An Investigation into the Pole–Slot Ratio and Optimization of a Low-Speed and High-Torque Permanent Magnet Motor

: At present, low-speed high-torque permanent magnet motors are widely used in the sampling industry, manufacturing industry and energy industry. However, the research on low-speed high-torque permanent magnet motors is far from enough. The primary difficulty in the initial design of low-speed high-torque permanent magnet motors is the selection of pole–slot ratio. The pole–slot ratio has a great influence on the electromagnetic performance such as torque ripple and the maximum output torque of low-speed motors. Choosing the appropriate pole–slot ratio scheme can make the design of a low-speed motor more efficient. In addition, the optimization design of the motor is also a necessary process. At present, there are many studies on optimization algorithms. However, the research on sample point sampling and surrogate model fitting is not enough. Choosing the appropriate sample point sampling method and surrogate model fitting method can help one obtain a more accurate surrogate model, which lays a foundation for the optimization of the motor. Based on the above analysis, this paper first selects four representative pole–slot ratio schemes for comprehensive comparison of their electromagnetic performances. Sec-ondly, two sample point sampling methods and three surrogate model fitting methods are combined to obtain six surrogate models, and the accuracy of the six surrogate models is compared and analyzed. Finally, a 37kW,160rpm prototype is made, and the comparison of the surrogate model optimization prediction results, the finite element simulation calculation results and the measured results is carried out to further prove the accuracy of the selected surrogate model. The work performed in this paper provides a certain reference value for the initial design and optimization experiment design of low-speed high-torque permanent magnet motor.


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.

Four Kinds of Pole-Slot Ratio Motor Model
At present, low-speed high-torque permanent magnet motors are mostly designed with multi-pole and multi-slot.However, there are many schemes for pole-slot coordination, which makes the design of low-speed high-torque permanent magnet motors very complicated.As shown in Figure 1, the motor design schemes of 37kW,160rpm with four kinds of pole-slot combinations are listed.The unit motors of these four pole-slot ratios are 10-pole 12-slot, 10-pole 24-slot, 8-pole 9-slot and 8-pole 18-slot, respectively.The pole-slot matching schemes of these four true fractional slots are widely used at present, and include two factors of concentrated winding and distributed winding.Table 1 shows the design data and performance requirements of a 37kW,160rpm low-speed high-torque motor.

Comparison of Electromagnetic Performance of Four Kinds of Pole-Slot Motors
In order to compare the fairness and rigor, the current density, permanent magnet dosage, stator and rotor size and no-load back EMF of the four pole-slot ratio motors were kept similar or equal in this paper.By changing the winding setting, the four motors achieved rated performance.
As shown in Figure 2, the no-load back-EMFs of the four pole-slot ratio motors were basically the same, among which the no-load back-EMF of the 70P84S motor was higher, and the no-load back-EMF of the 70P168S was slightly lower.In addition, it can be seen from the harmonic distribution map that the harmonic content of the 70P84S motor was the most abundant, mainly including 5th, 7th, 9th, 11th, 13th and 15th harmonics.The 9th

