21] would thus serve as the

appropriate wear model to describe the wear as discussed by Lim and Ashby [22] as well as

Cantizano, et al. [23]. In that model, first published by Holm [24], the worn out volume, during

the process of wear, is considered to be proportional to the normal load. The model is express

mathematically as follows:

V F
=K ",(2-1)
s H









where V is the volume lost, s the sliding distance, K the dimensionless wear coefficient, H

the Brinell hardness of the softer material, and F, the normal force. Since the wear depth is the

quantity of interest, as opposed to the volume lost, Eq. 2-1 is usually written in the following

form :

hA
= kF,, (2-2)


where h is the wear depth and A is the contact area such that V = hA The non-dimensioned

wear coefficient K and the hardness are bundled up into a single dimensioned wear coefficient

k (Pa )~. It should be noted that the wear coefficient k is not an intrinsic material property but is

also dependent on the operating condition. The value of k for a specific operating condition and

given pair of materials may be obtained by experiments [25]. Also worth noting, is that measured

values of wear coefficients usually have large scatter and may affect wear predictions

significantly. Care should thus be taken in obtaining these values. Uncertainty analysis for

measured values of wear coefficients, such as those presented by Schmitz et al. [26], may be of

considerable benefit.

Equation 2-2 can further be simplified by noting that the contact pressure may be

expressed with the relation p = F,/A so that the wear model is expressed as


= kp (2-3)


The wear process is generally considered to be a dynamic process (rate of change of the

wear depth with respect to sliding distance) so that the first order differential form of Eq. 2-3 can

be expressed as:

dh
= kp(s), (2-4)









where the sliding distance is considered as the time in the dynamic process, and the contact

pressure is a function of the sliding distance.

A numerical solution for the wear depth may be obtained by estimating the derivative in

Eq. 2-4 with a finite divide difference to yield the depth as follows:

h, = h~,_+kpAs, (2-5)

In Eq. 2-5, hi refers to the wear depth at the jth iteration while hi,_ represents the wear depth at

the previous iteration. The last term of Eq. 2-5 is the incremental wear depth which is a function

of the contact pressure and incremental sliding distance (As, ) at the corresponding iteration.

If information about the wear coefficient k, the contact pressure p, and the sliding

distance As, is available at all iterations ( j), the wear depth on a contact interface for a specified

sliding distance s can be estimated using Eq. 2-5. Here the sliding distance is an accumulation

of the incremental sliding distance for all iterations (n iter ) as is expressed in Eq. 2-6.


s = As (2-6)


The contact pressure ( p) may be obtained through numerical methods. The finite element

method appears to be the most widely used method. This is probably due to its accuracy. Several

papers [3, 6, 27-28] have been written in which an elastic foundation model has been used in

place of the finite element method. The wear coefficient can be obtained through experiments

such as this explained by Kim et al. [18, 25] where as the incremental sliding distance may be

obtained from the finite element analysis or can be specified by the user.










Simulation Procedure

The most widely used procedure to simulate wear occurring at a contact interface is an

iterative procedure describe by the numerical integration in Eq. 2-5. A number of papers [1,2, 17-

19,25,29], that demonstrate the implementation of Eq. 2-5 in predicting wear, have been written.

Although the details of the various procedures differ, three main steps are common to all of

them. These include the following:

* Computation of the contact pressure resulting from the contact of bodies.

* Determination of the incremental wear amount based on the wear model.

* Update of geometry to reflect the wear amount and to provide the new geometry for the
next iteration.

The procedure developed for predicting wear on oscillatory contacts incorporates the

aforementioned steps.

As was mentioned earlier the pin-pivot assembly shown in Figure 2-1 will be used to

illustrate the simulation procedure. In this assembly the pin is fixed so that it does not translate in

any direction but is allowed to oscillate (in an axis perpendicular to the paper) from one extreme

to another (bounded by specified amplitude). Contrary to the conventional definition of a cycle,

in this work a cycle is defined as a rotation of the pin from one extreme angle to the other

(e.g.+60O). The goal is to develop a procedure that can predict the wear over several thousand

cycles. It is worth noting that most of the work present in the literature dealing with wear

simulation does not address this type of motion but rather, that which is of a continuous nature

such as in rotational contacts.

The simulation of wear at the contact interface of the pin-pivot assembly is achieved by

considering each cycle separately. The wear in any cycle can be obtained by discretizing the

cycle into a number of steps and thereafter applying Eq. 2-5. The discretization is such that each










step corresponds to a specific pin angle between the two extremes. In the application of Eq. 2-1,

the wear coefficient k and the incremental sliding distance As~ are taken to be constant where as

the contact pressure p, is computes by the finite element method. The pin-pivot finite element

model used to illustrate the simulation procedure will be described a later subsection.

At each step a finite element analysis is performed to determine the contact pressure over

the contact region. The wear depth during any cycle and at any point on the contact surface can

then be determined by Eq. 2-7 which is a modification of Eq. 2-5.

h,,l,,= h,,, ,+kpg,,As, (2-7)

In Eq. 2-7, n refers to surface nodes number (of the finite element model) which may or

may not establish contact with the opposing surface. The sub script i and j indicate the current

step and cycle, respectively. All other terms are as defined previously.

The geometry is then updated to reflect the amount of wear and to prepare the model for

the next step. Details of the geometry update procedure will be discussed in subsequent

subsection. At this point the simulation progresses to the next step and the oscillating pin

assumes a new position. This involves a rotation through an angle corresponding to the

incremental angle. The previously described processes are repeated up until all steps in a cycle

are completed. The direction of pin rotation is reversed and the simulation of the next cycle

commences. The term 'step update' is adopted for this procedure since the geometry is updated

after every step. The simulation process for the step update procedure is summarized in the

flowchart shown in Figure 2-2.









Pin-Pivot Finite Element Model

Two methods that have been used in the literature to calculate the contact pressure at the

contact surface were mentioned as the elastic foundation and the finite element method. The least

expensive of the two methods, in terms of computational costs, is the elastic foundation method.

This method is, however, the least preferred due to its level of accuracy especially for

complicated geometries. To illustrate the simulation procedure the finite element method has be

selected.

