IEEE TRANSACTIONS ON MAONRT‘ICS. VOI. 35 NO 5. SEFTEMBER 1999
37110
Application of Taguchi Method to Robust
Design of BLDC Motor Performance
H.T. Wang, Z.J. Liu, S.X.Chen and J.P. Yang
Data Storage Institute, National University of Singapore
10 Kent Ridge Crescent, Singapore 119260
Abstract-This paper describes an approach to design of
brushless de motors considering the cogging torque reduction
and running torque optimization to enhance the product
robustness. The approach is based on Tawchi method and
utilizes the orthogonal array for design of ‘experiments’, i.e.
the scheme for numerical simulations using a finite element
method. The concept of sienal-to-noise (SN)ratio is aDDlied to
evaluate the mot& performance. A comparison is made
between the robust solution and the result obtained using a
conventional optimization procedure to demonstrate the
effectiveness of the rohnst design approach.
Index Terns-Electrical Machine, FEM, Robust Design,
Taguchi Method
I. INTRODUCTION
With recent advances in high-speed magnetic recording
technology, the robustness of the spindle motor
performance becomes an increasingly critical issue. As the
design constraints are more stringent, the spindle motor is
to be designed to perform in accordance with design
specifications despite the variability in operating
conditions. For instance, the effect of cogging and
unbalanced magnetic pull developed in brushless DC
(BLDC) motors [l], which may cause vibration and
acoustic noises, must be controlled to the minimum
possible level even when the operating condition is subject
to variability in thermal condition, material properties, and
other noises. It should be noted that in practice the motor
performance is controlled by quality inspection means
during production process, and excessive cogging/UMP
remains as the main cause responsible for a high product
failure or re-work rate. Finite element methods ( E M ) are
routinely used in evaluation of engineering product
performance. Owing to rapid advancement in computer
power and CAE tools, development of FEM based design
and optimization techniques are gaining pace [Z]. Some
commercial FEM software has been implemented with
preliminary optimization tools such as those based on fullfactorial or fractional-factorial Design of ‘Experiments’
(DOE). However, it is known that DOE based optimization
is not suitable for handling the non-linearity or the effects
of noise factors. In this paper, an optimization technique
based on Taguchi method is applied to a robust design
problem concerning spindle motor performance. Taguchi
method is a system of cost-driven quality engineering that
emphasizes the effective application of engineering
strategies rather than advanced statistical techniques. It can
reduce variability and find cost-effective, robust designs of
engineering products using a comparatively small number
experiments. It essentially aims at achieving the optimal
design target while keeping the product performance
insensitive to the effects of noise factors that may be due
to variability in manufacturing process or environmental
conditions, The effectiveness of the technique was
demonstrated In the design examples presented below.
11. CONCEPTSANDMETHOD
A . Taguchi Method
As simulation of product performance using FEM
invariably takes considerable computing resources and
time, the major challenge encountered in FEM based
optimization process for a practical problem is that the
designer can only perform a limited number of design
trials before reaching the optimal. The concept of Taguchi
method that is proven to be effective in the quality
engineering involving an efficient planning of
experiments on physical prototypes, is now employed for
computer simulation based optimization procedure.
Application of Taguchi method to robust design problems
involves three main stages,
(a) Selection of the performance characteristics to be
optimized, the control factors that can be adjusted
in the optimization exercise, and noise factors;
(b) Design and execution of the experiments based on
orthogonal array to obtain information on the
product performance and its variability; and
(c) Using analysis of mean (ANOM) and variance
(ANOVA) techniques to obtain optimal setting of
parameters for robust. design.
Then, verification of the robust design result shall be
performed. One of the key features of the Taguchi method
is the use of signal-to-noise ratio (SN Ratio) to transform
the performance characteristic in the optimization process
[3]. For the design problem under investigation, the
cogging torque to running torque ratio is chosen as the
performance characteristic and the S N ratio can be
expressed as follows,
B. Simulation of Product Response
To evaluate a design performance, a parametric
description for a BLDC motor is made. Fig. I shows one
pole pitch of the cross-sectional view of BLDC motor.
The electromagnetic field in the motor can be analyzed by
using finite element method, and the electromagnetically
induced forces and torque can also be computed with
various techniques [l].
0018-9464/99$10,00 0 1999 IEEE
3701
Rg.1. Cross-sectional view of BLDC motor showing 112
Stator tooth and 1 magnet pole
referred to as product performance characteristics, is to be
simulated using FEM.
Simulation and Results
The FEM simulation of the electromagnetic field in
the spindle motor is straightforward, however particular
care must he taken in the computation of electromagnetic
forces using FEM based techniques. It will be noted that
since the effect of the noise factors is to be examined in
the optimization process, the accuracy of the numerical
simulation is of great concern. Therefore, a very detailed
modeling of the physical problems is usually necessary. A
typical mesh of FEM analysis for the spindle motor
optimization problem is shown in Fig. 2, and the magnetic
flux distribution in Fig. 3, respectively. The cogging
torque-to-running torque ratio is computed according to
the following equation
where T,i and Tri are cogging torque and running
torque of the ith run.
Fig.2. Mesh for FEM analysis
Computation and Analysis
The mean, standard deviation, mean square deviation
(MSD) and S/N ratio based on the numerical simulation
of the responses are computed, and the results are given in
TABLE I.
