Permanent magnet (PM) induced vibration is one of the major concerns for PM motors. This work aims at the identification and suppression of the vibration source from magnetic field distortions caused by magnet/slot combination, uneven-magnetization, and magnet shifting. Modulation method is employed to predict the relationships between parameters and unbalanced magnetic force (UMF) and cogging torque (CT). Motivated by the magnetic field periodicity and structure especially air-gap symmetry, a new concept of equivalent magnet (EM) wherein one or more real magnets are defined as an imaginary one is introduced to help predict the unexpected force harmonics normally lower than magnet number, and rotation-frequency is used to present unified interpretation on magnetic force regarding the three distortions. The results imply that the relationships are determined by magnet/EM/slot combination including their greatest common divisor (GCD). Compared with CT, the UMF is more sensitive to the uneven-magnetization and magnet shifting. Like ideal motors, if the GCD is greater than unity, the UMF is eliminated, but the CT is not simply via altering the combination. The results also show that magnetic forces for the same EM/slot combinations share similar behaviors regardless of specific magnetic field details. The results can be utilized to suppress undesirable force, or inspect magnetization and installation status by monitoring force frequency and its amplitude, or gain vibration suppression by magnet's selective assembly. The modulation method, EM concept, and main findings are successfully verified by the finite element method (FEM) and comparison with the existing results in the literature. Main contribution of this work is the unified explanation on the relationships between the three distortions and unique force behaviors, especially the prediction on those unexpected harmonic forces.
Issue Section:
Research Papers
References
1.
Williams
, M. M.
, Zariphopoulos
, G.
, and Macleod
, D. J.
, 1994
, “Performance Characteristics of Brushless Motor Slot/Pole Configurations
,” Incremental Motion Control Systems and Devices Symposium
(IMCSD 94), San Jose, CA
, June 14–16, pp. 145
–153
.2.
Hanselman
, D. C.
, 1997
, “Effect of Skew Pole, Pole Count and Slot Count on Brushless Motor Radial Force, Cogging Torque and Back EMF
,” IEEE Proc. Electr. Power Appl.
, 144
(5
), pp. 325
–330
.10.1049/ip-epa:199712053.
Huang
, B.
, and Hartman
, A.
, 1997
, “High Speed Ten Pole/Twelve Slot D. C. Brushless Motor With Minimized Net Radial Force and Low Cogging Torque
,” U.S. Patent No. 5,675,196.4.
Zhu
, Z. Q.
, and Howe
, D.
, 2000
, “Influence of Design Parameters on Cogging Torque in Permanent Magnet Machines
,” IEEE Trans. Energy Convers.
, 15
(4
), pp. 407
–412
.10.1109/60.9005015.
Islam
, M. S.
, Mir
, S.
, and Sebastian
, T.
, 2004
, “Issues in Reducing the Cogging Torque of Mass-Produced Permanent-Magnet Brushless DC Motor
,” IEEE Trans. Ind. Appl.
, 40
(3
), pp. 813
–820
.10.1109/TIA.2004.8274696.
Liu
, Z. J.
, Li
, J. T.
, and Jabbar
, M. A.
, 2005
, “Cogging Torque Prediction by Superposition of Torque Due to Pole Transition Over Slot
,” Electric Machines and Drives
, IEEE
International Conference, Electric Machines and Drives, San Antonio, TX
, May 15, pp. 1219
–1224
.10.1109/IEMDC.2005.1958777.
Bi
, C.
, Jiang
, Q.
, and Lin
, S.
, 2005
, “Unbalanced-Magnetic-Pull Induced by the EM Structure of PM Spindle Motor
,” 8th International Conference on Electrical Machines and Systems (ICEMS 2005
), Nanjing, P. R. China, Sept. 27–29, pp. 183
–187
.10.1109/ICEMS.2005.2025098.
Hu
, J. H.
, Zou
, J. B.
, and Chen
, X.
, 2005
, “The Ideal and Non-Ideal Cogging Torque in Brushless DC Motor and Its Comprehensive Reducing Methods
,” Proceedings of the CSEE
, 25
(22
), pp. 153
–157
.9.
Zhu
, Z. Q.
, Ruangsinchaiwanich
, S.
, Chen
, Y.
, and Howe
, D.
, 2006
, “Evaluation of Superposition Technique for Calculating Cogging Torque in Permanent-Magnet Brushless Machines
,” IEEE Trans. Magn.
, 42
(5
), pp. 1597
–1603
.10.1109/TMAG.2005.86183110.
Zhu
, Z. Q.
, Ruangsinchaiwanich
, S.
, and Howe
, D.
, 2006
, “Synthesis of Cogging-Torque Waveform From Analysis of a Single Stator Slot
,” IEEE Trans. Ind. Appl.
, 42
(3
), pp. 650
–657
.10.1109/TIA.2006.87293011.
Hwang
, C. C.
, Wu
, M. H.
, and Cheng
, S. P.
, 2006
, “Influence of Pole and Slot Combination on Cogging Torque in Fractional Slot PM Motors
,” J. Magn. Magn. Mater.
