design of switched reluctance machines for low-acoustic-noise and wide-speed-range operation

200 Pages·2009·1.45 MB·English

COGGING TORQUE, TORQUE RIPPLE AND RADIAL FORCE ANALYSIS OF
PERMANENT MAGNET SYNCHRONOUS MACHINES

A Dissertation
Presented to
The Graduate Faculty of The University of Akron

In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy

Mohammed Rakibul Islam
May, 2009
COGGING TORQUE, TORQUE RIPPLE AND RADIAL FORCE ANALYSIS OF
PERMANENT MAGNET SYNCHRONOUS MACHINES

Mohammed Rakibul Islam
Dissertation

Approved: Accepted:

_______________________ _______________________
Advisor Department Chair
Dr. Iqbal Husain Dr. Alexis De Abreu-Garcia

_______________________ _______________________
Committee Member Dean of the College
Dr. Tom Hartley Dr. George K. Haritos

_______________________ _______________________
Committee Member Dean of the Graduate School
Dr. Igor Tsukerman Dr. George R. Newkome

_______________________ _______________________
Committee Member Date
Dr. Graham Kelley

_______________________
Committee Member
Dr. Kevin Kreider

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ABSTRACT

This dissertation presents a methodology for designing low noise small permanent
magnet synchronous motor (PMSM) drives by addressing the issues of cogging torque,
torque ripple, acoustic noise and vibration. The methodology incorporates several pole
shaping and magnet skew schemes in different motor topologies with similar envelop
dimensions and output characteristics intended for an automotive application. The
developed methodology is verified with finite element analysis (FEA) and experiments.
A comprehensive design methodology has been developed for obtaining the
analytical design of the machine for a given set of output characteristics. Using the FEA,
the effects of various magnet shapes and skew arrangements on the machine
performances (e.g. cogging torque, torque ripple etc.) have been analyzed. The FEA and
experimental results show that for certain magnet designs and configurations the skewing
does not necessarily reduce the ripple in the electromagnetic torque, but may cause it to
increase. An analytical model to predict radial vibration due to magnetic radial pressure
on the motor structure has also been developed. This model is used for predicting the
noise power level for several motor topologies designed for similar power level
applications.
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The predicted noise levels are utilized to develop guidelines for selecting motor
configurations, internal dimensions and winding types for a low-noise PMSM.
The selection of low-noise PMSM is not a straightforward one; rather it is a
compromise between torque harmonics and radial vibration of the machine. Some PMSM
configurations with less radial vibration might posses excessive torque ripples and
thereby violate other requirements to be less noisy.
Experiments are conducted to record the torque ripple variation for different
magnet shapes and skew in order to validate the results of FE models. The experimental
results correlated well with the FE computations.

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ACKNOWLEDGEMENTS

My sincere gratitude to Dr. Iqbal Husain without whose ardent initiatives,
constant compassionate advice and astute guidance this research work would not have
materialized. Also I would like to thank all of the Committee Members for their
excellent suggestions for making this research a success. The financial support of The
University of Akron during my research period is also highly appreciated. The support
of TRW Automotive Sterling Heights Division in fabricating the two PMSM designs
used in the experiments is highly appreciated.
I would also like to thank my parents, my wife Ayesha, my son Areeb, my lab
mates and my brothers and sisters for their invaluable love and encouragement over the
years.

