The cogging torque of a permanent-magnet motor is an oscillatory torque that always induces vibration, acoustic noise, possible resonance and speed ripples, and its minimization is a major concern for electric motor designers. This paper presents an effective approach for the cogging torque reduction of interior permanent-magnet motors by modifying the magnet span angle of the rotor and the shoe depth and shoe ramp of the stator. The cogging torque is calculated by employing a commercial finite-element analysis software Ansoft/Maxwell. The results show that the peak value of the cogging torque for the modified design decreases 50% in comparison with that of the original design

Pei-Li  Tsai

Wan-Tsun  Tseng

Yi-Chang  Wu

English

Vibroengineering PROCEDIA

  ©VIBROENGINEERING. VIBROENGINEERING PROCEDIA. NOVEMBER 2013. VOLUME 2. ISSN 2345-0533 113 
Cogging Torque Reduction of Interior Permanent-Magnet 
Synchronous Motors by Finite-Element Method 
Yi-Chang Wu, Wan-Tsun Tseng and Pei-Li Tsai 
COGGING TORQUE REDUCTION OF INTERIOR PERMANENT-MAGNET SYNCHRONOUS MOTORS BY FINITE-ELEMENT METHOD.  
YI-CHANG WU, WAN-TSUN TSENG AND PEI-LI TSAI 
Yi-Chang Wu1, Wan-Tsun Tseng2 and Pei-Li Tsai3 
1, 3 Department of Mechanical Engineering, National Yunlin University of Science & Technology, 
Yunlin, Taiwan 640, R.O.C.  
2 Department of Electrical Engineering, National Yunlin University of Science & Technology, Yunlin, 
Taiwan 640, R.O.C. 
 
E-mail: wuyc@yuntech.edu.tw 
Abstract. The cogging torque of a permanent-magnet motor is an oscillatory torque that always induces 
vibration, acoustic noise, possible resonance and speed ripples, and its minimization is a major concern for 
electric motor designers. This paper presents an effective approach for the cogging torque reduction of interior 
permanent-magnet motors by modifying the magnet span angle of the rotor and the shoe depth and shoe ramp of 
the stator. The cogging torque is calculated by employing a commercial finite-element analysis software 
Ansoft/Maxwell. The results show that the peak value of the cogging torque for the modified design decreases 
50% in comparison with that of the original design.  
1. Introduction 
An electric motor is an electric device that converts electrical energy into mechanical energy. Among 
various types of electric motors, interior permanent-magnet (IPM) synchronous motors have attracted 
extensive interest due to the characteristics of high efficiency, high torque-to-volume ratio, low cost of 
maintenance and a long constant power operating range [1]. IPM synchronous motors generate not 
only electromagnetic torque but also reluctance torque by the rotor saliency, so they are widely used in 
traction motors of electric and hybrid vehicles and electrical power steering systems of automobiles. 
However, the IPM synchronous motor possesses an inherent cogging torque that causes the torque 
ripple as well as prevents a smooth rotation. The cogging torque is an oscillatory torque that always 
induces vibration, acoustic noise, possible resonance, speed ripples, and position inaccuracy, which is 
detrimental to the motor performance particularly at light load and low speed. Therefore, the reduction 
of the cogging torque becomes a major concern for electric motor designers. Several approaches have 
been developed to attempt minimizing the cogging torque of permanent-magnet motors, such as 
stepped skewing of permanent-magnet blocks [2], modifying permanent magnet arc [3, 4], providing 
different magnet widths [1], and shifting the pole pairs by half a slot pitch [5], etc. However, these 
methods are not available for IPM synchronous motors due to buried permanent magnets and 
geometric constraints of rotors. In this paper, an exterior-rotor IPM synchronous motor is introduced, 
and the effects of design parameters of the rotor and stator on the cogging torque are discussed by 
finite-element analysis. 
2. An exterior-rotor IPM synchronous motor 
For an exterior-rotor IPM synchronous motor, permanent magnets with even numbers are buried 
inside the rotor, while the stator with fixed polyphase windings appears on the inside of the rotor. 
Figure 1 shows a cross-sectional view of a 3-phase, 12-pole/18-slot IPM synchronous motor with a 
one-layer V-shape rotor topology. Such a kind of IPM motor has been widely used in electrical 
vehicles. The rotor is formed by laminating steel plates including magnetic barriers and magnet 
insertion holes in which permanent magnets are buried. The variation of the reluctance around the 
                                                     
