the design of moving magnet actuators for large-range flexure-based nanopositioning

317 Pages·2014·6.99 MB·English

THE DESIGN OF MOVING MAGNET ACTUATORS FOR
LARGE-RANGE FLEXURE-BASED NANOPOSITIONING

by

David B. Hiemstra

A thesis submitted in partial fulfillment of
the requirements for the degree of Master of
Science in Engineering (Mechanical
Engineering) at The University of Michigan

Advisor:
Professor Shorya Awtar

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© David B. Hiemstra 2014
All Rights Reserved

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ACKNOWLEDGEMENTS
Shorya, it will take me the rest of my life to learn all of what you have taught me
and see all the ways you have helped me grow. Thank you.
Thank you to many people who collaborated with me during this work, including
Gaurav Parmar1, Cory Welch, Yangbing Lou, Zhen Wu, Yi Chen, Yilong Wen, and
Adrian Adames. Your help, discussions, insights, support, and machine shop time spent
with me on this project are invaluable.
Everyone else who supported me during this adventure, especially my family, the
Precision Systems Design Laboratory, and all my friends—thank you.

1 A certain portion of this work was done in collaboration with Gaurav Parmar in the Precision Systems Design Laboratory at the
University of Michigan. This portion has been published in a journal paper in IEEE/ASME Transactions on Mechatronics [83].
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TABLE OF CONTENTS
ACKNOWLEDGEMENTS ............................................................................................ iii
TABLE OF CONTENTS ................................................................................................ iv
LIST OF FIGURES ......................................................................................................... ix
LIST OF TABLES .......................................................................................................... xv
ABSTRACT ..................................................................................................................... 16
CHAPTER 1 : Introduction and Motivation ............................................................... 18
1.1 Lorenz-force electromagnetic actuators ..................................................... 19
1.1.1 Moving magnet actuators (MMA) ...................................................... 20
1.1.2 Voice coil actuators (VCA) ................................................................ 22
1.1.3 Characteristics of Lorentz force actuators .......................................... 24
1.1.4 Applications ........................................................................................ 25
1.2 Nanopositioning ......................................................................................... 27
1.2.1 Large range flexure based nanopositioning ........................................ 27
1.2.2 Research goals and impact .................................................................. 30
1.2.3 Challenges in achieving large range nanopositioning ........................ 32
1.3 Design specifications .................................................................................. 34
1.3.1 Motion range ....................................................................................... 36
1.3.2 Motion quality ..................................................................................... 36
1.3.3 Speed ................................................................................................... 37
1.3.4 Temperature stability .......................................................................... 43
1.3.5 Additional considerations ................................................................... 43
1.4 Thesis outline ............................................................................................. 44
CHAPTER 2 : Actuators for Large Range Nanopositioning...................................... 46
2.1 Actuator comparison based on literature survey ........................................ 48
2.2 Actuator comparison using performance indices ....................................... 51
2.2.1 Maximize first natural frequency ........................................................ 57
2.2.2 Maximize scanning frequency ............................................................ 60
2.2.3 Minimize rise time in point to point positioning application .............. 65
2.2.4 Minimize power consumption ............................................................ 66
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2.2.5 Minimize positioning resolution ......................................................... 67
2.2.6 Conclusion .......................................................................................... 68
2.3 Piezoelectric actuators ................................................................................ 68
2.3.1 Piezoelectric stack actuators ............................................................... 70
2.3.2 Piezoelectric stacks with amplification mechanism ........................... 71
2.3.3 Comparison between electromagnetic and piezoelectric actuators .... 80
2.4 Piezomotors ................................................................................................ 84
2.4.1 Quasi-static piezomotors ..................................................................... 85
2.4.2 Dynamic piezomotors ......................................................................... 88
2.4.3 Ultrasonic piezomotors ....................................................................... 89
2.5 Magnetorestrictive actuators ...................................................................... 91
2.6 Electromagnetic actuators .......................................................................... 92
