Optimisation and Characterisation of a Thin. MEMS Micro Generator

Transcription

1 Optiisation and Characterisation of a Thin MEMS Micro Generator A thesis subitted in fulfilent of the requireents for the degree of Master of Engineering Surendran Devadoss M.Eng. School of Electrical and Coputer Engineering Science, Engineering and Technology Portfolio RMIT University Deceber, 9

2 Copyright by Surendran Devadoss 9 All Rights Reserved

3 Abstract Electrocheical batteries are liited by low gravietric & voluetric energy density (ED) and not suitable for scaling. Studies of MEMS icro-engine coupled generator power supplies for portable applications are undertaken by any research institutes to develop an alternative to electrocheical batteries. Micro systes that have been reported in the current literature produce output power in the range of 1µW to 1W at rotor speeds of 3, to 1, rp, but challenges and issues still reain in the area of engine and generator developent to overcoe low syste efficiency and low energy density. The ain contributions of the thesis are in the areas of thin icro generator developent suitable for planar MEMS technologies which can be integrated with icro cobustion engines. This developent of a thin MEMS axial generator topology to achieve high power density is presented in the thesis. A custoized luped paraeter analysis ethodology using paraetric equations is developed to select suitable paraeters for the MEMS Micro generator. The ethodology takes inputs fro agnetic circuit and planar coil analysis used in the thesis. The agnetic circuit analysis is done using a Pereance coefficient ethod to deterine air gap flux density (B g ), force and torque. This analysis ethod is siple with accuracies close to FEM siulation for -D analysis and avoids any repeated odelling for physical paraeter change like in FEM ethod. The planar coil analysis is perfored using an original analytical ethod to deterine winding paraeters like resistance, coil length, and no of coils to operate the syste within practical current density and current loading level. ANSYS FEA analysis is used to validate the theoretical ethod prediction of air gap flux density for the 5 rotor radius icro generator odel which showed accuracies of 93% to FEA prediction.

4 Equivalent circuit odel of the icro generator with the selected paraeters is developed for characterisation. The equivalent resistance and reactance of the equivalent circuit odel is found to be 573KΩ and 489Ω respectively. Characterisation for no load, full load and variable load is perfored and an estiated useful power output of 1.6W is achievable at 15 rp. The icro generator when operated at an increasing teperature of 1 o C would see reduction in O/P power fro 1.6.W to 1.3W due to teperature effect on both flux density at air gap and winding resistance. Generalised equations for the engine are derived and linked to the icro generator luped paraeter equations to for the analysis odel for integrated engine-generator syste. The odel was analysed for attainable energy density for a syste volue of 4e- 3*7e-3*5e-3. The estiated energy density fro the analysis was 4.3 WH/Kg. This estiated energy density is three ties the energy density that could be achievable fro existing icro generators for the sae volue. A sall iproveent in engine efficiency of 3-5% is believed to increase the energy density of the odule closer or higher than existing batteries. The capacity of the icro engine generator syste to be able to operate for 3.9 hours at 1.6W output power would still ake this syste a significant alternative source of power for portable applications with a huge scope for further iproveent

5 Declaration I certify that except where due acknowledgeent has been ade, the work is that of the author alone; the work has not been subitted previously, in whole or in part, to qualify for any other acadeic award; the content of the thesis is the result of work which has been carried out since the official coenceent date of the approved research progra; and, any editorial work, paid or unpaid, carried out by a third party is acknowledged. Surendran Devadoss Date: 15 th Deceber 9

6 Acknowledgeents This thesis would not appear in its present for without the kind assistance and support of the following individuals Senior Lecturer. Dr. Thurai Vinay, for his kind support and guidance after the retireent of y previous supervisor. I acknowledge his unstinting coittent to helping e coplete the thesis with his equally generous and wise guidance. Associate professor.theo Kangsanant, for his guidance during the first two years of research providing valuable contribution to strengthen the base work for the research. Professor. Ian Bates, for his financial and oral support for the research work fro initiation to copletion. The thesis ight have been ipossible without his suppport. I still use his research ethodololgy in practical situations at work to define and identify the best possible solution to a given proble. The staffs fro Microtechnology centre in RMIT for their friendly support. I relish the tie spend with the in technical discussions which was useful for the research work. My parents, who had been patient and supportive during y studies providing oral support and cofort during difficult situations. My wife, for her understanding and support while writing the thesis, she soeties would sit with e long nights while writing the thesis coforting e with her presence.

7 Noenclature A Ac Ai A Ag a B Area in general Area of the coil Current loading Area of the Magnet Area of the Air gap No of parallel paths Magnetic flux Density Bg Air gap Flux density Optial value Bg =.5 * Kfe * Bts * Kh1 B, B r B g Residual flux density, PM and Air gap Flux density (Tesla) B l, B f Leakage flux density, fringing flux density (Tesla) b C Ci Breath in general Specific heat capacity (j/g.k or W.S/g.K) Current Density of the syste C 1,C Constants for leakage and leakage reluctance C w Coil pitch factor Coil _ Pair No of coil pairs per stator D Den Used as Diaeter and also for rotor diaeter density D e Electrostatic density (volue) Dg Do Mean diaeter of the air gap Outer Diaeter of the rotor

8 Di dc Inner Diaeter of the rotor Diaeter of the coil E e Electric field (Length) E e = V e L ED Energy density Ed Ev E e F, F f Energy density of the syste Induced voltage Electric field (V/) Electron Charge f of the agnet, f fro a agnetic source Wavefor frequency h cv Coefficient of Convection heat transfer (W/.K or W/. o C) h rd Coefficient of Radiation Heat Transfer (W/.K or W/. o C) J I I a, I Kv Ki Ke Kew Current density over a surface Current Arature Current, Current in electrical circuit Noralized Voltage Wavefor factor Noralized Current Wavefor factor Steinertz constant 1.6 typical value Winding distribution factor K h Hysteresis loss constant 1.5 typical values ρt Kd Pereance factor = Total pereance/pereance at air gap ρ g Kh Reluctance factor

9 Kp = Do / Le Ratio of gen size to Equivalent length K cd Conduction theral conductivity (W/.k or W/. o C) K cv Convection Theral Conductivity (W/K or W/ o C) K rd Radiation Theral Conductivity (W/K or W/ o C) L Le Lg L f LL Ls Lsc Lr Length, Longitudinal length for heat loss analysis Equivalent length of the generator Length of Air gap Frequency Losses Inductance of the syste Length of stator Length of stator core Length of Rotor L w, L Inductance of winding, general inductance Lr M e Lorentz nuber (W.oh/K or W.oh/ o C)- copper- (.45 e-8) Magnetization of the agnet Mass of Electron Mass of the aterial Nt Ns N Ncoil n O/P No of windings No of winding stages or layers Nuber of turns Total no of coils per phase Speed in rp Machine Output

10 PD Pout Pech Pin PL Pe Ph Ps Pw PF Pf Power density Maxiu output power Mechanical power Maxiu Power input Power losses Eddy current Losses Hysteresis losses Stray agnetic field losses Winding losses Friction losses Power factor of the syste P p Pole pitch P c Coil pitch PL Ph Power losses No of phases of the syste P cr, P co Pereance of the agnet, Pereance coefficient p Nuber of Poles Q cd Conduction heat transfer Q cv Convection heat transfer Q rd Radiation Heat transfer Q e Specific heat energy Stored (Watts or Joules/sec or Cal/sec) R Ri Electrical Resistance Inner radius of the rotor

11 Ro R Rgc Outer Radius of the rotor Reluctance of the agnet Reluctance of the whole agnetic circuit at air gap R s, R core, R, R path Reluctance -sealing, core, agnet, and agnetic circuit flux path. R cd Resistance of conduction heat transfer (K/W) R cv Resistance of Convection heat transfer (K/W or o C/W) R rd Resistance of Radiation (K/W or o C/W) Ss Sr T T Stator stages Rotor stages Teperature Tie period t t c, e Thickness of core, and winding t U Thickness of the rotor Internal Energy Stored in the syste V Volue in general ( 3 ) Vf V Root Mean Square of electron or Feri level speed of electron Linear Volue vf Vd v w Voluetric air fuel ratio Drift voltage due to the applied voltage Voltage in general Width in general

12 Greek Sybols Ψ Magnetic oent- Ψ = I. A = J. A φ, φ, φ, φ Magnetic, Air gap, Leakage and fringing flux (Weber) g l f λ w Flux Linkage 7 µ, µ r Pereability of air 4π *1, Material Pereability σ, ρ Conductivity and resistively of a conductor under consideration ω, f Angular frequency in radians/sec, Frequency in hertz I ℵ τ η Weidan s Constant Theral Conductivity Torque of the electrical achine Efficiency in general ρ e Magnetic Charge density- ρ = q e v ε e Electric perittivity λ w Flux linkage of winding υ ϖ θ e Total syste volue Angular frequency of rotation of the rotor Electrical degree θ Mechanical degrees φ w Flux linking the winding η g Efficiency of the generator η e Efficiency of the engine

13 t η s Efficiency of the syste η c Conversion efficiency fro echanical to electrical η Λ Beta factor for winding interleavance β Ratio of (Do/Di) σ Conductivity copper 5.7 e7 (1/oh.) ρ r Resistively- Copper 1.68 e-8 (oh.) ρ Density of aterial σ b Boltzann s constant (5.67 e-8 W/.K 4 or W/.C 4 ) η Density of free electrons (Atos/ 3 ) l α ε α b Mean free path length Resistive teperature coefficient Eissivity of aterial Absorptivity of the aterial

14 Abbreviations AECM - Centre for icrotechnology, RMIT, Melbourne ANSYS - Coputer application for Physical Modeling and Finite Eleent Analysis DRIE- Deep Reactive Ion Etching EMF- Electrootive force FEA- Finite Eleent Analysis FEM Finite Eleent Method Li-Lithiu LIGA- Geran word which stands for Lithography, Electroforing, and olding LPCVD Low Pressure Cheical Vapor Deposition MEMS- Micro Electro Mechanical Systes PDA- Personal Digital Assistant PD- Power Density PM Peranent Magnet RMIT- Royal Melbourne Institute of Technology UV- Ultra violet

15 Contents Abstract Acknowledgeent Noenclature Abbreviations Table of Contents List of Figures List of Tables 1. Introduction and Scope Definfition 1.1. Present and Future for Sall Scale power supplies Energy sources for portable power supplies 1.3. Hydrocarbon fuel based rotary MEMS power supplies MEMS Micro battery Power Syste Concept Micro-Generator Scope and Research Contribution Thesis Outline 9. Literature Review.1. Electrical Generator technology 11.. Electrical Generator topology 1.3. Existing Micro, MEMS otors and Generators MEMS Motors and Generator Manufacturing of MEMS Generators Micro generator developent considerations Magnetic Materials for Macro and MEMS technology.4.1. Magnetic MEMS Soft Magnetic Materials Hard Magnetic Materials Magnetic MEMS Fabrication ethods Factors Affecting Magnetic Materials Losses in Magnetic aterials 8.5. Electrical circuit Considerations Desired Characteristics of Electrical Winding Micro coils for Micro generators.6. Mechanical Considerations Bearing for Micro Applications MEMS generator analysis ethodologies Micro generator integration with icro engine Suary 36

16 3. Micro Generator Scaling and Selection 3.1. Scaling of Electrical Rotary Relationship between agnetic and electrical paraeters to power density Generator Topologies for MEMS Planar Developent Radial Flux PM Machine (RFPM) Axial Machine Magnetic Circuit Analysis Pereance coefficient Pereance Deterination Methods used for Pereance deterination Coparison of Pereance Approxiation Methods Pereance calculation for generic flux paths Force and torque calculation using co-energy density ethod Accuracy of Pereance coefficient ethod using circular & parabolic ethod Significance of Pereance coefficient with leakage calculation at icro level Electrical circuit analysis Planar Winding Analytical odelling ethod Validation of Analytical ethod MEMS Generator odel presented in thesis Suary 7 4. Modelling & Magnetic circuit analysis 4.1 Thin MEMS Micro Generator Model Methodology for icro generator developent Luped Paraeter Modelling Validation of Micro generator developent ethodology Micro generator agnetic circuit analysis FEM Analysis and Validation Suary Characterization of Micro Generator and Integrated Engine-Generator Syste 5.1. Selection of paraeters for Micro generator Effect of functional outputs to change in Beta factors Paraeters for axiu voltage, power and power density Characterisation of Micro generator Equivalent circuit odel of the icro generator Characterization of Micro generator for variable load Integration of Micro Engine-Generator Syste Energy Density of integrated Micro Engine Generator syste Suary Fabrication of MEMS icro generator

17 MEMS Micro Generator Fabrication Rotor Fabrication Stator Fabrication Suary Conclusion & Suggestions for future iproveent 17 BIBLIOGRAPHY APPENDIX A - Luped Paraeter Model APPENDIX B - Magnetic Circuit APPENDIX C Electric Circuit Analysis APPENDIX D Siulation Code

18 List of Figures Figure 1.1 Model of a icro battery power supply 5 Figure.1 (A) Radial achine topology (B) Axial achine topology (C) Transverse flux Machine topology Figure. B-H Characteristic curves Figure.3 Effect of teperature over Br and H of a selected NdFeb agnet 7 Figure.3.1 Effect of direct scaling of diensions to power density and 41 Figure.3. Figure.3.3 Figure 3.4 Power density & efficiency iproveent with linear increase in speed and current density Power density iproveent with increase in speed and current density 1 (A) Linear PD & diension relationship with J & N 1 (B) 3-D Power density & diension relationship with J & N (C) Efficiency without eddy currents considered for scaling 1 with J & N (D) Efficiency with eddy currents considered for scaling 1 with J & N Figure 3.5 Figure.3.6 Model Radial two pole Synchronous PM Micro Generator Machine (RFPM) and Cross-sectional view of RFPM under consideration (Not on Scale). (A) Load Vs Output power, copper loss and calculated input power, (B) Watts characteristics plotted as a function of arature current, (C) Efficiency and Output power as a function of load resistance, (D)Area spectru of O/P power with increase in turns, (E) Induced &Terinal voltage with Nuber of Arature Turns, (F) Power density, O/P power & Losses With Characteristics with change in turns Figure 3.7 Axial flux Thin PM Micro Generator (AFMEG) (Not on Scale). 5 Figure. 3.8 (A) Load (Ohs) Vs Output power (watts) and Efficiency (%) (B) Output power, losses and Power Density as a function of Turns (C) Output power, losses and Power Density as a function of Layers (D) Area spectru of O/P power with increase in turns and Layers (E) O/P power spectru with change in Air gap Length (F) Induced ef E & Terinal Voltage V t and Power density with change in turns. 54

19 Figure Coparison of different Micro Generators Configurations 55 Figure 3.1 Seicircular cylinder Pereance deterinations (circular) 58 Figure 3.11 Seicircular cylinder Pereance coefficient deterination (Parabolic) Figure 3.1 Seicircular cylinder Pereance coefficient deterinations 6 (Diagonal) Figure 3.13 Coparison between approxiation ethods for deterining ean 61 flux length for Pereance coefficient deterination Figure 3.14 Magnetic circuits for Pereance coefficient ethod accuracy 63 deonstration Figure 3.15 Coparison between theoretical ethod used and ANSYS results 65 (A) Force Vs Displaceent (B) Bg Vs Displaceent Figure 3.16 Coparison of force deterination ethods 66 Figure Planar winding topology A. Rectangular & B. trapezoidal 68 Figure 3.18 (A) 3d view of icro generator assebly 71 (B) Micro generator -d cross-sectional view (not on scale) Figure 4.1 Planar Micro generator cross-sectional view 75 Figure 4. (A) Superiposed view of poles and winding 75 (B) Side view of showing flux loop and induced ef direction Figure 4.3 Flow diagra of the ethodology for icro generator developent 77 Figure 4.4 (A)Generated voltage predicted by luped paraeter odel and copared with experiental & test bed result data for the reported icro generator for validation (B) Output Power predicted by luped paraeter odel and copared with Experiental & test bed result data for the reported icro generator for validation Figure 4.5 -D agnetic network for the thin MEMS icro generator (Figure 84 Figure.4.6 (A) Pereance factor to change in Rotor Radius (B) Airgap flux density fro pereance co-efficient deterination Figure.4.7 (A) Leakage pereance to change in Rotor radius and t1 for fixed t 9 (B) Fringing/airgap pereance percentage for change in Rotor Radius and t1for fixed t. Figure.4.8 Pereance at air gap G fro PM source to poles 91

20 Figure.4.9 Figure 4.1 Figure 4.11 (A) Flux density deterination using direct ethod (B) Flux density achievable using pereance factor calculation Leakage/Airgap pereance ratio with change in t1 and t for rotor radius of 1 Airgap flux density to change in t1 and t for a fixed rotor radius of Figure 4.1 Micro Generator -D Ansys odel 93 Figure 4.13 B-H curves of peranent agnet odels 94 Figure 4.14 Meshed Micro Generator odel 95 Figure 4.15 (A) -D flux lines for one half of the icro generator and the air gap path selected for PATH operation in ANSYS (B) -D flux lines for the Micro generator odel. Figure 4.16 Air gap flux density obtained using PATH operation in ANSYS 97 Figure 5.1 Do/Di ratio constants to obtain A. Maxiu voltage and B. 11 Figure 5. Nuber of coils to change in liacon rotor radius and Inter 1 Figure 5.3 Nuber of coils to change Gauge diension and Inter winding 13 Figure 5.4 Coil gauge value to width and coil area 14 Figure 5.5 Generated voltage to change in speed and liacon rotor radius 14 Figure 5.6 Generated voltage to change in Do/Di ratio and liacon rotor 15 Figure 5.7 Generated voltages to change in liacon rotor radius at a constant 16 Figure 5.8 No of coils/coil group/phase/layer vs liacon rotor radius for a fixed winding diension and coil pairs of Figure 5.9 Figure 5.1 (A) Total winding length (B) Total Coil resistance (A) Current density for a given coil profile at different rotor radius (B) Total Constant Losses for fixed profile of icro generator agnetic circuit at different rotor radius Figure 5.11 Equivalent circuit of the icro generator for characterisation 11 Figure 5.1 Characterisation of icro generator for variable load 111 Figure 5.13 Generated voltage to change in speed 111 Figure 5.14 (A) Terinal Voltage Vs Z L 11 (B) Terinal Voltage Vs Change in N rp and Z L

21 11 Figure 5.15 (A) Coil Current Vs Load Resistance (B) Coil Current Vs Change in N rp and Z L Figure 5.16 (A) Total Losses Vs Load Resistance 114 (B) Total Losses Vs Change in Speed and load resistance Figure 5.17 (A) O/P power Vs Load Resistance 114 (B) O/P power Vs Change in Speed and load resistance Figure 5.18 Efficiency Vs Load Resistance 115 Figure 6.1 MEMS Micro generator fabrication odel 1 Figure 6. Superiposed view of poles and winding 1 Figure 6.3 Magnetization characteristics of Iron 11 Figure 6.4 Saturation agnetization VS Theral expansion coefficient of 13 Figure 6.5 SEM photograph showing top layer of a stator coil prior to deposition of the protective SU8 layer[5] 16

22 Tables Table 1.1 Specific energy available in Hydrocarbon fuels 4 Table.1 Suary of MEMS rotational and linear icro otors 16 Table. Suary of MEMS rotational and linear icro Generators 17 Table.3 Soft agnetic aterials Table.4 Hard agnetic aterials 3 Table. 5 Coparison of hard agnetic aterial properties 4 Table.6 Skin depth of agnetic aterials at 1 Hz 8 Table 3.1 Micro generator paraeter relationship to icro generator specifications 47 Table 3. A. Ansys results for flux flow, flux density and force 65 Table 3.3 Paraeter deterination for planar winding using theoretical odeling 69 Table D pereance deterination for the icro generator odel 87 Table 5.1 Paraeters Selected for MEMS icro generator 19 Table 6.1 Properties of soft agnetic aterials 1 Table 6. Properties of selected hard agnetic source 15

23 Chapter.1 Introduction Chapter1: Introduction and Scope Definition Micro achining technology and Microelectroechanical systes (MEMS) have seen a steep growth in the past two decades. This growth has led to anufacturing of iniature devices and circuits to iprove their portability. However, the benefits of the reduction in size of MEMS and icro devices have not been fully exploited due to the relatively large size of power supplies used to power these devices. The power supplies, coonly electrocheical batteries, have seen very little iproveent in energy density and reduction in size and had failed to keep up with the shrinking size of electronic devices. This lead to a need for iproveent in electrocheical batteries as power sources, and an opportunity for the developent of suitable alternative power sources as an alternative to electrocheical batteries. 1.1 Present and Future for Sall scale power supplies Priary Lithiu Ion battery is coonly used as a power source for consuer electronics industry. The batteries for this application are selected to supply power for up to 3 to 4 hours of continuous operation. The battery weight for a Dell inspiron 51 at.8 Kg is close to 1.3Kg with the battery contributing to one third of the laptop weight [1]. Motorola c sli phone with a total ass of 84 gras has a Lithiu-Ion battery weighing 15 gras contributing to close to one fourth of the handset weight[]. Power supplies for ilitary applications are required to be light for soldiers to carry and to possess large stored energy to last long in battle fields. Batteries are proven bulkier for this application. For exaple, a soldier under 7 hour ission requiring an average power of Watts currently needs 1 to 13 Kg of rechargeable battery or 9 kg of non-rechargeable battery[3-5]. 1

24 Chapter.1 Introduction Power supplies with generation capacity in ill watts and watts range has applications in electronic devices (like Wristwatches, PDA s etc), icro-echatronics and echanical systes (robots, airplanes, etc.). Power generation at icro watt has applications in icro-electronic devices to power sensors (Bio & Cheical), actuators, drug delivery, industrial robots etc[6-8]. The full potential of the above entioned icro and acro applications can be achieved with a power supply which has 1 High energy density than batteries to provide long operating hours and power requireents.. Low density (ass/ volue) to reduce the ass of the syste and iprove portability. This will also help in power supplies keeping up with the shrinking size of electronics in odern icro and acro portable applications. 1. Energy Sources for portable power supplies. Radioactive fuels has the highest stored energy available (4.17e8 W-hr/L typically for uraniu) with hydrocarbon fuels following the (9.7e3W-hr/L typically for butane). Radioactive fuels are hazardous, less environentally friendly and difficult to handle which akes the unsuitable for power supplies at icro and acro level. The popular choice of energy storage ethods used for power supplies for the past three decades is electrocheical batteries which provide siple direct conversion to electrical energy. Lithiu- Thionyl chloride (3 Wh/Kg and 7 Wh/L )[5] and zinc air (5 Wh/Kg and 1 Wh/L) have the highest practical specific energy aong priary batteries, Lithiu-ion ( Wh/Kg and 3 Wh/L)[5] secondary batteries having the highest energy density in secondary batteries. The theoretical energy density of Lithiu-Thionyl chloride is 1489 Wh/Kg[5] which is alost 5 ties ore than the practical Lithiu-Thionyl chloride battery and the case is siilar with other batteries. This shows that there is a huge difference between what is theoretically possible fro batteries and what is available in practice.

