Design and optimization of high-speed permanent magnet synchronous motors

In this paper, a 30 kW and 60, 000 r/min high-speed permanent magnet synchronous motor (HSPMSM) was studied. We use the knowledge of motor design to determine the structural dimensions and materials of each part of the machine to create the electromagnetic design of the motor. The FEM model of the motor was created by finite element software, and the no-load and load characteristics for the motor were modeled and analyzed, which verifies the reasonableness of the design of the motor. A genetic algorithm was applied to carry out multi-objective optimization of the motor to obtain the optimized design solution, and the performance of the high-speed motor before and after the optimized design was compared. The simulation results indicate that the rated torque of the motor has been increased through the optimization, while the torque pulsation and the groove torque of the motor have been decreased, which effectively enhances the magnetic characteristic of the designed machine.


Introduction
Unlike ordinary motors, high-speed motors have the benefits of high rotational speed, little volume, and high capacity density, which are widely used in the fields of flywheel energy storage, blowers, compressors, circulating refrigeration systems, ship power supply systems, and aerospace engines [1][2][3][4] .High-speed permanent magnet motors are increasingly applied for high-speed fields because of their outstanding benefits with high efficiency and high-capacity density level, as well as the advantages of stator and rotor diversified structure and good control features [5][6][7] .Because of high rotational speed, fast temperature rise, heat dissipation difficulties, and other characteristics of high-speed permanent magnet motors, there are many differences between the design and the traditional motors, which rely more on the design experience of the designer, without a set of systematic design methods.Therefore, this paper determines the basic process of motor design based on the basic principles of motor design.The initial model for the machine is difficult to satisfy the requirements, which requires further optimization of the motor design.The commonly used optimization algorithms are genetic algorithms, ant colony optimization algorithms, simulated annealing optimization algorithms, particle swarm optimization algorithms, and so on [8][9][10] .Among them, the genetic algorithm has stronger applicability, the operation is simple, and the optimization effect is good.Therefore, in this paper, for the issues of excessive torque pulsation and groove torque in the simulation results, the genetic algorithm was applied to optimize the machine structure, and the best structural scheme was gained after evaluation.

Electromagnetic design of HSPMSM
The performance requirements of the HSPMSM designed in this paper are listed in Table 1.
where D is the internal diameter for the stator core, KNm is the factor of the wave shape of the air-gap magnetic field, Lef is the armature length, α'p is the computational pole-arc coefficient, A is the line load, Bδ is the air-gap magnetic density, Kdp is the winding factor of the armature, n is the rated rotational speed, and P' is the calculated power and P'=Ea•Ia, which can be estimated by Equation ( 2) in the actual design of the motor.
' 12  3 where ηN is the rated efficiency and PN is the rated power.
The line load of the machine is selected according to Equation (3).The initial air-gap magnetic density is set to 0.5 T.
16.4 8.3 lg( ) After approximating the volume D 2 Lef of the motor, for further identification of the thickness and length of the motor, it is essential to estimate the principal dimension ratio λ, defined as the proportion of Lef to the pole spacing τ, which is expressed in Equation (4).

Stator core and winding selection
The designed motor in this study adopts a multi-slot stator core structure with 24 slots.The stator winding is designed as a double-layer distributed winding with short coil pitch, and efforts are made to minimize the wire diameter during the design process.The stator slots are designed in a pear-shaped configuration, with detailed parameters of the slot shape listed in Table 2.

Selection of permanent magnetic materials
Cobalt permanent magnet material's magnetic stability is good, and it is very suitable for manufacturing all kinds of high-performance permanent magnet motors.However, cobalt is a strategic material, and the price is more expensive, resulting in a higher cost for the motor.NdFeB has higher magnetic performance than rare-earth cobalt materials.Neodymium in the rare earth content is an abundant resource, and iron and boron price is cheap, so NdFeB permanent magnet material is widely used.In this design, NdFe35 is used as the permanent magnet material [11] .

Modelling of the motor
From the above analysis, the initial design scheme of the HSPMSM can be taken, which is presented in Table 3.

Simulation and analysis of electromagnetic characteristics of the HSPMSM
We use FEM software to simulate motors.Figure 1 shows the distribution of magnetic flux lines of the motor, and it can be seen that there is almost no magnetic leakage in the motor.Figure 2 shows the distribution of the magnetic flux density of the motor, and it can be found that the maximum value of the magnetic flux density is 1.49 T, which has not reached saturation.Figure 3 shows the air-gap magnetic density waveshape of the motor under no-load conditions, which is a sawtooth wave with flat tops due to stator slots.Figure 4 shows the no-load counter potential waveform, with an RMS value of 179.01 V and some fluctuations at the top, which is close to sine. Figure 5 presents the waveshape of groove torque under no-load conditions, with a peak-to-peak value of 0.13 N•m.The groove torque is relatively large, which may cause vibration and noise problems for the motor.

Motor optimization based on genetic algorithm
A genetic algorithm is applied in this study to optimize the machine and solve the problem of excessive groove torque and torque pulsation in HSPMSM motors [12] .The optimization parameters are shown in Table 4, with the optimization objectives to maximize the output torque, minimize the torque pulsation, and minimize the groove torque.Furthermore, the parameterized machine model of the selected motor can be seen in Figure 7.The initial population size in the genetic algorithm was set to 100 and the minimum value of the iteration number is 80.The first generation's adaptive intersection probability was placed at 0.9 and adaptive mutation probability was set to 0.04.The last generation's adaptive intersection probability was placed at 0.5 and adaptive mutation probability was set to 0.07.The comparison of motor optimization parameters and objectives before and after optimization is shown in Table 5.It can be observed that with the multi-objective optimization applied to the preliminary design of the motor by means of a genetic algorithm, the average torque increased from 4.66 N•m to 4.99 N•m, with an increase of 7.14%.The torque pulsation decreased from 9.76% to 2.92%.The groove torque was significantly reduced from 0.13 N•m to 0.002 N•m.Additionally, the no-load counter potential waveform comparison is shown in Figure 8.After optimization, the waveform became smoother at the top, and the effective value of the back EMF increased to 179.01 V, showing a noticeable improvement compared to before.

Conclusion
Based on the design requirements and fundamental theories of motor design, the structural parameters of the motor were designed, and a 2D structural model was built by using simulation software.The electromagnetic performance of the motor was analyzed based on this model.To address the impact of the motor structure on its electromagnetic performance, this paper proposes an optimization method based on a genetic algorithm.Firstly, an optimization simulation model was established, and then a multi-objective optimization was performed by using a genetic algorithm.The optimized motors have less groove torque and output torque pulsation but have greater output torque.This has a significant improvement on the motor's vibration and noise problems, and the operating performance is significantly improved.

Figure 6
shows the waveform of electromagnetic torque under load, which fluctuates between 4.42 N•m and 4.88 N•m, with a torque pulsation of 9.76%.The output torque has an average value of 4.66 N•m, which is similar to the rated 4.78 N•m torque, meeting the design requirements.

Figure 1 .
Figure 1.Line of magnetic flux distribution.Figure 2. Magnetic flux density distribution.

Figure 2 .
Figure 1.Line of magnetic flux distribution.Figure 2. Magnetic flux density distribution.

Figure 3 .
Figure 3.The waveforms of radial air-gap flux density of the motor at no load state.

Figure 6 .
Figure 6.The torque waveform at full-load condition.

Table 2 .
Size parameters of stator slot.

Table 3 .
The main parameters of the motor.

Table 5 .
Comparison of data.