2.6.1 Voice coil actuators............................................................................. 94
2.6.2 Moving magnet actuators .................................................................... 99
2.6.3 Multi-phase electromagnetic actuators (linear motors) .................... 103
2.6.4 Additional electromagnetic actuator types ........................................ 104
2.7 Conclusion ................................................................................................ 105
CHAPTER 3 : Prior art concerning moving magnet actuators ............................... 106
3.1 Common MMA architectures ................................................................... 106
3.1.1 Slotting .............................................................................................. 107
3.1.2 Traditional MMA architecture .......................................................... 110
3.1.3 Linear motor MMA architecture ....................................................... 111
3.1.4 “Air” core MMA architecture ........................................................... 113
3.1.5 Slotted MMA (compressor architecture) .......................................... 115
3.2 Additional MMA architectures and design ideas ..................................... 118
3.3 Voice coil actuator designs ....................................................................... 127
3.4 Coil design ................................................................................................ 130
CHAPTER 4 : Design considerations and methodologies ........................................ 134
4.1 Actuator design considerations ................................................................ 134
4.1.1 Force uniformity over stroke ............................................................ 134
4.1.2 Armature reaction ............................................................................. 139
4.1.3 Shorted turn ....................................................................................... 141
4.1.4 Wire selection ................................................................................... 142
4.1.5 Magnetic saturation of circuit components ....................................... 143
4.1.6 Magnet material ................................................................................ 144
4.1.7 Radial instability ............................................................................... 149
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4.1.8 Thermal management........................................................................ 150
4.1.9 Actuator design considerations map ................................................. 150
4.2 System design considerations ................................................................... 153
4.2.1 Open-loop bandwidth........................................................................ 153
4.2.2 Actuator force ................................................................................... 153
4.2.3 Actuator force uniformity ................................................................. 154
4.2.4 Mechanical load on flexure bearing .................................................. 154
4.2.5 Thermal management........................................................................ 155
4.2.6 System design considerations map ................................................... 156
4.3 Design methodologies .............................................................................. 158
4.4 Figures of merit ........................................................................................ 160
CHAPTER 5 : Dynamic Actuator Constant .............................................................. 162
5.1 Derivation ................................................................................................. 163
5.2 Impact on motion system performance .................................................... 170
CHAPTER 6 : Electromagnetic modeling of an MMA ............................................. 176
6.1 Model neglecting magnetic fringing ........................................................ 180
6.2 Models incorporating magnetic fringing via Rotor’s method .................. 183
6.2.1 Circular flux paths............................................................................. 184
6.2.2 Improved magnetic leakage estimation ............................................ 186
6.2.3 Improved magnetic fringing estimation ............................................ 187
CHAPTER 7 : Actuator design and fabrication ........................................................ 192
7.1 Detailed design ......................................................................................... 194
7.1.1 Pole piece .......................................................................................... 195
7.1.2 Magnet length ................................................................................... 196
7.1.3 Magnet radius and coil thickness ...................................................... 197
7.1.4 Coil length ......................................................................................... 199
7.1.5 Wire gauge ........................................................................................ 200
7.1.6 Back iron ........................................................................................... 201
7.1.7 Coil bobbin........................................................................................ 203
7.1.8 Off-axis attraction forces .................................................................. 205
7.1.9 Mover shaft ....................................................................................... 206
7.1.10 Summary ........................................................................................... 208
7.2 Practical design considerations ................................................................ 208
