Research on multi-objective optimization of permanent magnet brushless DC motor

Rui QI，Hong ZENG，Zhi-hua ZHANG

（1School of Mechanical Engineering and Automation，Liaoning University of Technology，Jinzhou 121001，China）

（2 Jinzhou Halla Electrical Equipment Co.，Ltd.，Jinzhou 121001，China）

Abstract：CVVL motor is a permanent magnet brushless DC motor used to improve engine performance and reduce vehicle fuel consumption.With the CVVL motor as the optimization object in this paper，the optimization variable is based on five structural parameters of the permanent magnet thickness，the outer diameter of rotor，the inner diameter of stator，the stator slot body width and the stator slot height，and improving rated torque and motor efficiency，reducing torque ripple and stator slot full factor are optimization objectives.Based on the platform of simulation software ANSYS，the multi-objective optimization of permanent magnetic brushless DC motor structure has been done，and the optimal solution set is obtained.Finally，the feasibility of the optimization method is verified by simulation and test，and the results show that the optimized motor performance is improved to meet the optimization target.The multi-objective optimization method in this paper can provide the reference for the structural optimization of permanent magnetic brushless DC motor.

Key words：Permanent magnet brushless DC motor，RMxprt，OptiSLang，Multi-objective optimization，CVVL motor

Permanent magnet brushless DC motors are widely used in many fields，however there are also some defects and performance deficiencies in practical applications.CVVL（Continuously Variable Valve Lift）motor is a permanent magnet brushless DCmotor used to reduce vehicle fuel consumption and improve engine performance，but the motor in practical application sits in a certain defect and performance deficiency point，such as motor heating phenomenon is serious，motor efficiency needs to be improved，torque ripple is large，it is urgent to optimize its related structure［1-3］.At present，in the optimization design of motor，due to the overall motor development lag，the optimization method and effect need to be perfected［4-6］.

1 The process of multi-objective optimization

Based on the working characteristics and performance defects of CVVL motor，this paper finds the optimization variables that affect performance by theoretical calculation，uses the parameterization model of RMxprt module of ANSYS software，establishes the multi-objective optimization model of the motor with the motor model under the OptiSLang module，uses the particle swarm optimization（PSO）to optimize the structure of the CVVL motor，obtains the optimal solution set，and finally tests the feasibility of the optimi-zation method.

The motor optimization process for this paper is shown in Fig.1.

2 Selection of optimization variables and objectives

2.1 CVVL motor research and analysis

The optimized object of this paper，CVVL motor，is a permanent magnetic brushless DC motor，mainly composed of components such as worm shaft，rotor，stator，Hall sensor，bearings，motor shell，front cover casted by aluminum and electric drive winding［7-8］.The initial parameters of the CVVL motor in this paper are shown in Table 1.

Table 1 lnitial parameters

After the enterprise visit and test found that there are insufficient output torque，low motor efficiency，high torque ripple and serious heating phenomenon in CVVL motor，it is very important to optimize its multiobjective.

2.2 Optimization objectives

Because the tooth cogging torque is so large that it is an important factor causing the higher torque ripple［9-10］，the stator slot full factor is so high that it is the main reason for the serious heating of the motor winding［11］，low output torque caused by the rated torque is insufficient，and the motor efficiency is low，thus it can be determined the optimization target of this paper.Setting output parameters in optimization makes it easy to verify that the optimization results meet the target requirements，so the optimization output parameters corresponding to the optimization objectives are established，as shown in Table 2.

Table 2 Optimization objectives

2.3 Optimization variables

2.3.1 Find related variables

1）Relationship between performance and viscous damping coefficient

The average electromagnetic torque，which is also the formula of the mechanical characteristics of a permanent magnet brushless DC motor as follows，

In the formula，Tavis the average electromagnetic torque under a state angle，Tsis the blocking torque（when the rotor angle speedΩis 0），D is the viscous damping coefficient，andΩis the mechanical angle speed of the rotor.

