Modelling of Interior Permanent Magnet Motor and Optimization of its
Torque Ripple and Cogging Torque Based on Design of Experiments and Artificial
Neural Networks
Ganesh C. J.,^{1 }Vijay G. S.^{1} and Siddappa I. Bekinal^{1,*}
^{ }
^{1}Department of Mechanical and Industrial Engineering,
Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal
576104, Udupi, Karnataka, India.
*Email: siddappa.bekinal@manipal.edu
(S. I. Bekinal)
Abstract
Interior permanent magnet
(IPM) motors are the class of synchronous motors. They are known for their
highpower density and effective speed control performance along with efficient
torque per rotor volume. They are also capable of giving wide constant power
operating range which makes them best suitable for electric vehicle
applications (EV sector). However, the major task in the design of any IPM
motor is the optimization of torque ripple and reducing the undesirable cogging
torques. Rotor geometry is the primary design criteria in reducing the torque
pulsations. In this work, the orthogonal experimental design (OED) is used for
optimizing rotor geometry to discover the ideal combination of geometric
parameters to reduce torque pulsations and cogging torques. Artificial neural
network (ANN) is then modelled to find the optimum design for rotor geometry
using metaheuristic algorithms. Finally, the results of the optimization
process are verified by the conventional finite element analysis (FEA) method.
Torque ripple and cogging torque are reduced by 65% and 12% respectively on
postoptimization.
Table of Contents
Keywords: IPM
Motor; cogging torque; Torque ripple; Design of Experiments; Artificial Neural
Networks.
1.
Introduction
An electric motor is a machine that converts electrical energy into mechanical energy by rotation of shaft giving a torque output. This happens due to the interaction between the magnetic field present in the rotor and the current flowing through the winding. The major problem encountered is the generation of torque pulsation resulting in vibration of motor, which is optimized to a certain level that will yield a low noise of motor during its operation.^{[1]} Electric machines that produce magnetic fields by permanent magnets are called permanent magnet (PM) machines. The highpower density and speed control properties of interior permanent magnet synchronous motors (IPMSM) are wellknown. Minimizing the torque ripple or pulsation is always one of the major trends in the design of IPMSM.^{[2]} When IPMSM is rotated there exists always a certain level of torque ripple or pulsation which is one of the major drawbacks of operating interior permanent magnet (IPM) machine, resulting in the noise and vibration of the motor. There are various methods of optimizing such torque pulsation and undesirable cogging torques. Electric parameters can be varied to optimize the torque pulsation by varying the winding distributions.^{[3]} Another reason for torque pulsation is due to variation in the reluctance of the magnetic circuit during the full rotation of the rotor which can be influenced by magnetization direction, the number of slots, winding distribution, and skew angle.^{[4]}
The major reason for undesirable torque ripple could
be the nonideal magnetic field distribution which may be due to the poor
design of the electric motor. This will also result in the cogging torque which
will ultimately reduce the desired torque output of the motor. Another method
of optimizing the torque pulsation and the undesirable cogging torques is the
geometry of the rotor of the IPM. Optimization of rotor geometry is one of the
vital design criteria of electric machines. Several such design parameters were
analyzed by various researchers. Zhu et al. adjusted the geometry of the
motors employing the response surface technique and the Taguchi method after
studying the design variables of IPMSM based on the relevance of the parameters
to be optimized.^{[5]} They
were able to optimize the torque ripples, keeping the motor output torque
constant. Kioumarsi et al. proposed a method of drilling minor holes in
the rotor to minimize the torque pulsation in IPM.^{[6]}
The influence of rotor pole on pole pitch ratio of
the cogging torque of an IPM machine was presented by Zhu et al.^{[7]} Hwang et al. proposed the design and
electromechanical properties of IPM motors as a function of rotor shape.^{[8]} They considered speed, torque, torque ripple, and back electromotive force
(BEMF) voltage as various factors for their comparison. Ma et
al. study focused on flux weakening techniques and reducing the vibrations
of IPM motors.^{[9]} They
optimized cogging torque and torque ripples successfully.
Torque control and design optimization of the motor
using advanced computer simulation to enhance the performance and efficiency of
the electric motor is the latest trend. Zhang et al. offered a study
focusing on the optimization of cogging torques and torque ripple, which cause
vibrations and electromagnetic flux variations.^{[10]} They
attempted to optimize the dimensions of the rotor's essential geometries.
Configuring the design of the rotor involves the positioning of the magnets,
types of permanent magnet materials, robustness, and simplicity of construction
to get optimum output. The rotor arrangement of an IPM motor is a critical
aspect in determining the motor's overall performance. Zhu et al.
investigated and compared the electromagnetic behavior of multilayered IPM
devices for EV applications.^{[11]} The threelayered IPM machine has reduced torque
ripple and core loss because the harmonics of airgap density are lowered as
the number of magnet layers increases.
