Experimental and Modeling Study of Micro-Pump Direct Current Motors for Portable Direct Methanol Fuel Cell Applications

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Title:
Experimental and Modeling Study of Micro-Pump Direct Current Motors for Portable Direct Methanol Fuel Cell Applications
Physical Description:
1 online resource (80 p.)
Language:
english
Creator:
Patil,Anupam Vilas
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University of Florida
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Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Mechanical Engineering, Mechanical and Aerospace Engineering
Committee Chair:
Lear, William E
Committee Members:
Crisalle, Oscar D
Ingley, Herbert A

Subjects

Subjects / Keywords:
dc -- direct -- friction -- microdynamometer
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
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Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract:
A portable direct methanol fuel cell system is under investigation at the University of Florida Fuel Cell Research Laboratory. The anode recirculation pump-motor unit is a vital part of the system and is also among the highest parasitic loads. The losses can be split into pump fluid dynamic losses and motor electromagnetic and frictional losses. An experimental apparatus was built to test micro-pumps. One of the commercial pumps showing promising results is driven by a permanent magnet brush type DC motor. After decoupling from the pump, this motor was tested separately. Data from both experiments was used to obtain performance maps for the pump and the motor. A finite element two-dimensional quasi-steady state model of the electromagnetic effects in the DC motor was constructed and the results were compared with the experimental results. The resulting model couples geometrical and material property effects to the performance, enabling improved motor design.
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In the series University of Florida Digital Collections.
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Includes vita.
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Description based on online resource; title from PDF title page.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Anupam Vilas Patil.
Thesis:
Thesis (M.S.)--University of Florida, 2011.
Local:
Adviser: Lear, William E.
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RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2012-08-31

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lcc - LD1780 2011
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UFE0043373:00001


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1 EXPERIMENTAL AND MODELING STUDY OF MICRO PUMP D IRECT C URRENT MOTORS FOR PORTABLE DIRECT METHANOL FUEL CELL APPLICATIONS By ANUPAM VILAS PATIL A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIA L FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2011

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2 2011 Anupam Vilas Patil

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3 To my parents, Mrs. Vasudha and Dr. Vilas Patil; and my sister Abhilasha Patil Tandel This work would not have been poss ible without your love and support You have inspi red me to become who I am today I dedicate this work to you

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4 ACKNOWLEDGMENTS The completion of this work was possible only because of immense contribution from Dr. William Lear. I am extremely grateful to Dr. William Lear and Dr. James Fletcher for encouraging, advising and supporting me right from my first day of the masters program. I am also grateful to Dr. Oscar Crisalle for his guidance throughout the project. I would also like to thank Dr. Herbert Ingley for serving on my committee. I would like to thank the most important people in my life, my parents and my sister for their constant support and love. I am indebted to my colleagues at the University of for th eir invaluable guidance. Without assistance of Praneeth Pillarisetti, the experimentation portion of this work would not have been possible. Sydni Credle has always been a very patient mentor. Cheng Chan Kuo has provided me with his incredible insights on several occasions. The professionalism of everyone in this research facility will continue to inspire me throughout my career. I would also like to thank my colleagues at the University of North Florida for their assistance on several occasions. I also ta ke this opportunity to thank my all my friends especially Aditya Karnik, Kshitij Padhye, Akshay Bharadwaj, Ashwini Khade, Asmita Chitale, Sumi t Bhangdiya and Samiksha Shinde for being like a family I would also like to thank my friends back home for their support. Last but not the least; I would like to thank God for giving me this opportunity. Nothing was possible without his love.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURE S ................................ ................................ ................................ .......... 9 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 12 1.1 Overview ................................ ................................ ................................ ........... 12 1.2 Recirculation Pump ................................ ................................ ........................... 14 1.3 Goals and O bjectives ................................ ................................ ........................ 15 1.4 Thesis Organization ................................ ................................ .......................... 15 2 EXPERIMENTATION INVESTIGATION ................................ ................................ 17 2.1 Pump u nder C onsideration ................................ ................................ ............... 17 2.1.1 Market R esearch ................................ ................................ ..................... 17 2.1.2 Candidate P ump ................................ ................................ ...................... 17 2.2 General Purpose Micro Pump Test Rig ................................ ............................ 18 2.2.1 Experimental A pparatus ................................ ................................ .......... 18 2.2.2 Hardware Components ................................ ................................ ............ 21 2.2.3 Hardware f or Data Acquisition a nd Control o f Test Parameters .............. 22 2.2.3.1 Differential pressure head across the p ump ................................ 22 2.2.3.2 Pressure g auge c alibration ................................ .......................... 23 2.2.3.3 Differential p ressure g auge c alibration c urves ............................. 24 2.2.3.4 Upstream p ressure ................................ ................................ ...... 24 2.2.3.5 Flow r ate ................................ ................................ ...................... 24 2.2.3.6 Flow m eter c alibrat ion ................................ ................................ .. 25 2.2.3.7 Actuation v oltage ................................ ................................ ......... 25 2.2.3.8 Current to d rive the p ump ................................ ............................ 25 2.2.3.9 Motor s peed ................................ ................................ ................. 25 2.2.3.10 Data acquisition ................................ ................................ ......... 26 2.2.4 Test Procedure ................................ ................................ ........................ 26 2.2.5 Data Reduction ................................ ................................ ........................ 27 2.3 D.C. Motor Test S etup ................................ ................................ ...................... 28 2.3.1 Hardware Components ................................ ................................ ............ 29 2.3.1.1 Rotating a ssembly ................................ ................................ .......... 29 2.3.1.2 Pendulum a ssembly ................................ ................................ ....... 29 2.3.2 Hardware for D ata C ollectio n and C ontrol of T est P arameters ................ 30 2.3.2.1 Optical t achometer ................................ ................................ ......... 30

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6 2.3.2.2 Rotary e ncoder ................................ ................................ .............. 30 2.3.2.3 Current s hunt ................................ ................................ ................. 30 2.3.2.4 Data a cquisition ................................ ................................ ............. 30 2.3.3 Test Procedure ................................ ................................ ........................ 30 2.3.4 Data Reduction ................................ ................................ ........................ 31 2.3.4.1 Angle of deflection of the pendulum ................................ ............... 31 2.3.4.2 Torque ................................ ................................ ............................ 32 2.3.4.3 Motor s peed ................................ ................................ ................... 32 2.3.4.4 Input p ower ................................ ................................ .................... 32 2.3.4.5 Output p ower ................................ ................................ ................. 33 2.3.4.6 E fficiency ................................ ................................ ........................ 33 3 EXPERIMENTAL RESULTS ................................ ................................ ................... 34 3.1 Gene ral Purpose Micro Pump Test Rig ................................ ............................ 34 3.2 D.C. Motor Test Rig ................................ ................................ .......................... 37 3.3 Experimental results for pump ................................ ................................ .......... 40 4 DIRECT CURRENT MOTOR MODEL ................................ ................................ .... 43 4.1 Need for Finite Element Analysis ................................ ................................ ...... 43 4.2 Finite Element Me thod Magnetics ................................ ................................ ..... 44 4.3 Application of FEMM to DC M otor M odel ................................ .......................... 44 4.3.1 Pre processing ................................ ................................ ........................ 44 4.3.2 Boundary Conditions ................................ ................................ ............... 47 4.3.3 Mesh Generation ................................ ................................ .................... 49 4.3.4 Solution Scheme ................................ ................................ ..................... 50 4.4 DC Motor Model ................................ ................................ ................................ 51 4.4.1 Determination of Torque C onstant ................................ .......................... 51 4.4.2 Determination of Vol tage Constant ................................ .......................... 54 4.4.3 Motor Speed Calculation ................................ ................................ ......... 57 4.4.4 Parameterization of Voltage Constant ................................ ..................... 57 4.4.5 Friction Model ................................ ................................ .......................... 58 4.4.6 FEM and DC Motor Model Results ................................ .......................... 59 5 MODELING RESULTS ................................ ................................ ........................... 60 5.1 FEM Results ................................ ................................ ................................ ..... 60 5.2 Application of DC M otor M odel to FEM R esults ................................ ................ 65 6 C ONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK ................... 69 APPENDIX A UNCERTAINTY ANALYSIS ................................ ................................ ....................... 72 1.1 UF Pump Test Apparatus ................................ ................................ ................. 72 1.1.1 Energizing Voltage for P ump M otor C ombination ................................ ... 72

