GENICHI TAGUCHI developed statistical methods for quality improvement of engineering products, marketing, etc. This method is called Taguchi method that more recently applied to engineering and applied science. The Taguchi experiment design method for optimal design to mitigate cogging torque of a surface permanent magnet (SPM) motor is used in this article. In this paper, an efficient algorithm to the solutions for shape of PM is proposed and applied to optimize the shape of PMs in a surface-mounted PM motor to reduce the cogging torque. Finally, Simulation results are presented that indicates the reduction of magnitude of cogging torque.

1. International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 2013
DOI:10.5121/ijcsa.2013.3204 31
Application of Taguchi Experiment Design for
Decrease of Cogging Torque in Permanent
Magnet motors
A.Noori Shirazi1
, B. Yousefi2
, S. Asghar Gholamian3*
and S. Rashidaee3
1
Department of Engineering, Islamic Azad University-Nour Branch,Nour , Iran.
abdoreza.noori@gmail.com
2
Department of Engineering, Islamic Azad University-Nour Branch,Nour , Iran.
borzoyou@yahoo.com
3
Babol University of Technology, Faculty of Electrical and
Computer Engineering, Babol, Iran
*
Corresponding author: S. Asghar Gholamian
ABSTRACT:
GENICHI TAGUCHI developed statistical methods for quality improvement of engineering products,
marketing, etc. This method is called Taguchi method that more recently applied to engineering and
applied science. The Taguchi experiment design method for optimal design to mitigate cogging torque of a
surface permanent magnet (SPM) motor is used in this article. In this paper, an efficient algorithm to the
solutions for shape of PM is proposed and applied to optimize the shape of PMs in a surface-mounted PM
motor to reduce the cogging torque. Finally, Simulation results are presented that indicates the reduction
of magnitude of cogging torque.
KEYWORD:
TAGUCHI METHOD, PM MOTOR, PERMANENT MAGNET POLE
LIST OF SYMBOLS
PM Permanent Magnet
FEA finite element analysis
MMF magnetomotive force
SPM Surface-mounted permanent magnet
A the ratio of magnet pole arc to pole pitch
B the distance from motor centre
C the slot opening height
D the slot opening width
E the air gap length
DOE design of experiments
ANOM analysis of means
ANOVAanalysis of variance
f converter frequency
p machine pole pairs

