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CMP-451
Multiobjective Sequential Design Optimization of PM-SMC Motors for Six Sigma Quality Manufacturing
Gang Lei1, J. G. Zhu1, Y. G. Guo1, J. F. Hu1, Wei Xu2, K. R. Shao3
1
School of Electrical, Mechanical and Mechatronic Systems, University of Technology, Sydney, NSW 2007, Australia
2
Platform Technologies Research Institute, RMIT University, Melbourne, VIC 3001, Australia
3
College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China
In our previous work, two kinds of permanent magnet (PM) synchronous motors, transverse flux motor (TFM) and claw pole motor
were designed and fabricated by using the soft magnetic composite (SMC) cores. This paper presents the multiobjective and robust
design optimization for high quality manufacturing of these PM-SMC motors to improve their industrial applications. Meanwhile, an
improved multiobjective sequential optimization method is presented to reduce the computation cost. Thereafter, a PM TFM with SMC
core is investigated to illustrate the performance of the proposed method. From the discussion, it can be found that six sigma quality
manufacturing was achieved for all Pareto design schemes of this motor by using the proposed method, and the reliability of the motor
has increased significantly. Furthermore, manufacturing cost and computation cost have been reduced a lot.
Index Terms— Design optimization, PM transverse flux motor, six sigma quality manufacturing, soft magnetic material (SMC).
I. INTRODUCTION
S
OFT magnetic composite (SMC) is a relatively new kind of
magnetic material which is made of iron powder particles.
It has been introduced as an alternative to electrical steel
sheets and ferrites for a wide range of applications, for
example, electrical machines. Since this material is rather new,
the development of material, process and application is
ongoing at a high pace [1]. Compared with traditional steel
sheets, SMC cores have many merits, such as low eddy current
loss, low cost and environmentally friendliness. Furthermore,
they are suitable for the design of 3-D flux path as they are
isotropic both mechanically and magnetically. Therefore, SMC
is a promising material for the design of PM motors with
complex structure and 3-D flux path, such as PM transverse
flux motor (TFM) and claw pole motor [2]-[4].
In our previous work, two kinds of PM-SMC motors, TFM
and claw pole motor have been designed, fabricated and tested
[4]-[7]. We found that these motors can make full use of the
characteristics of SMC and provide good performances.
Meanwhile, their performances highly depend on the material
and manufacturing method. SMC cores are manufactured by
modules which are different from the core’s manufacturing
method with the traditional steel sheets. Therefore, besides
structure parameters, material and manufacturing parameters
must be investigated for the PM-SMC motors as well. A robust
analysis method was presented to include manufacturing
condition in the design optimization of PM-SMC motors [7].
From the discussion, it can be found that the manufacturing
quality of these motors has been increased a lot.
However, two other issues are needed to investigate for the
industrial applications of these motors besides robust analysis.
Firstly, multiobjective design schemes are necessary as it is
hard to determine the weights for different objectives without
detailed information of industrial applications. Secondly, high
computation cost is also an important issue as this is a high
dimensional optimization problem and 3-D finite element
analysis is involved. Therefore, this paper presents an
improved multiobjective sequential optimization method for
six sigma manufacturing quality design optimization of these
PM-SMC motors to improve their industrial applications.
II. MANUFACTURING OF PM-SMC MOTORS AND
OPTIMIZATION MODELS
Considering the manufacturing of PM-SMC motors, two
issues, namely manufacturing quality and cost, are needed to
investigate as they are different from traditional motors made
of steel sheets. Fig. 1 illustrates three magnetization curves for
a type of SMC core with different density values [1]. From this
figure, it can be found that there are significant differences of
B-H data between different density’s cores. Actually, the
density of SMC core depends on the manufacturing condition,
namely the compaction pressure. And it has great effect on the
electromagnetic field analysis of motors. Therefore, all these
parameters and issues should be taken as design optimization
factors for the industrial applications of these motors to
improve their manufacturing quality.
Fig. 2 shows the manufacturing cost and productivity of this
SMC core by using different pressures. As the SMC core is
compressed by module, SMC core’s density can be calculated
by the compacting pressure applied on the core’s surface and
the pressure is related to the compaction pressure. Therefore,
core’s density, manufacturing cost and productivity directly
depend on the pressure, which must be selected as a design as
well as a noise factor for the robust design of these motors.