Comparison of Electromagnetic Performance of Four Kinds of Pole-Slot Motors
In order to compare the fairness and rigor, the current density, permanent magnet dosage, stator and rotor size and no-load back EMF of the four pole-slot ratio motors were kept similar or equal in this paper.By changing the winding setting, the four motors achieved rated performance.
As shown in Figure 2, the no-load back-EMFs of the four pole-slot ratio motors were basically the same, among which the no-load back-EMF of the 70P84S motor was higher, and the no-load back-EMF of the 70P168S was slightly lower.In addition, it can be seen from the harmonic distribution map that the harmonic content of the 70P84S motor was the most abundant, mainly including 5th, 7th, 9th, 11th, 13th and 15th harmonics.The 9th harmonic of 70P168S motor was larger.The high-order harmonics of the 80P90S motor accounted for a relatively small proportion.The high-order harmonics of 80P180S accounted for a large proportion.
Appl.Sci.2024, 14, x FOR PEER REVIEW 5 of 19 harmonic of 70P168S motor was larger.The high-order harmonics of the 80P90S motor accounted for a relatively small proportion.The high-order harmonics of 80P180S accounted for a large proportion.
(a) (b) Figure 3 describes the no-load radial air gap flux density and harmonic distribution of four pole-slot ratio motors.It can be seen that the air gap flux density of the 70P168S and 80P180S pole-slot ratio motors was higher.Therefore, the distributed winding can improve the air gap flux density of the motor.In addition, the air gap flux density mainly contained 3rd, 5th, 7th, 9th, 11th and 13th harmonics.Among them, the motor of 70P84S had a greater high-order harmonic content.The harmonic content of 70P168S motor was small.The no-load magnetic density and magnetic line cloud diagram of the four pole-slot ratio motors are shown in Figure 4.It can be seen from the figure that the tooth magnetic density of the 70P168S motor was close to saturation, and the magnetic flux leakage are more.The 80P180S motor had the largest number of slots, but the saturation of the teeth was not serious, and the magnetic flux leakage was the least.The teeth of the 70P84S motor and the 80P90S motor were basically not saturated.Figure 3 describes the no-load radial air gap flux density and harmonic distribution of four pole-slot ratio motors.It can be seen that the air gap flux density of the 70P168S and 80P180S pole-slot ratio motors was higher.Therefore, the distributed winding can improve the air gap flux density of the motor.In addition, the air gap flux density mainly contained 3rd, 5th, 7th, 9th, 11th and 13th harmonics.Among them, the motor of 70P84S had a greater high-order harmonic content.The harmonic content of 70P168S motor was small.Figure 3 describes the no-load radial air gap flux density and harmonic distribution of four pole-slot ratio motors.It can be seen that the air gap flux density of the 70P168S and 80P180S pole-slot ratio motors was higher.Therefore, the distributed winding can improve the air gap flux density of the motor.In addition, the air gap flux density mainly contained 3rd, 5th, 7th, 9th, 11th and 13th harmonics.Among them, the motor of 70P84S had a greater high-order harmonic content.The harmonic content of 70P168S motor was small.The no-load magnetic density and magnetic line cloud diagram of the four pole-slot ratio motors are shown in Figure 4.It can be seen from the figure that the tooth magnetic density of the 70P168S motor was close to saturation, and the magnetic flux leakage are more.The 80P180S motor had the largest number of slots, but the saturation of the teeth was not serious, and the magnetic flux leakage was the least.The teeth of the 70P84S motor and the 80P90S motor were basically not saturated.The no-load magnetic density and magnetic line cloud diagram of the four pole-slot ratio motors are shown in Figure 4.It can be seen from the figure that the tooth magnetic density of the 70P168S motor was close to saturation, and the magnetic flux leakage are more.The 80P180S motor had the largest number of slots, but the saturation of the teeth was not serious, and the magnetic flux leakage was the least.The teeth of the 70P84S motor and the 80P90S motor were basically not saturated.
The load simulation was carried out by using the voltage source.The output torque and maximum torque curves of the four pole-slot ratio motors are shown in Figure 5.When the four motors all reached the rated performance, the torque ripple of the 70P84S motor was the largest, which was 7.9%, while the torque ripple of the 70P168S motor was 1.4%, which is the smallest.In addition, the maximum output torque of 80P168S was 9.9 kNm, and the overload multiple was 4.48 times.The maximum output torques of the 70P84S motor and the 80P90S motor were similar, no more than 8 kNm, and the overload multiple was far less than four times.It can be seen that the distributed winding motor can put out greater torque.The load simulation was carried out by using the voltage source.The output torque and maximum torque curves of the four pole-slot ratio motors are shown in Figure 5.When the four motors all reached the rated performance, the torque ripple of the 70P84S motor was the largest, which was 7.9%, while the torque ripple of the 70P168S motor was 1.4%, which is the smallest.In addition, the maximum output torque of 80P168S was 9.9 kNm, and the overload multiple was 4.48 times.The maximum output torques of the 70P84S motor and the 80P90S motor were similar, no more than 8 kNm, and the overload multiple was far less than four times.It can be seen that the distributed winding motor can put out greater torque.The load simulation was carried out by using the voltage source.The output torque and maximum torque curves of the four pole-slot ratio motors are shown in Figure 5.When the four motors all reached the rated performance, the torque ripple of the 70P84S motor was the largest, which was 7.9%, while the torque ripple of the 70P168S motor was 1.4%, which is the smallest.In addition, the maximum output torque of 80P168S was 9.9 kNm, and the overload multiple was 4.48 times.The maximum output torques of the 70P84S motor and the 80P90S motor were similar, no more than 8 kNm, and the overload multiple was far less than four times.It can be seen that the distributed winding motor can put out greater torque.Figure 6 shows the power factor, efficiency and loss of the four pole-slot ratio motors.It can be seen from this figure that the efficiencies of the four motors were not much different, and the efficiencies of the 70P84S motor and the 80P90S motor were the highest, reaching more than 96%.However, the power factor of the 70P168S motor was much lower than those of the other three motors, only 0.915.In addition, because the end of the distributed winding was longer, the copper loss of the 70P168S motor was the largest, reaching 857 W. Due to the rich harmonic content, the eddy current loss of the permanent magnet of the 70P84S motor and the 80P90S motor was the largest, both exceeding 100 W. The iron loss of 80P180S motor was the largest, reaching 723 W.
ferent, and the efficiencies of the 70P84S motor and the 80P90S motor were the highest, reaching more than 96%.However, the power factor of the 70P168S motor was much lower than those of the other three motors, only 0.915.In addition, because the end of the distributed winding was longer, the copper loss of the 70P168S motor was the largest, reaching 857 W. Due to the rich harmonic content, the eddy current loss of the permanent magnet of the 70P84S motor and the 80P90S motor was the largest, both exceeding 100 W. The iron loss of 80P180S motor was the largest, reaching 723 W. The electromagnetic performance of the four pole-slot ratio motors is summarized in Table 2.When the size of the stator and rotor, the current density, the amount of permanent magnet and the no-load back EMF were equal or similar, the efficiencies of the four motors were basically the same.The power factor of the 70P168S motor was low, but it met the performance requirements of the motor.In addition, the torque ripple of the 70P168S motor was only 1.4%, and the maximum output torque ratio reached 4.48 times.These two performances were excellent.The electromagnetic performance of the four pole-slot ratio motors is summarized in Table 2.When the size of the stator and rotor, the current density, the amount of permanent magnet and the no-load back EMF were equal or similar, the efficiencies of the four motors were basically the same.The power factor of the 70P168S motor was low, but it met the performance requirements of the motor.In addition, the torque ripple of the 70P168S motor was only 1.4%, and the maximum output torque ratio reached 4.48 times.These two performances were excellent.

