Shape Optimization of Permanent Magnet Motors Using the Reduced Basis Technique
In this paper, a tooth shape optimization method for
cogging torque reduction in Permanent Magnet (PM) motors is
developed by using the Reduced Basis Technique (RBT) coupled by
Finite Element Analysis (FEA) and Design of Experiments (DOE)
methods. The primary objective of the method is to reduce the
enormous number of design variables required to define the tooth
shape. RBT is a weighted combination of several basis shapes. The
aim of the method is to find the best combination using the weights
for each tooth shape as the design variables. A multi-level design
process is developed to find suitable basis shapes or trial shapes at
each level that can be used in the reduced basis technique. Each level
is treated as a separated optimization problem until the required
objective – minimum cogging torque – is achieved. The process is
started with geometrically simple basis shapes that are defined by
their shape co-ordinates. The experimental design of Taguchi method
is used to build the approximation model and to perform
optimization. This method is demonstrated on the tooth shape
optimization of a 8-poles/12-slots PM motor.
[1] Chang Seop Koh, Hee Soo Yoon, Ki Woong Nam, and Hong Soon Choi,
"Magnetic pole shape optimization of permanent magnet motor for
reduction of cogging torque," IEEE Trans. On Magnetics, vol. 33, No.2,
Mar 1997.
[2] Tae Kyung Chung, Suk Ki Kim, and Song-Yop Hahn, "Optimal pole
shape design for the reduction of cogging torque of brushless DC motor
using evolution strategy," IEEE Transactions on Magnetics, Vol.33,
No.2, Mar 1997.
[3] Jang-Sung Chun,Hyun-Kyo Jung, and Joong-Suk Yoon, "Shape
optimization of closed slot type permanent magnet motors for cogging
torque reduction using evolution strategy," IEEE Transactions On
Magnetics, Vol.33, No.2, Mar 1997.
[4] Semyung Wang, Soonkyu Jeong, and Heesoo Yoon, "Continuum shape
design sensitivity analysis of magnetostatic field using finite element
method," IEEE Transactions on Magnetics, vol. 35, No. 3, May 1999.
[5] Yao, Y.D., Huang, D.R., Wang, J.C., Liou, S.H., Wang, S.J., Ying, T.F.
and Chiang, D.Y., " Simulation study of the reduction of cogging torque
in permanent magnet motors," IEEE Transactions on Magnetics, Vol.
33, No. 5, Sep 1997.
[6] Yao, Y.D. Huang, D.R. Wang, J.C. Wang, S.J. Ying, T.F. and
Chiang, D.Y., "Study of a high efficiency and low cogging torque
spindle motor, " IEEE Transactions on Magnetics, Vol.34, No. 2, Mar
1998.
[7] Der-Ray Huang, Tai-Fa Ying, Shyh-Jier Wang, Chi-mou Zhou, Yin
Kwang Lin, Kai-Wen Su, and Hsu, C.-I.G., "Cogging torque reduction
of a single-phase brushless DC motor," IEEE Transactions on
Magnetics, Vol. 34, No. 4, Jul 1998.
[8] Liang-Yi Hsu and Mi-Ching Tsai, "Tooth shape optimization of
brushless permanent magnet motors for reducing torque ripples,"
Journal of Magnetism and Magnetic Materials, Vol. 282, , Pages 193-
197.,November 2004.
[9] S. Wang, and J. Kang, "Shape optimization of BLDC motor using 3-D
finite element method," IEEE Transactions on Magnetics, Vol.36, No.4,
Jul 2ooo.
[10] D. R. Huang, C.Y Fan, S. J. Wang, H.P Pan, T. F. Ying, C. M. Chao, and
E. G. Lean, "A new type single-phase spindle motor for HDD and
DVD," IEEE Transactions on Magnetics, Vol. 35, No. 2, Mar 1999.
[11] J. Y. Lee., J.H Chang, D.-H Kang, S.-I Kim, and J. P. Hong. "Tooth
Shape Optimization for Cogging Torque Reduction of Transverse Flux
Rotary Motor Using Design of Experiment and Response Surface
Methodology," IEEE Transaction on Magnetics, Vol. 43, No. 4, April
2007.
[12] M.A. Jabbar and Azmi Bin Azeman "Fast optimization of
electromagnetic problems: The reduced basis finite element
approach", IEEE Trans. Magn, Vol.40, No. 4, pp.2161-2163, July
2004.
[13] M.A. Jabbar and Azmi Bin Azeman "Multi-variable torque
optimization for small spindle motors based on reduced-basis
finite element formulation", International Conference on Power
Electronics, Machines and Drives, 2002. Date: 4-7 June 2002,on pp.
269- 274.
[14] M.A. Jabbar and Azmi Bin Azeman, "Torque optimisation for
small spindle motors based on reduced-basis finite element
formulation" International Journal of Applied Electromagnetics
and Mechanics, Vol.19, no.1-4, pp.355-360. 2004.
[15] N. Thiyagarajan, and R. V. Grandhi, "Multi-level design process for 3-D
preform shape optimization in metal forming," Journal of Material
Processing Technology, vol.170, pp. 421-429. 2005.
[16] Roy, R.K., 2001. Design of Experiments Using the Taguchi Approach.
Wiley-Interscience Publication.