Electromagnetic power Pemcan be expressed as：

Pemis electromagnetic power，Kuis speed ratio，KEis back-emf coefficient，and the output power formula of the motor is as follows：

Where P2is the output power and P0is the loss power.The motor efficiency formula is：

Whereηis the motor efficiency and P1is the input power.

In summary，it can be seen that the mechanical characteristics of the permanent magnetic brushless DCmotor，the average electromagnetic torque Tav，the electromagnetic power Pem，the output power P2and the motor efficiencyηof the moth is closely related to the viscous damping coefficient D.

2）Relationship between viscous damping coefficient D and optimization variables

The viscous damping coefficient D formula is：

The back-emf coefficient of a phase winding is：

Where Kwis the fundamental wave coefficient of a phase winding，Wpis the number of one-phase winding turns-in-series，Bmis the fundamental wave coefficient of the air gap flux density，Dais the center diameter of the stator iron，and L is the stator iron core length.

The equivalent winding resistor Reqis：

Whereρis th specific resistances of winding，m is the number of motor phases，Kris the specific resistivityt of winding，Lavis the half-turn length of winding elements，Kδis the Stator slot full factor，Asis a stator slot area，Z for the number of stator slots.

In summary，the viscosity damping coefficient D can be expressed as：

Due to the working environment and requirements of the CVVL motor，and the fundamental wave coefficient of the air gap flux density Bmis related to the air gap length，the air gap area and the permanent magnet thickness（magnetization length）［12-14］.In this paper，the relevant variables are selected as 10 variables which are the stator iron core diameter Dband the rotor outer diameter Dc（both reflect the length of the air gap），the stator slot area related variable（Hs1，Hs2，Bs0 and Bs2），the average half-turnl length of the winding Lav，the permanent magnet thickness hm，the stator iron center diameter Daand the stator iron center length L.

2.3.2 Determining optimization variables

In order to determine the best optimization variable，the 10 variables identified above are analyzed for sensitivity analysis as shown in Fig.2.

Fig.2 Sensitivity analysis

According to the sensitivity analysis，it can be seen that the stator slot body width Bs2，the stator slot height Hs2，the inner diameter of stator Db，the rotor outer diameter Dcand the permanent magnet thickness hmhave a relatively large influence on the optimization target.Because the optimization variables and the target variables affect each other and restrict each other，this paper adopts the multi-objective optimization method，and thus determines that the optimization variables in this paper are shown in Table 3.

Table 3 Optimization variables

2.4 Parametric modeling

Input the optimized front motor parameters into theRMxprt module in ANSYSin turn and create parameterized variables，as shown in Fig.3，the basic structure of the motor and the armature winding structure are visually viewable.

Fig.3 Basic structure of motor

The simulation environment is set to linear load，the initial value is the motor parameter value before optimization for the sake of comparison，and the parametric variables defined in parametric modeling correspond to the optimization variables above.The variable name and initial value are shown in Table 3.

3 Multi-objective optimization

3.1 Optimization method

In order to make the optimization results more accurate and reliable，OptiSlang is a powerful multi-objective optimization analysis software，and it is also the most reliable and robust rotation machinery optimization.In this paper，DesignXplorer is mainly used to establish optimized variables and find reasonable ranges of variables quickly，and import into OptiSlang module to establish an optimization model.It is based on Latin hypercube sampling to avoid sample aggregation，and uses particle swarm optimization algorithm to find optimal solution.

3.2 Establish multi-objective optimization model

After solving the motor model，this paper create an association with the OptiSLang optimization module under the workbench platform via Parameter Set.Then import the optimization variables in Parameter Set and set them as input variables，and import the above output variables.

Import the input variables and output variables described above in the optimization module and define the constraints of the optimization model，as shown in Fig.4.

Fig.4 Establish optimization model

It will lead to serious heating phenomenon and even damage to the motor components，and directly affect the overall performance of the motor when the motor winding current is too large or the stator slot full factor is too high［15］.So the constraints of this paper are：

1）The series winding current is less than 44 A；

2）The stator slot full factor is less than 95%；

3）The structure variable takes value range constraints.