25 Chapter.1 Introduction Batteries have energy density one order less than that of hydrocarbon fuels and uch less than radioactive fuels. Apart fro its low energy density, batteries have any other disadvantages which hinder their application versatility for odern portable applications. Their power transfer capability is reduced by internal resistance, energy loss due to leakage, cheical erosion and ageing. They are environentally hazardous and difficult to dispose; the voltage reduces as the stored energy is consued; life cycle and discharge affected by teperature [9]. Due to the disadvantages listed above, research inclination in recent years had gone towards power supply technologies using hydrocarbon fuels and energy scavenging for alternative power supplies[1-1]. Fuel cells are an alternative source of portable power supply which uses hydrogen fuel to produce electricity using siple cobustion reaction process. The popular fuel cells at present are Direct ethanol fuel cell (DMFC), Proton Exchange ebrane fuel cell (PEMFC), and Solid oxide fuel cell (SOFC)[5]. The energy density of odern icro PEMFC, DMFC and SOFC fuel cells is close to 5-1 Wh/Kg with an operating efficiencies ranging -6% [5]. Fuel cells suffer fro any issues like water anageent and leakage of unreacted fuel across ebrane, catalyst with good tolerance to ipurities, storage and handling of hydrogen which hinder their developent at icro scale. Energy scavenging looks at generating electricity fro naturally occurring phenoena and has been explored by various research labs around the world for alternative source of power to batteries. Various power sources have been developed fro different energy sources like radio frequency, abient light, theroelectric, hand generators and heel strikes [13]. The power capacity of such devices was in the range of icro watts to illi watts and can supply liited icro applications. The low power capacity and usability constraint akes their application narrow and not universally suitable. 3

26 Chapter.1 Introduction Hydrocarbon fuel based power supplies have been seen with increased interest aong the research counity around the world to look for a ethod to convert the cheical energy available in hydrocarbon fuels to useful electrical energy. Hydrocarbon fuel based rotary MEMS power supplies falls under this scope with a high potential for a high energy density power supply for icro applications. 1.3 Hydrocarbon fuel based rotary MEMS power supplies The specific energy of hydrocarbon fuels, for exaple pure hydrogen, is 33.3e3 Wh/kg (Table 1.1) is 1 ties ore than what is available fro the highest energy density Lithiu -Thionyl chloride priary battery (3 Wh/kg) and 165 ties ore than Li/organosulfide secondary battery ( Wh/Kg). A syste which can convert the cheical energy in fuels to electrical energy with even 5-1% efficiency would provide two to three tie higher energy densities than existing battery power supplies. Hydrocarbon Fuels Specific energy (Wh/Kg) Hydrogen 33.3e3 Propane 1.9e3 Butane 1.7e3 Diesel 11.9e3 Gasoline 1.4e3 Methanol 5.5e3 Ethanol 7.5e3 Table 1.1 Specific energy available in Hydrocarbon fuels Hydrocarbon fuel based rotary MEMS power supplies evolve with generation of electricity by converting cheical energy available in fuels to echanical energy either transitional or rotational energy as in engines or turbines. The echanical energy is then converted to electrical energy using generators coupled with the echanical drives. Recent research efforts have reported on the developent of these power systes using icro generators driven by icro turbines and engines [6, 14-19]. Typically, the icro generator systes driven by icro engines generate an open circuit voltage of.6 volts and 375 µwatts power [14]. The syste energy density was ~6 Wh/Kg with engine efficiency of <1% and generator efficiency of -3%. This energy density was lower 4

27 Chapter.1 Introduction than what was available in current batteries. This was due to issues in theral, fluid and cobustion anageent on the engine developent and issues with electroechanical conversion icro generator developent [6, 14, 16, 19]. Ongoing research efforts has been taken by several research institutes to iprove on the developent of icro engines[6, 13, 19] with little or no research efforts undertaken to iprove icro generators integrated to echanical drives. The thesis presented looks at iproveents in icro generator developent to be integrated with icro engines. Specific contribution is provided to theoretical and analytical ethodologies for icro generator developent. 1.4 MEMS Micro battery Power Syste Concept MEMS icro battery syste uses hydrocarbon fuels and power MEMS technology to generate electrical energy for power supplies. A scheatic showing the key coponents of such a syste being researched at AECM icro technology centre in RMIT is shown in Figure 1.1. The energy density of the syste can be written as v fuel E. D = η s * E. D fuel * (1.1) v syste Where η = η * η * η and s engine generator syste = vengine _ Generator accessories v + v + v fuel accessories 5 ENGINE-GENERATOR (H o and Co Exhaust and air intake logics ebedded) O/P Controller & Energy anageent FUEL TANK (Included with ethods to avoid gravitational orientation for fluid hauling) 7 4 Figure 1.1. Model of a icro battery power supply 5

28 Chapter.1 Introduction The IC engine in this case is a icro fabricated rotary engine of katrix type[]. The advantage of rotary engines is its planar orientation and fewer oving parts aking it easier to fabricate, asseble and package. Reported odels are available for siilar icro fabricated wankel engine fabricated using Deep Reactive Ion Etching (DRIE) and UV lithography ethods [6, 13, 18, 1] establishing the possibility of batch anufacturing such systes. The generator unit is integrated with the engine structure to reduce volue of the syste and to iprove the energy density. All or ost of the research contribution presented in the thesis is within the scope of such a icro generator developent. Fuel anageent for preset air-fuel ixture to engine chaber for better cobustion is achieved by delivering fuels through icro channels and using the engine waste heat to preheat the fuels []. Signal processing and conditioning circuit is a requireent to iprove the quality and reliability of power generated by these power supplies. The centre had planned to use existing conditioning technologies available for presented syste [-5]. Assebly and packaging were done to provide theral sealing and robustness to the syste using currently available ethods [6, 13, 14, 18]. Theral insulation using aerogel aterial with low theral conductivity is used to therally seal and aintain low teperature at generator end achieving efficient generator operation protecting agnetic and electrical coponents Micro-Generator Micro-generator in liquid battery power supplies is used to generate useful electrical energy and in aintaining the power density and energy density of the power supply. Micro generators can either be coupled to rotary engines as an independent entity or be integrated to engine unit by ebedding agnetic and electric circuit into engine physical structure. The later has advantages of reduction in volue of engine generator unit. This reduction in volue would increase the power density of the 6

29 Chapter.1 Introduction engine-generator syste. This ethod of integration would also iprove energy density of the power supply when attached with fuel tank and other accessories. The reported cases of icro generators coupled to engines for power generation has a volue of 1.1*.8*.5c operating at shaft speed of 13,3 rp producing an open circuit voltage of.63 volts and 375 icrowatt with syste energy density of 6 W-h/Kg [3]. The energy density of current engine-generator systes is 5 ties less than batteries. This reduction is attributed to both engine and generator shortcoings. The generator factors were generator having a large volue for windings(coiled structures) and agnetic circuit with large cores, hoopolar agnetic circuit[8], high agnetic leakage, analysis ethods to select suitable agnetic circuit and electric circuit paraeters[4] etc. These factors had reduced the icro generator perforance than theoretically expected[14]. The research contribution looks at providing novel solutions in the area of icro generator developent and analysis ethodology. 1.5 Scope and Research Contribution The dissertation focuses on an analytical ethodology for the developent of high power density icro generators to be integrated with icro internal cobustion engines such as the Katrix engine [19]. The original contributions ade in the dissertation are: Developent of a pereance factor analytical ethod for agnetic circuit analysis and deterination of airgap flux density forces and torques. This ethod provides a sipler and quicker alternative to FEA analysis of agnetic circuit analysis. The ethod is validated by coparing the results of -D FEA analysis and found to achieve 9-98% accuracy to FEA results. Developent of a odified luped paraeter using generalized equations cobining both agnetic and electric circuit analyses ethods. The agnetic circuit analysis is done using a pereance coefficient ethod to iprove 7

30 Chapter.1 Introduction accuracy in the deterination of air gap flux density. An original analytical ethod to obtain winding paraeters is developed. The above ethods are cobined with the luped paraeter analysis ethod to select best suitable winding paraeters for better power density. Synthesis of a novel sandwiched MEMS planar icro generator design with better agnetic and electric circuit topology for sipler anufacturing and attain better energy density. The odel fro synthesis is found to achieve seven ties greater energy than existing icro generators of siilar type. Characterisation of the icro generator is done for no load, fixed and variable load to deterine the useful output power and axiu efficiency attainable fro the icro generator. Developent of anufacturing process to fabricate and asseble individual coponents of the icro generators. 1.6 Thesis Outline Chapter gives an overview of the state of the art in MEMS icro otors and generators with key ephasis on available MEMS generators. Manufacturing of Micro generator and issues relating to anufacturing and integration with icro engines are discussed. Micro generator scaling and paraetric analysis ethodologies to select optial paraeters for icro generator developent to attain high power density are discussed. This will for as the rationale for the choice of luped paraeter odelling for icro generator developent reported in the thesis. Chapter 3 discusses the scaling strategies for icro generator to achieve axiu power density in generators at icro scale. Analysis of radial, axial achine, reluctance achines for the selection of suitable icro generator topology is perfored. Pereance co-efficient or pereance factor ethod for agnetic circuit analysis used in the thesis is briefed.three different ethods of calculating air gap, leakage and 8

31 Chapter.1 Introduction fringing pereance for two diensional structures are developed and validated with ANSYS FEM results. A theoretical analysis ethod is developed to calculate planar coil paraeters is developed and validated. Finally, the icro generator developed in the research is introduced and the advantage of the odel to existing technology is explained. Chapter 4 is dedicated to the ethodology for developent of the thin MEMS axial generator odel for integration with a icro engine. The ethodology uses a odified luped paraeter odel. The odel takes independent inputs fro agnetic circuit analysis and electric circuit analysis at icro scale fro chapter 3 to iprove the accuracy of the analytical developent. The developed ethodology is validated by applying it on a reported odel available in literature to deterine voltage, power and winding paraeters. The results fro the analysis are copared with practical and theoretical results obtained for the literature odel. FEM analysis is done to validate agnetic circuit analysis results obtained fro theoretical analysis. Results show that the theoretical ethod for air gap flux density prediction is 93% accurate to FEA results fro ANSYS 11. Chapter 5 deals with the selection of icro generator paraeters fro the ethodology developed in chapter 4. Equivalent odel of the icro generator is developed by deterining the equivalent resistance and reactance for characterisation. Characterisation of the MEMS icro generator with the selected paraeters is perfored for icro generator operation at no load, fixed and variable load conditions. Theoretical odelling of the engine functional paraeters is cobined with the icrogenerator paraeter odel to for an integrated icro engine-generator theoretical odel. This odel is then analysed for achievable energy density for a given volue (4e-3*7e-3*5e-3) of engine-generator package. 9

32 Chapter.1 Introduction Chapter 6 deals with the anufacturing feasibility of the icro generator coponents using existing fabrication technologies and the issues that need to be addressed while anufacturing. The choice of aterials for the anufacturing of the icro generator fro existing technologies is reviewed. Manufacturing process for individual coponents and assebly of the package using existing fabrication technologies is also briefed in this chapter. Chapter 7 suarises key conclusions ade fro the research and discusses recoendations for future work and areas of iproveent. 1

33 Chapter. Literature Review Chapter : Literature review This chapter provides an overview of electrical achine technology and generator topologies for MEMS icro generators. An overview of the state of the art in MEMS icro otors and generators are provided with key ephasis on available MEMS generators. Manufacturing of the icro generator and issues relating to anufacturing and integration with icro engines are discussed and considered for the developent of the icro generator presented in the later chapters. Micro generator scaling and paraetric analysis ethodologies to select ideal paraeters for icro generator developent to attain high power density are discussed. This fors the rationale for the choice of luped paraeter odelling for icro generator developent reported in the thesis..1 Electrical Generator Technology The different technologies in the operation of electrical achines for electrical power generation can be explained with the well known Faraday s laws of electroagnetic and agnetic flux equations given by.1. To induce voltage or EMF a change in flux linkage is essential and this change in flux linkage can be achieved by varying MMF or reluctance in the achine. Thus the technologies in electrical achines were naed after their ethod of achieving change in agnetic flux linkage as synchronous, induction, reluctance and peranent agnet (PM) generators. dφ e = -n Where dt F φ = (.1) R Different fors of electrical generator technology include synchronous generators; Induction generators, Reluctance achines and Peranent agnet generators and otors. Peranent agnet achine delivers high power density, torque 11

34 Chapter. Literature Review density and efficiency than other types because of higher induction achieved by the PM s and less variable losses due to exclusion of field windings [1, ].. Electrical Generator Topologies The electrical generator topologies were naed based on the direction in which the flux flows to link the windings to generate EMF or voltage in the achine. Radial achines are of synchronous, induction, reluctance or peranent agnet. Flux in these achines flows radially through the air gap perpendicular to the axis of rotation fro stator to rotor or vice versa to induce ef in the generator as show in Figure.1.A. Flux in axial achines flows in axial direction through the air gap and noral to the axis to induce voltage. The axial achines norally have peranent agnets ebedded in disc shaped rotors and windings in stator for convenience. The fact that stator and rotor are not concentric inside each other, the axial achines have greater variability and flexibility in topology and inclusion of ultiple rotor and stator cobinations as typically shown in Figure.1.B. Flux in the transverse flux achines flow radially though the airgap and axially throughout the circuference for power generation. In depth incite on all the achines can be obtained fro reading into references [3-7]. Stator winding Stator core arrangeent Winding Peranent Magnet Rotor with agnetic core Current direction Flux N in rp Rotor (A) (B) (C) Figure.1 A. Radial achine topology B. Axial achine topology C. Transverse flux Machine topology 1

35 .3 Existing Micro, MEMS otors and Generators Chapter. Literature Review Recent advanceent in the field of icro achining and MEMS anufacturing technologies have led the way to the advent of any icro, MEMS and hybrid achines (both generator and otors) with power levels in the range of upto hundred of watts. Many of the icro achines use peranent agnets as the ain source for field excitation to achieve better power density..3.1 MEMS Motors and Generator MEMS otors and generators have been under research fro the early 198 s with the first report of such achines in 1988 (Table.). The report described an IC processed Electrostatic Synchronous icro otor developed by U.C.Berkeley operating at a speed of 5 rp. Since then, the field of icro fabrication and icroachining had long iproved with the advent of new techniques and ethods to process and realise both low and high aspect echanical structures for icroelectroechanical systes. A list of MEMS otors is available in Table.. The first MEMS otors reported were processed by the sae ethod used for processing integrated circuits (IC) fro where the anufacturing technologies had grown with interediate passing techniques to recent popular techniques used for anufacturing like DRIE (Direct Reactive Ion Etching), LIGA and LPCVD. There are very few coercial MEMS otors available and they work under piezoelectric and Ultrasonic principles and developed by Flex Motors Corporation with proising PD in the range of.e5 to 6.6e5 W/3. The reported research odels listed in Table. vary in topology fro radial synchronous, radial and axial induction, reluctance and BLDC s with a 6 phase axial induction icro otor developed by MIT, USA-6 containing 131 pole pairs in stator and a tethered rotor giving a higher PD of 5.9e6 W/3. 13

36 Chapter. Literature Review A list of MEMS icro generators are available in Table.3. The advent of icro generator developent started alost a decade later to icro otors because of the need for better energy density power supplies to conventional batteries for portable and icro electronic devices. Early reports on developent of such generator coe fro Faculty of Engineering, Chiba, Japan [8] where a axial generator odel is developed as a power source for iplanted edical devices to replace batteries. The generator operated with etal agnets excited by coils carrying low frequency excitation currents producing an output power of 14 Watts at 1 rp with an open circuit voltage of ~1 volts. There has been a handful of icro generators developed since the first reported odel with ajor contribution fro research institutes in USA. The key developent objective of icro generators is only as an integrating or coupled unit to icro turbines, icro engines and other rotary transducers. The priary source for the rotary transducers is hydrocarbon fuel cheical energy or other high energy density sources to be converted to kinetic energy on the shaft which is coupled or integrated with the icro generator [9, 1-13]. The icro generators developent concentrated ore towards eeting operational specifications and objectives than achieving high power density. Due to this reason, PD of MEMS Generators has seen lesser iproveent over years. MEMS generators reported in Table.3 are of synchronous, reluctance, induction and peranent agnet which are ainly of radial and axial topologies with differences in topologies coing fro the stator and rotor arrangeents to achieve a high PD [9-17]. Peranent agnet axial topologies fro Table.3 can be seen to provide better PD than radial and reluctance topologies with reluctance topologies reported exhibiting low PD due to less achievable agnetic flux density at air gap due to lack of back iron, big cores and high reluctance path for flux flow [1]. 14

37 Chapter. Literature Review It can inferred fro Table. that otors using peranent agnets as the source for ain field exhibit a higher PD than otors with less or non use of peranent agnets. Topologies with planar profiles indicating iproved PD and anufacturing flexibility and ease. High PD s are associated with high speeds in coparison to syste total volue which can be a valid consideration for developent of MEMS generators. Soe of the iproveents suggested by the literature [9, 1] was the need for better agnetic circuits and analysis ethods to select better agnetic circuit and icro generator paraeters to achieve high PD. 15

38 Manufacturers and Reported Years Technology & Topology Max Speed (rp) Power (W) Diaeter () Thickness () Voluetric Power density (W/3) Manufacturing ethod Flex otors[] Piezoelectric E+5 - Flex Motors[] Ultrasonic E+5 - University of California, Berkeley, USA- 1988[1] Ic processed Electrostatic icro otorsynchronous E-3 Wet and RIE etching IMT, Berlin 1993 [] Georgia tech, USA [3] University of wisconsin, USA [4] U.C.Berkeley, USA 1995 [9] MIT, USA-1 [1] Braunschweig, gerany- 3 [1] Korea Electronics Technology Institute (KETI), Korea-4 [11] MIT, USA- 5 [9] National Taiwan University Taiwan- 6 Purdue University, USA- 7 [3] Dielectric Induction Microotor E E-3 8.E+3 LPCVD sacrificial process Reluctance Magnetic Microotor E E+3 Variable Reluctance Stepper Motor 3 LPCVD sacrificial process and cavity etching 1.44(No losses assued) E+1 Sacrificial LIGA process Electrostatic Micro Motor 3pN. 1.5E-3 Electrostatic Induction Micro Motor E+5 Linear Variable Reluctance Micro Motor _ 1.11N(Torque) Area = 8*7 1.5 _ UV Lithography 1. Thin and thick fil processing. DRIE Etching 3. Fusion Bonding Micro BLDC Motor E+4 Micro Milling and LIGA technology Induction Micro Motor ~ E+6 LPCVD pattering anf DRIE Micro Peranent Magnet Motor E+6 - Hoopolar Micro otor 1 5.E E+1 DRIE Table.1. Suary of MEMS rotational and linear icro otors 16

39 Manufacturers and Reported years Technology & Topology Max Speed (rp) Power (W) O/p Voltage-No load (V) Diaeter () Chapter. Literature Review Voluetric Power Thickness density () (W/3) Faculty of Engineering, chiba, Japan-1999 [11] Axial Peranent agnet generator ~1 14 ~1 _ Katholieke Universiteit Leuven, Belgiu- 4 [1] Radial E+6 UC Berkeley, USA-4 [9] Reluctance Generator E E+4 Iperial college, UK 5 [1] Planar Axial Generator E+4 LEG, France-5 [13] Planar Micro generator E+8 Eth Zurich/ ATE leutkirch, Gerany -5 [14] Radial, 3-phase E+7 Georgia Tech/MIT, USA-6 [37] Axial Peranent agnet generator E+6 Georgia Tech/MIT, USA-6 [38] Axial Peranent agnet generator E+6 Georgia Tech, FRANCE 7 [39] Axial Peranent agnet generator E+5 national sun yat sen- 7 [18] Peranent agnet 4.1E E+4 Kinetron MG4 Coercial [41] Radial E+5 Table.. Suary of MEMS rotational and linear icro Generators 17

40 .3. Manufacturing of MEMS Generators The advanceent in MEMS anufacturing technology to develop high aspect ratio structures, bulk icro achining and bonding has ade developent of electrical and echanical structures and integration possible. Most of the reported literature uses DRIE, surface icro achining, UV lithography and bonding techniques to realise structures for anufacturing and packaging. The first reported generator syste was that of a planar icro turbine syste by Wiegele in 1996 [19]. The icro turbine was of 3.5 in diaeter capable of operating at 4.5 Krp and fabricated using LIGA ethod. Hoes et al [1] at iperial college, London reported an axial flow icro turbine generator syste. The fabricateion was done using a cobination of silicon icroachining. The generator rotor which was developed on SU-8 and laser etched to ebedded illietre sized NdfeB PMs. The rotor was then sandwiched with two stators with electroplated CU using PCB techniques. Kinetron a dutch copany anufactures claw pole style icro generators with SCo or Ferrite PM rotors and Cu ulti-turned windings [41]. Achotee et al [48,49] reported a planar icro otor for use as a generator by integration with icro turbine. A 8- solid SCo or NdFeb was achined using icro EDM process to be used as stator with CU winding anufactured using electroplating technique. D.P.Arnold et.al [37-38] fro Georgia tech reported a planar icro generator using an electroplated surface winding on a soft agnetic substrate. The rotor was ade of an annular PM with back iron to iprove agnetic field on the air gap. An axial flux PM achine was reported by Pan et al [18] which use layers of windings ade of filaent winding ethod to create stacked Cu winding for stator and an arc shaped NdfeB agnet for rotor. The icro generator odel which is appropriate for the current research was by Senesky et al [9] fro university of Berkley. They developed an reluctance type 18