1  To whom any correspondence should be addressed. 
COGGING TORQUE REDUCTION OF INTERIOR PERMANENT-MAGNET SYNCHRONOUS MOTORS BY FINITE-ELEMENT METHOD.  
YI-CHANG WU, WAN-TSUN TSENG AND PEI-LI TSAI 
114 ©VIBROENGINEERING. VIBROENGINEERING PROCEDIA. NOVEMBER 2013. VOLUME 2. ISSN 2345-0533  
rotor creates saliency in the rotor structure of an IPM synchronous motor. Therefore, the IPM rotor 
generates reluctance torque in addition to electromagnetic torque due to magnetic saliency.  
3. Cogging torque analysis 
By definition, no stator current excitation is involved in the cogging torque production. The cogging 
torque directly arises from the mutual interaction of permanent magnets and the stator slotted structure 
of the IPM motor as the rotor rotates relative to the stator. Therefore, it is greatly affected by the 
configurations and dimensions of the rotor and stator. In this section, the effects of several design 
parameters, including the magnet span angle α of the rotor, the shoe depth d1 and the shoe ramp d2 of 
the stator, on the cogging torque are discussed by finite-element analysis. Figure 2 shows geometric 
parameters of the exterior-rotor IPM synchronous motor. The corresponding values of the magnetic 
properties and geometrical dimensions are given in table 1. The Ansoft/Maxwell 2D field simulator is 
employed to the cogging torque analysis of the two-dimensional IPM motor configuration. The period 
of the cogging torque for this IPM motor is 360º/lcm(P, S)= 360º/lcm(12, 18)=360º/36=10º. The 
symbol P is the number of magnet poles, the symbol S is the number of stator slots, and lcm(P, S) is 
the least common multiplier between P and S. The computed cogging torque of the IPM motor 
between 0º and 10º is given in figure 3. The peak value of the cogging torque is 2.14Nm, which occurs 
at about 1.5 mechanical degrees, and not half of 5 mechanical degrees.  
 
 
Figure 1. A cross-sectional view of 
an exterior-rotor IPM synchronous 
motor. 
 
The discrepancy of the peak position is mainly caused by the salient effects of the salient poles of the 
IPM synchronous motor. We set the total volume of permanent magnets of each design case as 
identical for comparison purposes. Figure 4 shows the cogging torque versus the magnet span angle α 
of the rotor. It is noted that with an increase of the magnet span angle, the peak value of the cogging 
torque increase. Figure 5 shows the cogging torque versus the shoe depth d1 of the stator. It can be 
seen that the peak values of the cogging torque decrease with the increase of the shoe depth. 
Influences of the shoe ramp d2 of the stator on the cogging torque are shown in figure 6. It is 
interesting to find that the peak values of the cogging torque decrease with the increase of the shoe 
ramp. The cogging torque can be expressed by the integration of the normal and tangential magnetic 
flux components within the air gap [6]. Because the normal and tangential magnetic flux components 
within the air gap vary with the geometry shape of pole shoes of the stator, the reduction of the 
cogging torque can be achieved by modifying pole shoes. By selecting the magnet span angle 
COGGING TORQUE REDUCTION OF INTERIOR PERMANENT-MAGNET SYNCHRONOUS MOTORS BY FINITE-ELEMENT METHOD.  
YI-CHANG WU, WAN-TSUN TSENG AND PEI-LI TSAI 
 ©VIBROENGINEERING. VIBROENGINEERING PROCEDIA. NOVEMBER 2013. VOLUME 2. ISSN 2345-0533 115 
α=80º, the shoe depth d1=4mm and the shoe ramp d2=30º, the peak value of the cogging torque 
reduces to 1.05Nm, which decreases 50% in comparison with that of the original design shown in 
table 1. 
 