A finite element analysis (FEA) method was utilized
by Hwang et al. to investigate the properties of IPMSM that are employed
as drive motors in electric cars in their study.^{[12]} The
stator and rotor's external diameters were adjusted to be the same so that
various parameters including cogging torque, torque ripple, and back emf
voltage could be compared depending on the position of a notch on the rotor
shape. In their study, Hwang et al.^{[13]} developed an effective method of optimizing the
rotor design in such a way that the flux distribution in the core is changed.
K. I. Laskaris and A. G. Kladas presented an
improved IPM motor with high torque and exceptionally high efficiency in the
same working area.^{[14]} When
compared to a surface permanent magnet (SPM) motor of the same size, the
proposed technique has the advantage of magnetic flux concentration in the air
gap, allowing for significantly higher magnetic flux density values. Zheng et
al. suggested an IPM machine with numerous rotor topologies, and the
various IPM machines were assessed, notably for drive applications.^{[15]} All IPM machines were discovered to have been tuned
to generate high torques while decreasing pulsation and cogging torques.
Because of the extremely nonlinear magnetic
behavior, conducting an exact analytical computation to predict motor
performance is quite difficult. In the design of any IPM machine, conventional
numerical methods, including FEA, are frequently employed. In optimizing the
design of a rotor or any component, one of the most commonly used methods in
industries is one factor at a time (OFAT), in which most design factors are
maintained constant, and one factor is modified until the desired output is
reached. This approach is timeconsuming and inefficient at times owing to its
inability to consider more than one variable at the same time.
Another effective method of optimizing the design
variables is the design of experiments (DOE) where we can study the behavior of
multiple factors changing simultaneously and also the interactions between
these variables. However, when optimization of IPMSM with one or more of the
design factors to minimize torque ripple, the motor architecture becomes more
complicated, and the structural parameters linked to motor output performance
become higher, making IPMSM topology optimization very challenging. When there
are many structural features to be changed, the response surface approach
becomes extremely difficult.^{[16]}
One of the challenges in PM electric machine design
is reducing cogging torque. To improve the performance of brushless direct
current motors using the DOE technique, a novel method for designing motor
magnets is provided. The DOE approach is used to screen the design space and
generate approximation models with response surface techniques.^{[17]} When
there are numerous structural variables to be improved, an optimization
technique that combines an algorithm with FEA software takes a long time.^{[18,19]} The
Taguchi approach can execute multiobjective optimization on an IPMSM; however,
it is unable to find the optimum parameter combination, resulting in a poor
optimization result.
In motor design, the selection of suitable design
parameters to match the specified operating requirements is essential. As a
result, regression analysis stated in terms of design variables is necessary
for design optimization. The purpose of regression analysis is to determine how
an objective function changes in response to changes in design factors. The use
of such regression analysis in conjunction with optimization techniques yields
the best design parameters.
Because ANN training requires a significant quantity
of data and gathering data takes a long time when the number of structural
variables to be optimized is enormous.^{[20]} In recent years, IPM machine rotor was optimized
based on genetic algorithms (GA).^{[21]} The nonlinear characteristics of diverse systems
can be estimated using an ANN. It has been used in several research projects to
aid in the design of various electric machines. The size of the induction
motor, as well as the cost of manufacture, are optimized using ANNbased
design.^{[22]} It is
also used to design an induction motor based on FEA results to optimize the
rotor slot geometry to maximize the average torque.^{[23]} To
reduce the torque ripple of an IPMSM, Hao et al. performed range analysis
on the data obtained from the orthogonal experiments to calculate the optimum
combination of geometric parameters using multiisland genetic algorithm (MIGA)
and radial basis function (RBF) neural networks.^{[24]}
The main objective of this article is to overcome
undesirable cogging torque and torque ripple by a systematic design of geometry
for IPM machines using DOE and ANN. It’s been observed that while trying to
reduce the cogging torque, the torque ripple tends to increase and vice versa
resulting in a conflicting behavior. Training an ANN model requires collecting
numerous existing and established sets of simulation data. But to make the
optimization process more flexible and adaptable for machines with various
sizes and requirements, this study employs an effective way of extracting
regression equation from orthogonal experimental design and later using it with
metaheuristic algorithms such as multiobjective particle swarm optimization
(MOPSO) and JAYA algorithm to reduce cogging torque
and torque ripple simultaneously.^{[2528]}
2. Methodology
2.1
Optimization process
The proposed optimization process to lower the motor
torque ripple and cogging torque is presented in the form of a flow chart as
shown in Fig. S1. The steps followed in the
optimization process are given below:
1. The objectives of the optimization were defined
at first;
2. The geometric parameters to be optimized were
selected based on the objectives;
3. An orthogonal array for the design of experiments
was defined based on the number of design variables and their levels;
4. The orthogonal experimentbased simulations were
conducted using Ansys MotorCAD software;
5. A multiobjectivebased regression equation was
extracted;
6. Discrete data from the DOE was then converted
into continuous form by applying ANN methods;
7. Metaheuristic algorithms were developed and used
to carry out the optimization to identify the optimal values of the design
variables;
8. The result of the above process was then verified
using conventional methods.