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TABLE OF CONTENTS
Page
LIST OF TABLES.............................................................................................................xi
LIST OF FIGURES..........................................................................................................xii
CHAPTER
I. INTRODUCTION..........................................................................................................1
1.1 Classification of PM Machines......................................................................2
1.1.1 Common Types of Permanent Magnets..........................................5
1.2 Advantages of PMSM....................................................................................7
1.3 Basic PMSM Operation.................................................................................8
1.4 Application of PMSMs..................................................................................9
1.5 Scope of PMSM Design...............................................................................10
1.5.1 Noise and Vibration Issues ..........................................................11
1.5.2 Torque Ripple Issues ....................................................................13
1.5.3 PMSM Design...............................................................................15
1.6 Research Objectives.....................................................................................16
1.7 Dissertation Organization............................................................................17
II. PMSM TORQUE RIPPLE, NOISE AND VIBRATION...........................................20
2.1 PMSM Structure..........................................................................................20
2.2 PMSM Drive System...................................................................................21
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2.3 PMSM d-q Model........................................................................................23
2.4 Principle of Operation..................................................................................26
2.5 Noise and Vibration in PMSM....................................................................31
2.5.1 Electromagnetic ...........................................................................31
2.5.2 Mechanical....................................................................................32
2.5.3 Aerodynamic ................................................................................33
2.6 Improving Torque Ripple, Noise and Vibration..........................................35
2.6.1 Design Based Methods ................................................................36
2.6.2 Control Based Methods ................................................................49
2.7 Shortcomings in Existing Research.............................................................50
2.8 Research Motivation....................................................................................51
2.9 Research Objectives.....................................................................................53
2.10 Conclusions..................................................................................................54
III. COMPREHENSIVE DESIGN METHODOLOGY..................................................55
3.1 Design Methodology....................................................................................56
3.2 Design Steps.................................................................................................60
3.2.1 Design Ratios ...............................................................................60
3.2.2 Envelope Sizing ...........................................................................63
3.2.3 Stator and Rotor Sizing ................................................................64
3.2.4 RMS Current Density ..................................................................65
3.2.5 Computation of Maximum Number of Turns in the Slot.............66
3.2.6 Calculation of Maximum Demagnetization Current I ..........67
demag
3.2.7 Choice of Magnet and Magnet Thickness l ...............................67
m
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3.2.8 Computation of Phase Resistance ................................................71
3.2.9 Number of Phases and Slot/Pole Combinations ..........................72
3.2.10 Example Design ...........................................................................74
3.2.11 Critical Issues ...............................................................................77
3.3 Design Data of PMSM.................................................................................81
3.4 Conclusions..................................................................................................84
IV. TORQUE RIPPLE AND COGGING TORQUE ANALYSIS..................................85
4.1 Torque Ripple and Cogging Torque............................................................86
4.2 BEMF and Torque Ripples..........................................................................87
4.3 PMSM Design Choices................................................................................90
4.3.1 Magnet Shapes .............................................................................91
4.3.2 Geometry Selection .....................................................................93
4.4 Torque Variation with Design Choices .......................................................94
4.4.1 Cogging Torque Variation with Configurations ..........................94
4.4.2 Effect of Magnet Shapes ..............................................................95
4.4.3 Average Torque Variation ...........................................................98
4.5 Torque Variation with Magnet Skewing......................................................99
4.5.1 Cogging Torque Reduction ........................................................100
4.5.2 Step Skewing .............................................................................100
4.5.3 Cogging Torque Results ............................................................101
4.6 Skewing with Variation in Magnet Shapes................................................103
4.7 BEMF and Torque Ripple Harmonics ......................................................107
4.7.1 Effect of Saturation ....................................................................111
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4.8 Simulation and Experimental Results .......................................................115
4.9 Conclusions ...............................................................................................118
V. RADIAL FORCE AND VIBRATION ANALYSIS................................................119
5.1 Radial Force, Stator Vibration, and Acoustic Noise .................................119
5.2 Unbalanced Radial Forces in Modular Machines .....................................121
5.3 Radial Force Density .................................................................................123
5.3.1 Calculation of Radial Pressure ...................................................127
5.4 Radial Vibration and Dominant Mode Shapes .........................................129
5.4.1 Radial Pressure and Mode Shapes under No-load
Conditions ....................................................................................131
5.4.2 Radial Pressure and Mode Shapes under Full-load
Conditions ....................................................................................134
5.4.3 Mode Shapes and Radial Force under No-load and
Full-load Conditions ....................................................................139
5.5 Radial Displacement .................................................................................142
5.5.1 Analytical Model .......................................................................142
5.5.2 Estimation and Validation of Radial Displacement ...................146
5.6 Vibration and Noise due to Radial Displacement .....................................151
5.6.1 Condition of Maximum Vibration .............................................152
5.6.2 Calculation of Natural Mode Frequency ....................................153
5.6.3 Acoustic Noise and Sound Power Level ....................................155
5.7 Conclusions ...............................................................................................157
VI. SUMMARY AND FUTURE WORK.....................................................................159
6.1 Summary ...................................................................................................159
6.1.1 Research Contributions ..............................................................161
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6.2 Future Works ............................................................................................163
REFERENCES................................................................................................................165
APPENDICES.................................................................................................................170
APPENDIX A. GLOSSARY OF SYMBOLS ..................................................171
APPENDIX B. SEVERAL WINDING TOPOLOGIES ..................................175
APPENDIX C. CANCELLATION OF EVEN HARMONICS IN
TORQUE FOR A 3-PHASE PMSM .....................................178
APPENDIX D. TYPICAL B-H CHARACTERISTICS OF
LAMINATION STEEL ..........................................................181
APPENDIX E. DIFFERENTIAL EQUATION OF VIBRATION
MODEL....................................................................................182
APPENDIX F. SOUND POWER LEVELS IN dB FOR SOME
COMMON NOISE SOURCES................................................184
APPENDIX G. SCHEMATICS OF A TYPICAL ELECTRIC
POWER STEERING SYSTEM .............................................185

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