 
Figure 2. Geometric parameters of 
an exterior-rotor IPM synchronous 
motor. 
 
Table 1. Specifications of an exterior-rotor IPM synchronous motor. 
NdFeB magnet properties (BNP 12) 
Items Symbol Values 
Remanence (T) Br 0.76 
Relative permeability µr 1.26 
Direction of magnetization -- Parallel 
Magnet thickness (mm) lm 6 
Magnet width (mm) τm 24.5 
Width between two magnets (mm) τf 10.95 
Motor parameters 
Items Symbol Values 
Number of phases Nph 3 
Number of magnet poles P 12 
Number of armature slots S 18 
Air gap length (mm) g 1 
Slot opening arc (degree) Ws 3 
Outer radius of rotor (mm) Rro 134 
Inner radius of rotor (mm) Rri 101 
Outer radius of stator (mm) Rso 100 
Inner radius of stator (mm) Rsi 40 
Bridge width (mm) t 1 
Air barrier length 1 (mm) h1 3.75 
Air barrier length 2 (mm) h2 1.38 
Air barrier width (mm) D 2 
magnet span angle (degree) α 90 
shoe depth (mm) d1 2 
shoe ramp (degree) d2 0 
Tooth width of stator wtb 12 
Stack length (mm) L 25 
 
COGGING TORQUE REDUCTION OF INTERIOR PERMANENT-MAGNET SYNCHRONOUS MOTORS BY FINITE-ELEMENT METHOD.  
YI-CHANG WU, WAN-TSUN TSENG AND PEI-LI TSAI 
116 ©VIBROENGINEERING. VIBROENGINEERING PROCEDIA. NOVEMBER 2013. VOLUME 2. ISSN 2345-0533  
 
 
 
Figure 3. Cogging torque distribution of the 
IPM synchronous motor shown in figure 1. 
(α=90º, d1= 2mm and d2=0º) 
 Figure 4. Cogging torque versus the magnet 
span angle α of the rotor. 
 
 
 
 
Figure 5. Cogging torque versus the shoe depth 
d1 of the stator. 
 Figure 6. Cogging torque versus the shoe ramp 
d2 of the stator. 
4. Conclusion 
In this paper, the reduction of the cogging torque for an exterior-rotor IPM synchronous motor has 
been presented by modifying pole shoes of the stator and adjusting the magnet span angle of the rotor. 
The proposed approach can also be applied for the cogging torque reduction of other permanent-
magnet motors with interior-rotor or exterior-rotor configurations.   
Acknowledgement 
The authors are grateful to the National Science Council (Taiwan, R.O.C) for supporting this research 
under grant NSC 102-2221-E-224-016-MY2. 
References 
[1] Wang D, Wang X and Jung S Y 2013 IEEE Trans. Magn. 49 2295 
[2] Jahns T M and Soong W L 1996 IEEE Trans. Ind. Electron. 43 321 
[3] Li T and Slemon G 1988 IEEE Trans. Magn. 24 2901 
[4] Eom J B, Hwang S M, Kim T J, Jeong W B and Kang B S 2001 J. Magn. Magn. Mater. 226 
1229 
[5] Ishikawa T and Slemon G R 1993 IEEE Trans. Magn. 29 2028 
[6] Lin Y K, Hu Y N, Lin T K, Lin H N, Chang Y H, Chen C Y, Wang S J and Ying T F 2000 J. 
Magn. Magn. Mater. 209 180 


Cogging Torque Reduction of Interior Permanent-Magnet Synchronous Motors by Finite-Element Method

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Cogging Torque Reduction of Interior Permanent-Magnet Synchronous Motors by Finite-Element Method

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