2.2
Initial IPM model
A 3phase, 10pole, 12slot IPM motor as shown in Fig. 1 was modelled for this study. The geometric
design parameters which were to be optimized per the objective are shown in Table 1. To design and optimize the rotor dimensions
and to perform simulations, Ansys MotorCAD software was used. The initial
design of the IPM was limited to a 1 kW application with an average peak power
of 1.1 kW and the parameters selected are given in Table
2.
Table
1. Motor Design Variables.
Design Variable 
Abbreviation 
Value 
Unit 
Magnet
thickness 
t 
4 
mm 
Magnets embed
depth 
d 
2.5 
mm 
Magnet arc
(ED) 
α 
140 
Degree 
Air gap 
Ag 
0.7 
mm 
Several parameters such as magnet thickness, depth
from rotor periphery, air gap, and magnet arc can be taken as inputs for
evaluating the outputs such as cogging torque, torque ripple as per Eq. (1).
𝑦 = 𝑓 (𝑡, 𝑑, 𝛼, 𝐴𝑔) (1)
Each of these design variables is defined within certain
limits: lower limit ≤ x ≤ upper limit.
Table
2. Parameters of IPM.
Design Variable 
Value 
Unit 
Poles 
10 

Slots 
12 

Stator lam diameter 
130 
mm 
Stator bore diameter 
80 
mm 
Magnet length 
40 
mm 
Magnet Br 
1.31 
Tesla 
Rated shaft speed 
2000 
RPM 
Fig. 1 Crosssection of IPM.
The limits for the design variables are considered
based on the prior calculations and boundary limits of the design of the motor
and other mechanical constraints to avoid any possible conflicts. The objective
functions are set to minimize the cogging torque and torque ripple.
3.
Optimization of cogging torque and torque ripple
3.1 Orthogonal experimental design
Orthogonal experimental design is one of the widely
used methods to determine the optimal values for the variables. Experiments
here are referred to the computerbased motor CAD simulations. While evaluating
the effects of various design variables or parameters on any system response, a
systematic method must be adopted which involves a series of simulations to
cover all possible domains of the design considered.
The traditional design process is ineffective for a
variety of reasons, including the fact that the number of experiments to be run
will be too vast to implement with the number of design parameters available. Instead
of performing prototype simulations or a thorough experimental design, which is
timeconsuming and inefficient, the OED approach can be utilized as an
effective way for conducting computer simulations, providing adequate system
knowledge for further usage.
The reduction in the number of experiments is one of
the most notable benefits of using the OED optimization approach. The OED
approach makes use of a matrix called an orthogonal array (OA). The parameter
values in each combination are represented by each row of the matrix, and the
number of rows indicates the predicted number of experiments in each design.
The orthogonal array's columns represent a parameter, and the number of columns
equals the number of design parameters.
Once the design variables are finalized, OED can be
set up and design experiments can be evaluated by following the steps given
below:
1. Consider only the critical design variables;
2. Decide the number of values\levels each variable
must carry;
3. Generate the orthogonal array for the considered
design variables and their levels based on the principles of DOE;
4. Perform simulations for each set of experiments
of OA to extract their respective responses;
5. The system is then modelled using ANN
methodologies with the aid of regression analysis to obtain optimal design by
applying metaheuristic algorithms.
Four critical rotor design
variables are defined to apply orthogonal array DOE for the IPM machine under
consideration. The present experimental design aims to find the optimal values
for the rotor geometry for which the IPM motor has minimum cogging torque and
torque ripple. The cogging torque and the torque ripple are made as to the
system output response. The values for 4 different rotor geometries are
tabulated in Table 3. Now by considering 5
levels for each parameter an L25 (5^{4}) orthogonal array (Table S1) had been designed and MotorCAD simulations
were carried.
L: Orthogonal Array 25:
Number of experiments
5: Number of values 4:
Number of Parameters
Table 3. Values for Design Parameters of IPM.