Comparison of Different Surrogate Models and Motor Optimization Design
Considering that the 37kW,160rpm low-speed high-torque permanent magnet motor needs to be used on the pumping unit, the output torque of the motor needs to be more than four times the overload multiple.Considering the performance requirements and application scenarios of this motor, the pole-slot ratio scheme of 70P168S is more suitable.The 70P168S pole-slot ratio and motor were selected for the comparison of different surrogate models and the motor optimization design.
Figure 7 is the cross section of the stator and rotor unit motor of the 70P168S motor.Among them, Wt is the tooth width, Bs0 is the slot opening, Tp is the thickness of the permanent magnet, α p is the pole arc coefficient of the permanent magnet, and δ is the air gap length.
The 70P168S pole-slot ratio and motor were selected for the comparison of different surrogate models and the motor optimization design.
Figure 7 is the cross section of the stator and rotor unit motor of the 70P168S motor.Among them, Wt is the tooth width, Bs0 is the slot opening, Tp is the thickness of the permanent magnet, αp is the pole arc coefficient of the permanent magnet, and δ is the air gap length.

The Influence of Design Parameters on Electromagnetic Performance
The influence of stator tooth width on the electromagnetic performance of the motor is shown in Figure 8.The size of the stator tooth width determines the saturation degree of the tooth magnetic density and the utilization rate of the permanent magnet.As the tooth width increases from 7 mm to 9 mm, the no-load back EMF and power factor of the motor increase first and then decrease.The output torque increases continuously, and the torque ripple decreases first and then increases.In addition, with the increase in tooth width, the magnetic density of the tooth decreases, so the corresponding iron loss will continue to decrease, and the change in efficiency is small.Figure 9 shows the influence of the stator slot opening on the electromagnetic performance of the motor.As the slot opening increased from 2.5 mm to 3.5 mm, the no-load back EMF and efficiency of the motor decreased slightly, but the torque ripple decreased from 1.1% to 0.75%.In addition, the power factor increased from 0.85 to 0.89, the output torque increased from 2.16 kNm to 2.09 kNm, and the iron loss increased slightly.