The diagram of the 2D Einite element model for the pin-pivot assembly is shown in Figure

2-3. As can be seen from the diagram, three kinds of elements have been used. The eight-node

quadrilateral elements were used to model the pin and the pivot. Three-node contact elements

were used to represent the contact surface. It is worth noting that the contact elements coat the

outer and inner surface of the pin and pivot, respectively. It should also be noted that the contact

element do not add any new nodes to the model. Instead, the nodes of the quadrilateral elements

that appear on the surface make up contact elements. The third type of element that was used is

the link (truss) elements. This element was used to prevent rigid body motion (RBM). It was

mentioned earlier that the pin is Eixed from translating but allowed to rotate in a controlled

manner. Specifically the rotation is allowed only once the finite element analysis has been

completed. This means that the pin will not experience RBM. The pivot, however, is Eixed along

its lower edge to prevent any horizontal translations as well as rotation in any axis but is allowed

to translate in the vertical direction. This is also the direction of loading as is shown in Figure 2-

1. There is thus a potential for RBM to occur. The link element is used to eliminate this

possibility. The effect of the link element is reduced by assigning it a very small elastic modulus.









Geometry Update Procedure

The process of geometry update is necessary in order to correctly simulate and predict the

wear occurring at the contact interface. Indeed material removal changes the contact surface and

causes a redistribution of the contact pressure resulting from the contact. These changes can only

be captured if the surface is altered through a geometry update. Estimation of wear through an

extrapolation which is based on the original surface has been shown to produce erroneous

predictions [30]. It is therefore becoming as standard, as is evident in the literature [1-2, 17-19,

25, 29, and 3 1], that geometry updates are included in the process of wear simulation.

The procedure proposed to update the geometry in this research involves two steps. These

steps are outlined below:

* Determine the normal direction (vector) of the contact surface at the location of each
surface node (contact node).

* Shift the position of the surface nodes in the direction of the normal vector by an amount
equal to the wear increment.

The normal direction of the surface nodes at the location of the contact nodes can be

obtained by considering the locations of the contact elements. The contact elements at the

surface have three nodes each. This element is illustrated in Figure 2-4. The corresponding shape

functions for this element may be written as follows:


N, = (t -1) t

N2 = -(t -1)(t +1) (2-8)

N3 = ~(t +1) t


where t is the local coordinate parameter. The surface of an element can then be described in

terms of the nodal coordinates and as a function of the local coordinate. The expression for the

surface is given in Eq. 2-9.












Tx N 0 N, ON,O x1 ,X
y 0 N, O N, O Ni y,-9




where xk and yk are the coordinates of node k (k = 1, 2, 3 )for the element of interest. If the

vector tangent to the surface (contact element surface) is denoted as vt then its value for the

element can be obtained as follows:


vt = -i+ j+0 k (2-10)
dt dt

where the partial differentials is given in Eq. 2-11 or 2-12.




dt dt dt dt x,
(2-11)
Sy 8N, 8N, dN, y,
0 0 0
dt dt dt dt Ix,



or

Dx N,
dt ,= t
(2-12)

dt ,= dt

The vector normal (v ) to the surface (depicted in Figure 2-4) can be expressed as a cross

product of the tangent vector ( v,) and the vector perpendicular to the plane of the surface


(v, = (0, 0,1)). This cross product is expressed in Eq. 2-13.where n2 denotes the node number.










V,~ XV
von=tn p. (2-13)


The resulting unit normal vector then appears as follows:

(y 8x .
v = t Bt(2-14)

ax"t I B9'tl

or,

vo,n = vnorm~x,ni + vnorm~y,nj (2-15)

where v and v are the components of the vector normal to the surface. Once the

contact pressure distribution and normal vectors at all the nodes on the surface have been

determined, the geometry can then be updated. The update is done by moving the surface nodes

in the direction of the unit normal vector. The coordinate of the new node position at any step of

any cycle can be written as follows:

n,2, n,2 1, n Lz norm~x,n .(2 -16 )

n,, n,-,Jnr x,n


The process of the geometry update is shown in Figure 2-5. In this diagram the wear depth

is grossly exaggerated to illustrate the concept. The procedure for the geometry update has been

used successfully in the wear-simulation process. A possible problem that could be encountered

during model updates is mesh distortion. In the pin-pivot model, mesh distortion during model

update is minimized through a carefully created finite element model. The FE model is initially

created in such a way that all normal vectors at surface nodes, before any update is performed,

will be in a direction parallel to the element edge. This idea is illustrated in Figure 2-6. After










several geometry updates it can be expected that the vector will no longer be parallel to the edge.

The deviation is however small to be of any maj or consequence.

Conclusion

The procedure discussed was used to predict the wear occurring at the interface of the

pin-pivot assembly. Although this was a specific problem, the general framework outlined can be

extended and used to predict wear in other 2D oscillatory contact problems.

















,IIcillation Pin



< I l l i f i I I /~ ,

l1II 11I1


.1II Ir ~ I II PiVOt


Pressure .-]... Pi ..1~ 111 0th


Figure 2-1. Oscillatory contact for a pin-pivot assembly.











































Figure 2-2. Wear simulation flow chart for the 'step update' procedure.






















I
~A I


-Nodbe Contalct
elements


8-n~ade t:~ ':;i-:-l i
Elernen~s


Figure 2-3. Pin-pivot finite element model.

























Figure 2-4. A three-node contact element used to represent the contact surface.






















L


r "'


Figure 2-5. Geometry updates process.


Figure 2-6. Surface normal vector for the pin-pivot assembly prior to update









CHAPTER 3
EXTRAPOLATION SCHE1VES

Introduction

The procedure discussed in Chapter 2 provides a way to simulate the wear resulting from

oscillatory contacts. However, the process can be quite expensive. For instance, if one desires to

simulate 100,000 oscillatory cycles for a case in which each cycle is discretized into 10 steps

then 1,000,000 finite element analyses (nonlinear) as well as geometry updates would be

required. Clearly this may not be practical and the need for techniques to combat the

computational cost becomes immediately apparent. Techniques to tackle the problem of

computational costs will be discussed in the current and following Chapters.