Design
Parameter 

Levels of Design Parameter 


t 
3 
3.5 
4 
4.5 
5 
d 
1.5 
2 
2.5 
3 
3.5 
α_{} 
130 
135 
140 
145 
150 
Ag 
0.5 
0.6 
0.7 
0.8 
0.9 
By employing OED method, the number of experiments
is reduced from massive 5^{4} = 625 to 25 experiments. Even though
conventional full experimental design provides sufficient information, it may
require too much effort to set up and is timeconsuming. The suggested OED
technique will greatly cut computation time and design effort without
sacrificing critical information. If the complete experimental design approach
is utilized in the given PM machine example, the OED method requires less than
5% of the overall computation time. This will result in the efficient use of
resources to properly design the system within a stipulated time.
3.2 Regression model
Regression analysis is a predictive modelling
approach that examines the connection between a dependent (target) variable(s)
and an independent variable(s) (predictor). This technique uses forecasting,
time series modelling, and identifying the causal impact connection between
variables. In this work, a significant effect of each input variable on cogging
torque and torque pulsation is studied. Simulation results of an orthogonal
array are given in Table S2. It has been
observed that each of the 25 experiments has given different responses. Fitting
a regression model helps to analyze the significance of each of the input
factors. The link between two or more variables was estimated using regression
analysis. The degree of the impact of numerous independent factors on a
dependent variable can also be determined using regression analysis. It can be
seen from the simulated results that each of the different experiments is
giving different output for cogging torque and torque ripple. It is also
observed that optimizing the cogging torque is leading to the rise of torque
ripple and vice versa. To solve such a condition, we are adopting a
multiobjective optimization method.
Regression fit and ANOVA (Analysis of Variance) was
performed on the set of simulation data using Minitab software. The regression
equations for the fitted responses torque ripple and cogging torque are as per Eq. (2) and Eq. (3)
respectively.
𝑇𝑜𝑟𝑞𝑢𝑒 𝑟𝑖𝑝𝑝𝑙𝑒 = −10.04 + 0.153𝑡 + 0.333𝑑 + 0.1421𝛼 − 1.22𝐴𝑔 −
0.0089𝑡^{2} + 0.238𝑑^{2} −
0.000542𝛼^{2} + 0.773𝐴𝑔^{2} − 0.0966𝑡*𝑑 +
0.00258𝑡*𝛼 −
0.7791𝑡*𝐴𝑔 −
0.0149𝑑*𝐴𝑔 (2)
𝐶𝑜𝑔𝑔𝑖𝑛𝑔 𝑡𝑜𝑟𝑞𝑢𝑒 = 1.02 − 0.547𝑡 −
0.1994𝑑 + 0.0235𝛼 −
3.392𝐴𝑔 − 0.02439𝑡^{2} + 0.0182𝑑^{2} − 0.000163𝛼^{2} + 0.954𝐴𝑔^{2} − 0.0922𝑡*𝑑 +
0.00684𝑡*𝛼 + 0.0965𝑡*𝐴𝑔 + 0.4465𝑑*𝐴𝑔 (3)
Residual plots for the fitted regression equations
are shown in Fig. 2. The main effects plots of
all the four factors on the responses are shown in Fig.
3. The results of effect plots show that torque ripple increases
steadily with the thickness of the magnet. Cogging torque is minimal at a
certain optimal value for magnet thickness and beyond which it tends to
increase. Both torque ripple and cogging torque tend to decrease with an
increase in the air gap. Torque ripple will increase with the increase in the
magnetic arc angle and then decrease after a certain point. Cogging torque will
decrease with an increase in the magnetic arc angle and then increase after a
certain point. Torque ripple increases with an increase in the depth of magnet
placement, whereas the cogging torque decreases with the increase in depth of
magnet placement. Conflicting behavior is observed between the geometrical parameters
over the two measured responses.
Fig. 2
Residual plots (a) Torque ripple (b) Cogging torque.
Now on performing multiresponse optimization to
minimize torque ripple and cogging torque simultaneously. Limits are defined for
performing multiobjective response optimization. The goal is to minimize the
torque ripple and cogging torque. The predicted responses by DOE using Minitab
software are shown in Table 4 and the
respective experimental simulation results for the optimized set of values are
shown in Table 5. The shaft output torque for
the above DOE optimized setting was found to be 3.69 Nm with torque ripple
accounting for around 3.75%.
Table
4. Multiple response prediction.
Design Variable 
Abbreviation 
Value 
Unit 
Magnet thickness 
t 
3.505 
mm 
Magnets embed depth 
d 
1.5 
mm 
Magnet arc (ED) 
α 
141.11 
degree 
Air gap 
Ag 
0.9 
mm 
Table 5. Experimental simulation results for DOE optimized set of values.