The Influence of Design Parameters on Electromagnetic Performance
The influence of stator tooth width on the electromagnetic performance of the motor is shown in Figure 8.The size of the stator tooth width determines the saturation degree of the tooth magnetic density and the utilization rate of the permanent magnet.As the tooth width increases from 7 mm to 9 mm, the no-load back EMF and power factor of the motor increase first and then decrease.The output torque increases continuously, and the torque ripple decreases first and then increases.In addition, with the increase in tooth width, the magnetic density of the tooth decreases, so the corresponding iron loss will continue to decrease, and the change in efficiency is small.application scenarios of this motor, the pole-slot ratio scheme of 70P168S is more suitable.The 70P168S pole-slot ratio and motor were selected for the comparison of different surrogate models and the motor optimization design.
Figure 7 is the cross section of the stator and rotor unit motor of the 70P168S motor.Among them, Wt is the tooth width, Bs0 is the slot opening, Tp is the thickness of the permanent magnet, αp is the pole arc coefficient of the permanent magnet, and δ is the air gap length.

The Influence of Design Parameters on Electromagnetic Performance
The influence of stator tooth width on the electromagnetic performance of the motor is shown in Figure 8.The size of the stator tooth width determines the saturation degree of the tooth magnetic density and the utilization rate of the permanent magnet.As the tooth width increases from 7 mm to 9 mm, the no-load back EMF and power factor of the motor increase first and then decrease.The output torque increases continuously, and the torque ripple decreases first and then increases.In addition, with the increase in tooth width, the magnetic density of the tooth decreases, so the corresponding iron loss will continue to decrease, and the change in efficiency is small.Figure 9 shows the influence of the stator slot opening on the electromagnetic performance of the motor.As the slot opening increased from 2.5 mm to 3.5 mm, the no-load back EMF and efficiency of the motor decreased slightly, but the torque ripple decreased from 1.1% to 0.75%.In addition, the power factor increased from 0.85 to 0.89, the output torque increased from 2.16 kNm to 2.09 kNm, and the iron loss increased slightly.Figure 9 shows the influence of the stator slot opening on the electromagnetic performance of the motor.As the slot opening increased from 2.5 mm to 3.5 mm, the no-load back EMF and efficiency of the motor decreased slightly, but the torque ripple decreased from 1.1% to 0.75%.In addition, the power factor increased from 0.85 to 0.89, the output torque increased from 2.16 kNm to 2.09 kNm, and the iron loss increased slightly.
The pole arc coefficient of permanent magnet is a very important design parameter, which greatly affects the flux of each pole of the motor.The influence of the pole arc coefficient on the performance of the motor is shown in Figure 10.As the pole arc coefficient increased from 0.65 to 0.8, the no-load back EMF and efficiency of the motor continued to increase, and the increase was larger.The output torque increased from 2.15 kNm to 2.3 kNm, and the efficiency also increased from 95.2% to 96%.However, the torque ripple of the motor and the eddy current loss of the permanent magnet were greatly reduced.The pole arc coefficient of permanent magnet is a very important design parameter, which greatly affects the flux of each pole of the motor.The influence of the pole arc coefficient on the performance of the motor is shown in Figure 10.As the pole arc coefficient increased from 0.65 to 0.8, the no-load back EMF and efficiency of the motor continued to increase, and the increase was larger.The output torque increased from 2.15 kNm to 2.3 kNm, and the efficiency also increased from 95.2% to 96%.However, the torque ripple of the motor and the eddy current loss of the permanent magnet were greatly reduced.The thickness of the permanent magnet has little effect on the air gap flux density, but has a great influence on the working point of the permanent magnet.The influence of the thickness of the permanent magnet on the electromagnetic performance of the motor is shown in Figure 11.As the thickness of the permanent magnet increased from 5 mm to 10 mm, the no-load back EMF and power factor were increasing, and the output torque and efficiency were also improved.However, the influence of the thickness of the permanent magnet on the electromagnetic properties was smaller than that of the pole arc coefficient.Similarly, the torque ripple of the motor was reduced from 0.95% to 0.65%, and the eddy current loss of the permanent magnet was also reduced from 22 W to 18 W.The pole arc coefficient of permanent magnet is a very important design parameter, which greatly affects the flux of each pole of the motor.The influence of the pole