Constant Extrapolation

Extrapolations have been used in various forms with the goal of reducing computational

costs. In this work an extrapolation factor ( A) is used to proj ect the wear depth at a particular

cycle to that of several hundreds of cycles. Essentially, the extrapolation is the total number of

cycles for which extrapolation is desired. Thus according to this definition, the extrapolation

factor can only take on positive integers values.

The equation used to determine the amount of wear at a particular node during any step in

a cycle was expressed in Chapter 2 as;




Equation 3-1 can be modified slightly in order to incorporate an extrapolation factor. It is

first noted that the first term on the right hand side (R.H. S.) of Eq. 3-1 refers to the cumulative

wear depth from previous cycles whereas the last term refers to the incremental wear depth at the

current step and cycle. As way to minimize computational costs, it is assumed that the next A "

cycles (as many cycles as the value of the extrapolation) will have the same amount of wear










depth as that of the current step and cycle. The total incremental wear depth for those many

cycles may then be obtained by multiplying last term of Eq. 3-1 with the extrapolation factor.

The resulting expression is shown in the following equation:

hn,l,J+A hn,2-,l, + kApl~n~s, (3 -2)

Utilizing the same concept, a new expression can be written to describe the position of the

contact nodes during the wear-simulation process. This expression is as follows:


yn,l,J+A n,21, norm x,n 3)


Extrapolation and stability. As may be expected, the level of accuracy of the wear

simulation is reduced when extrapolations are used. This is directly related to the assumption that

the same value of incremental wear depth is maintained for several cycles. This is, however, not

the case since in reality the geometry would constantly evolve which in turn would lead to a

continuous redistribution of the contact pressure and thus a change in the incremental wear depth

at each cycle. However the difference is small enough that it may be neglected as is evident from

the overall error of simulation results.

Use of extrapolations may also cause problems in simulation stability. Here stability is

defined with regard to the contact pressure distribution and hence the wear profile. An ideally

stable wear simulation would be defined as one in which the contact pressure distribution

remained smooth (with no sharp or sudden changes in the distribution) for the entire duration of

the simulation. It is however unlikely to have smooth pressure distribution throughout the

simulation process. As a result a more relaxed definition of stability is adopted where by sudden

changes in the pressure distribution are allowed to occur. In Figure 3-1A, the contact pressure is

seen to vary smoothly over the contact region except for small peaks at the contact edges. The










peaks are attributed to the transition form a region of contact to a region of no contact. This

transition occurs at a point which can not be represented by a discrete model. The result is that

there is an abrupt change in the surface curvature which causes high pressure. If such contact

pressure distribution is maintained through out the simulation, the simulation can be referred to

as stable. On the contrary, the diagram in Figure 3-1B is representative of contact pressure

distribution that would constitute an unstable wear simulation. The two diagrams show the

contact pressure distribution for a stable and unstable wear simulation consistent with the

adopted definition of stability.

When very large extrapolation sizes are used, wavy pressure distributions (Figure 3-1B)

are observed and the simulation becomes unstable. The shift to instability due to the use of large

extrapolation sizes can be explained as follows. The contact pressure distribution (obtained from

the finite element analysis) is generally not perfectly smooth. This may be due to the

discretization error stemming form the finite element analysis. The use of an extrapolation factor

magnifies these imperfections so that when the geometry is updated the contact surface

smoothness is reduced. If large extrapolation sizes are used, the regions that experience high

contact pressure in a particular step of the simulation are worn out excessively so that in the

following step these regions experience little or no contact. On the other hand, the regions that

did not experience high contact pressure will be worn out less and thus will experience greater

contact pressure in the next step. This behavior will repeat in subsequent steps causing the

surface to become increasingly unsmooth. The simulation will then become unstable. If,

however, smaller extrapolation sizes are used the wearing process acts as an optimizer to

smoothen the surface.









A smooth contact surface is critical for two reasons. The first reason is that a smooth

contact surface is consistent with the actual case that is being simulated, and the second is that a

non-smooth surface would affect the solution of the finite element problem. Due to these

reasons, a condition is placed on the selection of the extrapolation size such that the selected size

would not severely affect the smoothness of the pressure distribution.

Extrapolations provide a solution to the computational cost problem but as has been

discussed its use may introduce other problems. The accuracy and stability of the simulation may

be jeopardized by using extrapolation sizes that are too large. Using small extrapolation sizes

will produce more reliable solutions but will result in a less than optimum use of resources. It

may also be argued that even if an appropriate extrapolation size was selected at the beginning of

the simulation it may be that at a different stage of the simulation a different extrapolation size

would be required to provide optimum use of the available resources. In the next subsection a

procedure is described that seeks for the largest extrapolation sized while maintaining stability

during the entire simulation process.

Adaptive Extrapolation Scheme

The adaptive extrapolation technique is an idea proposed as an alternative to the constant

extrapolation scheme. The idea behind it is to seek for the largest extrapolation size while

maintaining a state of stability (smooth pressure distribution) throughout the simulation process.

The scheme is a three-step process. In the first part an initial extrapolation size ( A,) is selected.

The selection is based on experience.

In the second part of the adaptive extrapolation scheme, a stability check is performed. A

single check, preferably at the center step of the cycle, is sufficient for an entire cycle. The

stability check involves monitoring the contact pressure distribution within an element for all









elements on the contact surface. This essentially translates to monitoring the local pressure

variation. If the contact pressure difference within an element is found to exceed a stated critical

pressure difference Apont then a state of instability is noted and vice versa. In the final step of the

adaptive scheme, the extrapolation size is altered based on the result of the stability check. That

is, the extrapolation size is increased for the stable case and a decrease for the unstable case. This

process can be summarized as follows:

SAi i + MAmr if Apele < Apcnt
A = (3-4)


It must be mentioned that in order to maintain consistency in the geometry update as well

as in the 'bookkeeping' of the number of simulated cycles, a single extrapolation size must be

maintained through out a cycle. That is, every step in a cycle will have the same extrapolation

size while different cycles may have different extrapolation sizes. Figure 3-2 shows a graph of

the extrapolation history for the oscillating pin-pivot assembly. From the graph, it can be seen

that the extrapolation took on a conservative initial value of about 3900 and increased steadily up

to the 12th cycle (actual computer cycles not considering the extrapolations). Thereafter the

extrapolation size oscillated about a mean of about 6000.