Design Variable 
Value 
Unit 
Torque Ripple 
0.13 
Nm 
Cogging Torque 
0.17 
Nm 
Fig. 3 Main effect plots (a) Torque
ripple (b) Cogging torque.
3.3
The artificial neural network model
The single hidden layered
feedforward ANN as shown Fig. S2 was used to
fit a predictive model between the four inputs (x_{1} = t, x_{2}
= d, x_{3} = a and x_{4} = Ag) and
the three outputs (O_{1} =
Torque ripple, O_{2} =
Cogging torque and O_{3} =
Shaft output torque). w_{ji}
is the weight on the arrow connecting the j^{th}
hidden neuron to the i^{th}
input neuron, and b_{jk} is the weight on the arrow connecting
the j^{th} hidden neuron to
the k^{th} output neuron. b_{hj} and b_{Ok} represent the weights on the biases of the hidden
neurons and the output neurons, respectively. The configuration of the ANN
design was designated as 4 : L : 3.
The number of hidden neurons L was
varied from 5 to 50. The termination criteria set are: the maximum number of
epochs = 1000, minimum mean square error (MSE) = 1 ´ 10^{8} and minimum gradient = 1 ´ 10^{12}. The ANN would terminate if any one of these criteria
were met. The configuration with least MSE and least mean absolute percentage
error (MAPE) was selected. The configuration with L = 11 was selected for the study as the corresponding MSE was
2.138 ´ 10^{8} and MAPE
was 4.21 ´ 10^{4}. Only 92
epochs were sufficient to train the ANN. The training stopped on reaching the
minimum gradient. Fig. S3 shows the MATLAB
representation of the ANN configuration 4:11:3. The training curve for the same
is shown in Fig. 4. The tansigmoid activation function was applied on the hidden layer output
whereas the purelin activation
function was applied on the output layer computations. The ANN model gave a
very good fit with R^{2} value of 0.9999, 0.9999 and 0.9999 for the
three outputs O_{1}, O_{2} and O_{3}, respectively. Table 6 compares
the quality of fit given by the regression model and the ANN model in terms of
the R^{2} values. The ANN model gives a better fit and thus the ANN
model is used to define the objective functions in the optimization algorithms.
For the trained ANN model, the weight matrix [w] on the hidden layer, the weight matrix [b] on the output layer, the
bias vector {b_{h}} on the
hidden layer, and the bias vector {b_{O}}
on the output layer are given Table S3.
3.4 Optimization
using metaheuristic algorithms: PSO and JAYA
Although computer simulations utilizing the OED
technique offer enough information with considerably fewer data points, the
optimal rotor design cannot be obtained based on the limited data points. This
is because there are only a few sparse spots accessible over the whole design
area, and there is a significant chance that the perfect point will be
overlooked. Furthermore, there are just a few discrete FEA data points
accessible. To find the global optimal rotor design, the values of each
parameter must be swept continuously. A mathematical model must be created to
anticipate torque pulsations and cogging torque for various rotor designs. Due
to the highly nonlinear behavior of the magnets used in the rotor, it becomes
difficult to match and bring a mathematical relation.
As the ANN model provides a better quality of fit
(evident from Table 6), this research employs
the ANN model to assist the optimization process by executing complicated tasks
that are hard to interpret using explicit mathematical equations. IPM motor optimization
was performed based on the Regression model and ANN model generated from
computer simulations with various rotor geometries. Three multiobjective
optimization techniques were compared:
The PSO technique is made up of a group of particles
that move throughout the search space based on their own best previous location
as well as the best past location of the entire swarm or a close neighbor. The
velocity of a particle was adjusted in each cycle using the Eq. (4),
V (𝑡 + 1) = (𝑡) + 𝐶1 ∗ rand(R1 ) ∗ (𝑃𝑖_𝑏𝑒𝑠𝑡 – (𝑡)) + 𝐶2 ∗ rand(R2 ) ∗ (𝑃𝑔_𝑏𝑒𝑠𝑡 – 𝑃𝑖(𝑡)) (4)
where Vi (t + 1) is the updated velocity for the i^{th}
particle. C1 and C2 are the personal best and global best weighting
coefficients, respectively. Pi(t) is the location of the i^{th}
particle at time t. R_{1} and R_{2} are random numbers in the
range 0 to 1. The most wellknown position is Pi_best. Pg_best is the most
wellknown swarm position.
Table 6. Quality of fit given by Regression model and the ANN model.