2. International Journal on Computational Sciences &
1. INTRODUCTION
Recently, because of high reliability, high efficiency and improvement of the torque density,
surface permanent magnet motors (SPM) are used in industrial applications.
However, cogging torque problem is one of the main
type of motors. The interaction of the stator teeth with magnets produced cogging torque that
causes the increasing the noise, vibration and ultimately reduces efficiency of SPM motor.
The stator slots shape and permanent magnet pole configuration in SPM motors is the main cause
of cogging torque production. Many
torque in SPM motors. Some of these techniques are to modify the permanent magnet poles
configuration [8]-[11] and some of the other methods are to modify the shape of stator teeth
[13].
Surface permanent magnet motor with four poles, due to reduced consumption of copper and easy
manufacturing process, now widely used in air conditioning compresso
techniques, such as genetic algorithm [15], [16], rosenbrocks method [18], [19] and [17] is used
for improvement of cogging torque in SPM motors. But, the Taguchi method has been proven
useful in applied science especially in engi
The Taguchi method does not require using additional programming
element method analysis (FEM). Hence, effects of
be investigated in this method [20].
2. SURFACE PM MOTOR
Surface-mounted permanent magnet (SPM) motors are widely used in industry.
problem in SPM motors is the cogging torque and it affects the performance, produces noise and
results in mechanical vibration, therefore
torque in SPM motors.
In this paper, the 2D view of SPM motor shown in Figure1 and the main parameters are shown in
Table1. This kind of stator and rotor configuration
force or flux density under the PM rotor
and rotor, which will increase the ripple and noise
torque) with variations in stator and PM shapes has
analysis (FEM), in this paper.
International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 2013
Recently, because of high reliability, high efficiency and improvement of the torque density,
surface permanent magnet motors (SPM) are used in industrial applications. [1]-[4].
However, cogging torque problem is one of the main restrictions in usage development in this
The interaction of the stator teeth with magnets produced cogging torque that
causes the increasing the noise, vibration and ultimately reduces efficiency of SPM motor.
permanent magnet pole configuration in SPM motors is the main cause
Many methods have been proposed to reduction of
Some of these techniques are to modify the permanent magnet poles
some of the other methods are to modify the shape of stator teeth
Surface permanent magnet motor with four poles, due to reduced consumption of copper and easy
manufacturing process, now widely used in air conditioning compressors [5]. Some optimization
techniques, such as genetic algorithm [15], [16], rosenbrocks method [18], [19] and [17] is used
for improvement of cogging torque in SPM motors. But, the Taguchi method has been proven
useful in applied science especially in engineering process to improve best quality.
does not require using additional programming algorithms aside from finite
). Hence, effects of many factors on cogging torque
[20].
OTOR MODEL
mounted permanent magnet (SPM) motors are widely used in industry. An important
cogging torque and it affects the performance, produces noise and
therefore it is necessary and important to reduction of
of SPM motor shown in Figure1 and the main parameters are shown in
and rotor configuration cannot produce symmetrical magnetomotive
PM rotor poles, and harmonics exist in the air gap between stator
, which will increase the ripple and noise in torque. Calculation of The torque (cogging
stator and PM shapes has been computed using finite element
Figure1. SPM motor
Applications (IJCSA) Vol.3, No.2, April 2013
32
Recently, because of high reliability, high efficiency and improvement of the torque density,
restrictions in usage development in this
The interaction of the stator teeth with magnets produced cogging torque that
causes the increasing the noise, vibration and ultimately reduces efficiency of SPM motor.
permanent magnet pole configuration in SPM motors is the main cause
tion of a cogging
Some of these techniques are to modify the permanent magnet poles
some of the other methods are to modify the shape of stator teeth [12],
Surface permanent magnet motor with four poles, due to reduced consumption of copper and easy
Some optimization
techniques, such as genetic algorithm [15], [16], rosenbrocks method [18], [19] and [17] is used
for improvement of cogging torque in SPM motors. But, the Taguchi method has been proven
aside from finite
reduction can
An important
cogging torque and it affects the performance, produces noise and
ecessary and important to reduction of the cogging
of SPM motor shown in Figure1 and the main parameters are shown in
trical magnetomotive
between stator
Calculation of The torque (cogging
been computed using finite element method

3. International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 2013
33
Table1. Main parameters of the SPM motor
30 HpRated power
120 mmStator outer diameter
60 mmStator inner diameter
70 mmLamination length
1.7 mmPM thickness
0.5 mmAir gap length
DW360-50Stator and rotor core material
NdFeB 30SHPM material
2. DESIGN OF EXPERIMENT
Experimental design or design of experiments (DOE) is the design of any information where
variation is present, whether under the full control or not. DOE often used in evaluating applied
physic, engineering and material science.
The Taguchi method extremely reduced the number of experiments by using orthogonal array
tables. This array is selected the special features among the total number of experiments [6],[7].
In this paper, the design factors and their respective levels are given in Table2.
Where,
A is the ratio of PM Pole arc to pole pitch
B is the distance from motor centre used as the centre of circle for PM (mm)
C is the slot opening height (mm)
D is the slot opening width (mm)
E is the air gap length (mm)
Table2. Design Factors
Level 4Level 3Level 2Level 1Factors
0.90.860.820.78A
0.450.30.150B [mm]
1.110.90.8C [mm]
21.91.81.7D [mm]
0.60.50.40.3E [mm]
The orthogonal array L-16 selected for the matrix experiments based on standard Taguchi is
shown in table 3. As shown in Table3, there are 16 experiments required to determine the
optimum combination of the levels of these factors.
If there are 5 variable each at 4 levels, full factorial approach needs 4 5
or 1024 experiments. To
2D FEM analysis is conducted to obtain the average values of torque and cogging torque for each
case.
Table4 shows the results of simulation results.