41 Chapter. Literature Review illietre scale generator to be integrated with icro engines with uses a PM core. The stator poles were ade of powdered iron aterial fored using electrical discharge technique (EDM). The windings were wound on a plastic bobbin and enclosed to a centre post ade of steel and epoxy for better theral insulation. The peranent agnets were achined fro bonded NdFeb and connected to the yoke with a variable fixture arrangeent to adjust sensitivity of the agnetic circuit to saturation effects. The above literature substantiates the developent of icro generator using existing anufacturing ethods with a cobination of DRIE, Photolithography, electroplating techniques etc. Even with such variability in anufacturing and aterial choices there were any liitations and anufacturing difficulties in anufacturing icro generators. The key difficulties in anufacturing were in the areas of bulk structures with good precision with the required echanical, electrical and agnetic properties [46]. Ongoing research is underway by any research facilities around the world to iprove anufacturing ethods and aterials for icro generator developent..3.3 Micro generator developent considerations In general in icro generator developent, the generated power can be increased by either increasing the nuber of poles, or by increasing the speed, and by increasing the resistance and nuber of windings to liit heat losses in the winding. Achieving all or any of the three ebedded in a icro generator developent has anufacturing liitations associated with it. This section ais at looking at icro generator developent considerations for aterials, fabrication ethods and liitations for echanical structures, agnetic MEMS, electrical circuit. 19

42 Chapter. Literature Review.3.4 Magnetic Materials for Macro and MEMS technology The recent advanceent in electrical achine technologies has offered any choices in aterials with variable agnetic properties for electrical achines developent to iprove PD and to suit anufacturing technologies. Materials with agnetic properties take their place in one of the three general classes used to define the naed as Ferroagnetic, Paraagnetic and Diaagnetic aterials. The classes are defined on the basis of pereability value of aterials, which represents the alignent of dipole oents to better relate agnetic field to flux density for a aterial as in equation.. B = µh, With µ = µ. µ r & 7 µ = 4π * (.) 1 B-H curves or hysteresis loop are characteristic curves based on equation. to deterine the pereability of the aterial at different operating conditions. The size and shape of the B-H curved differ with different aterials and used as a basis to select a particular agnetic aterial for a desired application. The difference in B-H curves for different aterials are in their saturation and hysteresis features due to alignents of dipole oents which for the agnetic doain structure for the aterial. nd Quadrant B 1 st Quadrant +Hc -Hc H Characteristic curves 3rd Quadrant -M 4th Quadrant Figure. B-H Characteristic curves

43 .3.5 Magnetic MEMS. Chapter. Literature Review The choice of agnetic aterials in MEMS depends on the anufacturing capability of agnetic structures to achieve bulk anufacturing, required precision and agnetic B-H characteristics achievable fro theory. In a ulti-pole agnetic rotor, N-S pole transition regions or oxidized zones which do not contribute to power generation can be tens to hundreds of icrons per pole. The extent of these unproductive regions is sall when copared to the perieter of a c-scale or larger rotor, but is a significant portion for a illieter scale achines[17]. The usage of agnetic aterials used in MEMS applications is quite liited due to the above reason. The field is still under investigation by research groups around the world for iproved aterials and anufacturing ethods to achieve better agnetic aterials and echanical properties for MEMS anufacturing..3.6 Soft Magnetic Materials Soft agnetic aterials are ferroagnetic aterials with narrow B-H characteristic exhibiting low pereability values and saturation liits. Most electrical achines work with flux passing through an air gap and soft agnetic aterials are generally used as cores to regulate and achieve axiu flux flow in a desired path within the achine. The selection of soft agnetic aterials for a particular application is dependent on their pereability values and iportantly their saturation liit as poised to achine developent. The properties of soft agnetic aterials with their pereability and Bs values are listed in Table.3 with ferrous and silicon steel having better pereability and Br values and diversely used in icro electrical achines applications. 1

44 Chapter. Literature Review Saturation Flux density Materials Pereability (Bs) Ferrous (Fe) 6.*[53] Cobalt (Co) *[53] Nickel 5.6[53] NI Peralloy (81% Ni,% Mo,17% Fe) 14 to 35.7* [54] Si Steel 58.4 [55] cobalt(5%)- iron(5%) alloy [53] Aluiniu(16%)- Iron Alloy 8.9 [53] * Values approxiated to one decial Table.3 Soft agnetic aterials Soft agnetic aterial is the ost coonly used agnetic aterial in MEMS with alloys like NiFe (Peralloy). They have relatively high saturation flux density, low hysteresis and less ipact on agnetic perforance fro stress effects. This aterial is often used in agnetic recording heads with their anufacturing technology well established fro industrial use [46]. Micro agnetic actuators use electro deposited ferroagnetic NiFe cores wrapped around with current carrying conductors to generate the field required for actuation [46]. Advanced icro otors use ferroagnetic aterials with on-chip coils with assebled windings [57]. There was recent reported case of 5:5 NiFe alloy electrodeposited into deep silicon olds for vertically lainated NiFe structures [58]. Nickel-iron-olybdenu (NiFeMo) alloy was also reported as an alternative to NiFe and addition of olybdenu to NiFe iproves both resistivity and initial pereability and allows for high heat treatent [6]. The alloy can be deposited using electroplating, gas flow sputtering [6] and can achieve a saturation flux density as high as 1.7 T [61]. There were also coercially available agneto eters which use agnetoresitive eleents which were thin fil low noise NiFe alloys to detect agnetic field as low as.16 A/ [46]. TbFe alloys and TbFe /Feco ultilayer were used in

45 Chapter. Literature Review icro actuator configurations using cantilevers with ebranes coated with these alloys on one side. Literature was also available on Alloys of CoFeb,CoFeCr,CoFeb,CoFeCu and CoNiFeb which were widely used in agnetic recording and data storage technologies [6]..3.7 Hard Magnetic Materials Hard agnetic aterials or peranent agnets (PM) are agnetic aterials which exhibit wider B-H characteristics with a capability of holding reenance agnetic field with the peranent reoval of external field and operate at second and third quadrant deagnetising path. The iportant paraeters are their residual agnetic capacity Br and coercive force required to deagnetize the agnet Hc. Other paraeters of interest which represent the available field quantities are B, H and BH ax. Table.3 shows the properties of popular used peranent agnetic aterials in electrical technology listing key paraetric quantities Br, Hc, B, BHax and curie teperature with Table.4 suarizes their suitability s to application criteria. Materials Br (t) Hc (KA/) Bhax (kj/3) Curie tep C Alnico5, ceraic 1 [54] Alnico, Sintered 5 [54] Alnicio Cast 5 [54] SCo5 [54] SCo17 [54] SCo17 Bonded [54] NdFeb MQ III [54] Ferrite Bonded Flexible [54] Ferrite Bonded Rigid[54] Materials Alnico Flux Density Table.4 BH product Hard agnetic aterials Theral stability Cost Mechanical stability low (Brittle) corrosion resistance High Low High Mediu Bonded Ferrites Low Low High Mediu Flexible Low Saariu Mediu High High Very Brittle High Mediu 3

46 cobalt NdFeb High High Low Table. 5 Chapter. Literature Review High Lesser to SCo Flexible High Coparison of hard agnetic aterial properties Most of the hard agnetic aterials were based on alloys of cobalt (Co) because of its high crystalline anisotropic structure. Co-based alloys with various other alloys were available in the literature [46]. The issue with eleents alloyed with Co tend to concentrate at the grain boundaries resulting in isolated grain boundaries. This causes icroscopic energy barriers that increase the coercivity of the fil aking the aterial agnetically harder. There were also reported cases of Pt and Pb alloying which increases agnetic crystalline anisotropy [6]. In the case of alloy depositions the net agnetization reduces with increase in non-agnetic alloy eleents [46]. There were reports of CoPt and FePt alloys deposited using vaccu processes in ultilayered structures and then annealed to produce ordered phases [63] [64]. Sputtering FePt was reported with coercivity and energy product of 637 ka/ and 16 Kj/3.Electroplated CoPtW and CoPtZn having coercivity of about 3Ka/ [65]. A ajor disadvantage of these applications was the requireent for high teperature annealing at around 5 C to 7 C and soe of the aterials coonly used in MEMS cannot survive at these teperatures. Strontiu ferrite (SrFe 1 O 19 ) deposition by ixing Fe1O19 powder with an epoxy resin binding agent was available in the literature. The later was spread into photo resist oulds to for coplete cylindrical structures. Structures which were 65 µ thick with a diaeter of 5 to µ showed coercivity of 356 ka/ and axiu energy product of.7 KJ/ 3 [66] Neodyiu-Iron Boron (NdFeB) is one of the popular aterial of choice for applications which are very cost effective without any rare eleents such as cobalt. Reported cases of NdFeB agnetic structure include relatively thick agnetic fils 4

47 Chapter. Literature Review upto 8 µ fored using tape casting. Thin fils of NdFeB and CoS can be vacuu deposited and in any cases the deposited fils were aorphous and had soft agnetic properties (Hc<1Oe). To enhance coercivity high teperature annealing (>6 o c) was required which was daaging for soe MEMS aterial [63, 64]. Saariu Cobalt (SCo) peranent agnet deposition was reported which requires annealing at high teperature of (>5 o c) which akes it difficult to incorporate into soe structures [6]. Fil structures of 5 µ on ceraic glass substrates and 3 µ for silicon (due to annealing liitation) were reported with achievable coercivity of 8 ka/, flux density and energy product of.5t and kj/3 respectively [68]. In cases where the peranent agnet aterial was susceptible for corrosion during anufacturing process, it was often coated with a layer of protective aterial [46]. Due to the anufacturing difficulties and high annealing teperatures associated with soe of the hard agnetic aterials, the applications of hard agnetic aterials in MEMS anufacturing were liited. Where ever necessary, especially with high aspect ratio MEMS structures coercially available hard agnetic aterials were used and bonded to substrates and other structures using bonding and assebly techniques as reported in the literature [9-14]. This technique was basically advantageous to preserve and exploit the agnetic characteristics of the peranent agnet as a source for agnetic energy..3.8 Magnetic MEMS Fabrication ethods There were different fabrication techniques available in the literature for icro achining agnetic structure [56]. Electro deposition is one of the popular ethods where the electroplating aterial (anode) is deposited on a aterial to be coated (cathode) iersed into an electrolytic bath. Electric current helps carry ions fro 5

48 Chapter. Literature Review anode to cathode creating a conforal coating. Sputtering is another ethod which is used to deposit etal fils. The deposition essentially is done by firing of ions at the target ade fro the deposition aterial. Particles deposited were then guided towards the wafer by electric or agnetic fields. Sputtering is conforal and can be done at relatively low teperatures. A drawback of such a ethod was the stress associated with the deposited fils and their control [56]. Evaporation is a thin- fil deposition ethod technique where a target is heated with an electrical current or electron bea to condense vaporized target aterial on the wafer. This process when the rotor is not rotated properly can result in shadowing effect. LIGA is ultistep process which cobines lithography, plating and olding to for high-aspect ratio etal structures. This process uses X-ray lithography which akes it expensive. There were other ethods used such as screen printing in ters of anufacturing planar coils for electric circuit design [56]. Soe of the anufacturing ethods which were used for the preparation of hard agnetic aterials were sintering, pressure bonding, injection olding, casting, extruding, electrodepositing, and sputtering and LPCVD technologies [56]. Detailed inforation on the fabrication ethods entioned in this section and ore is available in the literature for further reading [56]..3.9 Factors Affecting Magnetic Materials The axiu useful energy obtainable fro a agnetic aterial is affected by operational factors and surrounding circuits with the iportant ones influencing the energy delivered by the agnet to be teperature, skin effect and oderately corrosion. A. Teperature All agnetic aterials especially hard agnetic have a liit on axiu operating teperature given by axiu operating teperature and Currie 6

49 Chapter. Literature Review teperature. A list of Currie teperature liits for peranent agnet aterials is listed in Table.5. NdFeb is ost sensitive to teperature having the lowest Currie teperature of 31 o C and Alnico possessing good teperature withstanding capacity with a Currie teperature of 9 o C. Figure.3 shows that the effect of teperature on agnetic intensity and flux density, with agnetic intensity being significantly affected and collapsing the net agnetisation M of the agnet Teperature ( Deg.C ) Br (T) H (KA/) Magnetic Strength (H) (KA/) Figure.3 Effect of teperature over Br and H of a selected NdFeb agnet B. Corrosion Magnetic aterials were subjected to corrosion after a period of usage which causes weight loss and reduces the density and energy of the agnet. The corrosion resistive capacity of peranent agnets is presented in Table.5 with SCo and NdFeb having high corrosion resistance property. Corrosion can be reduced by coating agnetic aterials with corrosion resistance aterials with good agnetic property with recent reports on acceleration test results for a uncoated and coated NdFeB agnet with nickel showing that a reduction in weight loss due to corrosion by a factor or to 3 is achieved by coating NdFeB with nickel[17]. 7

50 C. Skin Effect Chapter. Literature Review Skin effect is described as the affinity of alternative fields to distribute heavily on the surface of a conductor and reducing towards the depth or thickness to produce agnetic field. Skin effect is due to eddy currents which oppose and cancel out agnetic field internally in a conductor. The skin effect as supposed to electrical circuit s increases the resistance of the conductor at higher frequencies and in agnetic circuits reduces the net agnetic field. In general if the thickness of the aterial is higher than the skin depth then the net agnetic field would be less than expected. Skin depth of a aterials, defined by equation.3, is a function of relative resistivity of copper ρ, net pereability of the aterial µ = µ. µ, angular frequency ω. Table 3.6 r shows the skin depth of iron and nickel at frequency of 1Hz. r s = (. ) /( µ. ω) (.3) ρ r Material ρ r ω µ r s Ferrous 9.7E E-5 Nickel 6.8E E-5 Table.6 Skin depth of agnetic aterials at 1 Hz.3.1 Losses in Magnetic aterials Losses in agnetic aterials are priarily due to hysteresis, eddy current losses and excess losses. Excess loss is due to eddy currents produced by oving agnetic doain wall due to an alternating agnetic field.[7] Hysteresis and excess loss are less dependent on size and shape of the aterial unlike eddy current effect which is seen throughout the volue of the saple[7]. The general for of iron loss is shown in equation 3.3 and a detailed look at these losses is presented in chapter 4 under loss deterination section. L f = C + (.4) f + C1 f C WithC, C 1, C are Hysteresis, Eddy current and Excess Loss constant respectively 8

51 Chapter. Literature Review.4 Electrical circuit Considerations Arature windings are arranged in electrical achines to achieve axiu flux linkage and keep copper losses to a iniu Proper deterination of equivalent resistance, current loading and losses would ensure desired physical and functional paraeters to achieve high power density..4.1 Desired Characteristics of Electrical Winding In general the paraeters for coil developent for power generation are the total resistance of the winding for power generation and losses. Losses in windings constitute the heat losses, losses due to skin and proxiity effect caused by eddy current and agnetic induction. There is always a coproise between the windings which could induce axiu power and windings which can keep the variable loss at a iniu. The winding developent for an electrical achines desires 1. The sallest winding size that will handle the specified short circuit current and operate within perissible load current liit for the size with less heat losses. Possess high resistance to electro igration, and high elting point for high teperature applications [71]..4. Micro coils for Micro generators Micro coils as used in icro generators have been in existence for decades used for other applications like icro sensors and actuator, agnetic recording, RF MEMS, Teleetry etc as used. Two type of winding structures were ost coonly used in MEMS; planar and three diensional.. Planar structures were anufactured using IC technologies, UV lithography, and electro deposition techniques. The IC technique includes photolithography, Si-surface icro achining, Si-bulk icro-achining, 9

52 Chapter. Literature Review icro-olding, wet ecthing and reactive plasa etching, ion illing, deep reactive ion etching (DRIE), and LIGA ethods. Three diensional windings can be anufactured using advanced approaches such as electro deposition, sputtering, and wafer bonding. Detailed inforation on the fabrication ethods entioned above is available in the literature and not covered in the thesis [56]. Materials for icro coils include copper, gold, aluiniu and ost recently carbon icro coils fabricated using cheical vapour deposition techniques having conductivities of several S/c to 1 4 S/c [7-75]. Winding structure for rotary icro generators reported in the literature were both planar and wound structures [9-15]. A two coil layer winding structure of Cu/Cr with coil diensions of 1µ*3µ with a coil pitch of 6µ anufactured using UV lithography and electroplating process was fabricated for a planar axial generator odel[1]. The ultilayer coils were fored using lithographically in each SU8 layers during coil fabrication and second level of coil were directly fabricated which eliinated the need for SU8 plasa etching [1, 76]. The insulating layers between the coils layers were fored by SU8 photolithography. SU8 layers were good for agnetic guides, ultilayer coil insulators and also useful for ebedding and planar arrangeent of high aspect ratio structures [76]. Ebedded electroplated Cu test coil structures of 35µ* µ were fabricated and tested to suit high teperature icro turbines. Copper was electroplated on 1 µ oxide with A Ta diffusion to reduce the reaction of Cu to Si foring Cu-Si layers. The coils were over plated with a layer of nickel or platinu to avoid oxidation and corrosion during high teperature operations[17]. Surface wound electrodeposited copper layers of µ thickness ebedded in SU-8 epoxy old was reported for a ill watt scale peranent agnet icro generator[17]. Fabrication of three-phase stator coils for a icro generator using deep lithography and silicon etching process was also reported to substantiate the feasibility of existing technology to fabricate three phase 3

53 Chapter. Literature Review coils [77]. A illietre scale icro generator developed for integration with a icro wankel engine uses a plastic bobbin winding structure with 4 turns of 5 AWG copper wires[9]..5 Mechanical considerations: The coon design engineering issues with the icro rotational achines were constraints posed by frictional forces and bearing issues. The speed is constrained by how uch stress the parts can take before getting daaged. The saller the part the ore is the stress and iportance should be given towards echanical stability. In addition friction becoes a doinant issue in rotating achines and special coating coonly of silicon carbide (SiC) [78-8] and tungsten and TiN was used to keep the co-efficient of friction and the wear resistance low [78, 79]. Fluid or electro echanical bearings look attractive at very sall sizes due to their non-contact operational characteristics[8]..5.1 Bearing for Micro Applications: Developent of High speed icro bearing is difficult and plays a key part in the success of icro generator and otor application. The stability of the bearings and the stress levels deterine the axiu rotational speed achievable fro the syste and in turn the attainable echanical power. Due consideration needs to be given to the design of the syste to keep the ass and coefficient of friction (drag forces) to a iniu to develop an efficient bearing syste to reduce drag forces. Different fors of bearing systes were reported in the literature for icro achine applications with their own pro s and con s. Ball bearing unlike in acro achines has also been seen as an entity to support icro achines. Micro actuators with rotor diaeters of 1 supported on encapsulated ball bearings structure with 1 stainless steel balls of 85 µ was reported. The bearing structure supports the encased rotor and a thrust balance fro 31

54 Chapter. Literature Review electro-pneuatic syste was used to iniize noral load. The syste was reported to perfor well at speeds fro 5rp to rp. The ball bearing syste suffers fro wear and deteriorates at high loads [83]. Micro turbine with rotor diaeter of 1 supported by two ball bearings was reported in research which runs at speeds of 16, rp. The ball bearings liit the operating speed of the turbine and also reduces the dynaic balance of the rotor at high speeds[83].the literature suggest that the operating speed of the syste for increased power can be achieved by air bearings or other non contact bearing ethods. Micro gas bearing for icro actuator application was reported in literature with groves fored on a.5 diaeter shaft. The grooves were designed to take in air when the shaft rotates and push it to the central part to create pressure to push the shaft up under operation. Special ion coating of TiN and CrN was used to iprove the wear resistance and to reduce contact friction during start and stop cycles[84]. Flange and centre pin bearings for haronic side drives or icro otors were reported in the literature. The bearings were tested with a icro otor airgap of 1.5 µ. The use of lubricating oil was reported to reduce the friction torque by an order of agnitude[85]. The issue with lubricating oil was high viscous drag associated with the which is one fold greater than air. Self pressurizing hydrostatic and hydrodynaic thrust bearings were tested for turbine rotor design and up to speeds of 45, rp. The issue with the bearings was the wear during start and stop cycles where it was subjected to surface rubbing prior to lift off [86, 87]. Hydro inertia bearing for icro turbines was reported in research which can support rotor speeds upto 77 rp with reduced wear during start and stop cycles [88]. Micro generator using flywheel energy storage syste with high teperature superconducting bearings has been reported in the literature [88]. The bearing operates using levitation forces fro a high teperature superconductor and a 3

55 Chapter. Literature Review bearing agnet attached to a flywheel. Reported experiental results done in vacuu condition shows axiu flywheel speeds of 51,rp and co-efficient of friction calculated as.1. [89]. These bearings were subjected to flux creeping generated at higher agnetic fields which reduces the levitation forces and contributes to drag forces. Diaagnetic bearing with peranent agnets were reported as a siple alternative for icro bearings at saller scales. These bearings have losses due to eddy current effects and the losses increases with reduction in size [9]. Use of conventional ball bearings of type (BOCAtypeSMF681) was reported in literature where the generator design revolved the bearing specifications and coercial NdBFe agnet. The literature suggests the use of aerodynaic bearing to iprove the design of the generator for better energy density [1]..6 MEMS generator analysis ethodologies There are different ethods available and used to deterine the perforance characteristics of achines for coparison like network analysis ethod[91], luped paraeter generalised odels[9], FEA odels[93]. The thesis uses an iproved luped paraeter odelling developed as part of original contribution which uses independent agnetic and electric circuit analysis feeding to the luped paraeter odel to take into effect the change in paraeters to provide better accuracy than other ethods and not available before. In-depth inforation on the basis of the developed luped paraeter odel for Axial and radial odel is available in Appendix A. MEMS electric achine analysis ethodologies available in the literature for the developent of the icro generator uses siplified techniques for their analysis [, 17]. In other literature the odelling ethodology was specific to the generator odel and agnetic circuit analysis was done for Bg and directly used to evaluate voltage and current using custo built equations specific to the achine. No attept 33

