1. Introduction
The low-speed high-torque permanent magnet motor has the advantages of high efficiency, a high power factor, high safety and stable operation [
1,
2,
3]. At present, low-speed high-torque permanent magnet motors are widely used in various industrial production situations such as mining, manufacturing and transportation, and have a very large application prospect [
4,
5]. However, due to the unique application and performance requirements of low-speed high-torque permanent magnet motors, there are few studies on low-speed high-torque permanent magnet motors at present, and there is a lack of a prototype with which to measure and verify the theory, so the research is still not comprehensive and in-depth.
At present, the research on low-speed and high-torque permanent magnet motors is mainly about the exploration of new structures, the improvement in motor performance and the optimization of motors. In [
6,
7,
8], a double-stator structure is proposed to improve the torque density of low-speed high-torque permanent magnet motors. The kriging response surface model coupled with MOGA is used to optimize the torque ripple [
6]. However, the design of the double-stator structure is more complex, and the initial design is a more difficult task. In [
9], a novel composite rotor dual-stator low-speed high-torque motor was proposed. The rotor consists of a synchronous reluctance rotor and a surface-mounted permanent magnet rotor. This structure makes full use of the internal space of the low-speed high-torque permanent magnet motor, but the structure is still too complex; design and control are a problem to be considered. There are many studies on the performance improvement in low-speed high-torque permanent magnet motors. The influence of rotor dynamic eccentricity on the performance of a low-speed high-torque permanent magnet motor has been studied [
10]. It was found that an increase in rotor eccentricity will lead to an increase in the harmonic distortion rate of air gap flux density and stator copper loss, and the other performance of the motor does not change much. Refs. [
11,
12] studied the new structure optimization of a low-speed high-torque motor with the concentrated winding of the true fractional slot and the influence of the circumferential segmentation of the permanent magnet on the rotor loss, which reflects the advantages of the concentrated winding of the true fractional slot, which is easy to be embedded, and the number of spans at the end of the winding is small. The comparison of different pole–slot ratio schemes has also been studied. Ref. [
13] comprehensively compared three kinds of pole slot ratio schemes, including the integer slot and fractional slot. The results show that the overall performance of the 32P132S true fractional slot is better. The harmonic distortion rate of the no-load back EMF of the motor under the three pole–slot ratios of 32P48S, 40P48S and 42P54S was compared, and it was found that the waveform of 40P48S was more sinusoidal [
14]. However, it is not enough to compare the no-load back EMF only. The pole–slot ratio has a great influence on the electromagnetic performance of the motor, such as torque ripple, maximum output torque and loss, which should be comprehensively compared.
The optimization research on low-speed high-torque permanent magnet motors mainly focuses on the exploration of different optimization algorithms. The differential evolution algorithm is used to optimize the multi-objective optimization of the motor, so that the output torque ripple of the fan is smaller and the operation is more stable [
15]. In [
16,
17], the combination of fuzzy theory and the Taguchi method was introduced to transform the multi-objective optimization problem into a single-objective problem, and the range of design variables was continuously updated during the optimization process. Then, the motor was optimized according to the new range of values, which effectively improved the optimization accuracy of the Taguchi method. Ref. [
18] analyzed the non-passive surrogate model, and finally used the random forest surrogate model and NSGA-II to optimize the target performance of the motor. Ref. [
19] proposed a strategy based on the combination of a high-precision combined surrogate model and the optimization method. In this paper, the Latin Hypercube Method (LHS) was used to sample the sample points, and then six algorithms were used to establish and compare the surrogate model. Finally, the NSGA-II and the Taguchi method were used to optimize the motor. A combination of neural network and genetic algorithm was used to optimize the topology of the motor, which effectively reduced the cogging torque [
20,
21]. The combination of common response surface method and NSGA-II to optimize the design parameters could also effectively improve the torque performance of the motor [
22,
23,
24].
At present, the research on low-speed high-torque permanent magnet motors is mostly the exploration of new structures, the improvement in electromagnetic performance and the exploration of new optimization methods. However, in the current literature, the research on the pole–slot ratio, which is the most important difficulty in the initial design of low-speed high-torque permanent magnet motor, is far from enough. This makes the designer unable to judge and select the appropriate pole–slot matching scheme. Under the premise of taking into account the electromagnetic performance of the low-speed high-torque motor, the reduction in torque ripple, the increase in maximum output torque and the reduction in the material cost, there is a need to select the appropriate pole–slot ratio scheme. In addition, in the optimization design, there are a variety of sample point sampling methods and surrogate model fitting methods. The accuracy of the surrogate model obtained by combining different sampling methods and surrogate model fitting methods is different. However, the existing literature mostly focuses on the exploration of new optimization algorithms, ignoring the importance of the correct establishment of the surrogate model, and the optimized results are not compared with the prototype. In summary, a comprehensive comparison of the pole–slot ratio scheme can provide a certain reference value for the design of low-speed high-torque permanent magnet motors; analysis of the influence of different sampling methods and surrogate model fitting methods on the accuracy of the surrogate model is also a solid foundation for motor optimization, which enables designers to adopt appropriate sampling methods and surrogate model fitting methods to establish a high-precision surrogate model when optimizing the motor.
In this paper, based on the 37kW,160rpm motor, a comprehensive comparative study of the pole–slot ratio and the influence of different sampling methods and surrogate model fitting methods on the surrogate model are analyzed. In
Section 2, four different types of motor models with representative pole–slot ratio schemes are established, and the electromagnetic performance of the four motors is comprehensively compared. In
Section 3, the influence of the design parameters of the surface-mounted low-speed high-torque permanent magnet motor on the electromagnetic performance of the motor is analyzed, and two commonly used sample point sampling schemes (CCD, LHS) and three surrogate model fitting methods (GA, Kriging, ANN) are selected. Six kinds of surrogate models are obtained by combining them, and the influence of different sampling methods and surrogate model fitting methods on the fitting accuracy of these six surrogate models is analyzed, and the motor is optimized. In
Section 4, according to the optimized results, a prototype is made to verify the finite element simulation results and the optimization results of the surrogate model. The comparison results of the pole–slot ratio scheme and the surrogate model in this paper are summarized in
Section 5. The work performed in this paper provides a certain reference significance for the initial design and optimization design of low-speed high-torque permanent magnet motor.