, 304
(1
), pp. e430
–e432
.10.1016/j.jmmm.2006.01.20712.
Chai
, F.
, Gao
, H. W.
, Yu
, Y. J.
, and Cheng
, S. K.
, 2008
, “The Research on Performances of Interior Permanent Magnet Synchronous Motor With Different Pole and Slot Combinations
,” International Conference on Electrical Machines and Systems (ICEMS)
, Wuhan
, China, Oct. 17–20, pp. 3724
–3727
.13.
Lee
, C. J.
, and Jang
, G. H.
, 2008
, “Distortion of Magnetic Field and Magnetic Force of a Brushless DC Motor Due to Deformed Rubber Magnet
,” J. Appl. Phys.
, 103
(7
), p. 07F115
.10.1063/1.283544514.
Zhu
, L.
, Jiang
, S. Z.
, Zhu
, Z. Q.
, and Chan
, C. C.
, 2009
, “Analytical Methods for Minimizing Cogging Torque in Permanent-Magnet Machines
,” IEEE Trans. Magn.
, 45
(4
), pp. 2023
–2031
.10.1109/TMAG.2008.201136315.
Guo
, Z.
, Chang
, L.
, and Xue
, Y.
, 2009
, “Cogging Torque of Permanent Magnet Electric Machines: An Overview
,” Canadian Conference on Electrical and Computer Engineering (CCECE '09
), St. John's, NL
, Canada, May 3–6, pp. 1172
–1177
.10.1109/CCECE.2009.509031016.
Chen
, D. L.
, Wang
, S. Y.
, Xiu
, J.
, and Liu
, J. P.
, 2011
, “Physical Explanation on Rotational Vibration Via Distorted Force Field of Multi-Cyclic Symmetric Systems
,” 13th World Congress in Mechanism and Machine Science
, Guanajuato, México
, June 19–25.17.
Wang
, S. Y.
, Xu
, J. Y.
, Xiu
, J.
, Liu
, J. P.
, Zhang
, C.
, and Yang
, Y. H.
, 2011
, “Elastic Wave Suppression of Permanent Magnet Motors by Pole/Slot Combination
,” ASME J. Vib. Acoust.
, 133
(2
), p. 024501
.10.1115/1.400295418.
Bianchini
, C.
, Immovilli
, F.
, Lorenzani
, E.
, Bellini
, A.
, and Davoli
, M.
, 2012
, “Review of Design Solutions for Internal Permanent-Magnet Machines Cogging Torque Reduction
,” IEEE Trans. Magn.
, 48
(10
), pp. 2685
–2693
.10.1109/TMAG.2012.219950919.
Huo
, M. N.
, Wang
, S. Y.
, Xiu
, J.
, and Cao
, S. Q.
, 2012
, “Effect of Magnet/Slot Combination on Triple-Frequency Magnetic Force and Vibration of Permanent Magnet Motors
,” J. Sound Vib.
, 332
(22
), pp. 5965
–5980
.10.1016/j.jsv.2013.05.02220.
Hartman
, A.
, and Lorimer
, W.
, 2001
, “Undriven Vibrations in Brushless DC Motors
,” IEEE Trans. Magn.
, 37
(2
), pp. 789
–792
.10.1109/20.91761721.
Lee
, C. I.
, and Jang
, G. H.
, 2008
, “Experimental Measurement and Simulated Verification of the Unbalanced Magnetic Force in Brushless DC Motors
,” IEEE Trans. Magn.
, 44
(11
), pp. 4377
–4380
.10.1109/TMAG.2008.200151222.
Lee
, C. I.
, and Jang
, G. H.
, 2009
, “Noninvasive Detection of Unevenly Magnetized Permanent Magnet of a Brushless DC Motor by Characterizing Back Electromotive Force
,” J. Appl. Phys.
, 105
(7
), p. 07F107
.10.1063/1.306854623.
Gašparin
, L.
, Černigoj
, A.
, Markič
, S.
, and Fišer
, R.
, 2009
, “Additional Cogging Torque Components in Permanent-Magnet Motors Due to Manufacturing Imperfections
,” IEEE Trans. Magn.
, 45
(3
), pp. 1210
–1213
.10.1109/TMAG.2009.201256124.
Lee
, C. J. J.
, Lee
, C. I.
, and Jang
, G. H.
, 2010
, “Source and Reduction of Uneven Magnetization of a Permanent Magnet of a HDD Spindle Motor
,” IEEE Trans. Magn.
, 47
(7
), pp. 1929
–1932
.10.1109/TMAG.2011.212387725.
Sung
, S. J.
, Park
, S. J.
, and Jang
, G. H.
, 2011
, “Cogging Torque of Brushless DC Motors Due to the Interaction Between the Uneven Magnetization of a Permanent Magnet and Teeth Curvature
,” IEEE Trans. Magn.
, 47
(7
), pp. 1923
–1928
.10.1109/TMAG.2011.212059926.
Coenen
, I.
, Giet
, M. V. D.
, and Hameyer
, K.
, 2012
, “Manufacturing Tolerances: Estimation and Prediction of Cogging Torque Influenced by Magnetization Faults
,” IEEE Trans. Magn.