56 Chapter. Literature Review has been ade to optiize the syste using any analysis ethod. In the literature luped paraeter was used to provide effect of diension and paraeters over power density and efficiency and they were also used to select optial paraeter to achieve better PD [6]. All the analysis ethodology used in the literature use the agnetic flux density as air gap as Br/ or fro experience or fro separate FEM analysis. The thesis presents an iproved luped paraeter analysis by linking both agnetic circuit analysis. This will achieve coplete realisation of the achine over paraeters and diensional changes. It also reduce the coplexity involved in FEM analysis which required repetitive odelling and eshing and analysis to see the effect of change in diension to change in airgap.the iproved ethod can also be widely used for acro achine analysis..7 Micro generator integration with icro engine The icro generator odel available in literature developed to be integrated with a icro engine was that of a illietre scale reluctance generator (11* 8* 5) developed at university of Berkeley [9]. The generator was tested on a test bed and there was no literature available on coplete integration and testing of the generator and the icro engine. Wankel engine was chosen in this case for its planar construction and its flexibility of anufacturing with only few oving parts [9]. The agnetic circuit of the illietre scale generator consists of centre connected and edge connected pole faces, electroplated rotor, and adjustable peranent agnet source. The pole faces were ade up of powdered iron aterial and ade fro electrical discharge achining (EDM) technique. Powdered iron was selected in this case for its low loss and high flux density saturation levels. The pole faces were positioned using teplates and sealed with epoxy [9]. The electroplated rotor had electroplated NiFe into trenches on a 5 icroeter silicon wafer. A 5:5 ratio of NiFe was used for better Curie teperature characteristics. The agnetic source cae fro an NdFeb peranent 34

57 Chapter. Literature Review agnetic core which can be adjusted laterally to provide varied agnetic excitation. The stator consists of centre post and a toroid. They were ade of copressed silicon steel into a layered structure with a final epoxy finish. The stator winding was a plastic bobbin consisting of 4 turns of Awg wire and the plastic was developed to fit inside the toroid. The generator was assebled on a test bed by and the gap length was anually adjusted by adjusting the peranent agnet source in the test bed to attain axiu back ef. The shaft when run at 13krp produced a axiu open circuit voltage and power generated were 3.8V and 375 icrowatts [9]. The illietre scale generator was developed to fit the icro engine configuration. This posed constraints in the generator design and coproised on the axiu power that could be achieved fro the generator. The powdered iron rotor even though with better Curie teperature characteristics have difficulty in ters of anufacturing due to its brittle and inhoogeneous characteristics which can cause fractures when icro achining. Powdered iron reduces the net achievable agnetic flux in air gap due to difficulties in getting the isotropic agnetic alignent properties right fro icroachining as see fro literature [95]. Powdered iron also causes stator saturation due to its low pereability saturation characteristics. The agnetic flux in the stator was hoopolar in the non-aligned rotor positions and also fro the stator to the agnetic core causing leakage fluxes. The net flux flow was also reduced by the high reluctance due to large yoke, back iron core and air gaps. The external larger yoke and back iron also increase the volue of the generator thus reducing the net power density achievable fro the generator. The literature suggests a peranent agnet circuit with reversing flux capabilities would have iproved the net alternating flux available for ef generation by a factor of two [9]. The electrical winding structure was designed to attain the hoopolar flux flow for the reluctance achine. In doing so, it had also increased the volue of the generator and contributing 35

58 Chapter. Literature Review towards the net power density achievable fro the generator. The agnetic circuit with one agnetic source has reduced BHax and net agnetic flux density attainable in the air gap attainable in the air gap in contract to achines with two agnetic sources [17]. Proper choice for agnetic circuit to obtain optial flux levels can iprove the power density of the generator [9]..8 Suary An overview of the electrical achine technology and generator topologies is provided in this chapter. As a suary the following can be stated The state of the art in icro and MEMS generators are investigated and icro generator with planar construction has been found to provide high PD. Materials and Manufacturing of MEMS icro generators were looked at to substantiate the feasibility of anufacturing of such devices with existing fabrication techniques. The key difficulties in anufacturing were in the areas of bulk structures with good precision with the required echanical, electrical and agnetic properties. The coon design engineering issues with the icro rotational achines were constrains posed by frictional forces and bearing issues. Special coating coonly of silicon carbide (SiC) and tungsten and TiN were used in literature to keep the coefficient of friction low. Magnetic and electrical consideration for anufacturing of MEMS icro generator was reviewed. Due to the anufacturing difficulties and high annealing teperatures associated with soe of the hard agnetic aterials, coercially available hard agnetic aterials were used in any cases. The developent of a illietre scale generator for integration with icro engine was done to fit the icro engine configuration. This posed constraints in the 36

59 Chapter. Literature Review generator design and coproised on the axiu power that could be achieved fro the generator. The agnetic flux in the stator of the reported illietre scale generator was hoopolar causing leakage fluxes. The net flux flow was also reduced by the high reluctance due to large yoke, back iron core and air gaps. The electrical winding was designed to attain hoopolar flux flow for the reluctance achine. In doing so, it had also increased the volue of the generator and contributing towards the net power density achievable fro the generator. The power density of the icro generator has been reduced due to the above issues. The literature recoends that iproveent in agnetic analysis ethod for paraetric selection would help select better paraeter for agnetic circuit to achieve power density. The sae should also be applied for electric circuit analysis to achieve further increase in power density of the MEMS icro generator. The thesis focuses on selection of paraeter for a axial thin MEMS icro generator to attain high power density to existing icro generators. In doing so, the thesis had attepted to addressed the issues identified fro literature and developed iproveents for better selection of agnetic and electric circuit for icro generator developent. The third chapter would look at scaling strategies and selection of suitable topology for icro generator developent. The agnetic and electric circuit analysis ethods are also dealt in detail in this chapter. 37

60 Chapter 3: Micro generator scaling and selection The scaling strategies for icro generator developent are discussed in this chapter to understand the effect of scaling to attainable power density. The analysis of radial and axial achines for the selection of suitable icro generator topology for high power density and efficiency is ade using luped paraeter analysis. The analysis results are copared with a reported reluctance icro generator odel to select the best topology for icro generator developent. Pereance co-efficient or Pereance factor ethod for agnetic circuit analysis used in the thesis is briefed. Three different ethods of calculating the air gap, leakage and fringing pereance for two diensional structures are developed and validated with ANSYS FEM results. A theoretical analytical ethod to calculate planar coil paraeters is developed and validated. Finally, the icro generator developed in the research is introduced and the advantage of the odel to existing technology is explained. 3.1 Scaling of Electrical Rotary Machines The key achine specifications over which a icro electrical rotary achine is developed are their power, efficiency and power density (power/ass and power/volue). Like acro achines, icro achines needs to have a coproise between power density and efficiency achievable as achines delivering axiu power do not generally operate at axiu achievable efficiency levels. The realisation of the effect of scaling over power density and efficiency can be analysed with the help of functional quantities and their characteristics equation for power generation like Torque, Power (both echanical and electrical), Generated ef, Losses, and Efficiency. These strategies are helpful for atching electrical and echanical torques for electrical achines. There are other scaling strategies reported in the 38

61 literature where direct ethod of scaling to axiize power density was done for a specific icro achine odel[1]. The agnitude of Torque T in a rotary achine in general is the product of flux density B and the area A over which flux links the winding with current I as T = B. I. A (3.1) Voltage generated by the electrical achine is product of change in flux linkage the winding over tie and is represented as dφ dλ db V = n = = n. A. dt dt dt (3.) db By representing due to change in angular speed, the agnitude of ef is dt V = n. B. A. N or siply V = B. A. N (3.3) Power generated by the electrical achine is the product of voltage and current while the input echanical power on shaft is the product of torque and speed as in P elec = V. I (3.4) and.. N. T P ech = π = T. N (3.5) 6 The above equation can also be represented by a ore useful equation for scaling using diensional paraeters for both electrical power generation (generators) and echanical power generation (otors) as P elec = Pech = N. B. J. A (3.6) The ain losses in a rotary achine for electrical and echanical power generation are ainly the eddy current losses, hysteresis losses which coprise the net iron loss (constant loss) and the copper or heat losses (variable loss). The iron losses are due to the change in agnetic field on ferroagnetic aterials which restrict the flux flow due to their electro-agnetic resistive property. Eddy current is due to local 39

62 currents produced in ferroagnetic aterials which produce fields opposing the ain field causing loss in the achines. Generally these losses are linked to the property of the aterials used and their diensions and often predicted by curve fitting to experiental data available which is often coplex. A noralized equation for these losses can be written by taking into consideration their dependency on frequency as P eddy = N. B. volue (3.7) & P hys = N. B. volue (3.8) The heat losses or copper losses can be written as a product of the second power of current induced in the winding and the resistance of the winding as P cu = I. R (3.9) The above equation can also be represented by a ore useful equation for scaling using current density ( J ) and diensional paraeters as. L P cu = I. R = J. A. A ρ (3.1) and total losses can be written as. L P loss = N. B. A. L + N. B. A. L + J. A. A ρ ( N. B ( N + 1) J.ρ) (3.11) P loss = A. L. + (3.1) For better analysis of scaling, a linear diension is considered which when ebedded with power and loss equations would take the fors P 4 elec = Pech = N. B. J. (3.13) ( ) 3 P loss =. N. B ( N + 1) + J.ρ (3.14) It can be seen fro the above equation that electrical power and echanical torque fro echanical power are proportional to Power density and loss density can be written as 4 and the losses are proportional to 3. The 4

63 P Pech = 3 N. B. J. (3.15) elec 3 = P loss (. ( 1).ρ) 3 = N B N + J + (3.16) Efficiency of the generator with respect to power density can be written as eff P loss = 1 (3.17) P elec The realisation of the effect of scaling on power density and efficiency can be achieved by considering their respective fors above. Most electrical achines are operated at flux density B close to saturation and it can be kept as a constant and by keeping speed, current density and resistivity as constant the relative change of power density to scaling of linear diension in diension is shown in Figure.3.1. It is ade clear fro Figure 3.1 that by direct scaling of linear diension the power density reduces linearly and there exist a situation to the left side of the plot where any further reduction causes the power density to go lower than the loss density and thus severely reducing the efficiency of the achine. This illustration clearly shows that the strategy of direct scaling would lead to a syste with lower efficiencies and reduced power densities. Figure.3.1 Effect of direct scaling of diensions to power density and efficiency 41

64 One strategy to iprove power density and aintain efficiency is by linearly increasing the speed and current density to linear diension. The result of such strategy can be seen fro Figure 3. and 3.3 which shows that there in a window in the graph where higher power densities achievable and efficiency levels aintained. The proble with the strategy is that on the area both to the left and right hand side of the window power density tends to reduce with scaling and so does efficiency. If this strategy has to be adopted then the achine needs to be developed to operate within this window of desired operation. Proportional scaling ethods to achieve higher power densities aintaining good efficiency levels within the window would often lead to a trial and error developent ethod or using optiization proble to select paraeters to achieve the sae which is coplex and ay not guarantee desired operation. power densities and effeciency change with linear change with w,,j Change in power, Net power and Loss and effeciency Power density fro power produced Power density fro net power after loss Loss density Effeciency (Negavtive values reduced to zero) Diension Scaling Figure.3. Power density & Efficiency iproveent with linear increase in speed and current density An intuitive way of finding a strategy to aintain the levels of power densities and efficiencies can be arrived by analysing efficiency and power density equations. The efficiency for better understanding can be written fro the power density fors as 4

65 eff B. ω B. ω J. ρ = N. J. B. N. J. B. N. J. B. B. N B J. ρ = (3.18). J. J. N. B. Change in power density to change in w,,j 3 5 Power desnity Linear Diension Angular Speed (R Figure.3.3 Power density iproveent with increase in speed and current density By looking at power density and efficiency equation a linear relation between the linear diension and power density can be achieved by varying current density J 1, and angular frequency N and with other paraeters in the equations B, ρ kept constant for the reasons given at the beginning. The above scaling approach would ensure scaling of power density proportional to scaling of linear diension and also help to keep the last two parts of the efficiency equation as a constant. This will drive the efficiency of the achine close to a constant with reduced variability achieved by reducing the eddy current losses using available ethods. Figure 3.4(A, B) shows that a linear relationship between power density and diension can be achieved which would iprove power and torque capacity of the achine at icro scales. Figure 3.5.C shows that efficiency reains stable over scaling when eddy current effects are considered negligible (least influence) on the achine perforance and have not been included for analysis. Figure 3.4.D. shows that efficiency still reains stable when eddy current is taken into consideration but shows variation or 43

66 reduction at reduced scales which illustrate the iportance of reducing eddy currents and its effects at icro scales by choosing proper aterials and ethods to aintain efficiency levels. 1 Power density with scaling of J=1/ and N=1/ Power density with scaling of J=1/ and N=1/ Power density Linear Diension- P o w e r d e n s ity Linear Diension Angular Speed-w (Rad/sec) (A) (B) Effeciency scaling with J=1/ and N=1/ Effeciency scaling with J=1/ and N=1/ with eddy current effect E ffe c ie n c y 1.5 Effeciency Linear Diension-w Angular Speed-w (Rad/sec) Linear Diension-w Angular Speed-w (Rad/sec) (C) (D) Figure 3.4 A. Linear PD & diension relationship with 1 Jα & Nα B. 3-D Power density & diension relationship with 1 Jα & Nα C. Efficiency without eddy currents considered for scaling with Jα 1 & Nα D. Efficiency with eddy currents considered for scaling with Jα 1 & Nα 44

67 3. Relationship between agnetic and electrical paraeters to power density The iportant agnetic paraeters for consideration in icro achine developent are the reanent flux density B r, Air gap length and nuber of poles. Reanent flux density in agnetic circuit is dependent on the agnetic aterial used as the agnetic source. Ndfeb and SCo are popular hard agnetic aterials for agnetic source used in icro generator developent fro literature available in chapter. The literature recoends the use of coercially available hard agnetic sources to deposition techniques because of difficulties involved in icro achining hard agnets. The scaling strategy used in the previous section is done by keeping the flux density as constant at axiu attainable reanent flux density levels. This is achieved by reducing the stator and rotor air gap in such as way the agnetic circuit is operated close to saturation on the load line curve as shown in Figure 3.6. There is a liitation to how sall the air gap needs to be to avoid saturation in the cores. Saturation can be reduced by using high pereability soft agnetic cores ade of Ni, Fe and their alloys which have high pereability and exhibit high saturation levels. Table 3.1 shows the effect of air gap length to voltage, power and power density. Reduction of air gap reduces the volue of the achine and iproves power density. This increase in power density due to airgap length reduction is only sall copared to its effect of proportional increase to voltage and power. The open circuit voltage generated by the icro generator can be proportionally increased by no of poles. The increase in poles increases frequency losses and adds coplexity to alignent of the coils and also depends on the profile of the integrating structure. In planar coil arrangeent, to attain axiu flux linkage the agnetic 45

68 source has to be at the centre and within the coil arrangeent. This will ensure equal flux distribution to the coils for ef generation. The iportant electrical paraeters which affect the power and power density of the icro generator are nuber of coils, Resistance of the winding and current density. An increase in coil nubers increases the generated ef and directly increases the generated power. A coil structure with increased windings of thinner guage length will also reduce the dynaic I R losses and also reduce the total eddy current effects. But, increasing the nuber of windings pose coplexity in anufacturing for high precision coil structures. Current density is an iportant factor which also defines the perissible current carried by the coil structure. Current density as a paraeter for scaling is looked at in previous section. Any reduction in current density would also help reduce dynaic I R losses and thus can help iprove power. The effect of agnetic and electrical paraeters to icro generator functional outputs is suarized in Table 3.1. Output Paraeter Voltage Power Efficiency Power density Air gap Length Lg Depend on no of poles Reanent flux density Br Increases frequency losses No of coils n Depends on the coil profile Speed N Depends on the agnitude of 46

69 speed losses Current Density No direct Power Depends on the J effect increases coil profile with dynaic losses - Reduce - Increase Table 3.1. Micro generator paraeter relationship to icro generator specifications 3.3 Generator Topologies for MEMS Planar Developent Planar developent of icro generator as seen fro chapter has shown to exhibit higher PD at icro scale. A valid and better coparison of icro generator is achieved when done between the popular axial and radial and reluctance topologies for achievable PD. Four different odels of sae volue are considered for the analysis for power density: Radial flux PM achine (RFPM) and two axial achines with PM outside and PM inside on a sandwiched arrangeent and coparison of power densities of the achines are copared with each other and with a reported reluctance odel fro U.C.Berkley to ake the coparisons coplete. The analysis is done using an iproved luped paraeter odelling approach used in the thesis available in chapter 4. The ethodology uses independent agnetic and electric circuit analysis feeding to the luped paraeter odel to take into effect the change in paraeters to provide better accuracy than other ethod. In-depth on the basis of the developed luped paraeter odel for Axial and radial odel is available in APPENDIX A Radial Flux PM Machine (RFPM) The RFPM odel chosen for analysis is a siple universal synchronous achine with two poles which could be altered upon developent suitability. An 47

70 equivalent reluctance odel and cross sectional view of a RFPM achine used for analysis is shown in Figure 3.5. The rotor configuration for analysis is assued as a black box or salient poles with PM s inside the to suit the configuration of the engine. The power density for the achine under consideration is deterined by solving for agnetic and electrical circuits and then noralizing for output power and density. In this analysis the generator is again considered to be integrated to an engine or turbine providing the necessary echanical torque for power generation. The agnetic saturation of the syste depends on the saturation characteristics of the sealing aterial. The saturation characteristics of the core are better than the conventional achines noral air gap saturation through stator back iron. _ NI + φ φ 1 R s R c R l F R R l R c F R + _ NI R g B C E D M C B F A A A - Micro engine Generator outer casing, B - Winding Structure, C - Envisaged Sealing Structure, D - Engine Rotor and Generator coon Shaft E - PM structure with Magnetization Vector M Figure 3.5 Model Radial two pole Synchronous PM Micro Generator Machine (RFPM) and Crosssectional view of RFPM under consideration (Not on Scale). 48

71 The paraeters of the odel considered for analysis above has a volue.5*.3*.3 3 with a rotor outer diaeter scale of.18, rotor thickness of 9 icro eters with capacity to produce 5 to 1 W of power is considered. The speed of the achine is taken to be as 13krp with fixed nuber of poles and the achine is considered to generate a sinusoidal ef wavefor. The agnetic circuit for the achine is characterized above in Figure 3.5 and the final generalised luped paraeter odel for the achine is shown in equation st 1 Cw. Bg. N. ωr. Ds. Le. I( t).sinwet [ pv.. B. f + I a ( t).( Rw + jx l ) ρ g = (3.19) V + pv.. t. B. f +.1. P +.3. P ] c o / p o / p t The generalised equation fored in this case is design independent with only φ g directly dependent on the physical arrangeent of agnetic circuit poles. This akes the odified luped odel analysis of the achine useful for analysing a ajority of radial flux achine odel and axial achine topologies as explained in next section. The current density of the windings are custoized and kept below axiu current density of 5A/ for perissible operation during analysis. The load characteristics and efficiency of the achine are shown in Figure 3.6(A,B). Maxiu efficiency occurs at approxiately 8% of the axiu power output and there is always a coproise between achines for axiu efficiency and achine output power. It can be observed that the losses in the syste are generally high due to increase in loss due to engine teperature with is unavoidable in this configuration of integrated engine generator syste. It can also be observed that there is a loss balance point available fro Figure 3.6.B, C where the axiu output is obtained keeping achine losses as iniu and this point would be of interest for developent of a syste for axiu output. The terinal voltage in the syste is a function of winding resistance and has a proportionate effect over increase in 49

72 teperature and the current, which causes the reduction in voltage gain between induced and available voltages and reduction in O/P power with increase in turns as perceived fro Figure.3.6.E, F. The agnitude of no load generated voltage of the achine fro analysis was found to be.8 volts with axiu output power ~ 4 µ W and voluetric power density of around 14 Watts/ 3. 3.E-4.5E-4.E-4 Output(Watts) Input(Watts) copper Loss 1.4E-3 1.E-3 1.E-3 1.4E-3 1.E-3 1.E-3 Po/p Losses(Watts) Pi/p Watts 1.5E-4 1.E-4 5.E-5 8.E-4 6.E-4 4.E-4.E-4 Watts 8.E-4 6.E-4 4.E-4.E-4.E+.E+ 1.E+4.E+4 3.E+4 4.E+4 5.E+4 Load (Ohs).E+.E+.E+ 1.E-4.E-4 3.E-4 4.E-4 Ia (Aps) (A) (B) % eff output.e+ 3.E+4 6.E+4 9.E+4 Ohs 3.E-4.4E-4 1.6E-4 8.E-5.E+ O /P p o w e r (W atts ) 5.E-4 O/P power 4.E-4 3.E-4.E E-4 4.E Turns (B) (D) 5

73 EMF (E), Terinal Voltage (Vt) (Volts) E Vt Watts P.Desnity(Watts/3).E+ 1.6E+ 1.E+ 8.E+1 4.E+1 Power Density(W/3) O/P (Watts) Losses (Watts).1E-3 O/P & Losses (Watts) 1 Turns.E Turns.E+ (E) (F) Figure.3.6 (A). Load Vs Output power, copper loss and calculated input power, (B). Watts characteristics plotted as a function of arature current, (C). Efficiency and Output power as a function of load resistance, (D). Area spectru of O/P power with increase in turns, (E). Induced ef & Terinal voltage with Nuber of Arature Turns, (F). Power density, O/P power & Losses With Characteristics with change in turns 3.3. Axial Machine: Axial achines are uch suitable for high aspect ratio achines, where the ratio between achine diaeters to length is high. Luped paraeter odels are developed by a siilar approach to radial achines and available in APPENDIX A. Two odels of axial achines are analysed one with agnets inside and the other with agnets outside. The achine under considerations has the arature windings isolated and kept as a separate unit to reduce the heat losses due to engine teperature and iprove the power density of the syste. This configuration allows for the flexibility of agnets used to achieve high agnetic flux density (B ). A cross-sectional view of one of the axial achine with PM agnets outside is shown Figure

74 F g A D r t w G d g 1 B C E C B Iw M A F A Disc Shaped PM with Magnetization Vector M, B Sealing Structure C Electrodeposited agnetic pole aterials, D Winding Structure E Shaft Structure of the engine F PM Magnetic structure with Magnetization Vector M Figure 3.7 Axial flux Thin PM Micro Generator (AFMEG) (Not on Scale). The odel taken into consideration is of the sae volue as the radial achine odel.5*.3*.3 3 with a rotor outer diaeter scale of.85 and rotor thickness of 9 icro eters with an objective to produce 5 to 1 W of power is considered. The speed of the achine is taken to be as 13krp with fixed nuber of poles and the achine is considered to generate a sinusoidal ef wavefor. The final for of the generalised power density equation to be used for analysis is shown in equation ρ g ( t) = V t o π. r CwC( t). ζ - pv.. B st. f + e w t B. I ( t). l.( R µ µ L w g1 g1 l. N. ωr + jx ) + p. M. t c. B. f +.1. P o / p +.3. P (3.) o / p The load characteristics and efficiency of the achine are shown in Figure. 3.8 A with the axiu efficiency of 7-9% and this is due to low core losses and 5