TABLE I
COMPUTATION ANDANALYSIS FOREACH RUNS
Run
1
2
'
3
4
5
6
7
R g 3 Plux Distnbution
8
9
mean
45.141%
49.266%
53.878%
59.785%
63.482%
65.195%
39.306%
42.668%
47.750%
Std. De".
0.029843
0.031780
0.033317
0,016776
0.017890
0.017403
0.024648
0.025757
0.0~4038
MSD
S/NRatio
0.204566 6.891657
0.243616 6.132947
0.291273 5.356992
0.357677 4.465089
0,403283 ,3.943902
0.425313 .3.712914
.0.155037 8.095657
0.182648 7.383841
0.228523 ' 6.410703
111.DESIGN OF EXPERMENTS ANALYSIS
Design of Experiments
In this paper, An 8-pole & 6-slot external rotor BLDC
motor was considered. The design objective is to achieve
the optimal cogging torque-to-running torque ratio, and in
the mean time the deviation due to the effects of all noise
factors should be maintained minimal.
Three design parameters were considered as the control
factors. They are Tooth Face Angle (TFA), Tooth Body
Height (HTB), and Magnet Thickness (HM). Other three
factors are considered as the noise factors, they are Magnet
Material (MM), Tooth Face Angle (TFA), and Air-Gap
Length (LA). Fig. 1 shows a partial cross-sectional view
with some parameter specified.
Two L9 orthogonal arrays (OA) were utilized to
structure the settings of the design parameters (control
factors) and noise factors, respectively. At each design
parameter setting the response, or otherwise may be
The sensitivity analysis for each control factor can
then be performed by calculating the average S/N ratio for
each factor at the same level. Additionally, the effects of
factors on the performance of the spindle motor can also
be found according to the S/N ratio. The results are given
in TABLE 11. At the same time, the percentage
contribution (PC) for all control factors can be computed
and presented using the ratio of factor SS to TSS, as
shown in TABLE 111. It can be observed that the tooth
face angle has larger Contribution and more pronounced
influence on the performance.
Prediction and verification
Based on the above analyses of control factors and
sensitivity, an optimal setting of the design parameters
can be determined. Predictions of the mean and deviation
of response can be obtained.
TABLE I1
COMPUTATION
ANDANALYSISFORFACTORS
Factor
Level
WN)
~~
1
TFA
2
3
HTB
2
3
LM
2
3
I
1
6,127199
4.040635
7.296734
6.484134
5.820230
5.I60203
5.996137
5.669580
5.798850
TABLE III
ANOVAFORCONTROL
FACTORS
SS
D . 0 . F Meansq.
F
PC'(%)
Factor
TFA
16.324
2
HTB
2.6292
2
LM
0.1623
2
'PC-percentage contribution
8.1619
1.3146
0.0811
TABLE IV
PREDICTION
ANDVERIPICATION
Prediction
Verification
Mean
39.13%
38.57%
STD.DEV
0.02321
0.02389
8.13396
CriuyTaw Vdiden
0045 ,""U"
143.18 84.89
23.061 13.67
1.4233 0.842
For the optimization problem under investigation, the
optimal setting is From: TFA is on level 3, HTB is on level
1, and LM is on level 1. That is, TFA is 51", HTB is 3.8
mm, and LM is 1.155 mm. This is also referred to as the
robust solution in the following. Figure 4 compares the
cogging torque profiles developed in the BLDC spindle
motor before and after robust design procedure being
applied. The percentage contribution of each control factor
to the performance characteristic can. also be evaluated
during the course of optimization using Taguchi method.
The variance of the cogging torque at different settings of
design parameters is plotted in Fig. 5. The robust design
point is also indicated in these figures. It can be seen that
the robust design process yields smaller cogging torque and
larger running torque, and in the meantime the performance
is less sensitive to noise factors at the settings of control
factors corresponding to the robust design point. Table IV
shows the prediction and verification on robust point.
SIN
Fig.4. A Cogging Torque Comparison between Normal Design and
Robust Design
8.26064
From these figures, it can be concluded that by
applying the robust design technique an improved product
performance, in this case reduced cogging torque or
cogging to running torque ratio, can be achieved. At the
robust design point the sensitivity level of the performance
to the noise factors, as reflected by the variance of the
performance, is also significantly reduced.
Fig.5. A Cornperison about Cogging Torque Variation
between Normal Design and Robust Design
IV. CONCLUSION
Design optimization of HDD spindle motors using a
Taguchi method is discussed. The robust solution that is
insensitive to the effects of noise factors is achieved. It is
shown that the technique is effective in the cases where
FEM simulation or other computationally expensive
technique is to be used to evaluate the product
performance as against each setting of design parameters.
It is especially true when a robust solution is to be found
and therefore a very detailed analysis of the physical
problem is necessary to account for the noise effects in
numerical simulation process. The technique is also seen
to be suitable for use in optimization problems involving
discrete design parameters.
REFERENCES
Z. J. Liu. S. X. Chen, Q. D. Zhang, 'Design of Brushless DC
spindle motors for high speed HDD Recording', IEEE Trans. on
Magnetics, vol. 34,No. 2,pp 483-485.1998.
K.Preis, C.Magele, and O.Biro, "FEM and evolution strategies m
the optimal-design of electromagnetic devices", B E E Trans. an
Maen.. Val. 26.No.9.~~2181-2183.
1990.
W.?.Fuwlkes 'et al. "Engineering .Methods for Robust Pmduct
Design': Addison-Wesley, 1995.