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7 1.1.2 Current ................................ ................................ ................................ .... 72 1.1.3 Flow R ate ................................ ................................ ................................ 72 1.1.4 Differential Pressure ................................ ................................ ................ 72 1.1.5 Input Power ................................ ................................ ............................. 73 1.1.6 Output Power ................................ ................................ .......................... 73 1.1.7 Efficiency ................................ ................................ ................................ 73 1.2 Micro D ynamometer ................................ ................................ ......................... 73 1.2.1 Voltage ................................ ................................ ................................ .... 73 1.2.2 Current ................................ ................................ ................................ .... 74 1.2.3 Angle of D eflection ................................ ................................ .................. 74 1.2.4 Torque ................................ ................................ ................................ ..... 74 1.2.5 Motor S peed ................................ ................................ ............................ 74 1.2.6 Input P ower ................................ ................................ ............................. 74 1. 2.7 Output P ower ................................ ................................ .......................... 75 1.2.8 Efficiency ................................ ................................ ................................ 75 1.3 Inferred Results ................................ ................................ ................................ 75 B MODEL GEOMETRY ................................ ................................ .............................. 76 2.1 Motor Rotor ................................ ................................ ................................ ....... 76 2.2 Motor Casing ................................ ................................ ................................ .... 77 2.3 P ermanent Magnet ................................ ................................ ........................... 78 LIST OF REFERENCES ................................ ................................ ............................... 79 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 80

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8 LIST OF TABLES Table page 4 1 Description of DC motor components ................................ ................................ ..... 47 5 1 Comparison of experimental and analytical values of motor parameters ................ 68

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9 LIST OF FIGURES Figure page 1 1 DMFC System Architecture ................................ ................................ ..................... 13 2 1 Micro pump experimental facility layout. ................................ ................................ 19 2 2 General purpose pump test apparatus at University of Florida ............................... 20 2 3 Constant pressure head reservoir sc hematic ................................ .......................... 22 2 4 Test schematic for differential pressure gauge calibration ................................ ...... 23 2 5 Motor Test Rig developed at University of North Florida ................................ ......... 28 2 6 Micro dynamometer in operation at the University of North Florida ........................ 29 2 7 Torque acting on a pendulum system comp rising of magnet and counter weight ... 32 3 1 Plot of flow rate of KNF pump as a function of differential pressure. ....................... 35 3 2 Plot of efficiency and power consumption of KNF pump as a function of differential pressure at two actuation voltages. ................................ ....................... 36 3 3 Plot of Torque as a function of rotational speed ................................ ...................... 38 3 4 Plot of Current and Efficiency as a function of rotational speed .............................. 39 3 5 Plot of torque versus current for the experimental data ................................ ........... 40 3 6 Plot of pump efficiency as a function of differential pressure. ................................ 41 4 1 FEMM Model of permanent magnet brush type D.C. motor with graphic il lustration ................................ ................................ ................................ ............... 45 4 2 Commutator Brush arrangement for D.C. motor. ................................ .................... 46 4 3 Comparison of the external boundary and the motor size ................................ ....... 48 4 4 Triangular mesh in the motor geometry. ................................ ................................ 49 4 5 A closer view at space between rotor and magnet depicting a finer mesh compare d to neighboring spaces ................................ ................................ ............ 50 4 6 Schematic of DC m otor coil A ) Single current coil in an external magnetic field. B ) Side view of the current carrying coil in external magnetic field. ........................ 52 4 7 Schematic of a single coil rotating in an external magnetic field. ............................ 55

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10 5 1 Magnetic flux densities at the reference orientation ................................ ................ 61 5 2 Magnetic field intensities at the reference location ................................ .................. 61 5 3 Magnetic field intensity at the air gap between magnet and rotor ........................... 62 5 4 Variation of torque with rotor angular position ................................ ......................... 63 5 5 Plot for electromagnetic torque and experimental torque versus current ................ 64 5 6 Comparison of experimental and analytical electromagnetic torque values for 4V and 6V ................................ ................................ ................................ .................... 65 5 7 Comparison of experimental and analytical load tor que values for 4V and 6V ....... 66 5 8 Comparison of experimental and analytical motor efficiency for 4V and 6V ............ 67 A p p endix 2 1 Laminated steel rotor in the DC Motor ................................ .................... 76 A ppe n dix 2 2 Steel casing in the DC motor ................................ ................................ ... 77 A ppendix 2 3 Ceramic magnet in the DC motor ................................ ............................ 78

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11 Abstract o f Thesis Presented t o t he Graduate School o f t he University o f Fl orida i n Partial Fulfillment o f t he Requirements f or t he Degree of Master o f Science EXPERIMENTAL AND MODELING STUDY OF MICRO PUMP D IRECT C URRENT MOTORS FOR PORTABLE DIRECT METHAN OL FUEL CELL APPLICATIONS By Anupam Vilas Patil August 2011 Chair: William Lear Cochair: Oscar Crisalle Major: Mechanical Engineering A portable direct methanol fuel cell system is under investigation at the University of Florida Fuel Cell Research Labo ratory. The anode recirculation pump motor unit is a vital part of the system and is also among the highest parasitic loads. The losses can be split into pump fluid dynamic losses and motor electromagnetic and frictional losses. An experimental apparatus was built to test micro pumps. One of the commercial pumps showing promising results is driven by a permanent magnet brush type DC motor. After decoupling from the pump, this motor was tested separately. Data from both experiments was used to obtain perfor mance maps for the pump and the motor. A finite element two dimensional quasi steady state model of the electromagnetic effects in the DC motor was constructed and the results were compared with the experimental results. The resulting model couples geomet rical and material property effects to the performance, enabling improved motor design.

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12 CHAPTER 1 INTRODUCTION 1.1 Overview Direct Methanol Fuel Cells (DMFCs) are a subcategory of Proton Exchange Membrane (PEM) fuel cells, using methanol as compared to hydrogen as a fuel for the direct production of electricity. The DMFC was discovered in 1990 by superacid specialist Dr. Surya Prakash and Nobel laureate Dr. George A. Olah at University of ce the energy density of methanol is ten times that of compressed hydrogen and fifteen times that of Lithium ion batteries, it alleviates several of the problems of using compressed hydrogen, such as transportability, storage and safety. Owing to the ease of transportation of methanol and its higher energy density, it would seem an ideal replacement for hydrogen fueled PEM fuel cells. However, the system efficiencies are relatively low due to reduced electrochemical potentials and due to additional transpor t limitations. Thus the application of direct methanol as a power source is limited to competition with low efficiency systems that demand compactness, such as portable electronics. DMFCs are available in two design configurations: closed cathode and open cathode. In closed cathode designs, oxygen is made available to the cathode through serpentine channels similar to that of the typical anode, and the exit is coupled to a water extraction system. In open cathode systems, the cathode is open to the atmosph ere at the exit. The fuel cell system under study at the DMFC Research Laboratory at the University of Florida power is intended eventually to power commercial laptops and is an open cathode type configuration.

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13 Figure 1 1 D MFC system architecture Figure 1 1 shows the architecture of the system. The flow path on the anode side of fuel cell is dilute methanol, with concentrations ranging from 0.5M to 1.2M. Dilute methanol is circula ted in the flow path by means of a recirculation pump. A Gas liquid separator, mentioned as CO 2 separator in Figure 1 1, is present in the cathode flow path. The concentrated methanol flow path is used to introduce ultra pure methanol in the cathode flow p ath using an injection pump. The cathode flow path consists of the open cathode channels, filter, and fans. Purpose of the fan is to provide air at cathode for reaction and cool the cell. Diluted methanol is oxidized on the catalyst layer to produce carb on dioxide. Water is consumed at anode and produced at cathode. In a open cathode type configuration, the water produced at the cathode permeates back at the anode. This

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14 water balance is extremely crucial in DMFC. Protons are transported from anode to cat hode through membrane and electrons are transported through an external circuit, thus driving an electrical load. The cell reactions are, Anode half reaction: (1 1) Cathode half reaction: (1 2) Overall cell reaction: (1 3) 1.2 Recirculation Pump The function of the recirculation pump in a portable DMFC application is to continuously circulate dilute methanol (fuel) in the anode flow path. T he recirculation pump should run continuously displacing about 50 ml/min with back pressure of about 3 psi 4 psi. The pump must tolerate bubbles and should be self priming. The recirculation pump should be quiet enough not to be noticed. Since the recircul ation pump is driven by the fuel cell, the parasitic power consumption should be as low as possible. Pump components should also be resistant to the corrosion caused by dilute methanol and carbonic acid which is formed when carbon dioxide dissolves in wate r. Since the DMFC system will be mass produced, the cost of production of individual components, including recirculation pump should be low. Since the pump is operated continuously, the wear on components should be low. Life expectancy of this pump is abou t 2000 4000 hours.

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15 1.3 Goals and O bjectives To completely analyze the recirculation pump, both wet and dry sides have to be studied. The pumping chamber, check valves, inlet and outlet valves form the wet side, while the actuation mechanism form the dry s ide. In a different study, the wet side of this pump is being studied and a fluid mechanics model is being developed. The goal of this research is to improve the design capability of pump and motor combination by studying and improving the actuation model. The approach used to achieve this objective is: Construct a test apparatus to test off the shelf and in house designed micro pumps components. Create a physics based model for a permanent magnet brush type D.C Motor. The model developed in this study alon g with the fluid mechanics model will together define a complete pump model. 1.4 Thesis Organization The remaining portion of this thesis is organized as follows: Chapter 2 discusses the experimentation apparatus for testing pump and motor coupled togethe r and experimental apparatus to discuss D.C. motor testing. In Chapter 3, results obtained from pump motor combination tests and from D.C. motor tests are discussed. Various parameters such as flow rate, power consumption and pump motor efficiency are obt ained as functions of differential pressure. Results from D.C. motor tests quantify torque, power consumption and efficiency as functions of rotational speed and energizing voltage. Based on these results, performance of pump is estimated in terms of power consumption and efficiency.