arc coefficient on the performance of the motor is shown in Figure 10.As the pole arc coefficient increased from 0.65 to 0.8, the no-load back EMF and efficiency of the motor continued to increase, and the increase was larger.The output torque increased from 2.15 kNm to 2.3 kNm, and the efficiency also increased from 95.2% to 96%.However, the torque ripple of the motor and the eddy current loss of the permanent magnet were greatly reduced.The thickness of the permanent magnet has little effect on the air gap flux density, but has a great influence on the working point of the permanent magnet.The influence of the thickness of the permanent magnet on the electromagnetic performance of the motor is shown in Figure 11.As the thickness of the permanent magnet increased from 5 mm to 10 mm, the no-load back EMF and power factor were increasing, and the output torque and efficiency were also improved.However, the influence of the thickness of the permanent magnet on the electromagnetic properties was smaller than that of the pole arc coefficient.Similarly, the torque ripple of the motor was reduced from 0.95% to 0.65%, and the eddy current loss of the permanent magnet was also reduced from 22 W to 18 W.The thickness of the permanent magnet has little effect on the air gap flux density, but has a great influence on the working point of the permanent magnet.The influence of the thickness of the permanent magnet on the electromagnetic performance of the motor is shown in Figure 11.As the thickness of the permanent magnet increased from 5 mm to 10 mm, the no-load back EMF and power factor were increasing, and the output torque and efficiency were also improved.However, the influence of the thickness of the permanent magnet on the electromagnetic properties was smaller than that of the pole arc coefficient.Similarly, the torque ripple of the motor was reduced from 0.95% to 0.65%, and the eddy current loss of the permanent magnet was also reduced from 22 W to 18 W.The pole arc coefficient of permanent magnet is a very important design parameter, which greatly affects the flux of each pole of the motor.The influence of the pole arc coefficient on the performance of the motor is shown in Figure 10.As the pole arc coefficient increased from 0.65 to 0.8, the no-load back EMF and efficiency of the motor continued to increase, and the increase was larger.The output torque increased from 2.15 kNm to 2.3 kNm, and the efficiency also increased from 95.2% to 96%.However, the torque ripple of the motor and the eddy current loss of the permanent magnet were greatly reduced.The thickness of the permanent magnet has little effect on the air gap flux density, but has a great influence on the working point of the permanent magnet.The influence of the thickness of the permanent magnet on the electromagnetic performance of the motor is shown in Figure 11.As the thickness of the permanent magnet increased from 5 mm to 10 mm, the no-load back EMF and power factor were increasing, and the output torque and efficiency were also improved.However, the influence of the thickness of the permanent magnet on the electromagnetic properties was smaller than that of the pole arc coefficient.Similarly, the torque ripple of the motor was reduced from 0.95% to 0.65%, and the eddy current loss of the permanent magnet was also reduced from 22 W to 18 W.As the most important parameter of motor design, the air gap length has a great influence on the performance of the motor.Figure 12 shows the influence of air gap length on the performance of the motor.When the air gap length of the motor increased from 1 mm to 3 mm, the torque ripple, iron loss and permanent magnet eddy current loss of the motor were greatly reduced.Because the air gap length increased, the air gap flux density harmonic content was greatly reduced.As the most important parameter of motor design, the air gap length has a great influence on the performance of the motor.Figure 12 shows the influence of air gap length on the performance of the motor.When the air gap length of the motor increased from 1 mm to 3 mm, the torque ripple, iron loss and permanent magnet eddy current loss of the motor were greatly reduced.Because the air gap length increased, the air gap flux density harmonic content was greatly reduced.

Electromagnetic Optimization Design of Motor
Figure 13 shows the optimization process of this motor.In this paper, two sample point sampling methods and three surrogate model fitting methods were selected for the optimization of the motor.By comparing different sample point sampling methods and surrogate model fitting methods, an optimization method suitable for this kind of motor with a high coupling degree of electromagnetic performance was found.According to the above section, the influence of each design parameter on the electromagnetic performance of the motor was analyzed, and the motor optimization parameters and parameter range were selected, as shown in Table 3.