Conclusion

The use of extrapolations is an efficient way to cut down on computational costs. Even

though no way of accounting for the error involved has been developed, the results observed

from simulation runs have shown acceptable error ranges. An adaptive extrapolation scheme was

proposed to govern the selection of the extrapolation size during the simulation. The scheme

ensures that the largest allowable extrapolation size is used during the simulation. The scheme

thus provides for a way to minimize computational costs while maintaining a stable simulation.














\j :


//
j


Extrapolation Vs Cycles (E=207Gpa & Pivot thikness t=19mm)


6000

5000

3 4000

k 3000

2000

1000


5 10 15 20 25
Cycles


30 35 40


Figure 3-2. Extrapolation history for a pin-pivot assembly.


i\\


A B

Figure 3-1. Contact pressure distribution on a pin-pivot assembly. A) The case of a stable wear
simulation. B) The case of an unstable wear simulation.










CHAPTER 4
PARALLEL COMPUTATION INT WEAR SIMULATION FOR OSCILLATORY CONTACTS

Introduction

Although the use of extrapolations is probably the most effective way to reduce the

computational costs, other ways are also available. A parallel processing implementation of the

simulation procedure is proposed as an additional way to remedy the problem of computational

costs. This technique may be used in conjunction with the extrapolation scheme to further reduce

computational costs. The discussion of parallel computation will be preceded by an introduction

to the concept of 'cycle-update and intermediate cycle-update' which are central ideas in the

parallel computation procedure.

Cycle- and Intermediate Cycle-Update

The wear-simulation procedure that was discussed earlier was termed as the 'step-updated'

for the reason that geometry updates were preformed after every step. An alternative to the step

update procedure would be to exclude all geometry updates during the entire cycle and perform a

single update at the end of the cycle. We term this procedure as the 'cycle-update'. The cycle-

update is a modification of the step-update where updates are performed at the end of each

step/analysis. For the cycle-update, information from each analysis performed at each step is

stored and later used to update the model at the end of the cycle. The equation for the wear depth

at the contact interface for the cycle-update is expressed as follows;

n2_step
h2,J+A -h,,,_z+Ml C pl_,,s;, (4-1)


where n step is the total number of steps in a cycle. All other terms are as defined previously.

The cycle-update procedure can be summarized in the flowchart shown in Figure 4-1.









It should be noted that in both the cycle- and step-update techniques, the material

removal is discrete which is at variance with the actual process of wear in which the material

removal is continuous. The situation is, however, worse for the cycle-update since the frequency

of material removal is much less than in the step-update procedure. The step-update therefore has

a closer resemblance to the to the actual wear process. It would therefore be expected that the use

of the cycle-update procedure in wear simulations would yield less reliable results in comparison

to the step-update counterpart. Indeed this is what is observed when the procedure is tested.

More specifically the smoothness of contact pressure distribution during the simulation is

severely affected by the cycle-update than is by the step-update. A simplified explanation for this

phenomenon is that the step-update, performed at each step, closely captures intermediate

geometry changes within a cycle and hence the contact between two mating surface is

approximately conforming throughout the simulation. The result is that the pressure distribution

remains reasonably smooth. In the case of the cycle-update, the geometry is updated once in an

entire cycle. This dose not allow for the contacting surface to evolve smoothly throughout the

cycle and hence resulting in a less conforming contact between the mating surfaces. In this case

the pressure distribution would be less smooth, putting the accuracy of the results to question.

Although the cycle-update technique may yield less than accurate results, the technique

may still be used with caution. A general observation can be made regarding the accuracy when

using the cycle-update procedure. It has been observed that for a fixed extrapolation size, as the

total sliding distance covered through a complete cycle increases, the smoothness of the pressure

distribution is affected and hence the stability and accuracy of the simulation. Based on the

observation, a critical sliding distance so, is defined which if exceed, during sliding, geometry

update must be performed. Determination of the critical sliding distance is unnecessary since









short simulation runs can determine if the cycle-update is the appropriate produce. Thus the

mention of the critical sliding distance is purely for academic reasons rather than for practical

reasons. It is concluded that the cycle-update is best suited for cases in which the total oscillation

angle is small so that the sliding distance in a single cycle is less than sent .

In the event that the total sliding distance for a complete cycle is larger than sent we may

still take advantage of the idea behind cycle-update procedure. Instead of performing a single

update at the end of the cycle we may perform several equally spaced updates within the cycle.

This can be considered to be a hybrid of the step- and cycle-update procedure and the name

intermediate cycle-update is used for the procedure. The advantage of this idea is that the number

of updates in a cycle is reduced without affecting the stability of the simulation. The intermediate

cycle-update procedure can be summarized as is shown in Figure 4-2.

Parallel Computation

Computers may be configured to operate in parallel mode with the advantage that results

can be produced at a quicker rate. The idea proposed as a cost cutting means is a direct parallel

implementation of the cycle-update and the intermediate cycle-update procedures. Since the

implementation of the two procedures is similar, only the parallel implementation of the cycle-

update is discussed.

The cycle-update procedure is centered on the idea that no update is performed on the

geometry during the entire cycle. This means that all the analysis performed at each step within a

cycle is done on same geometry. The difference between any two analyses within a cycle is the

angle at with the two bodies contact during the analysis. This information may be exploited to

construct the parallel computation equivalent of the wear-simulation procedure.










The parallel implementation works as follows. Several processors are dedicated to the

wear analysis simulation. One of these processors is assigned the duty of a master processor.

This will be the processor responsible for distributing tasks to other processors as well as

consolidating the results from other process. The remaining processors will be the slave

processors. Each of the processors, both slave and master processors, will represent a particular

step within a cycle. In the beginning of any cycle, the appropriate model of the assembly to be

analyzed for wear is fed into the master processor. The master processor then distributes the

same model to the remaining processors. The master processor also allocates contact angles

(each slave will have a different contact angle corresponds to a specific step in the cycle) and

corresponding analysis conditions to each of the slave processors. At this point the master

processor instructs the slave processor to solve their corresponding contact problem. Once the

analysis in the different slave processors is done the master node collects the results and

computes the wear amount for that cycle. The model geometry is then undated and thereafter a

new cycle commences. The parallel implementation of the cycle-update procedure is

summarized in the flowchart shown in Figure 4-3.