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16 Chapter 4 discusses the modeling of a permanent magnet brush type D.C. motor. The model dependent variables are identical to those obtained from experimentation, namely torque, power consumption, and efficiency as functions of rotational speed and energizing voltage. In Chapter 5, validation experiments are described, and the modeling results are validated using the experimental results. The agreement between the experimental data and analytical predictions is discussed in thi s section of the thesis. In addition, a complete experimental performance map for the pump is presented in this section. In Chapter 6, conclusions based on experimentation and modeling are presented. Sensitivities regarding various parameters are also dis cussed in this chapter. Recommendations for future work are also mentioned in this chapter.

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17 CHAPTER 2 EXPERIMENTATION INVE STIGATION 2.1 Pump u nder C onsideration 2.1.1 Market R esearch Several options for positive displacement micro pump were considere d for potential role of anode recirculation pump. The list includes vane pump, gear pump, screw pump peristaltic pump and diaphragm pump. Vane pump was eliminated because of the fact that the methanol solution has low lubricity hence the wear of vanes wou ld be of substantial amount. The worn off material from vane can be a potential hazard for the fuel cell stack. Gear pump solves the problem of lubricity. However, the gear pump exhibited poor pump characteristics. As explained later in this thesis, Gear p ump has a large slip i.e. drop in flow rate with rise in pressure. During the tests, it was observed that the power drawn to maintain flow rate was much higher than the permissible limit. Peristaltic pump too was eliminated because of its high power requir ement. 2.1.2 Candidate P ump After conducting a thorough market research d iaphragm type pump actuated by a brush type permanent magnet was chosen as a candidate pump because of its extremely small parasitic power consumption while delivering flow rate whic h is optimum for fuel cell application. The diaphragm pump works on the principle of an oscillating diaphragm member. Actuation is provided by a brush type permanent magnet D. C. motor. The recirculation pump nominally operates at 45 ml/min at a differenti al pressure of 1.37 KPa (3 psi), although the purpose on the current investigation is to provide complete information for future design purposes. The

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18 manufacturer rates maximum flow rate achieved by the pump is 70 ml/min and maximum back pressure of 98.04 KPa (14.22 psi). The D.C. motor driving the pump is rated at 6 V and 0.11 A. Concentration of methanol in the anode flow path varies from 0.6 to 1.5 M. Thus the pump should be corrosion resistant to methanol concentration up to 1.5 M. Another pump in the fuel cell system is the dosing pump, as shown in Figure 1.1. The purpose of this pump is to inject pure methanol in the recirculation loop when the concentration of the methanol in the system drops below a preordained set point decided by the on board cont rol system. The dosing pump operates nominally at incomplete, in addition to pump to pump variations, it was necessary to build a test rig to quantify the performance of these p umps. Similarly, a special test rig had to be built to determine the performance of the small D.C. motors. The University of North Florida [1], Jacksonville built a micro motor test rig based on the eddy current brake phenomenon. These rigs will be discuss ed in detail in this chapter. 2.2 General Purpose Micro Pump Test Rig 2.2.1 Experimental A pparatus Figure 2 1 describes the schematic of the general purpose pump test rig with components labeled. Figure 2 2 is an image of the pump test apparatus at UF.

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19 Figure 2 1 Micro pump experimental facility layout.

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20 Figure 2 2 General purpose pump test apparatus at the University of Florida Water was stored in a constant pressure reservoir located upstream of the pump. Wate r exited the constant head reservoir through the upstream back pressure valve. An inline flow meter measured the flow rate of the water entering the apparatus The pressure upstream of the pump was measured using a bourdon pressure gauge. The pressure upst ream of the pump was zero at all the times. This is necessary because

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21 different upstream pressures would result in different flow rates for a same amount of differential pressure. Hence all the measurements in flow rates were made with zero upstream gauge pressure as reference. Isolation valves were present upstream and downstream of the pump to facilitate the replacement of the test pump without having to prime the apparatus every time. Pressure across the test pump was measured by a differential pressure transducer powered by an external power supply. Back pressure was imposed on the test pump by using a downstream needle valve. Water exiting the downstream needle valve is directed back to the constant head reservoir tank thus completing the loop. Follow ing section gives out detailed information on each component. 2.2.2 Hardware Components 1. Needle valve Needle valve was used upstream and downstream of the pump needle va lves were used in the apparatus 2. Flow meter Inline flow meter is used to measure the flow rate through the pump. The flow meter used is an Omega rotameter, Model number 360 02, with a flow range of 150 ml/min. 3. Isolation valve Isolation valves we re used to prevent water from draining while changing the pumps. The valves and the downstream needle valve were closed when the pump was being replaced. 4. Constant Head Reservoir The purpose of this tank was to have a constant head at the upstream sid e of the pump. Water level was maintained at a fixed level above the tube entrance. Without this tank and by using a conventional reservoir at the

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22 suction side, the upstream pressure head would drop as pump operated. To avoid this, a constant head reservoi r was devised. Figure 2 2 shows a schematic of the tank. Figure 2 3 Constant pressure head reservoir schematic 2.2.3 Hardware for data acquisition and control of test parameters 2.2.3.1 Differential pressure head across the pump Pressure head across the pump is measured using a differential pressure transducer. In this case, two pressure transducers were used for the measurement. A low range, Omega PX2300 5DI with a range from 0 5psi for low pressure heads and a high range, Omega PX2300 25DI with a ra nge of 0 25 for higher pressure heads. Both transducers have a current output in range of 4 20 mA. This analog signal was read using LabVIEW software. When pressure gauges were calibrated, it was observed that the pressure versus current relationship f or PX2300 25DI was not linear at low differential pressures. Since the operating point for the pump is in the lower pressure ranges, PX2300 5DI was employed in that range. The pressure versus current relationship for this transducer was extremely linear ov er the entire region of operation.

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23 2.2.3.2 Pressure gauge calibration In the micro pump test rig, the pressure head generated by test pump is measured by a differential pressure gauge. The output from the gauge, i.e. current, is directly proportional to the pressure difference across the gauge. Figure 2 4 shows a schematic for pressure gauge calibration. Figure 2 4 Test schematic for differen tial pressure gauge calibration One end of differential pressure gauge is connected to an electronic pressur e calibrator. The device used in this case is an Ametek CAL PAL electronic pressure calibrator. Full scale reading of this device is 200 psi. Accuracy of this device is 0.1% of full scale. An apparatus as shown is Figure 2 4 is constructed. Using the CAL PAL, pressure is applied to one end of differential pressure gauge and corresponding current reading is noted on an ammeter. Pressure is gradually increased from 0 psi till maximum pressure of the gauge. Then, pressure is gradually released till 0 psi is reached. By

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24 following this method, back lash error is avoided. The data obtained for pressure and current is then plotted and a curve fit is obtained for the particular data set. Two pressure gauges were used in the pump testing. One with a pressure rang e form 0 5 psi and other with range from 0 25 psi. The reason to employ 0 5 psi gauge is that, the accuracy of the 0 25 psi pressure gauge is small at lower pressures. To avoid these errors, a gauge with lower range was used whenever a low pressure tests w ere performed. Both the gauges were manufactured by Omega. Pressure P is expressed in term of current I by following equations. 2.2.3.3 Differential Pressure Gauge Calibration curves 0 5 psi: (2.1 ) w here pressure P is m easured in psi while current I is measured in mA. 0 25 psi: (2.2 ) 2.2.3.4 Upstream pressure Upstream pressure is measured using a Bourdon gauge that reads gauge pressure. 2.2.3.5 Flow rate Flow rate through the pump is measured by an inline flow meter in series with the pump. Most inline flow meters cause a pressure drop across them. Hence the placement of the flow meter in the test rig might be crucial. In the scenario where the flow rate meter is placed downstream of the test pump, when the needle valve is fully open the exit of the flow meter is at ambient pressure. The exit of the pump is at the same pressure as that of the flow meter entrance, which is higher than ambient pressure. Hence the pump can never be tested at truly zero pressure head condition. Hence the flow meter has to be placed upstream of the pump.