Electromagnetic Optimization Design of Motor
Figure 13 shows the optimization process of this motor.In this paper, two sample point sampling methods and three surrogate model fitting methods were selected for the optimization of the motor.By comparing different sample point sampling methods and surrogate model fitting methods, an optimization method suitable for this kind of motor with a high coupling degree of electromagnetic performance was found.According to the above section, the influence of each design parameter on the electromagnetic performance of the motor was analyzed, and the motor optimization parameters and parameter range were selected, as shown in Table 3.As the most important parameter of motor design, the air gap length has a great influence on the performance of the motor.Figure 12 shows the influence of air gap length on the performance of the motor.When the air gap length of the motor increased from 1 mm to 3 mm, the torque ripple, iron loss and permanent magnet eddy current loss of the motor were greatly reduced.Because the air gap length increased, the air gap flux density harmonic content was greatly reduced.

Electromagnetic Optimization Design of Motor
Figure 13 shows the optimization process of this motor.In this paper, two sample point sampling methods and three surrogate model fitting methods were selected for the optimization of the motor.By comparing different sample point sampling methods and surrogate model fitting methods, an optimization method suitable for this kind of motor with a high coupling degree of electromagnetic performance was found.According to the above section, the influence of each design parameter on the electromagnetic performance of the motor was analyzed, and the motor optimization parameters and parameter range were selected, as shown in Table 3.  Length of air gap [1,3] The sensitivity of the optimized parameters of the motor structure was obtained by establishing a finite element model for calculation.The histogram of Figure 14 shows the sensitivity values of the two rotor structure optimization parameters.The sensitivity value was larger, indicating that it had a greater impact on the optimization goal.A positive sensitivity value indicates that the optimization objective increased with the increase in the optimization variable, and a negative sensitivity value indicates the opposite trend.Length of air gap [1,3] The sensitivity of the optimized parameters of the motor structure was obtained by establishing a finite element model for calculation.The histogram of Figure 14 shows the sensitivity values of the two rotor structure optimization parameters.The sensitivity value was larger, indicating that it had a greater impact on the optimization goal.A positive sensitivity value indicates that the optimization objective increased with the increase in the optimization variable, and a negative sensitivity value indicates the opposite trend.The multi-objective optimization of the motor mostly uses the surrogate model, and the optimization results are verified by the finite element method.This method can greatly reduce the multi-objective optimization calculation time.However, it is necessary to select a reasonable experimental design method and a surrogate model fitting method to improve the fitting accuracy of the surrogate model and ensure the accuracy of the optimization results.The central composite design (CCD) and Latin hypercube design (LHS) were selected as the experimental design methods, and the genetic aggregation method (GA), Kriging method and neural network method (ANN) were selected as the surrogate model fitting methods.The proxy model obtained by combining these methods is shown in Figure 15.
From Figure 15, it can be seen that the accuracy of the surrogate model fitted by CCD-GA was poor, and there was a normal concentration phenomenon in various electromagnetic properties; the electromagnetic properties such as iron loss and torque in the CCD-Kriging surrogate model were also too concentrated, which would have made the optimization results less accurate.The accuracy of the surrogate model of CCD-ANN fitting was very poor, and the fitting of the neural network surrogate model required a large sample space.In motor optimization, a large number of sample space means a huge calculation time, which is unreasonable.The electromagnetic properties such as eddy current loss and efficiency of the surrogate model fitted by LHS-GA also showed normal concentration.The accuracy of the surrogate model fitted by LHS-ANN was very poor; however, the accuracy of the surrogate model of LHS-Kriging fitting was better, which is also the advantage of the stratified sampling strategy of LHS sampling.The neural network The multi-objective optimization of the motor mostly uses the surrogate model, and the optimization results are verified by the finite element method.This method can greatly reduce the multi-objective optimization calculation time.However, it is necessary to select a reasonable experimental design method and a surrogate model fitting method to improve the fitting accuracy of the surrogate model and ensure the accuracy of the optimization results.The central composite design (CCD) and Latin hypercube design (LHS) were selected as the experimental design methods, and the genetic aggregation method (GA), Kriging method and neural network method (ANN) were selected as the surrogate model fitting methods.The proxy model obtained by combining these methods is shown in Figure 15.