From the flowchart it can be seen that considerable amount of time is saved by using the

parallel computational in comparison to the cycle-updating procedures. If the number of

processors available is equivalent to the number of steps selected for a cycle, then the time

required to complete a single cycle while using the parallel procedure is approximately equal to

the time required to complete a single step in the step and cycle updating procedures.













































Figure 4-1. Wear simulation flow chart for the 'cycle-update' procedure.



















































Figure 4-2. Wear simulation flow chart for the 'intermediate cycle-update' procedure.













41




























Wear Rule
Determine wear


Update Model


Input Model


Solve Contact problem
(Obtain Contact Pressure)

Step 1 Step 2 Step 3 ..


Figure 4-3. Wear simulation flow chart for the parallel implementation of the 'cycle-update'
procedure.


Step n








Cycle Count


End of
Simulation









CHAPTER 5
WEAR-SIMULATION PROGRAM

Introduction

A simulation program was written in order to execute the wear-simulation procedure that

has been discussed in Chapters 2-4. The programming language used was "C" and the Finite

Element Analysis software used was Ansys. Ansys Parametric Design Language (APDL) was

used to write the commands necessary for the analysis. It should be mentioned that the choice of

language and software for this task, was based on convenience rather than limitation. Other

languages and analysis software may be used. In this Chapter the basic structure of the program

will be discussed.

Wear-Simulation Program Format

The wear-simulation program is composed of two parts. The first part of the program is a

C-program responsible for managing the simulation process and the second part is an Ansys

analysis input file, written in APDL, consisting of a set of commands related to the finite element

analysis. There exists an interaction between the two programs in which information is

exchanged. The interaction is managed by the C-program. A representation of the interaction is

shown in Figure 5-1. These two parts will be discussed in the following subsections.

Ansys Input Code

The Ansys input code is composed of a set of commands necessary to perform an analysis

on the finite element model and output analysis results. The input code has two main functions

which include performing contact analysis and extracting results from the analysis. These will be

discussed in the following sub sections.









Contact analysis

When the simulation program is launched, the C- program invokes Ansys and the Ansys

input code is read. This will be the beginning of a step within the current cycle. The C-program

also sends information to Ansys which will be read-in by the input file. This information may

include the orientation of the oscillating body, the current step and cycle. Based on the

information from the C-program, the input file instructs Ansys to read-in the corresponding

model (the model is in a file format with extension "CDB") and prepare it for analysis. The

preparation includes reorienting the oscillating body into a position consistent with the current

step. Any gaps occurring due to wear in the previous step are also closed. This essentially means

that contact is established between the bodies before the analysis begins. This is a necessary step

since any gap may result in rigid body motion (RBM). At this point, the input code instructs

Ansys to solve the contact problem.

Output of results

The solution of the contact problem yield an enormous amount of information, most of

which is not of interest in the wear problem. The second task of the input code is to extract the

necessary information for the wear analysis. Specifically, the contact pressure at each node is

extracted from the contact analysis results. The input code also extracts the coordinates of the

contact node and computes the normal vector at each contact node. This information is required

for the model update.

The data extracted from the analysis as well as the model is written onto a text file in a

predefined format that is readable by the C-program. Creating the text output file serves as the

end of the step. Ansys software then shuts down and the C-program resumes command. A

summary of the work done by the input code is shown in Figure 2-2.









Simulation Managing Code

The other part of the wear-simulation program, written in C, act as the simulation manager.

The codes' main functions are to coordinating all the analysis performed by Ansys as well as

performing the wear calculations.

Once the simulation program is launched the C-program reads in a set of user defined

parameters that describe the desired simulation. These parameters include information such as

the value of the wear coefficient, the number of steps per cycle, the total cycles to be simulated

and the oscillation amplitude. The C-program then invokes Ansys, as describe in the previous

section, and stays dormant until the contact analysis is done. Results from the contact analysis

stored in the text output file are then read in by the C-program. Stability check and extrapolation

modifications are then performed as was outlined in Chapter 2. The wear rule is then applied.

This determines the amount of wear increment at each node consistent with the contact pressure

form the analysis and the wear coefficient. Base on the incremental wear depth geometry update

is updated and a data file in text format is created. Information such as the contact node number

and the corresponding contact pressure and wear depth are appended to the file as the simulation

progresses. At this stage a cycle is completed and a new cycle commences. The structure of the

simulation program is depicted in Figure 5-3.
































































Send analysis~
rsesults to C-fle~


Figure 5-2. Function of the Ansys input code.


Su~pply analdysis inafo.
e. g Chrrent cycle, stp etc










R2~etrna rsesults.
Cont~act Prs. NoJrmdal direction. etc.


C-Source Code
Manage Simulation

-Stability C control
-Wear Rule
-Up date Ge ometry
-Create Data File


... .. +0.
- I- *:1. I-'lls
.1 I rj I
-1..:.n .:1 anal 1:
-E::Ir .:IF e:- 11:
-1 i.:.rnail clare.:1l.:.n il.:


Figure 5-1. Interaction between the C code and the Ansys input code.


CDB Fdle


Info fromb C0-}le ~












Ipad~dad ~7arame~ers





'\



"
'" ''
... .I ..
.~ ~ ~
--

H
.- --

-
I .:

.-..?-
--



.I

"-
..~ :. :
'' '~
r ----
: ..
........


.I
r ~. ..?.


.1
'''~' "~'
.-


I


-- CDB F)1 -


-


1- 1


in Fe *. us .E-E Fl e


















I


Figure 5-3. Structure of the wear-simulation program.





























47









CHAPTER 6
EXPERIMENTAL VALIDATION OF THE WEAR-SIMULATION PROCEDURE

Introduction

Probably the most convincing way to validate the results of a simulation is to compare

them against those from an actual experiment. In this work the simulation procedure is validated

by comparing simulation results to results from a wear tests performed on an oscillating pin in

pivot assembly. The simulation procedure is then used to simulate the wear occurring at the pin

j points of a backhoe (construction equipment). The effect of wear on the performance of the

backhoe is then demonstrated.