75 low teperature losses due to isolation fro engine operating teperature and also the syste helps to exploit in full the energy available in the agnetic circuit. The developent of the generator is independent of the agnetic circuit and dependent on the flux density available in the air gap but the efficiency and power density of the syste depends on the operating point of the agnets. A plot showing the area spectru O/P power to change in air gap length, turns, layers of printed circuit winding structure is shown in Figure 3.8 D, E which illustrates the systes dependency on the above paraeters. The terinal voltage in the syste is a function of winding resistance and has litttle effect over the increase in engine teperature which akes the difference between the induce ef and the terinal voltage reduced as seen fro Figure 3.8.F. The no load generated voltage of the achine fro analysis was found to be 3-4 volts with axiu output power of ~.5W and voluetric power density of ~36 Watts/ 3. Percentage % 1.E+ 8.E+1 6.E+1 4.E+1.E+1 Eff O/P 3.E-3 3.E-3.E-3.E-3 1.E-3 5.E-4 Watts P.Desnity(W/3) 4.5E+ 3.6E+.7E+ 1.8E+ 9.E+1 P.Density O/P Losses.4E-3 1.6E-3 8.E-4 O/P & Losses (Watts).E+.E+ 4.E+4 8.E+4 1.E+5 Ohs.E+.E Turns(Watts).E+ (A) (B) P.D e snity(w / 3 ) 1.E+3 8.E+ 4.E+.E+ P.Density O/P Losses 1 3 Layers (C) 5.E-3 4.E-3 3.E-3.E-3 1.E-3.E+ O /P & L osse s (W a tts ) 1.3E-7 Turns Layers E E-3 8.3E-4 4.7E-4 3.1E-4 3.E-6 5.E-5 O/P Power (Watts) (D) T u r n s, L a y e r s 53

76 O /P p o w e r (W a t t s ) 1.5E-3 1.3E-3 1.1E-3 9.E-4 7.E-4 5.E-4 3.E-4 1.E-4-1.E-4 1.E-3 3.E-3 5.E-3 7.E-3 Airgap Length g1 () E f & T.V o ltage (V o lts) Turns (E) (F) Figure. 3.8 A. Load (Ohs) Vs Output power (watts) and Efficiency (%), B. Output power, losses and Power Density as a function of Turns, C. Output power, losses and Power Density as a function of Layers, D. Area spectru of O/P power with increase in turns and Layers, E. O/P power spectru with change in Air gap Length, F. Induced ef E & Terinal Voltage V t and Power density with change in turns. Figure 3.9 shows power densities obtained fro the analysis plotted against each other and including the interpreted power density fro a reported reluctance odel[5]. It can inferred fro Figure 3.9 that the power density of both axial achines considered produced the peak power higher than the radial and the reluctance achine reported. Radial achine analysed see to exhibit low power density values but the variation in energy density over the range of resistance is lesser which infers that these achines are stable over load variation and needs less optiization. The window of axiu power density achievable fro Figure 3.9 for axial generator is narrow which infers a requireent to finding ideal paraetric values to keep the generator operate within the window of operation. 54

77 P.Density(W-hr/3).1E+6 Radial Reluctance Model Axial1-Magnet Inside Axial-Machine Sandwich odel 1.4E+6 7.E+5.E+.E+ 1.5E+4 3.E+4 4.5E+4 6.E+4 Ohs Figure Coparison of different Micro Generators Configurations Magnetic and electric circuit are key coponents for electrical power generation in a icro or acro generator and in general electrical achines. Proper analysis of these circuits would ensure desired physical and functional paraeters to achieve high power density and specific power in electrical achines. 3. Magnetic Circuit Analysis Pereance coefficient Magnetic circuits in practical cases would exhibit easurable levels of leakage fluxes and fringing fluxes which are to be introduced into the agnetic circuit calculation to get an accurate deterination of agnetic circuit paraeters. These factors depend on the physical structure of the agnetic circuit and the surrounding ediu they operate in. Two general correction factors can be defined to represent the leakage factor L f 1 and other to represent the loss of f L f poles. in the soft iron core or 55

78 φ L f 1 = & φg L = F f (3.1) Fg These factors needs to be included in the slope for the peranent agnet load-line to accurately calculated the air gap flux density at air gap. Inclusion of these factors into the slope equation for the load line in APPENDIX B, slope will then odify to L l A L f 1 Pg slope = µ (3.) L P f 1 g. = µ. L f lg A f Siilarly the air gap flux density and field intensity fro the load line with leakage is B H g g Pg A = Br.. P A B = with.. P = P t r µ t. P g g g P + P + P l. + P l + P L L g 1. L f (3.3) The deterination of L f depends on the relative pereability of the cores and the poles in the agnetic circuit. Since, we have assued that the softiron core has an infinite relative pereability then L f is basically unity. But for practical circuits the copensation of L f can be achieved by increasing the length of the agnet L as in equation 3.1. The deterination of L f can be deterined by the physical agnetic characteristics and the relative pereability of the additional coponents by taking into consideration the agnetization of the aterial and the total agnetic field as M = µ V (3.4) aterial aterial / B = µ ( H + M ) (3.5) aterial aterial And fro equation 3.5 µ H represents the external field applied to agnetize the aterial or align the agnetic oent to achieve B agnet aterial. Adjusting length of the L can copensate for the sae loss. This can be done at the final stages of the 56

79 developent process as an coproise to the requireents of the design and generally for ost design analysis the core can be taken as with high pereability. Finite eleent analysis can then be used to deterine the µ aterial required to achieve the required flux density for a particular application and a suitable core aterial and physical configuration can be selected to eet design requireents. For exaple if the circuit requires the syste to operate at an air gap flux density of 1.5T, with known Bg and H of the agnet µ aterial of the core can be evaluated. Copensation can then be required to L or the core aterial to achieve ideal air gap flux density in the circuit. The deterination of L f 1 by evaluating φ and φg in the circuit is difficult and coplex for practical circuits and is often done using finite eleent analysis to provide proper accuracy. An alternative and less coplex ethod to include leakage and fringing coefficient for agnetic field analysis is using a ultiplication factor tered as Pereance coefficient which is a ratio of Pereance of useful air gap to the Pereance of the total circuit useful air gap as in equation 3.3 and the useful flux density at air gap can now be written including the Pereance coefficient as in 3.4. Pg P f = (3.6) P t A B. g = Br. Pf (3.7) Ag 3.4 Pereance Deterination Methods used for Pereance deterination: The ethod of ean flux path is used for deterination of Pereance of all possible fringing and leakage paths in a agnetic circuit by observing the characteristics of flux flow in a agnetic circuit detailed in literature[6]. A graphical approxiation 57

80 ethod was used in literature for reluctance calculation and verified using practical results for good accuracy [7]. Three other original ethods are analysed in the thesis circular, diagonal and parabolic for approxiation ethods of deterination of Pereance to provide closer approxiations with graphical ethod. The ethods developed in research are siple and can be easily applied for good approxiations for -D analysis of agnetic circuits which are perfored in the thesis. A. Circular approxiation ethod This approach uses the characteristic equations associates with the circle to deterine the Pereance of a ean flux path. A siple case of fringing Pereance near air gap as in Figure 3.1 is considered for Pereance deterination using this ethod Mean Flux path d L g Figure 3.1 Seicircular cylinder Pereance deterinations (circular) Fro the above diagra the ean flux line fro circular ethod is given by LL =. π.( L / 4) = 1. 57L (3.8) g g With a noralization of eans length being 8% the length of LL then And the area A ( π. Lg ). d = Volue / Length = (8) L =.9L g. g d And µ. A.9. L. d = L (3.9) g P = = µ. 3 L 1.6. Lg g 58

81 B. Graphical approxiation ethod A graphical approxiation approach is explained in reference [6]. Considering the sae odel for Pereance calculation, the ean flux line fro graphical approach is L = 1. L. The ean area and pereance is given by g π. Lg. d A = Volue / Length = =.3Lg. d 8*1.. L g µ. A.3. Lg. d P = = = µ. 6d L 1.. L g (3.3) C. Parabolic approxiation ethod In this ethod the flux paths are approxiated as parabolas with focus located at soe point fro the centre (, L g /) with a radius a. Y Mean Flux path f (, L g /) f (, L g /4) x Figure 3.11 Seicircular cylinder Pereance coefficient deterination (Parabolic) The ean length of the arc of the parabola fro (,) to a point (x,y) for this case is L ( / ) + ( / ) + 4 * ( / 4) g ( Lg / ) L Lg Lg L g g L = Log (3.31) 8 ( L / 4) 4 ( L / ) g g And the ean area is siply given as A π * Lg * d = Volue / Length = 8* L L g. d =.396. L 59

82 L g. d P =.396. µ. (3.3) L D. Diagonal intersection approxiation ethod In this ethod the flux path span is approxiated to be lie within squares or rectangles with the length of the diagonals for the approxiated shapes is considered as the ean length of the flux path. The scenario for finding the ean length using diagonal approxiation analysis is shown in Figure 3.1 Figure 3.1 Seicircular cylinder Pereance coefficient deterinations (Diagonal) The ean flux length be su of d 1 and d which is written as Lg Lg L = * = Lg + 4 (3.33) Considering the ean flux line falling below the lines of intersection, the ean flux line length is considered as 1.1 ties the su of the diagonals to calculate A and P as π * Lg * d A = Volue / Length = =.3166Lg. d 8*1.4* L g and µ. A.3166Lg. d. µ P = = = µ. 55d (3.34) L 1.4. L g 6

83 3.4. Coparison of Pereance Approxiation Methods: A MATLAB analysis is done to choose the best ethod to deterine the ean length for Pereance evaluation using the approxiation ethods considered in the previous sections. The analysis shows that the diagonal intersection ethod to deterine Pereance is closely atching to graphical approxiation and practical results. g L For analysis is taken as = [ :.5e 3 :.5e 3] L g one diensional atrix in MATLAB with Lg range fro to.5e-3). (representation of a Figure 3.13 shows the result fro the analysis and it can be inferred that diagonal, circular ethod and graphical ethod[7] showed close atch with very little difference. Parabolic approxiation ethod showed a high tolerance level which increase in ean flux path length with increase in air gap length fro the other ethods analysed and also the foration of ean flux path length and the Pereance equations are deterination is coplex in nature using this ethod. Diagonal, circular with soe graphical assuptions are used for Pereance evaluation in this thesis. Figure 3.13 Coparison between approxiation ethods for deterining ean flux length for Pereance coefficient deterination 61

84 3.4.3 Pereance calculation for generic flux paths (using circular ethod) Calculation of Pereance can be ade easier if generalised equations are fored for ore generic flux path shapes which can be applied to a broad area of agnetic circuit analysis applications. Generalised equations for generic flux path for static and displaced structures are done and available in APPENDIX B 3.5 Force and torque calculation using co-energy density ethod Force due to change in co-energy for an air gap length Lg is given by f dw c =, dl g where co-energy is given by the su of co-energy of the peranent agnet and the coenergy at air gap as discussed in APPENDIX B. W c v = = W cg + W cp g. µ H g + v 1 µ H B. H r (3.35) And force can now be written as d vg. µ H g 1 f + v µ H Br. H dlg = (3.36) Where v = L * A & v = A * L and equating it in equation 3.36 with the second g g g ter becoing zero because of constant Br and H, the force becoes B g. A g f = (3.37). µ 6

85 3.6 Accuracy of Pereance coefficient ethod using circular and parabolic ethod Accuracy of Pereance coefficient ethod is deonstrated using a agnetic circuit with arature keeper. Force at displaceents is deterined using pereance coefficient ethod and copared with results fro ANSYS FEA by Virtual work, Maxwell stress tensor and Lorentz force ethod. L t r Peranent agnet L g t y L y Yoke t Arature L Figure 3.15 Magnetic circuits for Pereance coefficient ethod accuracy deonstration The odel paraeters for the force calculation are defined as L r =.7e-3 (), L g =.75e-3 (), L y =.1e-3 (), L =.7e-3 () t r =.1e-3 (), t y =.15e-3 (), t =.1e-3 (), d = 1e-3 () A MATLAB analysis is done by foring pereance coefficient equations which are available in APPENDIX B to obtain the flux density at air gap and force for different displaceents. Forces are deterined for the sae odel using ANSYS for three different displaceents with x= [,.75e-3,.15e-3] by virtual work, Maxwell tensor and Lorentz force ethods and the average of these forces are taken for coparison with theoretical data. Fro Table 3. A and B and Figure 3.16(A, B) the results for coparison of force data fro theoretical and ANSYS are very close with <1% discrepancy. These discrepancies are due to the diensional approxiation tolerances ade for ean flux path length for pereance coefficient deterination. 63

86 Generally, the theoretical calculations agree with ANSYS results which validate the accuracy and usability of theoretical calculations for better deterination of air gap flux densities in agnetic circuits to finite eleent analysis results. Displaceent (x).75e-3().15e-3 Air gap Flux density ( B ) fro g 1.37 T 1.33 T 1.5 T theoretical analysis Air gap Flux density ( B ) fro g 1.4 T 1.36 T 1.6 T ANSYS Force fro ANSYS (N) 1. Virtual Work Force (Fvwy) Maxwell Stress tensor Lorentz force (Fagy) Average Force (N) Force(N) fro theoretical calculation using MATLAB Accuracy (Force) 93% 96% 98% Accuracy ( B ) g 93% 93% 9% 64

87 ITEMS -Offset.75e-3 ()-Offset.15 e-3 ()offset Flux Flow plot Flux density Force at arature (Vector Plot) Table 3. Ansys results for flux flow, flux density and force - Force evaluated by theoretical approach - Force evaluated by ANSYS (A) (B) Figure 3.16 Coparison between theoretical ethod used and ANSYS results A. Force Vs Displaceent, B. Bg Vs Displaceent 65

88 3.7 Significance of Pereance coefficient with leakage calculation at icro level: Pereance coefficient calculation is beneficial at both icro and acro level applications and ay affect the outcoe of the syste for both applications. Direct calculation of forces using only airgap fluxes see to give a force of.65n which is.7 ties ore than that obtained fro Pereance coefficient ethod and siilar fro ANSYS results, the flux density obtained was 1.91 T which is 1.41 ties respectively ore than that obtained by Pereance coefficient ethod and fro ANSYS results as shown in Figure The difference gradually reduces for higher displaceents because of the increase of percentage of useful flux to fringing flux as the agnitude of fringing flux diinishes at higher displaceents. The sae is also true for analysis done for the sae odel used in acro scale and siilar characteristics can be observed. Figure 3.17 Coparison of force deterination ethods Pereance coefficient calculation would introduce significant iproveent in icro level agnetic circuit analysis with its high accuracy and siplicity. This ethod would help achieve ideal paraeters at icro scale than direct ethod to iprove the net power generated by the syste. This iproveent is significant at 66

89 icro level because of the low agnitude of power generation at illi and icro watts. The Pereance coefficient ethod would alleviate the need for separate forulations for forces for in parallel and perpendicular displaceents. The deterination of air gap agnetic field would take care of variations in flux linkage for perpendicular or parallel displaceent in deterining force with good accuracies for siulation realisation as seen fro previous section. 3.8 Electrical circuit analysis: Arature windings and the agnetic sources are oriented in electrical generators in such a way to attain axiu flux linkage and to keep copper loss at a iniu. Proper deterination of equivalent resistance, current loading and losses would ensure desired physical and functional paraeters to achieve high power density. This section describes an original analytical ethod used in the thesis to deterine equivalent resistance for planar windings adopted in the thesis for paraetric analysis. Heat loss deterination at icro scale using electron theory is detailed and continued with explanation of factors affecting electrical circuits at icro scale Planar Winding Analytical odelling ethod Winding paraeters like no of coils, resistance, length and current loading are deterined with the knowledge of average area of coil span, winding distribution factor and fill factor. For exaple, the equivalent length of winding for resistance calculation can be deterined easily for radial topology like wave, lap or ring types with fixed diensions per turn. But, this is not the case for planar windings whose diensions change with every turn. This ethod gives roo for analysis of planar winding with different fill factors, depths and areas. This ethod gives a very good approxiation of equivalent resistance and other paraeters to be used for luped paraeter analysis. 67

90 This would help develop better winding structures with desired paraeters in a sipler anner. b b1 h h u u b (A) (B) Figure.3.18 Planar winding topology A. Rectangular & B. trapezoidal Winding Paraeter Deterination b + h. x = Rectangular L coil = L ( x) = L ( x 1) 8u n old old x= 1 Lcoil ( x) = Lold ( x) + Lcoil ( x 1) x > Where n is no of turns per coil profile and u is space between turns Trapezoidal b 1 + b + * slope.. x = L coil = L ( x) = ( b1( x 1) + b( x 1)) 4u + * slope( x) n old x= 1 Lcoil ( x) = Lold ( x) + Lcoil ( x 1). x > Where slope = h + (( b1 b) / ) and slope( x) x = h( x) + ( b1( x) b( )) / ) with h( x) h( x 1) u =, b 1( x) = b1( x 1). u,and b ( x) = b( x 1). u b 1 (.. r / nc) tl1 = π, t l1 space between coil structure and outer radius 68

91 b = π, t 1 space between coil and inner radius (.. ri / nc) tl And nc of coil pairs per layer of coil structure Table 4.1 Paraeter deterination for planar winding using theoretical odelling The siplicity of the odel is further iproved by ebedding winding width and depth included with the interleavance space u. The algorith would deterine the A. The nuber of coil turns N coil for a given width and no of coil pairs in a winding layer structure which is used in luped paraeter odel for achine perforance analysis. B. Equivalent final length of the coil by including end connections as L = L + L final coil end C. Deterine resistance fro equivalent length and are winding as R eqv L final = ρ. A coil D. Analysis of Current density and current loading with knowledge of N coil and A coil Validation of Analytical ethod Validation of the planar winding analytical ethod for paraeter deterination is done by applying the ethod for paraeter deterination of an planar winding profile reported in literature[8]. The resistance of the trapezoidal winding structure obtained fro theoretical odel is 44.3 Ohs. The easured value of resistance for the fabricated winding structure reported in literature was 45 Ohs. This iplies that the analytical approach to obtaining winding paraeters for planar windings is close to easured results. This proves the accuracy of the theoretical odel and its validity for use for electric circuit paraetric analysis. 69

92 3.9 MEMS Generator odel presented in thesis The energy density (ED) of current engine-generator systes is 4 ties lesser than batteries. The energy density of the syste is dependent on efficiency and ratio of fuel to syste volue. An iproveent in ED can be attained by iproving the efficiency or fuel to syste volue ratio. If the desired ED to be attained is taken as X. For exaple X is to achieve two ties the energy density than batteries then it can be equated with respect to current systes as E.D Current *4 = (X/) (3.38) X= E.D Current *8 (3.39) Equation 3.34 shows that to attain an energy density two ties that of batteries an increase in eighty ties the ED of the current systes ay be required. The research looks at iproveent in icro generator developent with better efficiency and power density to iprove the ED of the syste by 1. Iproving efficiency of the icro generator to 7 to 8%.. Reducing the volue of the generator by a factor of to 3 for the sae power iproving power density of the icro generator. The above iproveents will increase the net syste efficiency to 1.4% and fuel to syste volue ratio by to 3. This will give a total iproveent to syste ED by a factor of 3.5 to 5 [A]. (A) 7

93 d6 d5 M t q t1 M gw gp g q1 d3 d1 d d4 PM South pole PM North Pole Poles Back Iron Winding (B) Figure A. 3d view of icro generator assebly B. Micro generator -d cross-sectional view (not on scale) The icro generator is developed for integration with a katrix rotary engine odel with its rotor structure the as shown in Fig.3.19 A. The rotor core and planar windings are sandwiched between the peranent agnet sources which are located outside the engine casing. The windings are developed to be electroplated directly to the agnetic circuit stator structure separated by an epoxy layer. This ethod would assist in further reduction of volue and increase in power density. The advantage of this proposed syste is 1. The net air gap flux density in the generator is increased with two peranent agnet sources. Better Flux shielding and distribution at air gap is achieved by different sizes for poles. 71

94 . The agnetic circuit allows for flux reversal iproving flux distribution. Leakage is reduced by reduction in air gap and total length of flux path. 3. The volue of agnetic circuit is reduced with thinner back iron cores. This set up will iprove the saturation characteristics of the icro generator cores and help reduce iron losses. 4. The volue of the winding is reduced with planar windings unlike wound structures used in developent for icro generators. 5. Reduction in fabrication steps by cobining winding and core structure. 6. Better flux distribution for EMF generation by cobining winding and core structure. 7. The coponents are siple and anufacturable using existing technologies and can be assebled with oderate ease. 8. The agnetic circuit like the other reported generators is susceptible to reduction in Hc due to high operational teperature of the generator. This could be reduced by using epoxy layers (with low theral conductivity) in the air gaps between the agnetic circuit and the engine cobustion chaber to protect the agnetic circuit. The above generator odel would iprove the power density of the icro generator and also reduce the volue and ass of the unit iproving the energy density of current engine integrated icro generator power supplies 3.8 Suary The following points can be suarized for the chapter Scaling strategies for icro generator developent is discussed. Fro the scaling strategy, the power density of the icro generator upon scaling can be increased by varying current density Jα 1, and angular frequency Nα. 7

95 The considerations and liitations of Magnetic and Electric functional paraeters for icro generator developent are briefed. Luped paraeter analysis on radial, axial and reluctance achine for best topology for icro generator developent is done. The analysis pointed to axial achine having the capability of producing high power density but in a narrow region with the necessity to select suitable paraeters to operate at the narrow region. Deterination of pereance using three different approxiation ethods is detailed and their accuracy to graphical approxiations is analysed with circular and diagonal approach providing closer results. Pereance co-efficient is an iportant factor for agnetic circuit analysis especially in icro generator odels where the volue of aterial of air gap volue is less. The accuracy and significance of the pereance coefficient ethod for peranent agnet circuit analysis is provided and validation using ANSYS FEA results. An accuracy of around 9 to 93% to FEA results is achievable using pereance coefficient ethod Planar analytical odel to deterine coil paraeters of a given coil profile for luped paraeter analysis is explained. The ethod when validated by applying it for resistance deterination of a planar winding profile reported in literature showed good agreeent with easureent value. The icro generator odels presented in the thesis is introduced. The developent strategies and advantages of the odels to achieve better power density than the existing icro generator odels for integration with icro engine are briefed. The next chapter would deal with the ethodology used for paraetric analysis of the icro generator. Magnetic circuit analysis of the icro generator odel presented also fors part of the chapter. 73