Considering the manufacturing condition and material
characteristic of SMC cores, the multiobjective design
optimization model of PM-SMC motors can be defined as
min :
s.t.
f
k
( x s , x mt , x mf ), k  1,..., M 
g i ( x s , x mt , x mf )  0, i  1,..., N ,
xl  x  [ x s , x mt , x mf ]  xu
(1)
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Define problem
2.5
2
Initial sampling process
Use NSGA II to generate the
initial sample set S(0)
and get Pareto optimal solution P(0)
B (T)
1.5
1
7.32 g/cm3
0.5
k th modeling process
Generate sample set S(k) and
construct Kriging model
7.16 g/cm3
6.69 g/cm3
0
0
20
40
60
H (kA/m)
80
100
Fig. 1. B-H curves with respect to different SMC density values
500
Update S(k) by
orthogonal design
technique with P(k)
NSGA II optimization
and get the Pareto solution P(k)
500
Cost ($/hr)
400
400
300
300
200
200
Productivity (pieces/hr)
Cost
Productivity
Compute the RMSEs for all
Kringing models
RMSEs   ?
No
Yes
100
100
200
300
Press size (ton)
400
100
500
End and output
Fig. 2. Manufacturing cost and productivity for SMC cores
Fig.3. The flowchart of improved MSOM
where xs, xmt, and xmf are the structure, material and
manufacturing parameters, and M and N are the numbers of
objectives and constraints, respectively. To achieve six sigma
quality manufacturing, the design model can be converted into
(2) within the framework of design for six sigma (DFSS)
technique [6].
min :
F ( 
s.t.
 gi (  f (x),  f (x))  0, i  1,..., N
 x  n    x  n
.
x
x
u
x
 l
   n  LSL
f
 f
  f  n f  USL

k
fk

( x),  fk ( x)) , k  1,..., M
(2)
where μ and σ are the mean and standard deviation of the
corresponding terms. LSL and USL are lower and supper
specification limits; n is the sigma level, which is generally
defined with respect to a probability value of a standard
normal distribution. In our work, the designed SMC motors are
expected to achieve six sigma manufacturing quality, so n will
be set as 6. For industrial manufacturing and quality control,
six sigma level manufacturing quality means 0.002 defects per
million for the “short term sigma quality”, and 3.4 defects per
million for the “long term sigma quality” [6], [7].
III. IMPROVED MSOM
For the practical design of motors, the implementation
process is usually quite time-consuming as finite element
model (FEM) is generally involved and the costs of FEM are
always very expensive and will take most of the optimization
time, especially for some complex electromagnetic devices,
e.g., PM-SMC motors. To deal with this problem, we
presented a multiobjective sequential optimization method
(MSOM) [8]. However, it is hard for that method to handle
high dimensional problems. Therefore, we present an
improved MSOM in this paper. Fig. 3 shows its flowchart,
which mainly includes four steps.
1) Generate an initial sample set S(0) and Pareto optimal
solutions P(0) by using NSGA II optimization method.
2) Update the samples. As we already got the Pareto optimal
solutions, we will use them to generate new samples. Firstly,
use orthogonal design technique to find the significant
parameters. Secondly, choose 2-level sampling method for the
significant factors. With the new samples, we can construct
new Kriging models for all objectives and constraints.
3) Optimize the obtained Kriging model by using NSGA II,
and we can get updated Pareto optimal solutions P(k).
4) Determine that if P(k) is the final Pareto solutions,
compute the root mean square error (RMSE) of the obtained
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

min : Fk   fk (x), k  1, 2
Pareto points for each Kriging model. If all RMSEs are no
more than ε, output the solution, otherwise go to step 2.
s.t.  gi (x)  n gi (x)  0, i  1,..., 4
,
(4)
TABLE I
MAIN DESIGN MATERIAL AND PARAMETERS
(a)
(b)
Fig. 4. Magnetically relevant parts of PM-SMC TFM (a) rotor, (b) stator
Parameter
Value
Number of phase
3
Number of poles
20
Number of stator teeth
60
Number of magnets
120
Stator core material (SMC)
SOMALOYTM 500
PM
NdFeB, N30M
850
IV. DESCRIPTION OF A PM-SMC TFM
A PM-SMC TFM is investigated to illustrate the efficiency
of the proposed method. Fig. 4 shows the magnetically
relevant parts of this machine. It is designed to deliver a power
of 640 W at 1800 r/min. Fig. 5 shows the region for 3D FEM
[5]. Table I lists several parameters and materials for this
machine. From our design experience, eight structure
parameters and one manufacturing parameter are needed to
investigate this motor. They are x1 and x2: circumferential
angle and axial length of PM; x3 to x5: circumferential width,
axial length and radial height of SMC tooth; x6 and x7: number
of turns and diameter of copper wire winding; and x8: air gap.
The last one, x9 is the pressure, which is selected as a design
factor as well as a noise factor for the robust manufacturing
quality optimization. And x1, x2, x6, x7 and x9 are significant
parameters. The deterministic optimization model can be
defined as,
 f (x)  Cost
min :  1
 f 2 (x)   Pout
 g1 (x)  0.795    0,
(3)
 g (x)  640  Pout  0,
 2
s.t. 
 g3 (x)  sf  0.8  0,
 g 4 (x)  J c  6  0.
where the Cost in objective mainly includes material costs of
PM, SMC core, wire winding, steel and manufacturing cost
of the core; η and Pout (unit: W) in g1 and g2 are the motor’s
efficiency and output power respectively; sf and Jc (unit:
A/mm2) in g3 and g4 are the fill factor and current density of
the winding respectively. Then we can get the robust
multiobjective optimization model of this motor within the
framework of (2).