Torque ripple 
Cogging torque 
R^{2} (Regression model) 
0.9983 
0.9975 
R^{2} (ANN model) 
0.9999 
0.9999 
This update equation's variants consider the optimal
placements inside a particle's immediate neighborhood at time t. The location of a particle was
updated using Eq. (5). A standard
multiobjective particle swarm optimization (MOPSO) algorithm was created using
MATLAB. The optimal values of the essential geometric parameters (Table 7) were determined using MOPSO in this work.
The objective function and constraints used in the optimization are given in Eq. (6).
Table
7. MOPSO Prediction.
Design Variable 
Abbreviation 
Value 
Unit 
Magnet thickness 
t 
3 
mm 
Magnets embed depth 
d 
1.5 
mm 
Magnet arc (ED) 
α 
130 
degree 
Air gap 
Ag 
0.873 
mm 
P (𝑡 + 1) = (𝑡) + (𝑡) (5)
(6)
Table 8 displays
the optimization outcomes. Post optimization by MOPSO, the torque ripple, and cogging
torque was reduced significantly, while the output torque remained
fundamentally unchanged at the desired range.
Table 8. Experimental simulation results for MOPSO optimized set of values.
Design Variable 
Value 
Unit 
Torque ripple 
0.12 
Nm 
Cogging torque 
0.15 
Nm 
The shaft output torque for the above MOPSO
optimized setting was found to be 3.65 Nm with torque ripple accounting for
around 3.6%.
The JAYA method integrates features of EA
(Evolutionary Algorithms) concerning survivability for the fittest concept,
along with SI (Swarm Intelligence), wherein the Swarm accompanies the leader
throughout the quest for the optimal solution. Rao^{[26]} proposed
the JAYA algorithm in 2016, and it has piqued the curiosity of a wide range of
research communities due to its amazing characteristics: It has simple concepts
and is straightforward to use. In the initial search, there is no derivative
information. It's a noparameter algorithm. It's versatile, flexible, and
wellrounded. As a consequence, the JAYA technique has been widely used for a
broad variety of optimization issues in a variety of fields.
MATLAB was used to build a proper JAYA algorithm for
multiobjective optimization. JAYA was employed in this study to determine the
best values of the essential design variables. The objective function and
constraints used in the optimization are given in Eq.
(7).
(7)
The Pareto optimal front for the Poloni function
obtained from the JAYA algorithm is shown in Fig. S4.
The proposed JAYA approach has been implemented to
optimize design variables simultaneously. The spread of the Paretooptimal set
over the tradeoff surface is seen in Fig. S4.
This method retains the variety of nondominated solutions over the
Paretooptimal front while solving the issue effectively. Table 9 shows one nondominated solution that
represents the best cost among the nondominated solutions obtained.
Experimental simulation results for MOPSO optimized set of values are shown in Table 10.
Table
9. JAYA Prediction.
Design Variable 
Abbreviation 
Value 
Unit 
Magnet thickness 
t 
3 
mm 
Magnets embed depth 
d 
1.5133 
mm 
Magnet arc (ED) 
α 
130 
degree 
Air gap 
Ag 
0.9 
mm 
Table 10. Experimental simulation results for MOPSO optimized set of values.
Design Variable 
Value 
Unit 
Torque ripple 
0.12 
Nm 
Cogging torque 
0.14 
Nm 
The shaft output torque for the above JAYA optimized
setting was found to be 3.6 Nm with torque ripple accounting around 3.5%.
4. Verification of results
MotorCAD software was used to carry out
calculations on the postoptimization motor torque ripple and cogging torque to
ensure the correctness of the optimization results. Fig.
5 depicts the magnetic field patterns of the motors. Except for the
higher flux concentration at the bridge, the magnetic field distribution of the
redesigned IPMSM remained essentially unchanged. The comparison of
postoptimization results of DOE, MOPSO, and JAYA techniques is shown in Table 11.
Table 11. Comparison of postoptimization results of DOE, MOPSO, and JAYA
techniques.


Predicted 
Results of the MotorCAD software 
Variation in % 
DOE 
Torque Ripple (Nm) 
0.13 
0.14 
7.69 
Cogging Torque (Nm) 
0.17 
0.178 
4.71 

Output Torque (Nm) 
3.69 
3.693 
0.08 

MOPSO 
Torque Ripple (Nm) 
0.12 
0.123 
2.5 
Cogging Torque (Nm) 
0.15 
0.156 
4.0 

Output Torque (Nm) 
3.65 
3.43 
6.03 

JAYA 
Torque Ripple (Nm) 
0.12 
0.12 
0.0 
Cogging Torque (Nm) 
0.14 
0.141 
0.71 

Output Torque (Nm) 
3.60 
3.404 
5.44 
Fig. 5 Flux distribution for various optimized designs (a)
original (b) DOE optimized (c) MOPSO optimized (d) JAYA optimized.