96 Chapter 4: Modelling & Magnetic circuit analysis The ethodology for developent of a thin MEMS axial generator odel for integration with a icro engine is discussed in this chapter. The ethodology uses a luped paraeter odel suitable for both icro and acro generator developent. The odel takes independent inputs fro agnetic circuit analysis using pereance factor ethod and electric circuit analysis at icro scale discussed in chapter 3 to iprove the accuracy of the analytical developent. The developed ethodology is validated by applying it on a reported odel available in literature[1] to deterine voltage, power and winding paraeters. The results fro the analysis are copared with practical and theoretical results obtained for the literature odel. FEM analysis is done to validate deterination of agnetic circuit analysis results obtained fro theoretical analysis. 4.1 Thin MEMS Micro Generator Model A cross-sectional view of the icro generator odel developed is shown in Figure 4.1. The odel is of an axial topology to exploit the advantage of achieving higher power density as discussed in chapter. The stator winding and the rotor ferroagnetic poles are sandwiched between peranent agnet structures foring the generator structure. Windings can either be connected in series or parallel according to the requireent and size of the ferroagnetic poles. The poles structure is selected to lay inside the winding structure for better flux linkage as shown in Figure 4..A. Magnetic back iron or cores are used for better flux flow between the peranent agnet sources as shown in Figure 4. B. 74

97 d6 d5 M t q t1 gw gp g M q1 d1 d3 d d4 PM South pole Poles Winding PM North Pole Back Iron Figure 4.1. Planar Micro generator cross-sectional view E E Ri ` L Ro ϖ Bg (A) (B) Figure 4. A. Superiposed view of poles and winding B. Side view of showing flux loop and induced ef direction 75

98 The net induced voltage for a single phase can be written in ters of the area of flux linkage the windings upon angular rotation ωn as Ro = coil v g n (4.1) Ri V ( t) N. K ( t). B. r. dr. ω.( p / ) Where ( p / ).N represent the nuber of coil turns per phase. (t) is represents the coil K v ration of V ( t) / V or siply for a sine wave can represent sin( t + (18 t)). Equation pk 4.1 is integrated to get V pk andv rs as in 4. and 4.3 V pk coil g i = (1/8). p. N. B.( D D ) ω (4.) n V rs coil g i =.88. p. N. B.( D D ) ω (4.3) n For exaple, to generate a voltage of 3V with assued inner and outer generator diaeter of 1 and 1 and a flux density level of 1. airgap, Ncoil required would be approxiately 74 for even nuber of turns. The current required to generate a power of 1W would be 3.33e-4 aps. The developent with such N coil nubers is possible using MEMS planar technology. The continuing sections in this chapter look at the ethodology and investigations for selecting best agnetic, electric circuit and physical paraeters to generate a voltage of -3Volts and 1-1W output power. Net flux density achievable at airgap is iproved by inclusion of two agnetic sources. The odel also achieves reduced leakage fluxes using the difference in pole diensions and regulates better flux flow. The difference in pole diensions also help in effectively reducing cogging torques generated at pole edges. Better and reduced size of winding structure using planar winding. Planar windings used in the icro generator developent will reduce size of winding structure and coplexity in assebly. 76

99 Additional layer of winding structures can be added to iprove power density and achine perforance upon requireent, which iproves the flexibility of the odel for iproveent. The net power density of the syste, the author believes will be iproved by the above inclusions in the developent of the icro generator. 4. Methodology for icro generator developent The ethod of luped paraeter analysis is used in this research to select suitable agnetic circuit and electric circuit paraeters for a given topology with given paraeter range and constraints. Start Micro-Generator Paraeter range and constraint Initialization Magnetic Circuit Analysis for Bg, Force and Torque Electric Circuit Analysis for Resistance, Current density Modified Luped paraeter odel analysis for Generated voltage, Current loading, Power and Energy density NO Check for paraeters within perissible liiting conditions Yes Characterisation of MEMS icro engine generator power supply using cobined luped paraeter odel Start Figure 4.3 Flow diagra of the ethodology for icro generator developent 77

100 Soe of the advantage of this ethodology provides are 1. Better accuracy with independent agnetic circuit and electric circuit analysis.. The coputation required to arrive at a local inia or axia for an objective function is less than optiization techniques and FEA techniques. 3. The odelling is siple and does not need specialised tools for analysis. 4. Multiple boundary conditions and constraints can be easily ebedded to the odel which is difficult with FEA or optiization algoriths. 5. Single coputation is enough to select paraeters for axiu power or axiu efficiency. 4.3 Luped Paraeter Modelling The luped paraeter odel is developed by foring generalised characteristics equations defining achine perforance for generated voltage, current and power. Diensional variations are ebedded into characteristic equation using a relative Beta factor defined by Do/Di ratio. This is used to analyse achine perforance to change in operational and physical paraeters and help choose best achine paraeters. The basis on the foration of generalised characteristic equations for luped paraeter odelling for axial achines is provided in chapter. Developent consideration specific to the presented icro generator is 1. The rotor takes 6% of the total achine area defined by π. Do / 4.Peranent agnet aterial ebedded to the rotor occupies 6% of the rotor space to achieve better flux density levels and is given by o A = ( π. D.(1- ς )) / 4 (4.4) Or = ( π. L -ς. π. L ) / (4.5) A 78

101 With ς being a factor which representing the area occupied by peranent agnet aterial core in the rotor. In this research is ς is taken to.6 in this case. The engine liacon rotor radius is the generator rotor radius ie., L = R. The area of planar coil boundary for stator per winding pattern is defined by e o A c = ( π. L -ς. π. L ) / Coil _ Pairs (4.6) The induced phase voltage when expanded and using β ratio would take the for ( β -1) V ( t) = N coil. K v ( t). Bg. Do.. ω. K.( p / ) n ew (4.7) 4β In the above equation K v (t) is a factor represent the ratio of peak voltage and V(t) as K v ( t) = V ( t) / V pk and ω n is the angular frequency. K ew is a voltage wavefor factor which takes in to account the winding distribution and written as K polearea = K w. K s & AirgapArea ew. sin( p * q / ) K w ( p, q) = (4.8) p *sin( q / ) With q representing coils/pole/phase and K s included with K ew for skewing in poles Ks = sin( σ / ) /( σ / ) (4.9) with σ being the skewing angle. The Peak values of voltage, current and power are iportant indicators of achine perforance and are the rating of the achine. In equation 4.7 peak voltage occurs when Kv = 1 and so V pk can be written as V pk ( β -1) = N coil. Bg. Do.. ω. K.( p / ) (4.1) n ew 4β Current loading is an iportant design paraeter in any electrical achine both icro and acro. It defines the perissible current level and current capacity of the achine. Ipk can be written using current loading and a wavefor factor Ki as Ai D ( β + 1) = π K (4.11) o I pk... a.. N coil β i 79

102 Where. N coil. I rs Ai = (A/) and K i = I pk / I rs π. D. a D above is defined as the average winding area ( D o + D D = i )to represent current loading. Current density can be obtained as J = I A pk coil I = π. D pk coil 4 (4.1) Maxiu power can now be written by cobining equation 4.1 and 4.11 which takes the for f Ai 3 ( β -1)( β + 1) P ax = Bg. π.( p / ).. K ew. a. K i. Ph. ηgen. Do. (4.13) 3 p. 8β With η Generator losses = 1- Pin ( β 1)( β + 1) Equation 4.13 suggest that axiu power occurs when =1 3 8β with < β < 1. β ratio has to be noralized to get better agnetic and electrical loading in the achine to achieve axiu power output in the achine. A. Loss deterination The losses in the syste are generally accounted for fixed and variable losses. The fixed losses in the syste include eddy current losses, hysteresis losses and windage losses or anoalous losses. The variable losses are generally the copper losses and stray losses etc. Eddy current loss at core and hysteresis loss can be written as n ec = Bg. f.( d / ρcore K e & P h Bg. f. K h P ) = (4.14) Where d and ρ are the thickness and resistively of the core. Hysteresis loss for a volue of core is usually obtained by curve fitting to experiental data available for aterial used. Equation 4.14 is an approxiation of 8

103 hysteresis loss for theoretical analysis with n a steinetz constant used to approxiate hysteresis loss to experiental data. n varies fro 1.5 to.5 and for acro achine analysis is taken as 1.6[] and icro etals is taken as.11[3]. Frictional losses, windage and stray losses are usually taken as an percentage of total losses P c = ( δ + δ + δ ). P (4.15) f w wd ax Withδ f, δ s, δ wd taken as.3. Copper loss or variable loss is written in ters of average coil area π. D and β as ( β + 1) P cu = π. I pk ( Ai / )[. Do / Dcoil ].. ρcoil. a. K i (4.16) 16β Substituting further for Ipk and introducing K = D L, P cu becoes p o / P cu 1 ( β + 1).( β + 1) = π.( Ai / )..( Do / Dcoil ).. K p L ρcoil a K i (4.17) N coil 3β It can be seen fro the equation that the copper loss is dependent on the D o /D coil ratio. An increase in conductor diaeter helps to reduce the total copper losses in the syste irrespective of no of turns in the stator. The above ratio is iportant in the selection of conductor gauge and helps to obtain a desired D coil to achieve reduced copper loss. The length of coil with end connection has to be taken into consideration with the end connection and inter winding connection for calculating copper loss. P ax with losses can be written as P ax = B. π. ω.( p / ). K g ( π.( Ai / ) n 1. N coil.( D o ew / D Ai. a. K i. Ph. K coil p. D o ( β + 1).( β + 1) ).. K 3 3β ( β -1)( β + 1). L. 3 8β p. L. ρ e coil. a. K - i ) - C (4.18) n With C = [ B f.( d / ρ ) K + B. f. K ] + P.( δ + δ + δ ) g. core e g h ax w f wd And power density of the achine is written as 81

104 Pax P. D = (4.19) v Gen With v = π. rf L where rf is the final outer radius and L the final achine length Gen. B. Inductance deterination Inductance of the arature windings helps to deterine the aount of agnetic energy stored in the circuit and can be written in ters of agnetic and electric circuit paraeters as L ar N coil. µ o. A = (4.) L coil And self inductance of the agnetic circuit is given by L si N coil. p. µ. A.( r ri ).( tw + ww ) = (4.1) 36. π 4.4 Validation of Micro generator developent ethodology Validation of the icro generator developent ethodology is done by applying the ethodology for perforance prediction of an axial achine icro generator reported in literature [1][95]. The paraeters taken for perforance prediction are sae as the build axial icro generator odel reported in literature [1, 4]. The analysis used in reference [1] uses direct equations to predict power fro easured resistance fro the icro fabricated coil structures. The agnetic circuit analysis in literature is not solved fro a agnetic proble prospective rather siply assues the flux densities to be unifor and equal to +/-B r / in any coil region lying above the peranent agnet. Figure 4.4.shows the results obtained fro the validation analysis. The prediction of generated voltage using the theoretical ethodology presented in thesis is close to experiental and the test bud results reported in the literature. The generated power predicted fro the ethodology reported in literature and used in the 8

105 thesis as shown in Figure 4.4.B is close and crosses over when the no of coil layers is oderate. The prediction shows soe visible difference when the coil layers are reduced or increased fro this oderate value. The variation can be reduced by noralizing the β ratio in the luped paraeter odel and using ore accurate values for K, p K and i K. ew 3 Generated Voltage[v] Prototype Result data Test Bed Result Luped paraeter odel prediction Generated Power[Watts] Experiental test result and predicted data Luped paraeter odel prediction Speed[] x Layers[] (A) (B) Figure 4.4.A. Generated voltage predicted by luped paraeter odel and copared with experiental & test bed result data for the reported icro generator for validation B. Output Power predicted by luped paraeter odel and copared with Experiental & test bed result data for the reported icro generator for validation 4.5 Micro generator agnetic circuit analysis Magnetic circuit analysis for the icro generator is done by developing a - D agnetic network including possible and iportant fringing and leakages paths. The network is expanded for 3-d pereance odel for useful airgap, fringing, and leakage are evaluated for pereance factor deterination. A -D agnetic network for the icro generator is shown in Figure 4.5.The network is represented in the for of circuit reluctances for siplicity of presentation and easier understanding. It should be noted that the agnitude of reluctance or pereance for the forward flux path (left hand side of the dotted line) in Figure 4.5 is equal and opposite 83

106 to the agnitude of pereance of right hand side. The calculation of pereance factor unlike to traditional resistance network analysis is accurate to deterine agnetic circuit functional paraeters and avoids needs for tie intensive FEA odelling and analysis. R cl R c R l R pwf R pg R p F R wg R s R pwf Ni R wl R wpl R pwl R wl R pwf Ni R p F R wg R pg R n R pwf R pwf 1 R l R nf R g R f R sf R g R sf F q 1 R n t 1 R c t q F R s R cl R cl1 Figure D agnetic network for the thin MEMS icro generator (Figure not on scale) *Note: Rcl1 is flux path between Rcl and R c. Siilar paths exist in parallel with all leakage reluctances above but not shown for clarity and better visibility The useful air gap pereance P in the icro generator is g P ( P + P + P )* (4.) g = pg g wg 84

107 The fringing pereance Pf is P ( P + P + P + P )* (4.3) f = nf pwnf pwsf sf Leakage pereance P l is P l = ( Pl + Pcl ) * + Pwl + Ppwl + Ppl + Pl + ( Pl 1 + Pcl 1 )* + Pwl 1 + Ppwl1 + Ppl 1 + Pl 1 (4.4) The deterination of 3-D pereance is given in tables below Flux profile Air Flux path 3-D Pereance A. Trapezoidal agnetic core structure Static P g ( r = - r )( w. g + w ) µ P pg ( r4 - r3 )( w1 + w ). µ =. g p P wg ( r = 4 - r )( w. g + w ). 3 1 µ w Dynaic wrt to angle of rotation P wg p ( r4 - r3 )( w1 + w ). µ.(1 ( θ. )) ( dynaic) =. π.( g + g ) p B. Rectangular agnetic core structure P g = (( r4 r3).(. π. r3/ cp)).µ g P = P = P can be taken to be of sae agnitude g pg wg 85

108 P wg p (( r4 r3).(. π. r3/ cp)). µ.(1 ( θ. )) ( dynaic) =. π ( g + g ) p Fringing flux paths: A. Trapezoidal agnetic core structure.6. µ.( r3 ( r1 + t1).(( w1 + w ) * + P nf = ( r ( r + t ) h + (( w 1 - w ) / ) ).6. µ.( r3 ( r1 + t).(( w1 + w ) * + P sf = ( r ( r + t ) 3 1 h + (( w 1 - w ) / ) ) P pwnf = 1 + w ) * + h + (( w1 w ) / ) ) (( Lpg + Lwg + t w ) + t1 ). µ.(( w - π. Ln t 1 P pwsf 1 + w ) * + h + (( w (( + + ) + 1 w ) / ) ) L pg Lwg t w t ). µ.(( w - = π. Ln t B. Rectangular agnetic core structure (used in dissertation) 1.. µ.( r3 ( r1 + t1).(( r4 r3) + (. π. r3/ cp)) P nf = ( r ( r + t ) µ.( r3 ( r1 + t).(( r4 r3) + (. π. r3/ cp)) P sf = ( r ( r + t ) 3 1 P pwnf 4. µ.(( r4 r3) + (. π. r3/ cp)) (( L =. Ln π pg + L wg t 1 + tw) + t1) P pwsf = 4. µ.(( r4 r3) + (. π. r3/ cp)) (( L. Ln π pg + L wg t + tw) + t) Leakage flux ( r5 (( r4 r3 ).( w1 + w )). µ Pl ( static) = paths 4.( h + g + g ) p 86

109 P l ( dynaic) = ( r 5 (( r 4 p r3 ).( w1 + w ).(1 θ. )). µ π 4.( h + g + g ) p P pwl =.69. µ. r 1.3(( r1 + t1 ) - r1 ). µ P pwl 1 = (( r + t ) - r ) (( r1 + t ) - r1 ). µ P pwsl 1 = (( r + t ) - r ) 1 1 P = pwl = Ppwl = Pwl Pwl since g p gw = g = are sae P pwl1 = Ppwl1 = Pwl 1 = Pwl 1 P cl =.69. µ. r 4 P cl 1 =.3( r6 - r5 ). µ ( r r ) 6 5 Table D pereance deterination for the icro generator odel The pereance factor with and without fringing flux taken in to consideration as in 4.6 and 4.7 as Pg P f = Where P t = Pg + Pf + Pl (4.5) P t P f Pg + Pf = (With fringing flux) (4.6) P t The flux density at airgap can then be evaluated using equation A B g = Br. Pf. (4.7) A g 87

110 The analysis of the agnetic circuit includes a ultidiensional analysis using Matlab siulation to see the effect of airgap flux density over change in rotor radius, t1 and t (APPENDIX B). The initial paraeters defined for analysis is % paraeter description% - All diensions in eters L=.9e-3; % Rotor peranent agnet pole length.15e-3< G <.5e-3.1e-3<t1<e-3,.1e-3<t<e-3 ;% distance t1 and t Core thickness=35e-6;% To sustain saturation with iron core with pereability of 5.5e-3<t<1e-3];% defined to keep L/Lg ratio >[1 15 ] Gcw=.5e-3; %coil to coil air gap distance and peranent agnet source distance 1e-3<L<e-3]; % liacon or rotor radius. Any variation in liacon radius varies the width of the peranent agnet source and the pole width. d1= 1e-3; % defined wrt to the iniu bearing of.3 or 3icron diaeter and for coercial bearing innner diaeter of 1 to shaft db=3e-3; % coercial ball bearing dia for 13 Krp [1] Br=1;% coercial grade SCo17 At first, analysis is done to deterine the effect of airgap flux density over change in rotor radius and distance t1 representing change in Q1 distance with fixed t and keeping the air gap at 5µ. The iplications fro Figure 4.6.A and B show that the airgap flux density levels achievable are high with a rotor radius of ore than 1. After this radius the slope of the flux density curve shows little iproveent with increase in rotor radius. Rotor radius of above 1 with high achievable flux density are well suited for objectives to generate axiu power O/P. The objective here is to select paraeters to achieve axiu power density. The flux density region and the rotor radius to the left of Figure in 4.6.B would be well suited. The reason for this reduction in slope of flux density change to rotor radius is due to the reduction pereance factor variation. 88

111 1.8 Perance Factor Rotor radius () (A) Region for high power density Airgap flux density (T) X:.5 Y: Region for high ouput power Rotor radius () (B) Figure.4.6 A. Pereance factor to change in Rotor Radius, B.Airgap flux density fro pereance co-efficient deterination to change in Rotor Radius Figure 4.7 iply that the leakage pereance agnitude increases and fringing pereance agnitude reduces with increase in t1 distance. This is because the agnet width represented by Q1 increases with t1 which akes the agnet width considerably larger than the peranent agnet poles which induces leakage flux paths 89

112 bypassing the peranent agnet poles. A siilar effect would be seen if t1 is fixed and t is varied. Leakage pereance increase in agnitude with increase in radius of the rotor as shown in Figure 4.7.A for a given air gap because of reduction in L g /A ratio. High flux density level would be achieved by controlling the fringing and leakage pereance paths with proper t1 and t distances. Leakage pereance x Rotor radius ().1. Distance t1() (Fringing pereance/airgap Pereance)* Distance t1() 1.5 x 1-3 Rotor radius () (A) (B) Figure.4.7 A. leakage pereance to change in Rotor radius and t1 for fixed t B. Fringing/air gap pereance percentage for change in Rotor Radius and t1for fixed t. Pereance between the peranent agnet source and the agnetic pole increases with increase in rotor radius as shown in Figure 4.8. This is due to increase in area of the peranent agnet source and poles to increase in rotor radius. The air gap pereance also reduces with increase in air gap length. Air gap lengths between 1-3µ at rotor radius of ore than 1 will achieve stable axiu flux density levels for axiu power O/P and the sae for radius less than 1 would help in achieving high power density. The sae condition could be seen for the pereance between the peranent agnet pole and the winding structure. The air gap can be adjusted to suit accuracy in anufacturing process and other constraints like drag forces at icro scale. 9

113 Pereance fro PMcore to poles in airgap G Pereance at airgap Rotor radius() Airgap G () 5 6 x 1-5 Figure.4.8 Pereance at air gap G fro PM source to poles Magnetic circuit calculations used in literature assues flux densities to be unifor and equal to +/-B r / in any coil region lying above the peranent agnet[1]. With this assuption the achievable flux density levels at air gap for this agnetic circuit will be 1T as shown in Figure 4.9(A). By using pereance factor to deterine air gap flux density gives a clear picture to variation of air gap flux to rotor radius and distance t1 as shown in Figure 4.9(B). The axiu achievable flux density varies with rotor radius and distance t1. Calculation using the earlier ethod with air gap flux density as +/-B r / will cause errors in theoretical analysis results. Flux at airgap with pereance factor(t) Rotor Radius() X:.11 Y:.11 Z: x 1-3 Distance t1 () Flux at airgap (T) Rotor Radius() x 1-3 Distance t1()() (A) (B) Figure.4.9 A. Flux density deterination using direct ethod, B. Flux density achievable using pereance factor calculation 91

114 Figure 5.8 and 5.9 shows the analysis to see the effect on air gap to change in t1 and t done for a fixed rotor radius of 1. Figure 5.8 shows that a reduction in leakage can be achieved with a t/t1 ratio of between to. The reduction in leakage by a higher ratio of t/t1 will cause increase in fringing flux and affects the length to width ratio for better field intensity and deagnetisation characteristics. It is also evident fro Figure 5.9 that a reasonable low t/t1 or siply t ratio between to 3 would provide axiu flux density, not affecting the length to width ratio of the peranent agnet and control leakage and fringing flux. leakage/airgap pereance percentage X:.1 Y:.1 Z: x 1-3 Distance t1 () X:. Y:.1 Z: 19.5 X:.9 Y:.16 Z: 4.63 X:. Y:.9 Z:.31 1 x 1-3 Distance t () Figure 4.1.Leakage/Airgap pereance ratio with change in t1 and t for rotor radius of 1 Airgap Flux density (T) X:. Y:. Z:.9753 X:. Y:.9 Z: 1.15 X:. X:. Y:.1 X:.16 Y:.5 Z: Y:.1 Z: X:.1 Z: Y:.1 Z: X:.11 Y:.1 Z: 1.14 X:.1 Y:.1 Z: x 1-3 Distance t1 () Distance t () x 1-3 Figure 4.11 Air gap flux density to change in t1 and t for a fixed rotor radius of 1 9