7.2.1 Mover ................................................................................................ 208
7.2.2 Back iron ........................................................................................... 209
7.2.3 Bobbin ............................................................................................... 210
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7.3 Fabrication ................................................................................................ 211
7.3.1 Bobbin ............................................................................................... 211
7.3.2 Coil winding...................................................................................... 212
7.3.3 Back iron ........................................................................................... 215
7.3.4 Magnets ............................................................................................. 215
CHAPTER 8 : Thermal management system ............................................................ 216
8.1 Concept selection ..................................................................................... 218
8.2 Detailed design ......................................................................................... 221
8.2.1 Latent heat sink ................................................................................. 221
8.2.2 Thermal bridge .................................................................................. 224
8.2.3 Thermal housing ............................................................................... 225
8.2.4 TMS thermal model .......................................................................... 226
8.3 Fabrication ................................................................................................ 231
CHAPTER 9 : Double-parallelogram flexure bearing .............................................. 233
9.1 Detailed design ......................................................................................... 234
9.1.1 Material selection .............................................................................. 235
9.1.2 Motion stage design .......................................................................... 235
9.1.3 Beam dimensions .............................................................................. 236
9.1.4 Off-axis stability ............................................................................... 239
9.1.5 Bearing dynamics.............................................................................. 241
9.2 Practical design considerations ................................................................ 243
9.3 Fabrication ................................................................................................ 244
CHAPTER 10 : Experimental Results ........................................................................ 247
10.1 Experimental setup ................................................................................... 248
10.2 Moving magnet actuator ........................................................................... 251
10.2.1 MMA static force characteristics ...................................................... 251
10.2.2 Effect of bobbin material on dynamic response ............................... 252
10.3 Thermal management system ................................................................... 253
10.4 Nanopositioning ....................................................................................... 254
10.4.1 System characterization .................................................................... 255
10.4.2 Nanopositioning performance ........................................................... 255
CHAPTER 11 : Innovations in Actuator Design ....................................................... 259
11.1 Concentric coil ring magnet (CCRM) moving magnet actuator .............. 259
11.1.1 Optimal MMA topology ................................................................... 260
11.1.2 Concentric coil radial magnet (CCRM) module ............................... 263
11.1.3 Single CCRM open face MMA (preferred embodiment) ................. 265
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11.1.4 Integrated thermal management ........................................................ 269
11.1.5 Single CCRM closed face MMA design .......................................... 270
11.1.6 Axially spaced dual CCRM MMA designs ...................................... 272
11.1.7 Radially spaced dual CCRM MMA designs ..................................... 274
11.1.8 Planar topologies ............................................................................... 276
11.2 Actuator integration with motion system ................................................. 278
11.3 Coil designs .............................................................................................. 279
11.3.1 MMA featuring non-uniform coil windings ..................................... 279
11.3.2 High-efficiency planar coils .............................................................. 280
11.4 Voice coil actuator concepts ..................................................................... 282
11.4.1 Flexure coil leads .............................................................................. 283
11.4.2 VCA for nanopositioning .................................................................. 284
CHAPTER 12 : Conclusion.......................................................................................... 285
REFERENCES .............................................................................................................. 287
APPENDIX A: Analytical MMA model MATLAB code .......................................... 309
APPENDIX B: Analytical thermal model for selection of heat pipes ...................... 316