To validate the optimization results, the newly predicted
set of inputs were fed into MotorCAD software, and responses were extracted
and compared with that of predicted results of optimization. A maximum
deviation of 7.69 % was observed between the results of MotorCAD and
optimization.
The results revealed that the motor torque ripples
were reduced by 65% after the optimization when compared to the initial design.
Also, the cogging torque was reduced by 12% after optimization as compared to
the original design. Further to that, the simulation results revealed that
after the optimization, motor output torque was appreciably improved from that
of the original design.
It is observed from Fig. 6 that
postoptimization the shaft output torque had been significantly increased
along with reduced torque pulsations.
Fig. 6 Comparison of shaft output
torque in terms of torque ripple.
Also, the mechanical reliability of the optimized
model was cross verified to ensure a safe design postoptimization of rotor
geometry. Rotor Material: M25035A (Yield Strength = 455 MPa). Mechanical
stress and distortions were calculated using FEM methods in MotorCAD software.
The von Mises stress was 1 MPa, which was substantially smaller than the yield
strength, indicating that the rotor design was both safe and durable. As demonstrated
in Fig. 7 for the MOPSO optimized model, the
maximum rotor distortion was substantially low at 0.00006 mm.
Fig. 7 FEA results of MOPSO optimized model. (a) Stress,
(b) Displacement.
Similarly, the von Mises stress is observed to be 1
MPa in JAYA optimized model, which is also substantially smaller than the yield
strength, ensuring the safe and reliable rotor design. The maximum distortion
of the rotor was found to be significantly low 0.00006 mm as shown from Fig. 8 for JAYA optimized model.
Fig. 8 FEA results of JAYA optimized model (a) Stress (b)
Displacement.
5. Conclusions
In this work, torque ripples and cogging torque in
IPMSM were significantly reduced utilizing PSO, JAYA, ANN, and the orthogonal experimental
approach. Initially, in the orthogonal experiment technique, motor geometric
parameters were employed as factors, while torque ripples, cogging torque, and
shaft output torque were utilized as responses. Later the regression equations
were obtained for the responses using MINITAB software and the ANN model. The
ANN provided a better fit. Finally, the ANN model was employed in the
multiobjective optimization PSO and JAYA algorithms. Torque ripples and
cogging torque were reduced by 65% and 12%, respectively, after optimization.
The shaft output torque was increased by 9%. The optimization outcomes
demonstrated that the methods used in this study were capable of obtaining
optimal design variables with reduced IPMSM torque ripple and cogging torque.
The results show that the design goal of finding optimal variables can be
successfully satisfied using the proposed hybrid method of optimization using
ANN in conjunction with the design of experiments.
Acknowledgements
The authors acknowledge the support provided by
Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal,
for carrying out the research work.
Conflict of Interest
The
authors declare no conflict of interest.
Supporting information
Applicable.
References
[1] M. Li and W. Wang, Micromotors, 2018, 51, 11–14.
[2]
Q. Liu and K. Hameyer, IEEE T. Ind. Appl., 2016, 52, 4855–4864, doi: 10.1109/TIA.2016.2599902
[3]
J. Wang, Z. P. Xia, D. Howe and S. A. Long, 3^{rd}
IET International Conference on Power Electronics, Machines and Drives  PEMD 2006, 489493.
[4]
L. Parsa and L. Hao, IEEE T. Ind. Electron., 2008, 55, 602609, doi:
10.1109/TIE.2007.911953.
[5]
X. Zhu, W. Wu, L. Quan, Z. Xiang and W. Gu, IEEE T. Energy Conver., 2019,
34, 11781189, doi:
10.1109/TEC.2018.2886316.
[6]
A. Kioumarsi, M. Moallem and B. Fahimi, IEEE T. Magn., 2006, 42, 37063711, doi: 10.1109/TMAG.2006.881093.
[7]
Z. Q. Zhu, S. Ruangsinchaiwanich, N. Schofield and D. Howe, IEEE T. Magn.,
2003, 39, 32383240 doi: 10.1109/INTMAG.2003.1230613.
[8]
M. H. Hwang, J. H. Han, D. H. Kim and H. R. Cha, Energies, 2018, 11, 2601, doi: 10.3390/en11102601.
[9]
F. Ma, H. Yin, L. Wei, G. Tian and H. Gao, Sustainability, 2018, 10, 1533, doi: 10.3390/su10051533.
[10]
G. Zhang, W. Yu, W. Hua, R. Cao, H. Qiu and A. Guo,
Appl. Sci., 2019, 9, 3634, doi: 10.3390/app9173634.