, 48
(5
), pp. 1932
–1936
.10.1109/TMAG.2011.217825227.
Lee
, C. J.
, and Jang
, G. H.
, 2011
, “Development of a New Magnetizing Fixture for the Permanent Magnet Brushless DC Motors to Reduce the Cogging Torque
,” IEEE Trans. Magn.
, 47
(10
), pp. 2410
–2413
.10.1109/TMAG.2011.215430628.
Černigoj
, A.
, Gašparin
, L.
, and Fišer
, R.
, 2010
, “Native and Additional Cogging Torque Components of PM Synchronous Motors—Evaluation and Reduction
,” Atkaff
, 51
(2
), pp. 157
–165
.29.
Tudorache
, T.
, and Trifu
, I.
, 2012
, “Permanent-Magnet Synchronous Machine Cogging Torque Reduction Using a Hybrid Model
,” IEEE Trans. Magn.
, 48
(10
), pp. 2627
–2632
.10.1109/TMAG.2012.219848530.
Dosiek
, L.
, and Pillay
, P.
, 2007
, “Cogging Torque Reduction in Permanent Magnet Machines
,” IEEE Trans. Ind. Appl.
, 43
(6
), pp. 1565
–1571
.10.1109/TIA.2007.90816031.
Schlensok
, C.
, Riesen
, D. V.
, Schmülling
, B.
, Schöning
, M. C.
, and Hameyer
, K.
, 2007
, “Cogging-Torque Analysis on Permanent-Magnet Machines by Simulation and Measurement
,” Tech. Mess.
, 74
(7–8
), pp. 393
–401
.10.1524/teme.2007.74.7-8.39332.
Saied
, S. A.
, Abbaszadeh
, K.
, Hemmati
, S.
, and Fadaie
, M.
, 2009
, “A New Approach to Cogging Torque Reduction in Surface-Mounted Permanent-Magnet Motors
,” Eur. J. Sci. Res.
, 26
(4
), pp. 499
–509
.33.
Wang
, D. H.
, Wang
, X. H.
, and Sang-Yong
, J.
, 2013
, “Cogging Torque Minimization and Torque Ripple Suppression in Surface-Mounted Permanent Magnet Synchronous Machines Using Different Magnet Widths
,” IEEE Trans. Magn.
, 49
(5
), pp. 2295
–2298
.10.1109/TMAG.2013.224245434.
Aydin
, M.
, Zhu
, Z. Q.
, Lipo
, T. A.
, and Howe
, D.
, 2007
, “Minimization of Cogging Torque in Axial-Flux Permanent-Magnet Machines: Design Concepts
,” IEEE Trans. Magn.
, 43
(9
), pp. 3614
–3622
.10.1109/TMAG.2007.90281835.
Gulec
, M.
, and Aydin
, M.
, 2012
, “Influence of Magnet Grouping in Reduction of Cogging Torque for a Slotted Double-Rotor Axial-Flux PM Motors
,” International Symposium on Power Electronics, Electrical Drives
, Automation and Motion (SPEEDAM
), Sorrento, Italy
, June 20–22, pp. 812
–817
.10.1109/SPEEDAM.2012.626441536.
Wang
, S. Y.
, Xiu
, J.
, Cao
, S. Q.
, and Liu
, J. P.
, 2014
, “Analytical Treatment With Rigid-Elastic Vibration of Permanent Magnet Motors With Expanding Application to Cyclically Symmetric
,” ASME J. Vib. Acoust.
, 136
(2
), p. 021014
.10.1115/1.402599337.
Wang
, S. Y.
, Huo
, M. N.
, Zhang
, C.
, Liu
, J. P.
, Song
, Y. M.
, Cao
, S. Q.
, and Yang
, Y. H.
, 2011
, “Effect of Mesh Phase on Wave Vibration of Spur Planetary Ring Gear
,” Eur. J. Mech. A-Solid
, 30
(6
), pp. 820
–827
.10.1016/j.euromechsol.2011.06.00438.
Parker
, R. G.
, 2000
, “A Physical Explanation for the Effectiveness of Planet Phasing to Suppress Planetary Gear Vibration
,” J. Sound Vib.
, 236
(4
), pp. 561
–573
.10.1006/jsvi.1999.285939.
Nicolet
, C.
, Ruchonnet
, N.
, and Avellan
, F.
, 2006
, “One-Dimensional Modeling of Rotor Stator Interaction in Francis Pump-Turbine
,” 23rd IAHR Symposium on Hydraulic Machinery and Systems
, Yokohama, Japan
, Oct. 18–21, pp. 1
–15
.40.
Nicolet
, C.
, Ruchonnet
, N.
, Alligné
, S.
, Koutnik
, J.
, and Avellan
, F.
, 2010
, “Hydroacoustic Simulation of Rotor-Stator Interaction in Resonance Conditions in Francis Pump-Turbine
,” IOP
Conference Series: Earth and Environmental Science
, Barcelona, Spain, June 28–30.10.1088/1755-1315/12/1/012005Copyright © 2015 by ASME
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