[1] Chang Seop Koh, Hee Soo Yoon, Ki Woong Nam, and Hong Soon Choi,
"Magnetic pole shape optimization of permanent magnet motor for
reduction of cogging torque," IEEE Trans. On Magnetics, vol. 33, No.2,
Mar 1997.
[2] Tae Kyung Chung, Suk Ki Kim, and Song-Yop Hahn, "Optimal pole
shape design for the reduction of cogging torque of brushless DC motor
using evolution strategy," IEEE Transactions on Magnetics, Vol.33,
No.2, Mar 1997.
[3] Jang-Sung Chun,Hyun-Kyo Jung, and Joong-Suk Yoon, "Shape
optimization of closed slot type permanent magnet motors for cogging
torque reduction using evolution strategy," IEEE Transactions On
Magnetics, Vol.33, No.2, Mar 1997.
[4] Semyung Wang, Soonkyu Jeong, and Heesoo Yoon, "Continuum shape
design sensitivity analysis of magnetostatic field using finite element
method," IEEE Transactions on Magnetics, vol. 35, No. 3, May 1999.
[5] Yao, Y.D., Huang, D.R., Wang, J.C., Liou, S.H., Wang, S.J., Ying, T.F.
and Chiang, D.Y., " Simulation study of the reduction of cogging torque
in permanent magnet motors," IEEE Transactions on Magnetics, Vol.
33, No. 5, Sep 1997.
[6] Yao, Y.D. Huang, D.R. Wang, J.C. Wang, S.J. Ying, T.F. and
Chiang, D.Y., "Study of a high efficiency and low cogging torque
spindle motor, " IEEE Transactions on Magnetics, Vol.34, No. 2, Mar
1998.
[7] Der-Ray Huang, Tai-Fa Ying, Shyh-Jier Wang, Chi-mou Zhou, Yin
Kwang Lin, Kai-Wen Su, and Hsu, C.-I.G., "Cogging torque reduction
of a single-phase brushless DC motor," IEEE Transactions on
Magnetics, Vol. 34, No. 4, Jul 1998.
[8] Liang-Yi Hsu and Mi-Ching Tsai, "Tooth shape optimization of
brushless permanent magnet motors for reducing torque ripples,"
Journal of Magnetism and Magnetic Materials, Vol. 282, , Pages 193-
197.,November 2004.
[9] S. Wang, and J. Kang, "Shape optimization of BLDC motor using 3-D
finite element method," IEEE Transactions on Magnetics, Vol.36, No.4,
Jul 2ooo.
[10] D. R. Huang, C.Y Fan, S. J. Wang, H.P Pan, T. F. Ying, C. M. Chao, and
E. G. Lean, "A new type single-phase spindle motor for HDD and
DVD," IEEE Transactions on Magnetics, Vol. 35, No. 2, Mar 1999.
[11] J. Y. Lee., J.H Chang, D.-H Kang, S.-I Kim, and J. P. Hong. "Tooth
Shape Optimization for Cogging Torque Reduction of Transverse Flux
Rotary Motor Using Design of Experiment and Response Surface
Methodology," IEEE Transaction on Magnetics, Vol. 43, No. 4, April
2007.
[12] M.A. Jabbar and Azmi Bin Azeman "Fast optimization of
electromagnetic problems: The reduced basis finite element
approach", IEEE Trans. Magn, Vol.40, No. 4, pp.2161-2163, July
2004.
[13] M.A. Jabbar and Azmi Bin Azeman "Multi-variable torque
optimization for small spindle motors based on reduced-basis
finite element formulation", International Conference on Power
Electronics, Machines and Drives, 2002. Date: 4-7 June 2002,on pp.
269- 274.
[14] M.A. Jabbar and Azmi Bin Azeman, "Torque optimisation for
small spindle motors based on reduced-basis finite element
formulation" International Journal of Applied Electromagnetics
and Mechanics, Vol.19, no.1-4, pp.355-360. 2004.
[15] N. Thiyagarajan, and R. V. Grandhi, "Multi-level design process for 3-D
preform shape optimization in metal forming," Journal of Material
Processing Technology, vol.170, pp. 421-429. 2005.
[16] Roy, R.K., 2001. Design of Experiments Using the Taguchi Approach.
Wiley-Interscience Publication.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:54001", author = "A. Jabbari and M. Shakeri and A. Nabavi", title = "Shape Optimization of Permanent Magnet Motors Using the Reduced Basis Technique", abstract = "In this paper, a tooth shape optimization method for
cogging torque reduction in Permanent Magnet (PM) motors is
developed by using the Reduced Basis Technique (RBT) coupled by
Finite Element Analysis (FEA) and Design of Experiments (DOE)
methods. The primary objective of the method is to reduce the
enormous number of design variables required to define the tooth
shape. RBT is a weighted combination of several basis shapes. The
aim of the method is to find the best combination using the weights
for each tooth shape as the design variables. A multi-level design
process is developed to find suitable basis shapes or trial shapes at
each level that can be used in the reduced basis technique. Each level
is treated as a separated optimization problem until the required
objective – minimum cogging torque – is achieved. The process is
started with geometrically simple basis shapes that are defined by
their shape co-ordinates. The experimental design of Taguchi method
is used to build the approximation model and to perform
optimization. This method is demonstrated on the tooth shape
optimization of a 8-poles/12-slots PM motor.", keywords = "PM motor, cogging torque, tooth shape optimization,
RBT, FEA, DOE.", volume = "3", number = "1", pages = "27-6", }