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25 2.2.3.6 Flow meter calibration Calibration data for this inline flow meter, an Omega Rotameter, was provided by the manufacturer. The flow meter used has a 65 mm scale and has accuracy of 2 % of full scale deflection. Flow rates up to 150 ml/min can be measured by this Rotameter. Using the calibration data provided, a curve fit was achieved with an R 2 = 1. Flow rate F is expressed in term of scale reading R by E quation (2.3) (2.3 ) where F is measured in ml/min. 2.2.3.7 Actuation voltage The actuation voltage is provided by the D.C. power supply rated at 24 V and 5 W. The voltage is measured using National Instrument d ata acquisition systems. The data is logged using the LabVIEW software. 2.2.3.8 Current to drive the pump D epending on the back pressure imposed on the pump, the motor draws the current to drive the pump. This current can be measured by National Instrument s data acquisitions system by employing a precision shunt resistor. This data is logged using the LabVIEW software. 2.2.3.9 Motor speed Motor speed or motor frequency was not measured. However the current consumed by pump and motor was recorded. DC motor tests were carried out separately to identify the relation between motor current and rotational speed.

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26 2.2.3.10 Data acquisition The data acquisition system employed to retrieve the data was a National Instrument Compact FieldPoint. The data acquisition s ystem has two analog input, two analog outputs and thermocouple input and pulse width measurement module. Pump voltage and pump current was acquired using analog input module. Current generated using differential pressure gauge was acquired using an anal og input module. In the formula node of LabVIEW, calibration curves were entered and thus readings of differential pressure were obtained for the respective current signal generated. Depending on the pressure transducer used, the calibrations equations wer e modified. Flow meter readings were manually entered in the excel sheet and the curve fit equation was used to obtain the flow readings. Current was measured using a prec ision shunt resistor. Appendix 1 describes the experimental uncertainty in measurin g voltage and current. 2.2.4 Test Procedure In an actual test, water stored in the constant pressure reservoir entered the apparatus through the upstream back pressure valve. The entire apparatus was primed and ensured that no air bubble was present in any part of the apparatus Power sources for data acquisition system and differential pressure transducer were set to 24V. Both the upstream and the downstream needle valve were completely open. Power source for test pump was set to a desired energizing vo ltage. The pump was turned on by activating its power source. As the pump started operating, upstream pressure rises. The upstream needle valve was adjusted in such a way that the bourdon gauge read zero gauge pressure. The pump was allowed to run in this state till steady state was achieved. Voltage across the motor, current flowing through the motor and the

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27 differential pressure across the pump was recorded using the LabVIEW VI. Flow rate readings were manually recorded. Later, the back pressure valve was adjusted in such a way that the differential pressure gauge read a pressure 0.5 psi higher than the earlier test. It was ensured that upstream gauge pressure was zero by adjusting upstream needle valve. The procedure was repeated until the downstream need le valve is completely closed or the test pump stalls, whichever happens earlier. 2.2.5 Data Reduction Flow meter scale readings are then entered for every test point. Using calibration Equation (2.3), flow meter readings in ml/min are calculated. Flow rate, Q is measured with a Rotameter. Pressure is calculated using Equation ( 2.1 ) and Equation ( 2.2 ) depending on the pressure range the pump is being tested. Input power P IN is given by, (2.4 ) w here P IN is measured in Watt, voltage V is measure n Volt and current I measured in Ampere. Output power P OUT is given by, (2.5 ) where P OUT is measured in Watt, then equivalent pressure is achieved usi ng calibration Equation (2.1) and Equation (2.2 ) The units for pressure in this equation is psi and flow rate Q is measured in ml/min. The Efficiency (2.6 )

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28 Results were achieved for flow rate, power consumption and efficiency as functions of the differential pressure. These results are discussed in the next chapter in form of plots. 2.3 D.C Motor Test S etup The pump testing rig was developed in house at the University of Florida, while the test rig for D.C. motor was constructed by the Mechanical Engineering Department at the University of North Florida. Figure 2 5 shows an image of the sche matics of the apparatus Figure 2 6 shows a closer view of the micro dynamometer. Figure 2 5 Motor Test Rig developed at University of North Florida An eddy current dynamometer design is used to test the motor. The motor speed is measured using an opt ical tachometer. The dynamometer can be used for motors with power less than 4W.

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29 Figure 2 6 Micro dynamometer in operation at the University of North Florida 2.3.1 Hardware Components 2.3.1.1 Rotating a ssembly Rotating assembly consists of an aluminum disk driven by the test motor. Since torque produced by these motors is extremely small, a very light weight disk is required. The specifications for the components used in the micro dynamometer can be found in the project report for the micro dynamometer [1] 2.3.1.2 Pendulum a ssembly As the motor rotates the aluminum disk, torque is transmitted back to the source of magnetization. This causes the pendulum to rotate. Torque induced is calculated by measuring the weight of the pendulum assembly and the angl e of rotations. Neodymium magnets are used in this application because of the magnetic potential and low weight.

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30 2.3.2 Hardware for D ata C ollection and C ontrol of T est P arameters 2.3.2.1 Optical t achometer An optical tachometer was used to measure the sp eed of the rotating disc. The optical tachometer used in this application is Monarch ROS W. Maximum speed that can be measured by this tachometer is 250,000 RPM and has a TTL output signal. 2.3.2.2 Rotary e ncoder An encoder was used to measure the angular position of the pendulum, thus estimate the torque. The rotary encoder used in this application is US Digital MAE3. The encoder has a resolution of 8192 counts/rev and has output of 12 bit PWM signal. 2.3.2.3 Current s hunt Current consumed by the motor i s measured by measuring the voltage across a current shunt. The current shunt used in this application is manufactured by Packet Flux Technologies and is rated at 0.5A and 100 mV. 2.3.2.4 Data a cquisition National Instrument CompactDAQ NI 9401 is a digi tal input/output module and is employed to acquire encoder and tachometer signals. NI 9215 is an analog input module and was employed to acquire motor voltage and motor current. Software National Instrument LabVIEW is the data acquisition tool used in th is case. The Virtual Instrument (V.I.) was created by students at the University of North Florida. 2.3.3 Test Procedure The motor drove a non ferrous disc, aluminum in this case, which rotated in a magnetic field generated by a neodymium magnet. The proxi mity of the rotor to the permanent magnet affected the motor loading. The resistive torque on the motor increased as the disc approached the neodymium magnet. The magnetic field

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31 interaction with induced eddy current in the disc causes the pendulum to defle ct. The pendulum was measured using an optical encoder. Initially, the pendulum assembly was kept at the distance farthest from the disc. The rail system was used to adjust the distance between different mounts. The distance between pendulum assembly and disc was gradually rotated and the resulting drop in the motor speed was noted in the LabVIEW VI. Once the speed dropped by 100 rpm, the pendulum assembly was locked in the position, and the motor was allowed to run for some time to achieve steady state. Torque is calculated as a function of the deflection of the pendulum assembly. Once the torque versus time curve achieved steady state, data logging was turned ON. Data compr ising of motor current, motor voltage, deflection of pendulum and motor speed was noted. Data logging is kept turned ON for about 5 seconds so that sufficient data points are available for each test point. The data achieved for those five seconds is averag ed out to obtain a unique data point. 2.3.4 Data Reduction 2.3.4.1 Angle of deflection of the pendulum The angle of deflection of the pendulum is measured using a rotary encoder. The output of an encoder is 12 bit PWM signal. Using NI 9401 Digital I/O modu le, width w of the pulse generated by the encoder is measured. Angle of deflection in degrees is then given by, (2. 7)

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32 2.3.4.2 Torque Figure 2 7 Torque acting on a pendulum system comprising of magn et and counter weight [1] Torque is calculated by applying law of conservation of angular momentum and is given by (2. 8) w here g is the acceleration due to gravity in m/s, l is lengt h of pendulum in meter, is angle of deflection measured in radians. m CW is the counter weight mass attached to the pendulum and m Mag is the mass of the neodymium magnets. 2.3.4.3 Motor s peed Motor speed is measured by a remote optical tachometer. The sensor is powered by an external power supply and generates a negative pulse every of time light emitted by sensor bounces off the reflective tape on the disk. 2.3.4.4 Input p ower (2.9 ) w here P IN is measured in Watt, Voltage V is measure n Volt and Current I measured in Ampere

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33 2.3.4.5 Output p ower Output power for a motor is given a product of its rotational speed and the torque generated. (2.10 ) 2.3. 4.6 Efficiency Efficiency is defined as (2.11 ) Data achieved from the DC motor tests using the micro dynamometer is the Torque, power consumption and efficiency as functions of energ izing voltage and motor speed. These results are discussed in detail in the next chapter.