[11]
S. Zhu, W. Chen, M. Xie, C. Liu and K. Wang, IEEE T. Magn., 2018, 54, 15, doi: 10.1109/TMAG.2018.2841851.
[12] M. H. Hwang, H. S. Lee and H.
R. Cha, 2018, Energies,
11, 3053, doi: 10.3390/en11113053.
[13]
C. Hwang, C Chang, P. Li and C.
Liu, J. Phys.
Conf. Ser. 2011, 266,
12068, doi: 10.1088/17426596/266/1/012068.
[14]
K. I. Laskaris and A. G. Kladas, IEEE T. Ind. Electron., 2010, 57, 138145, doi:
10.1109/TIE.2009.2033086.
[15]
J. Zheng, W. Zhao, C. H. T. Lee, J. Ji and G. Xu, CES Trans. Electr. Mach. Ssyst.,
2019, 3, 1218, doi:
10.30941/CESTEMS.2019.00003.
[16] G. Lei, J. Zhu, Y. Guo, C.
Liu and B. Ma, Energies,
2017, 10, 1962, doi: 10.3390/en10121962.
[17]
K. Abbaszadeh, F. Rezaee Alam and S. A. Saied, Energy Convers. Manag., 2011, 52. 30753082, doi:
10.1016/j.enconman.2011.04.009.
[18]
T. Song, Z. Zhang, H. Liu and W. Hu, IET Electr. Power App.,
2019, 13, 1157–1166, doi: 10.1049/ietepa.2019.0069.
[19]
S. Shimokawa, H. Oshima, K. Shimizu, Y. Uehara, J. Fujisaki, A. Furuya and H.
Igarashi, IEEE
T. Magn., 2018, 54, 14,
doi: 10.1109/TMAG.2018.2841364.
[20]
H. Sasaki and H. Igarashi, Int. J. Appl. Electrom.,
2019, 59, 8796, doi:
10.3233/JAE171164.
[21]
D. Sim, D. Cho, J. Chun, H. Jung and T. Chung, IEEE T. Magn., 1997, 33, 18801883, doi: 10.1109/20.582651.
[22]
M. Ikeda and T. Hiyama, IEE proc., Electr. power appl., 2005, 152, 1595–1602, doi: 10.1049/ipepa:20050173.
[23]
D. Bae, D. Kim, H. Jung, S. Hahn and C. Koh, IEEE T. Magn., 1997, 33, 19241927, doi: 10.1109/20.582668.
[24]
J. Hao, S. Suo, Y. Yang, Y. Wang, W. Wang and X. Chen,
IEEE Access, 2020, 8, 2720227209, doi:
10.1109/ACCESS.2020.2971473.
[25]
Y. Zhang, S. Wang and G. Ji, Math. Probl. Eng., 2015, 931256, 138, doi:
10.1155/2015/931256.
[26]
M. A. Abido, Electr. Power Syst. Res., 2009, 79, 11051113, doi:
10.1016/j.epsr.2009.02.005.
[27]
R. Venkata Rao, Int. J. Ind. Eng.
2016, 7, 19–34, doi: 10.5267/j.ijiec.2015.8.004.
[28]
R. A. Zitar, M. A. AlBetar, M. A. Awadallah, I. A. Doush and K. Assaleh, Arch. Comput. Methods Eng., 2021,
130, doi: 10.1007/s11831021095858.
Author Information
Mr. Ganesh C. J. is pursuing his Master of Technology
in Computer Aided Analysis and Design at Manipal Institute of Technology, MAHE,
Manipal. His current interests include Design of Experiments, Optimization
methods and Product design & analysis.
Dr.
Vijay G. S.
is Professor in the Department of Mechanical and Industrial Engineering at
Manipal Institute of Technology, MAHE, Manipal, India. Bearing Diagnostics;
Application of Soft Computing Techniques to Engineering and nonEngineering
domains; Machinery Vibration Signal Processing and Analysis; Finite Element
Analysis; Geometric Modelling for CAD; Mechanical Vibrations; Fluid Mechanics;
Operations Research; Material Science and Metallurgy are the areas of his
expertise.
Dr.
Siddappa Bekinal
is an Associate Professor in the Department of Mechanical and Industrial
Engineering at Manipal Institute of Technology, MAHE, Manipal, India. Passive
Magnetic Bearings; Mechanical Vibrations; Rotor Dynamics; Turbomachinery and
Mechanical Vibrations Energy Harvesting are the areas of his expertise.
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