The optimization algorithm selected in this paper is the standard particle swarm optimization.The initial population size set in this paper is 10，and the maximum population size is 200.

Based on distributed computing DSO，the software activates distributed computing to greatly improve the optimization efficiency，and can set the number of points of distributed parallel computing as needed.After the optimization model is completed，the solution is returned，the intermediate distributed calculation process can be viewed during the solution process.If there are interference or other model errors caused by parameter combinations，the program will automatically skip，the calculation of the successful data store down for viewing.

3.3 Optimization results

The basic results of optimization are shown in the following figure.Fig.5 is a Pareto 2D graph.The curve formed by the red line in the figure is called the Pareto front surface，the significance is to optimize the algorithm to obtain a feasible solution，from which the user can choose the appropriate solution for their own needs.

In Fig.6 and Fig.7，the resulting optimization variable value and the output variable value selected in Fig.5 where the 99th group is shown，and this group of optimal solution is also the most direct result ofmulti-objective optimization.It can be seen from the figure that the optimal solution values are：the magnet thickness hm2.06 mm，the rotor outer diameter Dc23.77 mm，the inner diameter of stator Db24.54 mm，the stator slot body width Bs2 7.61 mm，the stator slot height Hs2 is 6.28 mm.

Fig.5 Results（Pareto 2D）

Fig.6 Results（optimization variables）

Fig.7 Results（optimization objectives）

Table 4 shows the comparative analysis of simulation experiment results between before and after optimization.

Table 4 Comparison of simulation results

4 Practical test of CVVL motor

4.1 Motor test

Make test motor according to optimized parameter value，then prepare the measuring torque machine，power supply，driver，etc.to start the test.

Fig.8 CVVL motor and the test bench

Connect the host computer，driver，power supply，motor and Hall sensors in turn，as shown in Figure 8.Plug the motor into the power supply and install the motor on the test bench，connecting the rotor output of the motor to the measuring torque machine.During the experiment，the load is increased from0，measuring parameters such as speed，armature current and rotor output torque.Due to the limitation slack of test conditions，this test verifies the optimization objectives of the rated torque and the motor efficiency.

4.2 The result about torque

The test data shows that the rated torque of the rotor can reach 0.469 N·m（In order to prevent motor damage，the test is measured at the limit current.），the rated torque before optimization is 0.448 N·m，and the optimization is improved by 4.68%.With the rotor output torque and current are used as the longitudinal axis and the lateral axis respectively，the test results are compared in a curve form between before and after optimization，as shown in Fig.9.

Fig.9 Test comparison chart（torque）

From the comparison chart，it can be seen that the optimized output torque of the rotor is smooth，the torque ripple is small，and it rises linearly，which is stronger than the output torque before optimization.

4.3 The result about torque

The efficiency of the motor is affected by the objective reason of the current measurement in the test.The efficiency value cannot be numerically analyzed but can be comparatively analyzed，and this paper only makes curve comparative analysis.Taking the motor efficiency and current as the main reference values，comparing the motor efficiency curves before and after optimization，the comparison curve can be obtained as shown in Fig.10.

Fig.10 Test comparison chart（efficiency）

It can be seen from the comparison chart that the optimized motor efficiency curve rises smoothly and steadily，and the optimized efficiency is higher than the motor efficiency before，which can verify that the optimization method is very reasonable and reliable.

5 Conclusion

The rationality of the structural parameters of the permanent magnet brushless DC motor directly affects the performance of the entire motor.Therefore，this paper uses the simulation software ANSYSplatform for the multi-objective optimization of the CVVL motor structure.In order to verify the rationality of the optimization，the optimized motor was simulated and tested.The results show that the optimized motor meets the requirements of the optimization objectives，and the test results show that the optimized motor has advantages in the rotor torque and the motor efficiency，which can provide the reference for the structural optimization of permanent magnetic brushless DC motor.Therefore，the multi-objective optimization of permanent magnet brushless DC motors is of great significance.