115 4.6 FEM Analysis and Validation FEM analysis using ANSYS 11 is done to validate the results obtained fro theoretical agnetic circuit analysis. A -D axis syetric agnetic nodal analysis for the icro generator is perfored to predict the flux density levels achievable at the air gap. Literature results have shown that -D FEM agnetic circuit analysis gives closer results to 3-D analysis and also easier to develop and analyse[1]. The eleents are defined by eleent type agnetic vector solid plane 53 and the key-options are selected for axi-syeric analysis. Figure 4.1 Micro Generator -D Ansys odel Figure 4.1 shows the developed -D odel of 5 scale icro generator odel in ANSYS for analysis. Paraeter selection for the icro generator fro the odified luped paraeter analysis which is detailed in chapter 5 has shown that a 5 rotor 93

116 radius icro generator can produce.8v and W. The FEM analysis done for the final odel is illustrated here for validation. A t/t1 ratio of is considered for analysis and the agnetic poles are odelled to be at the centre of the winding structure for axiu flux linkage. The physical paraeters used for the icro generator odel is available in chapter 5. Figure 4.13 shows the peranent agnet B-H curves were the characteristics of an coercial grade SCo17[5] with Br=1.38 is used for analysis. The poles alignents are defined by the orthographic coercive force paraeters MGXX and MGYY. The pereability of the PM agnet taken for analysis in this case is 7 and that of the agnetic aterials as 5 siilar of Ni:Fe alloys to achieve high saturation levels. The air gap for analysis is taken as 3µ between the PM source and the poles and 6 µ between the poles, windings and the opposite PM source. Figure 4.13 B-H curves of peranent agnet odels The odel was initially fored in eter scale and scaled down after eshing for icro eter scale. This is because difficulties were experienced while fine eshing icro structures with liitations posed by the size of the quad eleents. The eshed 94

117 odel for analysis is shown in Quad esh is developed with eleent lengths of.1 and eleent nubers of 5. The air gap is finely eshed for accurate results in this case the eleent length was set at.1. Figure 4.14 Meshed Micro Generator odel Static solution analysis is done to deterine the no load flux density levels of the icro generator to validate the results obtained fro theoretical analysis. Figure 4.15A shows -D flux lines for the icro generator odel and the air gap path defined to obtain air gap flux density using PATH function in ANSYS. Figure 4.15B shows the flux lines for the coplete odel. Figure 4.16 shows the result obtained for no-load flux density at one half of the air-gap obtained by the PATH function. The flux flow is regulated and the leakage fluxes are reduced by using back iron and different lengths of peranent agnet source as shown in Figure 4.15 A and B. A trapezoidal air-gap flux density characteristic is observed with axiu achievable flux density levels of 1.64 T. The theoretical results fro previous section predicted axiu air gap flux density level of T at 5 rotor radius which is 93% accurate to FEM results which validates the theoretical ethod. 95

118 (A) (B) Figure 4.15 A. -D flux lines for one half of the icro generator and the air gap path selected for PATH operation in ANSYS. B. -D flux lines for the Micro generator odel. 96

119 4.7 Suary Figure 4.16 Air gap flux density obtained using PATH operation in ANSYS. The ethodology for developent of a thin MEMS axial achine odel for integration with a icro engine is discussed and validated. The result fro validation when copared with prototype results reported in literature was found to have close atch with little discrepancy which can be avoided by proper selection of β factor. Magnetic circuit analysis for the icro generator is a -D agnetic network which is expanded for 3-d pereance odel to deterine useful air gap, fringing, and leakage fluxes fro pereance factor deterination. Iplications fro analysis show that the air gap flux density levels achievable are high with rotor radius of ore than 1. After this radius the slope of the flux 97

120 density curve iprove less with change in rotor radius Air gap flux densities achievable at air gap lengths of 1-3µ is high for rotor radius ore than 1 which could be considered for designs with the objective to generate axiu power. Rotor radius of less than 1 with an increasing slope of air gap flux density is a good choice for icro generator to achieve axiu power density The analysis to see the effect on air gap to change in t1 and t done for a fixed rotor radius of 5 show that a reduction in leakage and better flux regulation can be obtained with a t/t1 ratio of between to. FEM analysis is done using ANSYS 11 for a icro generator odel with a rotor radius of 5 to validate theoretical agnetic circuit analysis ethod. Predicted results for air gap flux density fro theoretical analysis are 93% closer to FEM analysis results which validated the results obtained fro theoretical analysis. The next chapter would continue with the paraetric analysis of the icro generator and the integrated engine-generator odel for high power density and energy density. The analysis is aied at ideal selection of paraeters for the syste and to characterize the operation of the syste. 98

121 Chapter 5: Characterisation of Micro Generator and Integrated Engine-Generator Syste The selection of icro generator paraeters fro the ethodology developed in chapter 4 is continued in this chapter. Characterisation of the MEMS icro generator with the selected paraeters is perfored for icro generator operation at no load, fixed and variable load conditions. Theoretical odelling of the engine functional paraeters is cobined with the icro-generator paraeter odel to for an integrated icro enginegenerator theoretical odel. This odel is then analysed for achievable energy density for a given volue of engine-generator odule. Finally, energy anageent for the Micro MEMS generator is discussed to choose a suitable energy anageent strategy for the syste. 5.1 Selection of paraeters for icro generator The selection of paraeter is based on the outcoe to develop a high power density icro generator which generates 1-1W at 3V to be used for portable applications. The objective is to select paraeters to generate axiu power at a sallest volue possible to increase power density achievable fro the syste. Suitable paraeters are selected by cobining agnetic and electric circuit analysis available in chapter 3 and 4 with the generalised luped paraeter odel for the icro generator developed in chapter 4. A ultivariable analysis is done using Matlab to select the paraeters (Code available in APPENDIX E). The key initial paraeters used for analysis are 1e-3<Rotor radius<e-3 <Eccentricity<.5L %eccentricity atrix of the rotor <Speed<4% speed atrix in rp 99

122 Volue=4e-3*7e-3*.5e-3; % volue of the engine-generator syste Area =4e-3*7e-3; % Area of the engine-generator syste Lr=9e-6; %Thickness of the peranent agnet rotor 1<Beta<1.5 %Do/Di ratio.1<air gap<.1% Air gap atrix 3<winding gauge diension<6; % Winding Gauge paraeters (Area obtained fro gauge diension of the winding) The analysis for flux densities at air gap for the agnetic circuit as shown in Figure 5.1 inferred that a rotor radius of <1 with increasing slope in flux densities would help achieve axiu power density. This analysis is used as an input for analysing and selection of other functional paraeters of the generator. The ethodology used in deterining the coil paraeters such as nuber of coils, length and resistance of coil is done with the help of the theoretical ethod defined in chapter 4. A planar trapezoidal winding structure to suit the circular profile of the stator is selected for analysis. This winding structure is selected to provide better copper fill that rectangular or circular winding structure. The inter winding space is defined with a variable beta factor as defined in chapter 4. The beta factor, winding profile, winding gauge specifications (the width and height are derived fro circular gauge diaeter to keep the area the sae) are used to deterine icro generator electric circuit paraeters. The paraeters are selected to generate the required functional outputs and to keep the current density within practical liits of 35A/ for printed circuit board winding structures. 5. Effect of functional outputs to change in Beta factors Two key beta factors which are defined fro chapter 4 to define Do/Di ratio, inter winding spacing. Do/Di defines and deterines the voltage, power and power density of 1

123 the icro generator. An increase in this ratio would increase the voltage because of increase in winding fill area. This increase in will winding fill space will also help in reducing the copper losses by increase in resistance of the winding depending on the winding diensions and reduce the copper losses. Figure 5.1.A and B shows the Do/Di ratio constants fro the luped paraeter equations required to produce axiu power and voltage. It can be inferred fro the figures that to a Do/Di ratio of ore than.5 would help achieve high voltage, power and power density. The slope of increent in Do/Di constants reduces as Do/Di ratio increases which is an added advantage since this ratio is constrained by practically liitation of the shaft diaeter..5 Beta Ratio for axiu voltage generation.16 Beta ratio to achieve axiu power X: 4 Y: R a tio c o n s ta n t.15.1 Ratio constant Do/Di ratio[] Do/Di ratio[] (A) (B) Figure 5.1. Do/Di ratio constants to obtain A. Maxiu voltage and B. Maxiu power The other factor which influences the power generated by the MEMS icro generator is the inter winding spacing ultiplying beta factor. This factor along with the coil diensions deterine the winding fill capacity, current loading of the generator which are iportant functional paraeters for the generator. An increase in the winding interspacing ultiplying factor reduces the nuber of coils/coil 11

124 group/phase/layer as seen in Figure 5.. Siilarly an increase in gauge diension reduces the width and height of the coil and increases the nuber if coil or conductors fill space in the stator as shown in Figure 5.3. The gauge value to winding diaeter and winding area used in the thesis is shown in Figure 5.4. The beta factors needs to be noralised and adjusted to agnetic circuit results to achieve better voltage, power and power densities, which has been done in the next section. 45 nuber of coils/coil group/phase/layer Beta winding interspacing Factor Liacon Rotor Radius [] Figure 5.. Nuber of coils to change in rotor radius and Inter winding spacing beta factor 1

125 Nuber of coils/coil group/phase/layer Beta winding interspacing Guage Diension 6 Figure 5.3. Nuber of coils to change Gauge diension and Inter winding spacing Beta factor.35 Coil diaater 3.5 x 1-8 Coil Area Coil Width..15 Coil Area Guage [] Guage [] Figure 5.4. Coil gauge value to width and coil area 13

126 5.3 Paraeters for axiu voltage, power and power density Figure 5.4 shows the effect of change in speed to generated voltage. An increase in speed increases the generated voltage. The increase in speed is constrained by bearing and frictional losses associated with the achine. The analysis fro keeping a Do/Di ratio of 4 to provide balanced axiu voltage and power shows that a 5 rotor radius and can generate.8v at a speed of rp as show in Figure 5.4. In the later sections this speed is analysed to atch torques of the engine generator syste for axiu energy transfer. Bearing systes to run at this speed is achievable fro literature and is discussed in chapter. At this speed and with only two pole pairs, the syste will have low frequency losses and reduced frictional losses Voltage [V] Rotor Radius [] Speed[] x 1 4 Figure 5.5. Generated voltage to change in speed and rotor radius An increase in Do/Di ratio to rotor radius also presents an increental effect in voltage by proportional scaling of the agnetic circuit and the Do/ Di ratio which are 14

127 shown in Figure 5.5. This ratio is noralized to achieve the required voltage. In Figure 5.5 Do/Di ratios is noralized and a ratio of 5 will generate a voltages of.8v at rp. A further increase in Do/Di ratio would further increase the generated voltage and reduction in volue but would introduce coplexity in anufacturing of shaft and bearing design and deanding higher accuracy with little tolerance. 1 1 Voltage [V] Beta Ratio (Do/Di) Liaco Rotor Radius []. Figure 5.6. Generated voltage to change in Do/Di ratio and rotor radius to a constant speed of 15rp Figure 5.6 is the plot for generated voltage for different rotor radius and for different Do/Di ratio. A generated voltage of.8v is achievable with a rotor radius of 5 with Do/Di ratio of 5 and at rp as shown in Figure 5.7. The paraeter for the coils for the icro generator is selected by deploying the scaling strategy and analysing for suitable coil interspacing beta factor and coil diensions explained in the previous section and also available in chapter3. The no of turns/coil group/phase/layer at 5 rotor radius is 5 as shown in Figure 5.8. The paraeters of the coil gauge 15

128 value of 45 for circular and planar coil diension of 44µ *17µ was selected fro the electric circuit analysis for and coil area of 7.4e Generated Voltage[Volts] X:.5 Y: Liacon Radius [] Figure 5.7 Generated voltages to change in rotor radius at a constant speed of 15rp 16

129 4 No of turns for variable stator area with a define guage size of No of turns/coil group/phase/layer Liacon radius [] Figure 5.8 No of coils/coil group/phase/layer (vs) rotor radius for a fixed winding diension and coil pairs of The no of coils per pole/coil group/phase/layer was analysed to be 5 coils as shown in Figure 5.8. The no of coil pairs used in this case was as shown in the design of the icro generator. The total length and winding resistance for the coil structure fro analysis is 3.86 and 573Ω at 5 rotor radius as shown in Figure 5.9 A and B. The axiu current density of the winding is 1.13e7 A/ (Figure 5.1.A)which is well within the usual practical liits of 3.5e7 A/ for conductors fabricated using printed circuit board technology[1]. The constant losses which includes the hysteresis and the eddy current losses in the agnetic circuit is shown in Figure 5.1 B and the constant losses for rotor radius of 5 is 9e-5W. The available output power and power 17

130 density corresponding to the above paraeters was deterined to be and W and 6.36e3 W/ 3 based on a load of 57Ω L in 15 1 Total Resistance X:.5 Y: X:.5 Y: No of windings Liacon Radius (A) (B) Figure 5.9 A. Total winding length B. Total Coil resistance (For fixed Coil diension and variable liacine rotor radius) Current Density[A/] 7 x X:.5 Y: 1.59e+7 Total constant Losses 4 x Liacon Radius [] X:.5 Y: 9e Liacon Radius() (A) (B) Figure 5.1 A. Current density for a given coil profile at different rotor radius B. Total Constant Losses for fixed profile of icro generator agnetic circuit at different rotor radius 18

131 Table 5.1 shows the paraeters selected for the icro generator using the ethodology described in chapter 4. The power density can be increased further by increased nuber of coil pairs, coil layers and increasing speed proportionately which will also increase anufacturing coplexity. PARAMETERS VALUES Package Volue 4e-3*7e-3*5e-3 Rotor radius (L) 5 Pole piece thickness (Lr) 9µ Air gap between pole piece and winding 1-3 µ Air gap between PM source and poles(gp) 1-3 µ Air gap between winding and PM(Gc) 5 µ t1 Distance of PM fro Di 4 µ t Distance of PM fro Di 8 µ Outer rotor diaeter 1 Inner rotor diaeter 1.5 Inner radius of pole piece 1.75 Outer radius of pole piece 4 Do/Di ratio 5 Pole pairs (P) 1 No of coil turns/coil structure (Trapezoidal) 5 Inner radius of coil 1. Outer radius of coil 4.55 Coil pairs Coil Pitch 19 µ Coil Width 44 µ Coil Height 17 µ Interlayer spacing of coils 3 µ Table 5.1 Paraeters Selected for MEMS icro generator 5.4 Characterisation of Micro generator 19

132 5.4.1 Equivalent circuit odel of the icro generator The icro generator can be characterized using its potier equivalent circuit with induced voltage Vo, Equivalent resistance and reactance of the winding as shown in Figure The resistance of the windings fro analysis in the previous section is 573Ω. The inductance of the winding is calculated to be around 33H and the synchronous reactance Xs is calculated to be 489 by taking Vo to be constant is at constant Bg due to peranent agnet source. The no load voltage and the axiu short circuit current of 4.88A can already be obtained fro the previous section. Rc=573 KΩ X s = 489 Z s =573+j365 Z L Vo V T Figure 5.11 Equivalent circuit of the icro generator for characterisation 5.4. Characterisation of Micro generator for variable load The characterisation of the icro generator is done for a set variable resistive load as shown in Figure Characteristics equations developed fro chapter 4 are used to characterise the generator. Constant and variable losses are deterined for the icro generator fro the air gap flux densities and electric circuit paraeters obtained fro the odified luped paraeter analysis. Load resistance and speed are initialized with speed varying fro 1 to 4rp and load resistance fro 1 to 1KΩ. 11

133 Rc=573Ω X s = 489 Vo Z s =573+j365 V t 1<Z L < 1KΩ Vo=V t +Ic*(R c +jx s ) Figure 5.1 Characterisation of icro generator for variable load The analysis is done in two parts which one being a direct two diensional characterisation of the generator to variable load resistance. The other is a three diensional analysis of the icro generator to change in speed and variable load. Figure 5.13 shows that an increase in generated voltage is feasible with the sae profile with increase in speed with relaxed constraints fro bearing and frictional losses. 7 Generated Voltage [Volts] x 1 4 Speed [rp] Load Resistance (Ohs) Figure Generated voltage to change in speed Figure 5.14 A and B shows the terinal voltage obtained for variable load and the terinal voltage slope gradually reduces with increase in load resistance. The coil behaves inverse to terinal voltage characteristics which reduces with increase in load as shown in 111

134 Figure 5.15 A and B. The coil current and terinal voltages increase with speed in Figure 5.14.B and 5.15 B..5 1 Terinal Voltage [V] Terinal Voltage [V] Load Resistance (Ohs) x Speed [rp] Load Resistance (Ohs) 1 (A) (B) Figure 5.14 A. Terinal Voltage Vs Z L B. Terinal Voltage Vs Change in N rp and Z L 4 x 1-3 Coil Current for the MEMS icro generator Coil current at variable load [Aps] Load Resistance (Ohs) Coil Current [Aps] Load Resistance (Ohs) 1 1 Speed [rp] 3 x (A) (B) Figure 5.15 A. Coil Current Vs Load Resistance B. Coil Current Vs Change in N rp and Z L The total losses increases with increase in resistance as shown in Figure 5.16 A and B and reaches a point where the load resistance atches the coil resistance. This point represents the condition where variable losses is balanced and at iniu and is also the point where axiu efficiency is obtained as shown in Figure After this point the 11

135 total losses starts to reduce as the variable reduces with reduction in coil current as shown in Figure The O/P power of the generator follows total losses and specifically variable losses because constant losses are kept constant because of a fixed speed for analysis as shown in Figure 5.17.A. A axiu O/P power of 1.7 W can be achieved at the load resistance of 573Ω. The O/P power trend follows total losses including both fixed and variable loss when change in speed is included for analysis as shown in Figure 5.17 B. The axiu theoretical efficiency at the energy balance point where load resistance atches internal coil resistance is 8.% as shown in Figure The efficiency is calculated by assuing frictional losses being engine losses and not included in this analysis. The effect of operating teperature of the icro engine would affect both the electric circuit and agnetic circuit paraeters of the icro generator. For exaple, a icro generator coponent operated at a teperature of 1 o C would have an air gap flux density loss of 9% and in this case fro to 1.8 (Using air gap flux density Bg value calculated fro Br taken at 5 o C and Teperature reduction coefficient of selected SCO of.1%/ o C). Siilarly, the internal resistance of the coil would increase fro 573Ω to 74Ω. The generated voltage is estiated to have reduced fro.8v to.4v and the achievable O/P power fro 1.7 W to 1.3W. It is iportant that the icro generator coponents are sealed and isolated properly using epoxy aterial to avoid the teperature effects. 113

136 4.5 x 1-4 Total losses for the MEMS icro generator x 1-4 Total Losses [W] 3.5 Total Losses [W] Load Resistance (Ohs) x Speed [rp] Load Resistance (Ohs) (A) (B) Figure A. Total Losses Vs Load Resistance B. Total Losses Vs Change in Speed and load resistance 18 x X: 6 Y:.1687 x 1-3 O/P Power [W] Load Resistance (Ohs) Generated power [W] x 1 4 Speed [rp] Load Resistance (Ohs) (A) (B) Figure 5.17 A. O/P power Vs Load Resistance B. O/P power Vs Change in Speed and load resistance 114

137 8 8 X: 5 Y: 8. Effeciency [%] Load Resistance (Ohs) Figure 5.18 Efficiency Vs Load Resistance 5.5 Integration of Micro Engine-Generator Syste The integration of the icro engine generator syste is done by cobining paraetric equations for the engine with the icro generator luped paraeter odel. Mechanical power for the engine at engine shaft is defined fro engine displaceent and the fuel consued per revolution. A siplified displaceent equation for the katrix engine odel used in the thesis for integration is 3 Dp = 8* L * e * t [ ] (5.1) rev Where, L = Liacon radius, e = Eccentricity with eccentricity ratio = (L/e) t= thickness of the rotor 115

138 Fuel consued per revolution of the engine syste can be deterined fro engine displaceent and air/fuel ratio as in equation 5.. The echanical power and torque generated at the engine shaft is given by equation 5.3 fuel = vf * Dp * 3 n [ ] (5.) s sec Where, vf = Air/Fuel Ratio, s n = revolution per second Pech = fuel *η * t Lhv [ w ] (5.3) Where, η t = Engine Efficiency, Lhv = Latent heat N. Tech = Pech /ϖ [ ] (5.4) sec The operating tie of the engine syste fro fuel consuption can be written as in equation 5.4. The tank size is also iportant in defining the energy density of the syste tie taken for Tie per fuel tank. tie = 1 fuel * Tanksize sec (5.5) The engine efficiency for integration purpose is taken a conservative Figure as 1%[1] as seen fro literature. The engine efficiency as seen fro chapter 1 is instruental in defining the conversion efficiency of the engine generator syste. The fuel used for analysis is ethanol due to their environentally friendly nature and wide use in icro achine application. Assuption are ade for integration with vf = 1e-5 = [air/fuel] ratio, η t = 1%, Lhv = 588 Kw-h/3 (Ethanol as fuel). It has to be noted that echanical power generation can 116

139 be iproved and the tie per fuel tank for operation of the syste can be iproved by increasing the air fuel ration of the engine. 5.6 Energy Density of integrated Micro Engine Generator syste The theoretical echanical odel of the icro engine is with the icro generator theoretical ode. The calculation of echanical power, torque, fuel tank capacity and tie of operation, energy density is done using the integrated odel. The calculation is done based on an integrated engine-generator package volue of 7e-3*4e-3*5e-3. The generator shaft speed corresponds to twice the engine shaft speed because of the dual cobustion/revolution cycle in the katrix engine. The displaceent for the given rotor including the eccentricity is calculated to be 5.99e-8 [ 3 /rev]. The engine would consue 9.34e-4 liters per hour at this rate of displaceent. The fuel tank capsule can hold 3.61e-3 Liters which would give a total operating tie of 3.9 hours in continuous operation for the syste. The calculated echanical power is 5.5W. The echanical and electrical torques for engine-generator torque atching purpose is.9e-5 N. and 1.6e-6 N. respectively. The energy density of the integrated engine generator syste by taking ethanol as the energy source is found to be 4.3 Wh/Kg with an assue engine efficiency of 1% fro literature[]. This energy density is approxiately seven ties the energy density of the icro power battery syste available in literature []. The energy density of the icro engine-generator power syste is approxiately eight lesser than that of the highest energy density Lithiu -Thionyl chloride priary battery (3 Wh/kg) and 5 ties less than that of Li/organosulfide secondary battery ( Wh/Kg). Even a sall iproveent in engine efficiency of 3 to 4% 117