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34 CHAPTER 3 EXPERIMENTAL RESULTS The KNF pumps driven by a permanent magnet brush type D.C. motor were tested using the general purpose pump motor combination test rig described in Chapter 2. The D.C. motors were then tested separately using the motor test rig developed at the University of North Florida. Experimental uncertainty associated with each test has been discussed in Chapter 2. Using the data from these two test apparatus performance of the pump was inferred and can be used for modeling the fluid mechanics. The electromagnetic model developed in Chapter 4 using the finite element method is validated using the experimental data obtained from the D.C. motor t est. Results obtained from both of the rigs will be discussed in detail in this chapter. The motor driving the KNF pump is rated at 6V and 0.11 A. It is desirable to evaluate the performance of the pump motor combination at its rated specifications. Hence 6V was selected as one of the actuation voltage. As discussed in Chapter 2, the flow rate design requirement for the recirculation pump 45 ml/min with a back pressure of 3 psi. This operating point was achieved when the pump was run with energizing voltag e of at least 4V. Hence this voltage was selected as the other energizing voltage. The desired operating point cannot be achieved by energizing the pump with a voltage less than 4V. 3.1 General Purpose Micro Pump Test Rig Using the general purpose pump te st rig, characteristics of pump and motor combination like flow rate, power consumption and efficiency as a function of differential pressure were measured. Tests were run under different environmental conditions and

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35 by different operators. Figure 3 1 shows a plot of flow rate (ml/min) versus the differential pressure (psi). Figure 3 1 Plot of flow rate of KNF pump as a function of differential pressure. For a positive displacement pump like KNF, the flow rate shoul d ideally remain constant independent of back pressure, as long as the frequency and stroke are constant. The working principle of a KNF can be visualized by a piston inside a cylinder. As the inlet cavity of the pump expands, a low pressure region is crea ted and this region should be ideally filled by the fluid from the inlet line. If the valves do not seal outlet line as desired, the fluid from outlet line fills up this region. This causes the net flow at the outlet to drop. This drop in flow rate is call ed as Slip. As the back pressure increases, performance of valve drops, thus causing increase in slip. As the differential pressure rises, the force required to push the fluid rises as well. This causes the motor torque to increase with it. The motor spee d, according to the torque speed characteristics, drops thus the pump flow rate drops with it causing a slip.

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36 This physical phenomenon can be seen in Figure 3 1 for both 4V and 6V. The slip should be as low as possible for a positive displacement pump as i t affects the overall pump performance. When the pump is energized by 4V, a slip of 16% was observed at 3 psi and 40% at 14 psi. When the pump was energized by 6V, a slip of 2.4% percent was observed at 3 psi and 17% at 14 psi. The plots are derived by us ing linear fits to actual test data. Figure 3 2 shows a plot of the power consumption and efficiency (percent) versus the differential pressure (psi). Figure 3 2 Plot of efficiency and power consumption of KNF pump as a function of differential pressure at two actuation voltages. Efficiency of the pump motor combination is slightly higher for 4V energizing voltage at lower differential back pressure. As the back pressure increases, the pump becomes more efficient w hen operated at 6V. The pump motor combination is more efficient in lower back pressure region when operated at 4V because the power input is significantly smaller even if the slip is higher for 4V. As the back pressure rises, the

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37 advantage of lower input power drops as compared to higher losses because of slip. Thus the pump motor combination becomes efficient at higher back pressure region when operated at 6V because the slip is comparatively small even if the input power is higher. Energizing voltage a nd current drawn by the motor are logged using National Instrument Compact Field point data acquisition system as explained in Chapter 2. Accuracy of these devices is extremely high and hence the uncertainty in measuring the power consumption is extremely low. The efficiency measurement depends on the flow rate measurement. The device used for flow rate measurement, a rotameter, has comparatively higher uncertainty. Also the error in measuring flow rate is higher at lower flow rates. For this reason, the uncertainty in efficiency measurement increases as back pressure rises of flow rate drops. In case of fuel cell application, the pump should consume less power rather than being efficient at the design operating point. For this reason, it is advisable to operate the pump at lowest possible voltage that meets the design requirement i.e. 4V in this case. 3.2 D.C. Motor Test Rig As explained earlier, the D.C. motors were tested so that the experimental data obtained can be used to validate the electromagnet ic model developed later in Chapter 4. Using the D.C. motor test rig, characteristics of motor like torque, power consumption and efficiency as a function of rotational speed are measured. Figure 3 3 shows a plot of tor que as a function of rotational speed.

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38 Figure 3 3 Plot of Torque as a function of rotational speed For D.C. motor, torque varies linearly with motor speed. This trend can be seen in Figure 3 3 for both the actuation voltages. Uncertainty associated w ith the torque measurement is because of the uncertainty associated with measuring the angular position of the pendulum assembly. Uncertainty is highest at the lower torque readings because the angular deflection of the pendulum is very small, hence the er ror associated in angle measurement becomes comparable to the angle measured. The connection between motor and aluminum disc is made by flexible coupling. Measures are being taken during experimentation to minimize eccentricity to the maximum possible exte nt. However, some eccentricity would exist in the coupling. The uncertainty associated with this eccentricity is not discussed in this study. The experimental no load speed achieved when the motor was energized by 4V was 1966 rpm and for 6V was 2993 rpm. The optical tachometer measures the speed with accuracy of 0.05% of

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39 the reading. Hence the error associated with these readings would be approximately 1 1.5RPM. Figure 3 4 shows a plot of current drawn by the motor and its efficiency as a function of motor speed. Figure 3 4 Plot of c urrent and e fficiency as a function of rotational speed Like torque, current drawn by the motor is also linearly proportional to the motor speed. The linear nature of the current speed relation is governed by the DC motor theory. And the trend of the result is as expected. Stall current observed for 4V is about 169 mA and for 6V is about 249 mA. From these values, resistance of the motor can be calculated. The terminal resistance is t hus approximately 24 ohm. Resistance can also be calculated by physically measuring the resistance across the brush and rotating the shaft. It was observed that average resistance over a complete cycle was 25.3 ohm. Each brush contributed 0.3 ohm resistanc e. Thus resistance across coils was 24.7ohm,

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40 which agrees with experimental data within the experimental uncertainty. An error of 3% was seen in resistance calculated. The efficiency plot follows an expected parabolic profile. For 4V, peak efficiency ac hieved was about 31% at the speed of about 1500 rpm. For 6V, peak efficiency achieved was 35% at the speed of 2176 rpm. The current in motor test rig was logged using a precision current shunt and National Instrument analog input module 9215 with accuracy of 0.02%. Hence the uncertainty in current measurement is extremely small. The efficiency measurement, however, depends on the measurement of torque and rotational speed. Since the uncertainty in measuring torque is higher at lower speed, we see a higher uncertainty in efficiency measurement at lower motor speed. The uncertainty drops as the motor speed increases. 3.3 Experimental R esults for P ump Torque versus speed and current versus speed curves were obtained for the D.C. motor from the motor test appar atus Thus, torque versus current plot can be deduced from both of these data sets. Figure 3 5 shows this plot. Figure 3 5 Plot of torque versus current for the experimental data

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41 From Figure 3 5, it can be seen that torque is linearly dependent on the current drawn by the motor. Within the regime of experimental error, it can be said for a given amount of current flowing through the coils, only a certain constant amount of torque will be generated. The energizing voltage dictates the speed at which thi s torque is available. A linear curve fit can be obtained for torque and current relationship. From pump motor tests, data for the current drawn by the motor for varying pressure is also available, thus the motor torque can be related to the differential p ressure. Using these relations and Equation 3.1, pump efficiency and differential pressure can be correlated. (3.1) Figure 3 6 shows a plot of pump efficiency as a function of diff erential pressure. Figure 3 6 Plot of pump efficiency as a function of differential pressure.

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42 Uncertainty associated with pump efficiency measurement exists because of the uncertainty in measurement of the flow rate. As explained earlier, higher the b ack pressure, lower the flow rate thus higher the error. From experimental results, it can be seen that the pump is marginally efficient when operated at 4V. The results obtained for the pump chamber gives an indication of the pump hydrodynamic efficiency. This data can be used to validate hydrodynamic efficiency of the pump.

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43 CHAPTER 4 D.C. MOTOR MODEL testing rig and the motor driving the pump was tested at University of North F D.C. motor testing rig. Using the experimental data from both of these tests, experimental data for the pumping chamber was also obtained. To support the modeling efforts on the pump, a steady state model for the D.C. motor is generated. This chap ter will focus on discussing the physics of a permanent magnet brush D.C. motor and the model in detail. The purpose of this model is to relate the physical dimensions and material properties of motor components to the performance map, thus contributing to design optimization. The finite element method is used to model the electromagnetic actuation of the motor. A magnetostatic or steady state magnetic simulation is presented in this thesis. Flux linkage in each coil and torque produced a function of curr ent in coils, current at the terminal and position of the rotor is calculated. 4.1 Need for Finite Element Analysis how charges and current interact with electromagnetic field The forces acting on charge are given by the Lorentz law. Flux density, electromagnetic field intensity, force and torque can be calculated by solving these equations. However, to solve these equations analytically, geometry has to be comparatively simpl e. The equations become extremely difficult to solve if geometry becomes complicated. In case of a brush type permanent magnet D.C. motor, the geometry of components is extremely complex. Also, components are made of dissimilar materials thus making the an alytical analysis

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44 difficult. To identify the performance of the motor at different rotor positions, the equations would have to be solved with different initial and boundary conditions. Finite element method can be used for solving extremely complex geom etries. Approach to solve the problem does not alter when initial conditions or boundary conditions are changed. This is extremely helpful for calculating motor parameters for different orientations are coil currents. 4.2 Finite Element Method Magnetics F inite element package used in this study is an open source package called Finite Element Method Magnetics or FEMM [2] This package is used to solve two dimensional planar or axisymmetric problems. This package can, however, solve only steady state low fre quency problems. Thus this package is well suited for the problem under consideration. This package will be used to calculate torque generated by the rotor as a function of coil current and position of the rotor. The results obtained will be then compared with experimental results for this motor. The relevant partial differential equation governing the solution scheme ca n be found in the FEMM manual [2 ] 4.3 Application of FEMM to D.C. M otor M odel 4.3.1 Pre processing Pre processing step involves defining t he geometry of the model, adding material to the components and applying the boundary conditions. Figure 4 1 shows model of D.C. motor with dimensions exactly equal to the actual dimensions. The model is generated using graphical pre processor integrated in the FEMM package.