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LIST OF FIGURES
Figure 1.1: Conventional MMA cross section .................................................................. 20
Figure 1.2: Opposite coil winding directions produce unidirectional force in MMA ...... 21
Figure 1.3: Off-the-shelf MMAs [6] and [8] .................................................................... 22
Figure 1.4: Conventional VCA cross section and off-the-shelf product .......................... 23
Figure 1.5: Voice coil windings in air gap with radially oriented magnetic field
experience force in axial direction .................................................................................... 23
Figure 1.6: Off the shelf Voice Coil Actuator .................................................................. 24
Figure 1.7: Actuator integrated in a mechatronic motion system ([23][24][25]) ............. 26
Figure 1.8: Tradeoff between range and resolution in motion systems ............................ 28
Figure 1.9: Envisioned research impact ............................................................................ 31
Figure 1.10: Raster scanning over 10mm x 10mm sample (not to scale) ......................... 39
Figure 1.11: Motion profile and force requirements for point to point positioning ......... 42
Figure 2.1: Overview of final actuator candidates for large range nanopositioning ........ 47
Figure 2.2: Normalized actuator force-stroke and stress-strain curves ............................. 53
Figure 2.3: Flexure based motion system with amplification mechanism ........................ 55
Figure 2.4: Comparison of performance index E/ρ for various actuators (estimated
maximum and minimum ranges shown) ........................................................................... 60
Figure 2.5: Specific actuation stress vs. actuation strain [93]........................................... 62
Figure 2.6: Comparison between performance indices E/ρ and σε/ρ (estimate maximum
and minimum ranges shown) ............................................................................................ 64
Figure 2.7: Piezo stack actuator [102] .............................................................................. 70
Figure 2.8: Piezoelectric stack actuators with amplification a) [109] and b) [102] .......... 71
Figure 2.9: Piezo stack actuator model ............................................................................. 72
Figure 2.10: Piezo stack actuator integrated with motion system model ......................... 73
Figure 2.11: Effect of flexure and amplification mechanism stiffness on piezo actuator
displacement and force output .......................................................................................... 74
Figure 2.12: Effect of flexure and amplification mechanism stiffness on piezo actuator
blocking force output ........................................................................................................ 75
Figure 2.13: Force and displacement of piezo actuator integrated with motion
amplification ..................................................................................................................... 76
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Figure 2.14: First resonant frequency vs. free stroke of commercially available
mechanically amplified piezo actuators ............................................................................ 78
Figure 2.15: Blocking force vs. free stroke of commercially available mechanically
amplified piezo actuators .................................................................................................. 79
Figure 2.16: First resonant frequency and actuator stroke for an MMA and PZT actuator
(Model # P-025.40P) ......................................................................................................... 82
Figure 2.17: First resonant frequency and actuator stroke for an MMA and PZT actuator
(Model # P-056.80P) ......................................................................................................... 84
Figure 2.18: “Walker” type piezomotor from PiezoMotor AB [114][115] ...................... 86
Figure 2.19: Ultrasonic piezomotor [144] ........................................................................ 90
Figure 2.20: (Attempt!) at categorization of electromagnetic actuators ........................... 93
Figure 2.21: VCA in inverted configuration eliminates moving wires and reduces heat
transfer to the motion stage at cost of higher moving mass .............................................. 97
Figure 2.22: MMA derived from VCA architecture ......................................................... 99
Figure 2.23: Advantages of traditional MMA over VCA for large range nanopositioning
......................................................................................................................................... 102
Figure 3.1: Volumetric force output dependence on magnet material and actuator
dimensions (inner actuator diameter, D, and outer diameter D ) for slotted vs. non slotted
o
MMA architectures [193] ............................................................................................... 108
Figure 3.2: Conventional MMA cross section ................................................................ 110
Figure 3.3: Stacked MMA architecture .......................................................................... 112
Figure 3.4: Flux focusing MMA [197] ........................................................................... 113
Figure 3.5: Air core” MMA allows both axial and radial motion .................................. 114
Figure 3.6: Two axis MMA with maglev force and axial motion [177][56][178] ......... 115
Figure 3.7: Two axis MMA with maglev force and axial motion [57] ........................... 115
Figure 3.8: Slotted MMA for compressor applications showing force direction for
positive coil current......................................................................................................... 116
Figure 3.9: Highly variable force over stroke plot of typical slotted MMA [199] (top)
[200] (bottom) ................................................................................................................. 118
Figure 3.10: Reduction of cogging force via ferromagnetic end plates [50] .................. 119
Figure 3.11: MMA with fixed magnets at axial ends to increase spring force and system
resonant frequency [156] ................................................................................................ 120
Figure 3.12: Active end coils [217] ................................................................................ 121
Figure 3.13: Basic Halbach array.................................................................................... 122
Figure 3.14: Inversed MMA [218].................................................................................. 123
Figure 3.15: Stacked inverted MMA .............................................................................. 124
Figure 3.16: Radial magnet configuration [219]............................................................. 125
Figure 3.17: Radial and axial magnet [221].................................................................... 126
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