Wear-Simulation Validation

The wear simulation is validated through a comparison of simulation and test results. The

wear test consisted of a fixed steel pin inside an un-lubricated oscillating steel pivot. The pivot

was set to oscillate with amplitude of 30 and was loaded in the direction of its shoulder as shown

in Figure 6-1. The resulting pressure at the cross-sectional of the pivot was 601VPa. The pressure

was kept approximately constant through out the test. A total number of 408,000 cycles were

completed during the test to yield a maximum wear depth of about 2mm. It should be noted, for

the sake of comparison, that the definition of the test cycles is different from that of the

simulation cycles. Here a test cycle is defined as a complete rotation from one extreme to the

other and then back to the starting position (in this case -30 to 30 and back to -30). The test

information is summarized in Table 6-1 for convenience.

Three simulation experiments were performed to mimic the actual tests performed on the

pin and pivot assembly. The three simulations experiments were as follows:

* step-updating procedure

* intermediate cycle-update procedure










*parallel implementation of the intermediate cycle-update procedure

All three simulation tests were performed with the model shown in Figure 6-1. A wear

coefficient of 1.0 x 105 mm3/Nm (typical on un-lubricated steel on steel contact) was used. This

value is obtained from pin-on-disk tests results reported by Kim et al. [18]. In all three cases the

cycles were discretized into 10 steps. Both the step- and intermediate cycle-updating simulation

tests were performed on the same computer (for time comparison), however, the parallel

implementation was performed on a parallel cluster. The following is a brief discussion of these

simulation test and the corresponding results.

Step-Update Simulation Test

The step updating simulation test was performed with oscillation amplitude and loading

identical to that of the actual wear test. The simulation test was run for 100,000 cycles

(considering the extrapolation). The simulation test parameters are summarized in Table 6-2

below. In Figure 6-2, the history of wear for the pin and pivot nodes that experienced the most

wear is shown. From the figure, a transient and steady state wear regime can be identified as

discussed by Yang et al. [32].

The transient wear regime corresponds to the beginning of the simulation until the

contact between the pin and the pivot is conforming. Thereafter the wear transitions to the steady

state wear regime. The steady state wear regime in marked by an interesting phenomenon where

by the contact pressure distribution is observed to be approximately constant over the region of

contact. This is in contrast to the transient wear regime during which a range of contact pressure

values is observed over the contact region. This concept is illustrated in Figure 6-3.

Within the steady state wear regime, the wear is approximately linear with respect to the

cycles as can be seen in Figure 6-2. This information may be exploited to determine the wear on









the maximum wear nodes after 408,000 cycles. Noting that one test cycle has twice the sliding

distance in comparison to that of the simulation test, an extrapolation within the steady state can

be made to predict the wear depth at the 408,000th cycle. The expression for the predicted wear

depth is a follows;


h =21 (hm hFer[ ~,m ) e~st"'" m, hJ (6-1)


where, h is the predicted wear depth, ns,,, and ns,,,z are the total simulated cycles at two points

within the steady state regime whereas hFhi and h,, are the corresponding simulate wear

depths at these cycles. In this equation the experiment test cycles is denoted by neest .

A value of 1.867mm was predicted as the maximum wear depth on the pin. Although this

value underestimates the wear depth it is a reasonable prediction considering that the wear

phenomenon is a complex process. The variation of the extrapolation size is depicted in Figure 6-

4. The simulation took approximately 206 minutes.

Intermediate Cycle-Update: Parallel Computation

The Intermediate cycle-update procedure and its parallel implementation were performed

with the same parameter values as were used in the step-updating procedure (see Table 6-2).

However, in this procedure, the update was performed after every 3 steps so that 3 updates were

performed in each cycle. This is in contrast to the step-update procedure where 10 updates were

performed, one at the end of every step. The result for the intermediate cycle-update and the

corresponding parallel implementation are identical. The plot of the wear on the pin and pivot

nodes that experience the most wear is shown in Figure 6-5.

A maximum wear depth (on the pin) of 1.854mm was obtained from the intermediate

cycle-update procedure and its parallel implementation. A plot of the extrapolation during the










analysis is shown in Figure 6-6. A simulation time of 450 minutes was noted for the intermediate

cycle update procedure. This is slightly more than twice the time it took to complete the step-

update simulation test. This time difference can be explained by examining the extrapolation

history plots (Figure 6-4 and Figure 6-6) for the two procedures. The average extrapolation for

the step update is slightly greater than twice that of the intermediate cycle update procedure. This

is because the step update is a more stable procedure than the intermediate cycle updating

procedure. The stable characteristic of the step update allows for the use of larger extrapolation

and thus few simulations cycles are required to predict the wear depth. In the present case, only

19 cycles were required to complete the step-update simulation test whereas 49 cycles were

required to complete the intermediate cycle update simulation test. The parallel implementation

of the intermediate update procedure only took approximately 13 5 minutes to complete. Clearly

this procedure provides a time advantage. A comparison of the results form the simulation tests

and the actual tests are shown in Table 6-3.

Conclusion

The discussion in this Chapter focused on validating the wear-simulation procedure that

was presented previously. The validation is done by comparing the results from the simulation to

that of an experimental counterpart. The wear occurring at the contact interface of an oscillation

pin-pivot assembly was simulated. The predicted wear depth deviated from the actual

experimental wear depth by approximately 7%. Even though this deviation appears to be large

the predicted results is able to give a good insight into the wear occurring at the interface.

Indeed like any other approximation technique, errors are inherent. A number of factors

contribute to this discrepancy including the wear model, which is not an exact representation of

wear and the finite element analysis, which is an approximation technique.









Another contributor is the wear coefficient. The wear coefficient is obtained

experimentally and as was mentioned has a large scatter. Errors in the wear coefficient

considerably affect the results of the simulation. For instance, if instead a wear coefficient of

1.2 x 105 mm3/Nm WaS used the new predicted wear depth would be 2.028mm. The new wear

coefficient, which is still within the range of scatter according to Kim et al. [18], has a deviation

of about 1.4% from the experimental value. This is indeed a large improvement from the

previous predictions. It is thus concluded that even though the procedure does not accurately

predict the wear the results obtained are of the correct order of magnitude and can be used for

preliminary design.