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45 Figure 4 1 FEMM Model of permanent magnet brush type D.C. motor with graphic illustration The position of rotor with respect to the permanent magnet depicted in Figure 4 1 rm in this thesis should refer to the position of rotor as in Figure 4 1. It can be seen in Figure 4 1 that a sign exists next to a coil indicate the direction of the coil winding. Positive indicate that the current in the coil is coming out side the plane of paper, while negative indicate that current in the coil is go ing in side the plane of paper. With this particular schematic, if positive end of power source is connected to coil 1 and negative terminal partially to each of coil 2 and coil3, the rotor wil l rotate in clockwise direction. The indicated position of rotor in Figure 4 1 is a reference zero position. Appendix 2 has a detailed geometry of the components with dimensions. Figure 4 2 shows the commutator and brush arrangement for this motor.

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46 Figu re 4 2 Commutato r b rush arrangement for D.C. motor. The marking on the brush indicate the rotation for reference zero position in counter clockwise direction. The position of brush with respect to commutator dictates the current flowing through the coil in contact. For a given reference zero position, Coil1 will be energized with positive current and magnitude equal to the magnitude of terminal current. Negative current will be applied to Coil 2 and Coil 3 and magnitude equal to half the magnitude of term inal current. Thus Coil 2 and Coil 3 will be partially energized. If a brush is in contact with two coils, the current is divided equally between both the coils. It can be seen from the Figure 4 2 that for 30 degrees counter clockwise rotation, Coil 2 will lose contact with both the brushes. Thus Coil 2 will be de energized. This is a desired effect, because after 30 degrees rotation, angle between North Pole of magnet

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47 and Coil 2 will be zero. Thus any amount of current in Coil 2 will not contribute toward s generation of torque, since the angle between external magnetic field and current flow is zero, the cross product of these two quantities will be zero, thus zero force acting on the coil. Equation 4.1 governs this phenomenon. However, maximum possible to rque will be generated from both Coil 1 and Coil 3, since Coil 1 will be attracted to South Pole and Coil 3 will be repelled by the South Pole. Table 4 1 Description of DC motor c omponents Component Quantity Material Description Rotor 1 M 19 Steel Lam inated plates Coil 3 Copper Wire diameter: 0.16 mm Turns: 120 turn each Permanent Magnet 2 Ceramic Horse shoe type Casing 1 1018 Steel 4.3.2 Boundary Conditions The problem analyzed in this report is a planar problem, with a boundary surrounding t he geometry. The boundary is modeled in a way to simulate open space. Compared to the model geometry, the boundary is comparatively larger in size and thus models open space fairly accurately. Figure 4 3 shows a representation of motor and the boundary.

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48 Figure 4 3 Comparison of the external boundary and the motor size Equation 4.1 gives the mathematical representation of the boundary condition used in this problem and is applied to the circular section tagged as External Boundary in Figure 4 3. A = 0 (4.1) where A is a magnetic vector potential. By defining A=0, we disallow magnetic flux lines to cross the boundary. Thus the magnetic flux lines are always parallel to the boundary.

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49 4.3.3 Mesh Generation FEMM utilizes a triangular element for comput ation of flux density and flux Figure 4 4 shows the geometry of model with triangular mesh. Figure 4 4 Triangular mesh in the motor geometry In Figure 4.4, it c an be seen that permanent magnets are modeled as a collection of small individual magnets. This scheme is advantages compared to modeling them as single block because with this scheme the magnetization direction can be controlled more accurately. In this c ase, magnets have a radial magnetization direction. The direction of arrow on each block illustrates the direction of magnetization. Thus, the magnet on the left of the rotor is modeled as a North Pole while one on the right is modeled as a South Pole. To tal number of elements in this model is 215,769 and total number of nodes is 107,933. Figure 4.5 gives a closer look at the air gap between the rotor and the magnets.

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50 Figure 4 5 A closer view at space between rotor and magnet depicting a finer mesh co mpared to neighboring spaces It can be seen from Figure 4 5 that the density of mesh is very high at the air gap. This is essential since most of the electromagnetic interaction take place at the air gap. Triangular elements can also be more easily visuali zed in this figure 4.3.4 Solution S cheme for a given angular position of the rotor and current in the coil. Since the geometry consist of 3 yokes, after every 120 degrees, the so lution to the equations repeat. Hence the geometry is analyzed from 0 degree to 120 degree in steps of 2.5 degree. For a given angular position of the rotor, current in the terminal vary from 0 mA to 15 mA in steps of 3 mA. Using the finite element metho d, a plot for torque against rotor position is obtained for various values of current in the coil. By integrating the curve over entire

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51 cycle, a relationship between electromagnetic torque and current in the coil is established. This relationship together with one dimensional DC motor model is used describe a complete DC motor model. 4.4 DC Motor Model The electromagnetic torque versus current plot obtained from the finite element analysis is used to develop a complete DC motor model by using experimental a nd physical parameters. Relationships for obtaining speed characteristics will be discussed in this section. To establish a complete model, constants like torque constant and induced electromotive force constants are needed to be calculated. Also, the fini te element method did not consider the friction at the shaft. A suitable friction model will be also included in the DC motor model. 4.4.1 Det ermination of Torque C onstant The brush D.C. motor produces torque directly proportional to the power supplied to it. The core is located concentric to a set of permanent magnets. When current passes through the coils, a magnetic field is generated and this magnetic field interacts with external magnet field generated by the magnets. This interaction of the fields ca uses a torque to act on the rotor proportional to the current passing through the coils. The torque acting on the rotor is in effect caused by the Loren rotor [3] [4] [5]. Figure 4 1 illustrates the physics behind a D.C. motor takin g just one turn in the consideration.

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52 Figure 4 6 Schematic of D.C. Motor coil A ) Single current coil in an external magnetic field. B ) Side view of the current carrying coil in external magnetic field. The electromotive force F acting on a single co il is given by Lorentz force acting on a straight wire in external magnetic field. (4.2) w here F = Force, Newton = Current in coil Ampere L = Length of conductor, Meter B = Magneti c field Intensity, Tesla = Cross product Resolving the cross product, (4.3)

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53 w here = angle between vector along length L and magnetic field B. S ince both the vectors are always at right angle to each other Thus Equation (4.2) can be written as (4.4) Electromagnetic torque acting on the roto r can be given by a product of the force F acting on the rotor and the radial distance R from the axis of rotation. Since force F acts on two lengths of the conductor, total force acting on the conductor is 2F. Thus electromagnetic torque is given by, (4.5) Substituting Equation (4.4) in Equation (4.5), (4.6) Thus for n number of turns, Torque acting can be calculated by simply multiplying Equation (4.6) by n. (4.7) Analytically, it is difficult to estimate B. To do so, high precision magnetic flux density meters are used. However, the magnitude of magnetic field intensity B remains constant since it is property of the permanent magnet. More conve nient way of representing torque T is by expressing the multiple constant parameters collectively as a single constant. In case of motors, this constant is called motor constant or torque constant, K T This constant will be called torque constant hereafter in this report. Equation (4.7) is the representation of torque constant.

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54 (4.8) 4.4.2 Determination of Voltage Constant changing magnetic field, a voltage is induced in the coil. The voltage is called back electromotive force or back emf. The magnitude of back emf, V EMF is given by Equation (4.10) (4.9 ) w here = el ectromagnetic flux passing through the coil, Tesla. (meter) 2 t = time, Second. Flux is expressed as magnetic field intensity B in a unit area A. Thus Equation (4.9 ) can be modified and written as (4. 10 ) To simplify the model, it is assumed that magnetic field intensity is constant across the area under consideration. Since the size of magnets used is comparable to the size of the rotor, this assumption is fairly accurate. [3] [4] [5] [6] Thus back emf Equation (4.10 ) can be written as (4.11 ) Figure 4 7 gives a schematic of a single coil on a rotor placed in permanent magnetic field.