140 can increase the energy density icro engine-generator power syste to ore than energy densities available in portable batteries. 5.7 Suary The ethodology for developent of a thin MEMS axial achine odel for integration with a icro engine is continued fro chapter4. The following can be suarized as contributions fro the chapter. The paraeters for the icro generator odel to generate voltage of 3V at 1-1W are selected. The selected icro generator odel paraeter corresponds to a generated voltage of 3.V and available power of W with power density of 6.36e3 W/ 3. Electrical equivalent odel for the icro generator is derived and the equivalent resistance and reactance for the odel is calculated as 573Ω and 489 Ω respectively. The characterisation of the icro generator on variable load is perfored and the usable axiu power output when coil resistance is equal to load resistance is found to be 1.6W. The efficiency obtained at this point is 8.% and this efficiency is expected to reduce on practical cases due to the effect of teperature and frictional effects. Theoretical odel for the icro engine is developed for integration with the icro generator to deterine achievable energy density for a copletely integrated engine generator power syste. The displaceent for the given rotor including the eccentricity is calculated to be 5.99e-8 [ 3 /rev]. The fuel tank capsule can hold 118

141 3.61e-3 Liters which would give a total operating tie of 3.9 hours in continuous operation for the syste. The calculated energy density of the integrated engine generator syste by taking ethanol as the energy source is found to be 4.3 Wh/Kg. The energy density of the icro engine-generator power syste is seven ties greater than the energy density of odels reported in literature and seven lesser than the energy density available in portable priary and secondary batteries. A sall iproveent in engine efficiency of 3 to 4% would ensure the energy density of the icro engine-generator power syste to be ore than energy densities available in portable batteries. The capacity of the icro engine generator syste to operate for 3.9 hours at 3.W output power would still ake this syste a considerable alternative source of power for portable applications with a huge scope for further iproveent 119

142 Chapter 6: Fabrication of MEMS icro generator This chapter will discuss the fabrication process for the fabrication of MEMS icro generator coponents using existing anufacturing technologies. The choice of aterials for the anufacturing of the icro generator fro existing technologies is reviewed. The liitations and constraints posed by the fabrication ethods to anufacture the icro generator are briefed MEMS Micro Generator Fabrication The configuration of the MEMS icro generator to be fabricated is shown in Figure 6.1. The fabrication feasibility is divided into two parts, fabrication of rotor and fabrication of stator the coponents using bonding techniques. The design and fabrication objective is to iniize the no of oving structures and coponents to induce bulk icro achining. The anufacturing technologies had grown with interediate passing techniques to recent popular techniques used for anufacturing like DRIE (Direct Reactive Ion Etching), LIGA and LPCVD for anufacturing of high aspect ration coponents. A review on fabrication ethods available in literature for icro generator developent is available in chapter. The fabrication process like ost coon design is aied to be on a silicon SU-8 substrate base Rotor Fabrication The rotor is developed to axiize the aount of rotor area available for soft agnetic aterial. The rotor poles used in the design is rectangular to include siplicity in rotor fabrication and also to increase the pole area in rotor to suit the rotor profile. 119

143 d6 d5 M t q t1 M gw gp g q1 d3 d1 d d4 SCO SCO Ni:Fe poles Powdered Iron Copper Figure 6.1. MEMS icro generator fabrication odel E Ri ` L Ro Figure 6. Superiposed view of pole and winding A. Material selection for soft agnetic poles 1

144 The aterial for the soft agnetic poles apart fro high agnetic circuit characteristics also deands operation in a high teperature environent. Relative pereability and saturation agnetization are the key agnetic properties looked for in the soft agnetic poles. An increase in saturation agnetization when induction goes to infinity will iprove the flux flow in the icro generator for voltage generation. Any increase in flux flow above this capacity will cause pereability to go to zero causing no change in flux density for voltage generation. Materials with high pereability would also iprove flux flow and achieve high saturation agnetization. Figure 6.3. Magnetization characteristics of Iron [1] The aterial should possess high Curie teperature characteristics to be suitable to operate at high teperatures. Table 6.1 shows popular choices of ferroagnetic aterials reviewed in chapter with their theral expansion co-efficient and curie teperatures. Ideally the soft agnetic aterial can be ade fro powdered iron fro electro deposition process. The aterial on the other hand should posses atching theral expansion co- 11

145 efficient to silicon not to cause daage to the physical structures operating at high teperatures. Iron which is a popular soft agnetic aterial for generator developent has very good agnetization characteristics and Curie teperature as shown in Table 6.1. But, the theral expansion coefficient of iron is 6 ties that of silicon which ay cause the daage to the soft agnetic structure when operating at high teperatures. Theral Expansion C Magnetic saturation (Tesla) Curie Teperature ( C) Nickel 13e Cobalt 14e Peralloy(81%Ni,% Mo,17% Fe) 1e Ferrous 11e Table 6.1. Properties of soft agnetic aterials [1] Figure 6. shows typical saturation agnetisation characteristics and theral expansion co-efficient trade offs in Ni:Fe alloys. It can be seen fro the Figure that Ni:Fe alloys of 4:6 ratio exhibits siilar theral expansion coefficient as silicon but has lower saturation agnetization of 1.4T which ay cause saturation with the present design at low operating teperatures. An Ni:Fe ratio of 45:55 can be used to get high saturation agnetization of 1.6T and close to sae theral expansion coefficient as silicon. Addition of olybdenu to Ni:Fe alloy will increase the initial pereability of the aterial to further reduce avoid saturation effects and allows for high heat treatent as seen fro literature[]. This trade off in saturation agnetization is necessary to achieve better structural and agnetic balance of the rotor. 1

146 Figure 6.4 Saturation agnetisation VS Theral expansion coefficient of NiFe alloys B. Fabrication of Ni:Fe soft agnetic rotor poles Fabrication of Ni:Fe is coon and popular in MEMS in the developent of thin agnetic structures for agnetic sensors, actuators and agnetic recorders as reviewed fro chapter. The coon technique for fabrication of NI:Fe structures in MEMS is using electro deposition. There was recent reported case of 5:5 NiFe alloy electrodeposited into deep silicon 9µ oulds for vertically lainated NiFe structures for using electro deposition and DRIE etching techniques [3][4]. This confirs the feasibility of fabricating high aspect ration 45:55 Ni:Fe fabrication using electro deposition principle. The process as available in literature [3] and begins with a 5 µ silicon wafer. Trenches were etched in the shape of the rotor poles. The wafer was then bonded to a second wafer which has a copper seed layer, and the wafer stack was electroplated with a 5:5 ratio of nickel to iron The top surface of the plated wafer was then planarized, the seed wafer was reoved, and the reaining features of the rotor were etched using deep 13

147 reactive ion etching (DRIE). A siilar process can be used in fabricating the soft agnetic rotor structure Stator Fabrication The stator consists of two sections the botto section consists of agnetic poles and back iron and the top section consists of back iron, agnetic poles. The stator back iron and PM poles can be fabricated with the siilar process as the rotor soft iron poles. A siilar fabrication process to develop back iron cores is available in literature [6]. The process starts with two 1 diaeter 5icron thick silicon substrates. First, 3icron deep annular cavities were etched on the backside of one side of the wafer by DRIE using a photoresist ask. After reoxidation and sputter deposition of a Cr/Cu seed layer, the cavities would be filled with 45:55 Ni:Fe alloy by electroplating. A dry-fil photoresist ask would be used to confine the electrodepositing to the cavities. Chapter suggest that fabrication of hard agnetic structures using fabrication technologies was difficult to achieve due to heat treatent procedure involved in fabricating such structures. Coercially available peranent agnets were used where ever possible in literature to overcoe. The design also ake use of coercially available n48 grade Nd Feb or SCo17. The characteristics of the Trade show the design specs of the hard agnets. Nd Feb can be used as a agnetic source for the agnetic circuit to provide suitable isolation is provided for the poles fro the engine chaber. SCo17 is an alternative choice for NdFeb with relatively high saturation flux density level and high curie teperature characteristics. SCo could effectively be a good choice for agnetic source if suitable isolation is not provided to isolate the peranent agnet sources fro the cobustion chaber. SCo with low coercive force characteristics is sensitive to external fields and the net achievable flux density can be affected when influenced with external 14

148 fields. With the high Curie teperature characteristics SCo17 would suit this application to be fabricated closer to the engine structure. The other side of the substrate with the back iron could be etched by DRIE using a photoresist ask. Cavities were fored using patterning to for cavities for the peranent agnets. Peranent agnets then can anually be inserted into the cavities in the stator, and secured in place with SU8 which was applied using a needle and then cured by UV exposure and heating. Bhax Curie tep Materials Br (t) Hc (KA/) (kj/3) C SCo17 [54] NdFeb MQ III [54] Table 6.. Properties of selected hard agnetic source [6] Coil structures has been fored using MEMS technologies for ore than two decades and an literature review on the current ethods and capabilities are available in chapter.. The coil structure was integrated into the top part of the stator structure using electroplating. An insulation layer of SU-8 would be fored using UV photolithography and the copper windings were electroplated on to the. Siilar electroplated coil tracks of 1µ with a width of 3µ and a pitch of 6µ shown in Figure 6.3 which confirs the capability of fabrication coil structures of diensions selected in chapter4. The fabrication of coil structures and agnetic source in one single unit iproves flux distribution and flux linking the winding structure, reduces fabrication coplexity and volue of the syste. 15

149 Figure 6.5. SEM photograph showing top layer of a stator coil prior to deposition of the protective SU8 layer[5]. 6. Suary This chapter discussed the fabrication process to fabricate icro generator coponents using existing fabrication technologies. The following can be suarized fro this chapter The choice of aterials for pole structures show that an Ni:Fe ratio of 45:55 exhibits high saturation characteristics and theral expansion co-efficient close to silicon. This akes it suitable for pole structures to be operated at high teperatures of around 3 C [4]. The rotor poles can be fabricated using a cobination of DRIE and electrodepositing techniques. Coercially available SCo having high curie 16

150 teperatures is a practical choice for peranent agnet source close to be integrated close to engine structure. The stator structures can be fored using a cobination of DRIE, lithography techniques to include copper coil layers includes in the stator with an insulating layer separating the Peranent Magnet source and the coil structure. The chapter also substantiates that the 5 MEMS Micro generator coponents can be fabricated using existing fabrication ethods 17

151 Chapter 7: Conclusion & Suggestions for future iproveent The need for alternative source of power to existing battery for portable applications has been deonstrated in the thesis. An integrated engine generated power syste using hydrocarbon fuel is one of the alternatives for portable application to achieve higher energy density than in batteries. The literature on existing integrated icro engine generator syste showed that the achievable energy densities fro existing systes are 5 ties less than existing batteries. This is ainly due to reduction in efficiency and power densities of both the generator and the engine because of operational issues and fabrication liitations. The dissertation investigated on increasing the energy density of the engine-generator syste by increasing the syste power density and efficiency of the icro generator through proper selection of developent paraeters. Initially, analysis fro luped paraeter analysis on different electrical achine technologies to produce high power density at planar scale showed that axial achines were seen to provide better power density than radial or reluctance achine. The peak power density for axial achines is ten ties greater than radial achines and two ties greater than reluctance achines. A sandwiched axial achine odel presented in the thesis was estiated to provide better flux density characteristics, high power density and is easy to anufacture. An increase in power density of the icro generator upon scaling can be increased by varying current density by Jα 1, and angular frequency by Nα. A Pereance coefficient deterination ethod for theoretical analysis of agnetic circuit to deterine flux density and forces was presented. This co-efficient is significant in theoretical agnetic circuit analysis to achieve analysis results with accuracies of 9 to 93% to FEA results. An analytical ethod to deterine coil paraeters for a given coil profile for 17

152 luped paraeter analysis was explained and validated. These two ethods are used as independent inputs to the luped paraeter ethodology developed to select functional and physical paraeters for the MEMS icro generator. The icro generator with two stator cores and planar winding directly integrated on top of the stator structure on one side provide better air gap flux density levels, flux distribution and reduced the volue of the icro generator to increase power density. The ethodology for paraeter selection and developent of a thin MEMS axial achine odel was validated and results were in close atch with practical results for the validated odel available in literature. Magnetic circuit analysis for the MEMS icro generator using pereance coefficient ethod show that the airgap flux density levels achievable are high and ore than 1.185T (for a SCo agnet with Br of 1) with rotor radius of ore than 5. The theoretical odel is validated by analysing a icro generator odel with 5 radius in ANSYS FEA to predict air gap flux density. Result fro theoretical prediction of 1.184T is 93% accurate to 1.64T After this radius the slope of the flux density reduces with change in rotor radius. Air gap length between 1-3µ is found to achieve high air gap flux density levels at rotor radius ore than 5. A reduction in leakage pereance and better flux regulation for axiu air gap flux density is obtained with t/t1 of between to. The icro generator odel paraeters selected fro the analysis corresponds to a generated voltage of.8v and available power of W with power density of 6.36e3 W/ 3. Electrical equivalent circuit odel for the icro generator is derived for characterisation and the equivalent resistance and reactance for the odel is calculated as 573Ω and 489Ω respectively. The characterisation of the icro generator on variable load is perfored and the usable axiu power output is found to be 1.6W at, rp. The efficiency obtained at this point is 8.% and this efficiency is expected to reduce further with practical systes due to the effect of teperature and friction. The icro generator when operating at 18

153 an elevated teperature of 1 o C is estiated to loose air gap flux density levels by 9% and increase coil resistance fro 573Ω to 74Ω which will reduce the output power fro 1.6W to 1.3W. Theoretical odel for the icro engine is developed for integration with the icro generator to deterine energy density for a copletely integrated engine generator power supply package. The displaceent for the given rotor including the eccentricity is calculated to be 5.99e-8 [ 3 /rev]. The fuel tank capacity was estiated to hold 3.61e-3 Litres which would give a total operating tie of 3.9 hours in continuous operation for the syste. The calculated energy density of the integrated engine generator syste by taking ethanol as the energy source is found to be 4.3 Wh/Kg. This energy density is seven ties greater than the energy density of icro engine-generator odels reported in literature and seven ties lesser than the energy density available in portable priary and secondary batteries. A sall iproveent in engine efficiency of 3 to 4% would ensure the energy density of the icro engine-generator power syste to be ore than that of batteries. The capacity of the icro engine generator syste to operate for 3.9 hours at 1.6W output power would still ake the engine-generator power supply a considerable entity for alternative source of power for portable applications with a huge scope for further iproveent. The final chapter substantiates the feasibility of fabrication of the 5 Thin MEMS Micro generator coponents using exiting technologies. As a future Iproveent to the current work a practical odel of the MEMS icro generator could be built and test to validate the theoretical odel to practical results. An analysis on ultiple layers as supposed to single layer adopted in the thesis can be analysed for an iproveent in achievable power density. Inclusion of better isolating ediu with good theral properties between the agnetic circuit and the engine structure would help achieve high agnetic flux density and high power density. 19

154 APPENDIX APPENDIX A - LUMPED PARAMTER MODELLING A.1 Luped paraeter odelling- Radial Flux PM Machine (RFPM) The RFPM odel is siilar to a siple universal synchronous achine with two poles which could be altered upon developent suitability. An equivalent reluctance odel and cross sectional view of a RFPM achine used for analysis is shown in Figure The rotor configuration for analysis is assued as a black box or salient poles with PM s inside the to suit the configuration of the engine. The power density for the achine under consideration is deterined by solving for agnetic and electrical circuits and then noralizing for output power and density. The saturation of the syste depends on the saturation characteristics of the sealing aterial. _ + NI φ φ 1 R s R c R l F R R l R c F R + _ NI R g B C E D C B A A F M Figure A.1, A - Micro engine Generator outer casing, B - Winding Structure C - Envisaged Sealing Structure, D - Engine Rotor and Generator coon Shaft E - PM structure with Magnetization Vector M

155 APPENDIX Figure A.1 Model Radial two pole Synchronous PM Micro Generator Machine (RFPM) and Cross-sectional view of RFPM under consideration (Not on Scale). The assuptions ade for analysis are that the peranent Magnets follow linear characteristics and anisotropic in nature. For analysis, leakage is considered negligible and not taken into consideration for actual analysis due to its coplexity of deterination and to siplify the proble. The analysis done under static position with the f induced in the winding taken at zero potential to neglect arature reaction effects. The agnetic circuit given in figure 3.11 is solved using Kirchoffs Circuit laws (KCL) for φ,φ 1 the flux loops. The f equation for the network is written as F g 1 c ( φ, R ) + φ R - f + φ. R = (A.1) F g c ( φ, R ) + φ R - f + φ. R = (A.) φ φ = + φ 1 (A.3) With no leakage, φ & 1 φ are equal and are in the sae potential. So, φ φ 1 = φ = (A.4) Equation is solved using the relation 3.5 for deterining the agnetic flux ( φ ), f (F), Flux linkage ( λ ) and Inductance (L) on different parts of the achine and deterination of synchronous Reactance X s of the achine. with F =B.L / µ, R. R L /µ. A g = Lg / µ g Ag, and c c c c = on Eq 3.3 and 3.3φ becoes, 4Br. L / p φ = 4L (A.5) g Lc µ ( µ A + µ A ) g g c c

156 With λ w = NI* φ g /I = LI=N I / flux linkage per phase and per cycle using 3.6 becoes g APPENDIX R, the total flux linkage per pole with respect to the PM φ 4λ. H L =. Rc (A.6) 4Ip s. λ w φ Rg N + 4φ + φ The sealing flux φ g linking the winding per pole per phase can be obtained for a differential area by integrating the sae for a cycle tie period T, with the rotor angle θ variable fro to π / p. The sealing can also be deterined directly fro the flux in air gap over a cycle using the reenance flux density Br. The sealing flux was calculated using both the ethods and found to provide a siilar result approxiately e -5 Weber. The sealing flux φ g could then be used in the generalized equations for ef induced, peak ef, O/P power and power density. The induced ef over a tie period T can the be written as dφ s E (t) = N* dt The agnitude of peak ef is written as t d λ w = = C N dt dt t w. φs. ωr. = CwC( t). Bs N. ωr Ds Le. dt (A.7) E p = C. φ N. ω (A.8) w s r With C w being a constant to represent the coil pitch factor and ω being the angular frequency of the engine rotor. The terinal voltage for such achines using the direct and quadrature axis variable d & q can be written as in equation 3.4. V V V td tq to e Ra = R a I I R a I d q o di L d di + Lq di L d q dt dt dt (A.9)

157 APPENDIX The O/P power produced by the generator and the voluetric energy density can be written as in equation 3.31 and 3.3 as t P 1 op v( t) I ( t) = Pinduced _ Ploss = Generator. t η = P (A.1) ip t ρ = ( ) ( ) V1 v t I t (A.11) t The losses in the generator are grouped up and written as in equation A.1 identifying the paraeters influencing the losses. P = P p,v, t, B ) + P ( I, R, T ) + P ( P ) + P ( P ) (A.1) loss c ( c var a w s o / p f o / p st P = p.( f. B. V + f. t. B. V ) (A.13) c c P var = I a. R a (A.14) The core losses consist of the hysteresis and the eddy current loss represented P c in equation A.1 as a function of their influencing paraeters poles, frequency, flux density and thickness of the core is expanded in equation (A.13) for inclusion in the luped paraeter for future analysis. The eddy variable losses represented as P var is written as function of arature current I a, winding resistance Rw and teperature T and expanded in equation (A.14) for inclusion in the final luped paraeter generalised equation. The last two losses are the stray agnetic losses and friction losses which are considered the sae as in acro scale [54] achines to siplify the analysis. The reluctance forces for icro currents is considerably negligible and the torques produced by the are iniu in icro etre scale achines. Torque due to Lorenz forces are predoinant and are deterined using equation (A.15) and also using finite eleent analysis with the knowledge of Bg.

158 c a g w APPENDIX τ = Ν I B A (A.15) The generalized equation fored in this case is design independent with only directly dependent on the physical arrangeent of agnetic circuit poles. This akes the odified luped odel analysis of the achine useful for analysing a ajority of radial flux achine odel. The paraeters of the odel considered for analysis above has a volue.5*.3*.3 3 with a rotor outer diaeter scale of.18, rotor thickness of 9 icro eters with capacity to produce 5 to 1 W of power is considered. The speed of the achine is taken to be as 13krp with fixed nuber of poles and the achine is considered to generate a sinusoidal ef wavefor. The agnetic circuit for the achine is characterized above in figure 3.11 and the final generalised luped paraeter odel for the achine is shown in equation (A.16) φ g st 1 Cw. Bg. N. ωr. Ds. Le. I( t).sinwet [ pv.. B. f + I a ( t).( Rw + jx l ) ρ g = (A.16) V + pv.. t. B. f +.1. P +.3. P ] c o / p o / p t A. Axial Machine: The luped paraeter generalized equations are developed by a siilar approach to radial achines with odifications to analyse axial achines.. The achine under considerations is siilar to radial achines except that the arature windings are isolated and kept as a separate unit to reduce heat losses due to engine teperature and iprove the power density of the syste. This configuration allows for the flexibility of agnets used by achieving a better operating point with high agnetic flux density (B ). A cross-sectional view of the axial achine with PM agnets outside is shown figure A..

159 APPENDIX F g A D r t w G d g 1 B C E C B M A F Figure A., A Disc Shaped PM with Magnetization Vector M B Envisaged Sealing Structure C Electrodeposited agnetic pole aterials D Winding Structure E Shaft Structure of the engine F PM Magnetic structure with Magnetization Vector M Figure A. Axial Flux Thin PM Micro Generator Configuration (AFMEG) (Not on Scale). The assuptions ade for analysis of the syste are the sae as used in RFPM achine and have to be referred fro the previous section and not repeated to avoid redundancy. An equivalent reluctance network diagra of the odel under consideration is shown in figure.a.3. The equivalent reluctance odel is solved using the sae technique as that of RFPM achine in the previous section.