Table 6-1. Wear test information for the pin and pivot assembly.
Test Parameters Values


Oscillation amplitude 30

Load (cross-sectional pressure) 60MPa

Test condition Un-lubricated steel on steel

Total cycles 408,000

Max wear depth on pin ~2.00mm



Table 6-2. Simulation parameters for the pin in pivot simulation test.
Simulation Parameters Value

Oscillation amplitude 30

Load (cross-sectional pressure) 60MPa

Wear coefficient (k) 1.0 x105 mm3/Nm

Total cycles 100,000

Steps per cycle 10


Table 6-3. Comparison of results form the simulation tests and actual wear tests for the pin in
pivot assembly
Max. wear depth Simulation
(pin) (mm) time (min.)
Actual test 2.000 --

Step update 1.867 206
Inter. cycle update 1.854 450
Parallel 1.854 135


















* acillation Pin


II


:Iationlary Pivot


0.2




0.15
o
E


S0.1




0.05


01
01 23 4 5
cycles


6 7 8 9 10

x 104


Figure 6-2. Cumulative maximum wear on pin and pivot.


Pressure A-long Pivot WVidth


Figure 6-1. Pin-pivot assembly for the wear test.





Wear on pin & pint (Step Update)
0.25,











I :
I) I
I I I I I
: :


I I


Figure 6-3. Contact pressure distribution on the pin and pivot during wear analysis. A) Contact
pressure distribution in the transient wear regime. A range of pressure values is
observed. B) Contact pressure distribution within the steady wear regime. The
pressure distribution is approximately constant over the region of contact.













Extrapolation History (Step Update)


6000 - -- -


5000 L -



~4000 -~~I


e 3000


2000 -i


1000-



0 2 468 0
Cycles


14 16 18 20


Figure 6-4. Extrapolation history plot for the step updating simulation procedure.


Wear on pin & pint (Inter. Cycle Update)


E 0.





0.05


1 23 4 5
cycles


6 7 8 9 10
x 104


Figure 6-5. Cumulative maximum wear on pin and pivot for the intermediate cycle updating
procedure and the parallel implementation.















Extrapolation History (Intermediate Cycle Update)


3500


3000


2500


.2 2000


S1500
LL


0 5 10 15 20 25 30
Cycles


35 40 45 50


Figure 6-6. Extrapolation history plot for the intermediate cycle update procedure and its
parallel implementation.









CHAPTER 7
WEAR-SIMULATION EXAMPLE: ESTIMATION OF BACKHOE BUCKET TIP
DISPLACEMENT

Introduction

In Chapter 6, the wear-simulation procedure for oscillatory contact was validated through

experiments. It was found that the method can reasonably predict wear occurring at such

interfaces as long as accurate wear coefficients are obtained. In this Chapter, the usefulness of

the procedure will be demonstrated through an example. The example involves determining the

erroneous displacement at the tip of construction equipment due to wear at various joints.

Estimation of Tip Displacement

A backhoe system will be used to demonstrate how the simulation procedure can aid in

determining the effect of wear on the performance of a system. The system is a part of a

construction vehicle used in excavation work. The particular backhoe system to be used in this

example consists of three maj or parts (boom, dipper and bucket) as shown in Figure 7-1. The

sy stem consists of three j points; two connect the three parts together while the third one connects

the backhoe system to the vehicle (not shown in Figure 7-1). Each j oint consists of two

components that are in contact and experience relative oscillatory motion when the backhoe

undergoes a cycle of digging and loading. The contact at these joints can be considered as

oscillatory and as may be expected, large amounts of wear occur at these j points. The goal in this

example is to estimate the amount of control of the bucket tip that is lost due to wear at these

j points. The loss in control is quantified as the magnitude of the unwanted bucket tip displacement

that occurs when the backhoe is rotated about the rotation axis. The tip displacement is shown in

Figure 7-1.

The diagram in Figure 7-2 shows a pivot j oint before and after wear has occurred. In

Figure 7-2A diagram no wear has occurred and the pin sits snugly in the pivot hole. In such a









case the tip displacement is negligible. However, once wear has occurred at the j points, the pin is

able to rotate through an angle as shown in Figure 7-2B. This kind of rotation propagates through

all three j oint and eventually causes a bucket tip displacement. The magnitude of the tip

displacement is dependent on the amount of wear.

In this example the tip displacement will be obtained assuming that the backhoe has been

in operation for a period of one year. This corresponds to a total of 90,000 cycles of digging and

loading dirt. This is obtained by assuming that the backhoe executed 60 cycles an hour, 5 hours a

day for 300 days in a year. The tip displacement is obtained by first determining the amount of

wear at each of the j points. In this case the j points are represented by a pin and pivot assembly

similar to that used in the previous Chapters. The loading at each j oint is taken to be constant

throughout the entire cycle. A list of the loads applied at each pivot is shown in Table 7-1. Also

listed in Table 7-1, are the oscillation amplitudes of the each pin at each their corresponding

joint. It is worth noting that an assumption is made that no other factors contribute to the tip

displacement and that the initial tip displacement is zero.

The three joint are assumed to be made of steel and that no lubricant is used. A wear

coefficient with a value of 1.0 x105 mm3/Nm is thus used in the analysis. This choice is

consistent with experiments performed by Kim et al. [18]. A wear analysis is performed on all

the joints for the specified parameters. Only 52440 cycles are simulated and the final results are

linearly extrapolated. The wear depth at the j points obtained from the simulation is shown as a

function of the cycles in Figure 7-3. It can be seen from Table 7-2 that the wear on j oint 3 is

greatest. This is consistent with the fact the oscillation amplitude for the third j oint is the largest.

The maximum wear depth on the pin and pivot at 20,000 cycles and the extrapolated wear depths

at 90,000 cycles for the three j points are reported in Table 7-2. The wear depth at 90,000 cycles is










used to determine the bucket tip displacements of all the component parts from the centerline.

The component displacements as well as the overall backhoe tip displacement are listed in Table

7-3 and are depicted in Figure 7-4.

A maximum bucket tip displacement of 149mm is estimated. This can be interpreted as the

additional distance, from the desired position, that the bucket tip will travel be for coming to a

halt when the backhoe is rotated.

Conclusion

The value of the simulation procedure was demonstrated through an example in which the

erroneous bucket tip displacement, attributed to wear, for a backhoe system was estimated.