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55 Figure 4 7 Schematic of a single coil rotating in an externa l magnetic field. The area under the loop can be identified by areas A1 and A2. Assuming a sign convention that magnetic flux coming out of rotor is positive and flux going in the core is negative The back emf equation can be thus written as (4.12 ) Thus combining the area terms, since B is a constant parameter, (4.13 ) A1 and A2 can be expressed as (4.14 ) (4 .15 )

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56 where, R = radius of the rotor, meter L = Length of rotor measured in the plane of paper Thus E quation (4.1 3 ) can be written as (4.16 ) Since is a constant and or angular velocity measured in radian/second, Equation (4.16 ) is written as (4.17 ) Generalizing the model for n turns, (4.18 ) The term 2nRLB is collectively called back emf constant K EMF Thus back emf generated is given by Equation (4.19 ) in terms of back emf constant and rotational speed, (4.19 ) I n an ideal motor, when expr essed in a consistent unit system. However, in actual motors, values of and are not equal since there always exists a stray magnetic field

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57 4.4.3 Motor Speed Calculation Figure 4 8 shows an equivalent circuit model of a D.C. motor. Since all the experimental results are achieved at steady state, only a steady state model is constructed. Hence the equivalent D.C. motor circuit does not include inductance. Figure 4 8 Equivalent Ci rcuit for a D.C. electric motor [ 7 ] Voltage across the terminal can be expressed as (4.20 ) When no resisting torque is applied, the current passing through the motor is and the speed of rotation is The equation for back emf constant is thus g iven by combining Equation (4.19 ) and Equation (4. 20 ) and eliminating [8 ] (4.20) From Equation (4.9), (4.21) 4.4.4 Parameterization of Voltage Constant Parameterization of constant implies that it is expressed as a factor of other constant that can be either measured directly or can be calculated from the governing

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58 eq uations. In this case, the voltage constant is expressed as a factor of the factor is defined as Using the parameterization factor and taking a ratio of Eq uation (4.21) and Equation (4.20 ), (4.22) Re arranging the terms in Equation 4.22 can be thus expressed as (4.23) Equation (4.23 ) gives a model for electroma gnetic torque as a function of motor speed when energized by a voltage V. However, this model over predicts the torque since it does not include the effects with friction. Friction model is discussed in the following section. 4.4.5 Friction Model Several friction models have been discussed extensively in literature. Models for friction compens ation are proposed by Walrath [9 ] and Dahl [ 10 ]. Model proposed by Walrath does not consider the dynamic component of friction while the model proposed by Dahl does n ot account for static friction. A friction model used in this study wa s proposed by Canudas et al. [11 ] and includes both static (coulomb) friction and dynamic (viscous) friction. The model is given by, (4.24 ) Using th e experimental data, constants and can be determined. The actual friction model used is given by (4.25 )

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59 The load motor torque can be thus expressed as, (4.26 ) By using curve fit equations for speed and torque, free speed, and stalling torque can be calculated. Stalling can be ca lculated by knowing the value of motor terminal resistance R and actuation voltage V. (4.27 ) Thus current consumed by motor when no resisting torque is acting on the motor can be calculated using (4.28 ) Equation (4.26 ) can be used to plot the load torque and the motor speed curve. E fficiency of a DC Motor is given by, (4.29 ) 4.4.6 FEM and DC Motor Model Results In the next cha pter, results of the finite element analysis are discussed. The results obtained from this analysis are used to construct a steady state motor model as discussed earlier in this chapter. These results will be then compared to the experimental results.

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60 CH APTER 5 MODELING RESULTS In previous chapters, experimental data for DC motor was discussed. In last chapter it was discussed that an open source finite element analysis tool, FEMM can be the interaction between current and charges and the electromagnetic field. The motor geometry was discretized in triangular elements. A steady state DC motor model was also discussed. Finally a linear friction model was discussed. The solutions are explain ed in detail in this section. The torque current relation obtained from finite element method will be then used with the DC motor model and friction model to obtain motor characteristic curves. 5.1 FEM Results The FEMM code was used to solve the motor geo metry described in Figure 4 1 and the result shown in Figure 5 1 is a magnetic flux density plot with the rotor being at reference position. As explained in Figure 4 2, the commutator divides the current between coil 2 and coil3. Since the resistance of bo th the coils is equal, the current gets divided equally. Hence a current of 0.1 mA in flows through coil 1 and current of 0.05 mA flows through coil 2 and coil 3. Figure 5 2 Magnetic field intensities with flux lines superimposed at the reference orientati on

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61 Figure 5 1 Magnetic flux densities at the reference position Figure 5 2 Magnetic field intensities at the reference position

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62 It can be seen in Figure 5 1 that flux lines enter Yoke 3 and leave Yoke 2. The magnetic flux lines follow the north s outh direction passing through the electromagnetic field generated by rotor. In the rotor, the flux density is highest at the Yoke 2 and Yoke 3. This indicates that torque induced on these parts of rotor is more than any other on the rotor. The direction o Thus torque is induced on the rotor. Figure 5 2 shows the magnetic field intensities. The field intensities are high at the air gap, particularly between the magnet and the rotor. A closer look at the air gap can be seen in Figure 5 3 Figure 5 3 Magnetic field intensity at the air gap between magnet and rotor The magnetic field intensities are highest at the air gap because this region serves as the area where magnetic fields generated by electromagnet and permanent magnet interact. The vector product of both the fields results in higher magnetic intensity. The solution scheme explained in previous chapter was applied to the finite element model. A series of simulation as explained in t hat section was carried out and

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63 the values of torque obtained for each simulation are plotted in Figure 5 4. Figure 5 4 shows a plot of variation of instantaneous torque as a function of rotor angular position. Figure 5 4 Variation of torque with rotor angular position In Figure 5 4, six positive spikes and six negative spikes can be seen. Six spikes are the result of three rotor yokes rotating past two permanent magnets. Positive spikes in torque are caused by the electromagnet being attracted by the p ermanent magnet thus assisting the rotation. Momentary negative spikes are observed when the electromagnets are repelled by the permanent magnets. Since the magnitude and the duration torque being in positive region is more than it is in negative region, a net positive torque is experienced on the rotor. The value of torque generated at the shaft for a given current as a function of the position of the rotor, as shown in Figure 5 4 is fit. The averaged torque over the entire cycle, is then given by,

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64 (5.1) Figure 5 5 shows a plot of against current. The results presented in this plot are compared with the experimenta l results described earlier in C hapter 3. Figure 5 5 Plot for electromagnetic torque and experimental torque versus current The x intercept for th e experimental values shown in F igure 5 5 are the free current or the current consumed by motor when no resisting torque is applied. The electromagnetic torque, however, does not have this x intercept because the electromagnetic torque is the torque generated at the shaft while the experimental torque is the resisting t orque on the motor. For zero current passing through the coils, no electromagnetic torque is generated. The torque increases linearly with current in the coil and this phenomenon is also explained by Equation (4.8).

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65 5.2 Application of DC M otor M odel to FEM R esults A DC motor model was discussed in Chapter 4. Figure 5 6 shows a plot of torque versus speed for experimental and FEM results as given by Equation 4.26. The model was evaluated at the energizing voltages of 4V and 6V. Figure 5 6 Comparison of experimental and analytical electromagnetic torque values for 4V and 6V In the F igure 5 6, the model considers only the electromagnetic torque. It can be seen from the plot that the slope of the electromagnetic torque is much lesser then the experimenta l results. This can be seen for both the cases of actuation voltages. Free speed for electromagnetic torque in case of actuation voltage of 4Vis about 4000 rpm, where as in actual experiments, free speed recorded was about 2000 rpm. The difference in the s peed increases linearly as the resisting torque drops. The reason for high rotation speed for electromagnetic torque is because it does not take into

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66 consideration the friction. Figure 5 7 shows a plot of load torque when friction model described in previo us chapter is taken into account. Figure 5 7 Comparison of experimental and analytical load torque values for 4V and 6V From Figure 5 7 it can be seen that the model agrees with experimental results fairly well at lower speeds. However, the disagreeme nt increases as the motor speed increases. The variation in the experimental and analytical values increases exponentially with the increase in the speed. Using Equation (4.31), efficiency can be calculated and Figure 5 8 shoes a plot of analytical and exp erimental values of efficiency as a function of motor speed.

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67 Figure 5 8 Comparison of experimental and analytical motor efficiency for 4V and 6V From Figure 5 7 and Figure 5 8 it can be seen that the model predicts higher torque at higher rpm. And E quation (4.31) shows that for higher torque, the efficiency is also higher for same speed and input power. The efficiency predicted by the model is thus higher than the experimental values. This chapter discussed that by employing a magnetostatic finite element code, solutions for magnetic flux densities, magnetic field intensities and torque acting on current carrying conductors can be obtained. By using a steady state motor model and a linear friction model, an analytical map of DC motor performance can be obtained. The results obtained from the model were compared with the experimental values. By applying appropriate curve fit equations, analytical values for staling torque and free speed stalling current and free current can be obtained. Table 5 1 sh ows a comparison of experimental and analytical values of these parameters.