4. International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 2013
34
Table3. L-16 Orthogonal Array
EDCBAExperiment
111111
222212
333313
444414
432125
341226
214327
123428
243139
1342310
4213311
3124312
3241413
4132414
1423415
2314416
Table4. Motor Simulation Results
Tavg
(N.m)
Tc (N.m)Experiment
4.07470.79621
3.98300.73192
3.88270.67473
3.77780.62244
3.73310.65755
3.79760.72596
3.87230.65837
3.94540.72598
3.94860.83529
4.02420.833610
3.72970.535011
3.79850.520312
4.02200.669813
3.91330.522514
4.14480.806315
4.03040.644316
3. ANALYSIS OF SIMULATION RESULTS
After obtaining all the simulation results from the matrix experiment and, ANOM (analysis of
means) and ANOVA (analysis of variance) are carried out to estimation of the four design
parameters and determination of the relative importance of each design variable [21].
The means of all simulation results can be calculated by Equation1.
1 6
1
1
1 6
i
i
m T
=
= ∑
(1)

5. International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 2013
35
Table5 tabulates the results.
Table5. Analysis of Means
Tavg
(N.m)
Tc
(N.m)
3.91740.6850m
3.1. Average Effect
The average torque of variable A at level 3 is calculated by Equation2.
3
1
( ) ( (9) (10) (11) (12))
4
avg avg avg avg avgmA T T T T T= + + +
(2)
As shown in table3, the factor A is set to in experiments 9, 10, 11, 12 at level 3. Similar way can
be used for computing of Average torque of all variables.
Table 6 shows the results. A plot of main factors effects is illustrated in Figure2 It is seen that the
factor-level combination (A4, B1, C4, D2, and E1) contributes to maximization of average
torque.
Table6. Average torque for all levels of all factors
EiDiCiBiAii
4.04733.91473.90813.94963.92961
3.95863.92003.91483.9293.83712
3.87523.91763.923.90743.87533
3.7803.91723.92413.88804.02764
Figure2. Main factor effects on average torque
The peak to peak value of cogging torque for all levels of factors is shown in Table7. Main factor
effect on the peak to peak value of cogging torque is shown in Figure3
3.75
3.78
3.81
3.84
3.87
3.9
3.93
3.96
3.99
4.02
4.05
A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4 E1 E2 E3 E4
Tavg(N.m)
setting of factors

6. International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 2013
36
Table7. Peak to peak value of cogging torque for all levels of all factors
EiDiCiBiAii
0.19530.15900.17240.18740.17941
0.18130.16940.17280.17890.18032
0.16710.17920.17570.17040.17473
0.15440.19050.17710.16140.16364
Figure3. Main factor effects on peak to peak value of cogging torque
3.2. Analysis Of Variance (ANOVA)
To conduct Analysis Of Variance is calculated the sum of squares. It is measure of the deviation
of simulation data from the mean value of the data. The sum of squares (SSFA) due to various
factors can be calculated as:
4
2
1
4 ( )iA
i
SSFA m m
=
= −∑
(3)
SSFB, SSFC, SSFD and SSFE can be obtained in the same way. Table8 is shown the data of the
machine among the initial, Taguchi parameter designs and simulation results.
It can be seen that average torque increases from the initial design of 3.8276 Nm to Taguchi
parameter design of 4.1118 Nm, and to simulation result of 4.10 Nm. The cogging torque value
decreases from 0.7315 Nm to 0.6390 Nm in Taguchi parameter design, and to 0.6400 Nm in
simulation result.
Table 8. Comparison Results
Tc (N.m)Tavg. (N.m)
0.73153.8276Initial
0.63904.1118Taguchi results
0.6404.10Simulation results
0.15
0.154
0.158
0.162
0.166
0.17
0.174
0.178
0.182
0.186
0.19
0.194
0.198
A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4 E1 E2 E3 E4
Tc(N.m)
setting of factors

7. International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 2013
37
4. CONCLUSION
The Taguchi method applied to design optimization of SPM motor for the reduction of cogging
torque value. The peak to peak value of cogging torque decreases before and after optimization
by Taguchi method.
The peak to peak value of cogging torque decreases from 0.7315 Nm to 0.6390 Nm in Taguchi
parameter design, and to 0.6400 Nm in simulation result.
Proposed method for solving this problem is significantly reduced the peak to peak value of
cogging torque of SPM motor.
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