Although the input values for the backhoe system and thus the tip displacements are not from an

existing case, the example demonstrates how the performance of a system can be affected by

wear and how the simulation procedure can aid in quantifying the loss in performance.





Boom OBM~ 1.6880 LBMC 73.64

Dipper GD 0.4260 LD 55.34
Bucket GjBU 0.4320 LBU 20.00

Tip displacement 148.98mm


Table 7-1. List of loads and relative rotation angles at the joints of the backhoe.
Load (MPa) Oscillation amplitude

Joint 1 10.75 -150 to 150

Joint 2 10.40 -22.50 to 22.50

Joint 3 12.15 -350 to 350


Table 7-2. Summary of the wear depth at the j points after 20,000 cycles as well as the
extrapolated wear depth at 90,000cycles
Initial diameter Wear depth at e dp a
20000 cycles
(mm) 90000 cycles (mm)
(mm)
Pin Pivot Pin Pivot Pin Pivot

Joint 1 74.47 75.44 0.114 0.128 0.516 0.576

Joint 2 75.13 76.11 0.139 0.168 0.626 0.758

Joint 3 54.48 55.19 0.161 0.216 0.724 0.974


Table 7-3.

Part


Displacement of the boom component parts from the center line.
Distance from
Angle deflection
center (mm)




























Figure 7-1. Pin-pivot assembly for the wear test.


----- Diameter


D~-iameter after


Figure 7-2. Joint consisting of a pin and pivot: A) Joint before wear has occurred on both
components. B) Joint after wear has occurred on both components.













Wear on Pmn & P~vot (Joint 1)


2-3















U 05 1 15 2 25 3 35 4 45 5 55
cycles x 104


E

A
E


Wear on P n & Pivot (Joint 2)


04

O 35






B
























01


pin r
O pivot
















105 115 225 335 445 555
cycles x 104


Wear on Pmn & Plvot (Joint 3)


10 05 1 16 2 26 3 36 4 45 6 55
cycles x 104



Figure 7-3. Wear on the pin and pivot at the backhoe Joints. A) Wear at j oint 1. B) Wear at joint

2. C) Wear at j oint 3.












B~s~r~Tucket Tip

LE
Center lirne ----




r---------~Bucket















SwBoom.


Figure 7-4. Backhoe component displacement from the vehicle centerline.









CHAPTER 8
CONCLUDINTG REMARKS

The obj ectives in this work were two fold. One goal was to develop a wear-simulation

procedure to predict wear occurring on bodies experiencing oscillatory contact. The second goal

was to incorporate into the wear procedure, techniques that would minimize the associated

computational costs of the simulation process while ensuring stability through out the simulation

process.

The wear-prediction procedure was developed based on a modified form of Archard' s wear

law. It involves determining wear at incremental steps within a cycle for the total number of

cycles to be simulated. At the end of every step the geometry is updated to reflect the evolution

of the surface and thus account for changing contact conditions. This update procedure, termed

as step update, is a more stable procedure than the cycle and intermediate cycle update

procedures in which updates are delayed to the end of the cycle or after several steps have been

simulated.

Two techniques were proposed to minimize the computational costs of the simulation. The

first technique was an incorporation of an adaptive extrapolation scheme into the wear-prediction

procedure. The purpose of scheme was to optimize the selection of the extrapolation factor for

the best use of the available resources while ensuring stability in the simulation.

The second technique is a parallel implementation of the cycle and intermediate update

procedures. With no parallel implementation, step update approach is computationally cheaper

than the intermediate cycle update procedure. The reason for this is that the intermediate cycle-

update procedure is a less stable procedure (due to the reduced number of geometry updates in a

cycle) and thus requiring the use of smaller extrapolation sizes. This results in a longer

simulation time. When parallel computation is used, the intermediate cycle update procedure is a










cheaper alternative in terms of computational cost. It is deduced that in the absence of parallel

computing resources, the most reasonable simulation procedure to use is the step-updating

procedure where as the intermediate cycle updating procedure is best when parallel computing is

available.

In the simulation validation process, it was found that the wear depth on the pin predicted

by the simulation procedure was under predicted but within a reasonable range. This under

prediction is largely attributed to the wear coefficient used. The wear model used is a

phenomenological model in which the wear coefficient is determined through experiments.

Hence an inaccuracy in this coefficient has a great effect on the prediction process as was shown

in Chapter 6. Based on the results it is concluded that the procedure is a reasonable way to

predict wear on bodies experiencing oscillatory contact









CHAPTER 9
RECOMMENDATIONS FOR FUTURE WORK

The wear-prediction procedure presented in this work provides a way to determine the

wear occurring on bodies that experience oscillatory contacts. In the procedure, the changing

contact condition or evolving surface was accounted for by updating the surface as the

simulation progressed. This ensured for a more realistic simulation of the wear process.

The prediction process can be made even more realistic by considering how the wear

affects the kinematics and dynamics of a system and in turn how the kinematics and dynamics of

the system affects the wear process. In mechanisms, once wear has occurred at connection, the

initial paths through with components of the mechanism travel are no longer preserved. The

loads involved may also be affected. These changes occur due to the gap or change in geometry

that is introduced at the connections as wear occurs. It should also be noted that the changes in

the motion of the components, as well as the loading, will affect the wear process.

The procedure that has been presented is an idealized case in which the changing system

does not affect the wear process and vice versa. Essentially wear predicted by isolating the

region in which the wear occurs and thus neglecting any changes that the wear would have on

the overall system. A recommendation for future work is to study the effect of a continuously

changing system (changing due to wear) on the wear process itself.









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BIOGRAPHICAL SKETCH

Saad Mukras was born in Nairobi, Kenya. He was raised in Nairobi and partially in

Gaborone, Botswana, where he completed his secondary education. He then j oined University of

Botswana and then transferred to Embry Riddle Aeronautical University in Daytona Beach,

Florida. There, he studied aircraft engineering technology and received his bachelor' s degree in

2003. He then j oined the University of Florida to pursue a master' s degree in mechanical

engineering in 2004. He worked under the supervision of Dr. Nam-Ho Kim, completing several

research proj ects, earning his masters degree in 2006.