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68 Table 5 1. Comparison of experimental and analytical values of motor parameters 4V 6V Experiment Model Experiment Model ( m N. m ) 1.88 1.82 3.04 3.10 ( RPM ) 1966 2201 2993 3202 ( m A ) 170 162 250 243 ( m A ) 21.5 22.2 27.8 28.1

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69 CHAPTER 6 CONCLUSIONS AND RECO MMENDATIONS FOR FUTU RE WORK In this work, apparatus were built for testing micro pumps and DC motors. Characteristic curves for positive displacement micro pump and permanent magnet brush type DC motor were achieved with good repeatability. Uncertainty analysis was performed on the data obtained from these apparatus Using the results from both the apparatus inferred. The results obtained from these apparatus provide a good validation step for all future fluid dynamics modeling efforts. A steady state m odel for permanent magnet brush type DC motor was also introduced. The DC motor models discussed in the element analysis was done using an open source package, FEMM, to calculate the electromagnetic parameters for DC motor such as magnetic field density and magnetic field intensity. The code has a capability to calculate torque produced by the motor as functions of coil current, rotor position and material properties. By employing modeling techniques discussed by several authors, motor characteristic curves such as torque and efficiency as functions of motor speed and energizing voltage were constructed. A friction model, which accounted for coulomb and viscous friction, w as also added to the electromagnetic model to approximate the actual DC motor under consideration. The results obtained from this model were presented as a comparison with the experimentation results. It was seen that the analytical and experimental valu es of torque and efficiency as a function of speed matched closely at low speeds. However, at higher speeds, the difference between these results increased sharply. One of the possible reasons for this

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70 inconsistency can be the incomprehensive friction mode l. The friction model introduced in this work accounted for shaft friction. However, friction at brush commutator interface was not taken into consideration. Also, wear on the graphite brushes and its contribution to the friction was not taken into conside ration. The experimental techniques presented in this have allowed pump testing with flow rates up to 150 ml/min and back pressure up to 25 psi, and DC motor testing with power consumption up to 4W. The modeling techniques presented in this work allow a mo tor designer to vary the motor component dimensions and material properties to obtain approximate characteristic curves for design purposes. This model in conjunction with a fluid dynamics model will form a complete micro pump model. The main objective of this research was to support DMFC development activities. By employing the micro pump model, a fairly accurate estimate of parasitic power consumption can be achieved. Since the pump characteristic curves can be achieved analytically, the results can be u sed to create a pump performance map. This will assist a fuel cell control engineer to estimate flow rate and power consumption for recirculation pump as a function of external load. Some of the observations from the experimental results were The effect of head on pump power consumption was very small. Pump energizing voltage does not have any effect on pump efficiency till the head is 10 psi. I f hea d more than 10 psi is acting, the pump is more efficient when operated at 6V. The hydrodynamic efficiency is nearly insensitive to pump energizing voltage.

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71 For a given amount of current flowing through the coils, only a certain constant amount of torque will be generated. The energizing voltage dictates the speed at which this torque is available. In future, ph ysical phenomena that caused mismatch of analytical and experimental results at higher motor speeds can be investigated. O nly the bearing friction has been taken into consideration However, friction also exists at the interface of brush and commutator. Ex periments conducted on brush type motor have indicated the degradation of motor performance with time. The degradation of the brushes and the rate at which degradation occurs can be analyzed analytically. The finite element model presented in this study as sumes all materials to be homogenous. A more comprehensive model will also take into account the non homogeneity of these materials. The FEM tool, FEMM, is a steady state two dimensional analysis tool. Advanced FEM tools like ANSYS can be employed to get d ynamic, three dimensional results.

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72 APPENDIX 1 UNCERTAINTY ANALYSIS 1 .1 UF Pump Test Apparatus 1 .1.1 Energizing Voltage for pump motor combination Accuracy of the voltage input module is 0.07% of the reading [1]. Thus uncertainty in measuring Voltage is given by (A1 .1) 1 .1.2 Current The voltage across the shunt is measured by the voltage input module [1]. Thus uncertainty in current measurement is giv en by ( A1 .2) 1 .1.3 Flow rate The Rotameter used in the setup is an Omega Rotameter with an accuracy of 2% of full scale deflection. The full scale reading on flow meter is 150 ml/min. Thus the uncertainty in flow rate measurement, W (Q), ml/min (A1 .3) 1 .1.4 Differential Pressure Since the differential pressure is a function of current, uncertainty in the measured pressure is a function of current and the accuracy with which the curr ent is measured by the data acquisition hardware. Uncertainty in measuring differential pressure psi is given by

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73 For 0 5 psi gauge: (A1 .4) For 0 25 psi gauge: (A1 .5) 1 .1.5 Input Power Uncertainty is the Input Power Watt is given by ( A1 .6) 1 .1.6 Output Power Uncertainty in Output Power Watt is given by (A1 .7) 1 .1.7 Efficiency Uncertainty in efficiency is given by (A1 .8) 1 .2 Micro dynamometer 1 .2.1 Voltage Accuracy of the voltage input module is 0.2% of the reading. Thus uncertainty in measuring Voltage is given by (A1 .9)

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74 1 .2.2 Current Current is measured using a precision shunt resistor. The voltage across the sh unt is measured by the voltage input module. Thus uncertainty in current measurement is given by (A1 .10) 1 .2.3 Angle of deflection The accuracy of rotary encoder is 0.5 0 Deg or 0.00873 radians. Hence the uncertainty in measuring angle, in radians is (A1 .11) 1 .2.4 Torque Uncertainty in Torque in N m is given by, ( A1 .12) 1 .2.5 Motor speed Accuracy of optical tachometer as specified by manufacturer is 0.05% of the reading. Thus the uncertainty in measuring motor speed in RPM is (A1 .13) 1 .2.6 Input power Uncertainty is the Input Power, Watt is given by (A1 .14)

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75 1 .2.7 Output power Uncertainty in measuring output power in Watts is given by (A1 .15) 1 .2.8 Efficiency Uncertainty in efficiency is given by (A1 .16) 1 .3 Inferred Results 1 .3.1 Pump E fficiency Uncertainty associated with calculating pump efficiency is given by (A1 .17)

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76 APPENDIX 2 MODEL GEOMETRY 2.1 Motor Rotor Figure A ppendix 2 1 Laminated steel rotor in the DC Motor

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77 2.2 Motor Casing Figure A ppendix 2 2 Steel casing in the DC motor

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78 2.3 Permanent Magnet Figure A ppendix 2 3 Ceramic magnet in the DC motor

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79 LIST OF REFERENCES 1. University of North Florida, Micro dynamometer Project Report Internal document 2. D. C. Meeker, Finite Eleme nt Method Magnetics, Version 4.0.1 (03Dec2006 Build), http://www.femm.info 3. Chapman, S.J. Electric Machinery Fundamentals, McGraw Hill, New York, 1991 4. Chiasson, J. The Physics of DC Motor for Control Courses, Notes. Un iversity of Pittsburgh, PA 5. Matsch, L. Electromagnetic and Electromechanical Machines. Harper and Row, New York, 1977 6. Nise N. Control Systems Engineering, Appendix H. Wiley and sons, 2008 7. Mark D. First order DC electric motor model, MIT Aero & Astro, February 2007 8. Heinzmann, K. Mikus, K. Introduction to Motors, 2005 https://research.cc.gatech.edu/humanoids/sites/edu.humanoids/files/IntroToMotors.pdf 9. Walrath, C.D. "Adaptive Bearing Friction Compensation Based on Recent Knowledge of Dynamic Friction". Automatica. Vol. 20. No. 6, pp. 717 727, 1984. 10. Dahl, P.R. "Measurement of Solid Friction Parameters of Ball Bearings". Proceeding of 6th Annual Symposium on Incremental Motion Control Systems and Devices, University of Illinois, 1977. 11. Canudas, C. Astrom, K.J. and Braun, K. Adaptive Friction compensation in DC Motor Drives, IEEE International Conference on Robotics and Automation 1986

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80 BIOGRAPHICAL SKETC H Anupam Patil was born in Mumbai, India, in 1985 and was raised by a surgeon father and a banker mother in a scenic coastal town of Alibag, India Anupam completed his Bachelor of Engineering in mechanical engineering from Veermata Jijabai Technological I nstitute, Mumbai in 2007. After graduation, Anupam worked as a Product Development Engineer at the Automotive Sec tor of Mahindra and Mahindra where his work focused on vehicle performance and vehicle dynamics modeling. Anupam enrolled for the M asters of S cience program in m echanical e ngineering at University of Florida in August 2008 under guidance of Dr. William Lear, Dr. James Fletcher and Dr. Oscar Crisalle. During his M aster s program he served as a Research Assistant at the Fuel Cell Research Labo ratory. Anupam rec eived his Master of Science in m echanical e ngineering in August 2011. Upon completion of his degree, He started working fulltime for Cummins, Inc as a Fuel Systems Performance Engineer. Anupam intends to continue to contribute to the fiel d of clean energy.