750
700
650
600
25
Deterministic
Robust
27
29
31
Cost [$]
33
35
Fig. 6. Pareto solutions for both methods
1
Probability of Failure (POF)
Fig. 5. Region for the 3D field analysis of TFM
Pout [W]
800
Deterministic
Robust
0.8
0.6
0.4
0.2
0
0
10
20
30
40
Number of Pareto Points
50
Fig. 7. POFs for the Pareto solutions
V. RESULTS AND DISCUSSION
In the implementation, each parameter is defined to follow a
normal distribution with standard deviation as 1/3 of its
manufacturing tolerance. And 3000 points are selected as the
first sample set in the improved MSOM. Then 5 parameters
are selected as the significant parameters in the updating
processes as discussed in Section IV. Moreover, to illustrate
the performance of different methods, the probability of failure
(POF) is taken as a criterion, which is defined as
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1  i 1 P( gi  0) . Figs. 6-9 illustrate the optimization results
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for both deterministic and robust design optimization
approaches. We can draw the following conclusions from them.
Mean of current desnsity (A/mm2)
6.3
Deterministic (average = 5.99)
Robust (average = 5.87)
6.2
6.1
6
5.9
5.8
5.7
5.6
5.5
0
10
20
30
Number of Pareto Points
40
50
Fig. 8. Mean of current density for the Pareto solutions
Deterministic
Robust
Core's desnsity (g/cm3)
7.6
7.4
7.2
7
6.8
3) Fig. 8 shows the means of current density (JC) for all
Pareto points. It can be seen that deterministic design schemes
have higher means of JC compared with robust design schemes.
The means of JC of the robust schemes are obviously smaller
than the upper limit 6 A/mm2, and the average is 5.87 A/mm2.
However, many points are higher than the limit for the
deterministic approach; in this case the average is 5.99 A/mm2.
Meanwhile, the standard deviations of these JC for both
methods are 0.04 A/mm2. Therefore, the POF values of g4 of
deterministic approach are higher than those of robust
approach. For other constraints, we can also get their POFs,
means and standard deviations for all Pareto points. However,
not too much difference has founded for them. Therefore,
current density issue is the main reason why deterministic
schemes have higher POFs than robust schemes as shown in
the Fig. 7.
4) Fig. 9 illustrates the core’s density for all Pareto points. It
can be found that the core densities for deterministic schemes
are around 7.2 g/cm3, which means 200-ton pressure is needed
for compacting the cores with all deterministic schemes.
However, for the robust design schemes, 200ton pressure will
be used for the first to the 29th design scheme; and then only
100ton pressure will be needed for the rest design schemes,
and the core densities are around 6.6 g/cm3 for these schemes.
Therefore, robust approach needs less manufacturing condition
and cost.
5) For the computation cost, 3820 FEM points are needed by
using the proposed method. This is much less than the FEM
points required by using the direct optimization method of
NSGA II with FEM. For the latter case, it needs about 10000
FEM points.
6.6
0
10
20
30
Number of Pareto Points
40
VI. CONCLUSION
50
Fig. 9. SMC core’s density for the Pareto solutions
1) Fig. 6 illustrates the optimal Pareto solutions obtained
from deterministic and robust optimization models respectively. It can be found that the output power increases with the
increase of cost and vice versa. The front of the Pareto
solutions obtained from robust multiobjective approach is
obviously lower than that from the deterministic approach.
This means that to achieve the same output power, the needed
cost of robust design is higher than that of deterministic design.
2) Fig. 7 illustrates the POF values of all Pareto points for
both approaches. It can be found that the POF values of
deterministic design schemes (or Pareto points) are unstable
and obviously higher than those of robust schemes. Some of
them are even more than 50%. These are bad design schemes
from the point of view of high quality of industrial design.
For the robust multiobjective design schemes, the POF
values are almost 0. Therefore, though the needed cost for the
same output power of deterministic approach is less than that
of robust approach, its lower cost is at the cost of lower POF.
An improved MSOM was presented for the robust design
optimization of PM-SMC motors in this work. From the design
example, it can be found that the proposed method can
significantly improve the reliability and manufacturing quality
of the motor with lower manufacturing condition and cost. In
summary, robust multiobjective design optimization makes
products with higher reliability and manufacturing quality, and
will improve the industrial applications of PM-SMC motors.
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accepted and in press.
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optimization method for the design of industrial electromagnetic
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