From Figure 15, it can be seen that the accuracy of the surrogate model fitted by CCD-GA was poor, and there was a normal concentration phenomenon in various electromagnetic properties; the electromagnetic properties such as iron loss and torque in the CCD-Kriging surrogate model were also too concentrated, which would have made the optimization results less accurate.The accuracy of the surrogate model of CCD-ANN fitting was very poor, and the fitting of the neural network surrogate model required a large sample space.In motor optimization, a large number of sample space means a huge calculation time, which is unreasonable.The electromagnetic properties such as eddy current loss and efficiency of the surrogate model fitted by LHS-GA also showed normal concentration.The accuracy of the surrogate model fitted by LHS-ANN was very poor; however, the accuracy of the surrogate model of LHS-Kriging fitting was better, which is also the advantage of the stratified sampling strategy of LHS sampling.The neural network surrogate model is a non-parametric model, while CCD and Kriging are based on the data distribution characteristics of using the minimum sample space instead of the overall space, and the obtained sampling space has obvious Monte Carlo simulation characteristics.Finally, from the perspective of the fitting accuracy of the surrogate model, the LHS-Kriging fitting surrogate model was selected for the next multi-objective optimization.The response surface of the motor stator and rotor design parameters to the motor performance is shown in Figure 16.It can be seen that the influence of tooth width and slot opening on torque ripple and iron loss was significant.The pole arc coefficient of the permanent magnet and the thickness of the permanent magnet have a great influence on the kilometer citation, efficiency, torque ripple and eddy current loss of the motor.The air gap has a great influence on torque ripple and iron loss.Therefore, the optimization of the above five stator and rotor design parameters is very necessary.The response surface of the motor stator and rotor design parameters to the motor performance is shown in Figure 16.It can be seen that the influence of tooth width and slot opening on torque ripple and iron loss was significant.The pole arc coefficient of the permanent magnet and the thickness of the permanent magnet have a great influence on the kilometer citation, efficiency, torque ripple and eddy current loss of the motor.The air gap has a great influence on torque ripple and iron loss.Therefore, the optimization of the above five stator and rotor design parameters is very necessary.
Efficiency is an important criterion for judging the excellence of the motor.The reduction in the amount of permanent magnets can greatly reduce the manufacturing cost, and the suppression of torque ripple can ensure the smooth output torque of the motor.Therefore, the above three indicators were used as optimization objectives.Selecting the torque as the first constraint condition of the rated load should be greater than the rated torque.The no-load back electromotive force of the motor should be slightly less than the rated load voltage to ensure that there is a sufficient excitation magnetic field to complete the electromechanical energy conversion process.In addition, the power factor of the motor is a basic index.For the permanent magnet motor, the power factor should not be less than 0.9.
The response surface of the motor stator and rotor design parameters to the motor performance is shown in Figure 16.It can be seen that the influence of tooth width and slot opening on torque ripple and iron loss was significant.The pole arc coefficient of the permanent magnet and the thickness of the permanent magnet have a great influence on the kilometer citation, efficiency, torque ripple and eddy current loss of the motor.The air gap has a great influence on torque ripple and iron loss.Therefore, the optimization of the above five stator and rotor design parameters is very necessary.Efficiency is an important criterion for judging the excellence of the motor.The reduction in the amount of permanent magnets can greatly reduce the manufacturing cost, and the suppression of torque ripple can ensure the smooth output torque of the motor.Therefore, the above three indicators were used as optimization objectives.Selecting the torque as the first constraint condition of the rated load should be greater than the rated torque.The no-load back electromotive force of the motor should be slightly less than the rated load voltage to ensure that there is a sufficient excitation magnetic field to complete the electromechanical energy conversion process.In addition, the power factor of the motor is a basic index.For the permanent magnet motor, the power factor should not be less than 0.9.
Objectives: max( ) min( ) min( ) where η is the motor efficiency; PM-weight is the weight of the rare earth permanent magnet.Tr is the torque ripple of the motor.

Constrains:
22.1kNm 0.9 cos where η is the motor efficiency; PM-weight is the weight of the rare earth permanent magnet.
Tr is the torque ripple of the motor.
Constrains : where T is the output torque of the motor, cosφ is the power factor of the motor, and E LS is the no-load back EMF of the motor.
The LHS-Kriging surrogate model was used to optimize the multi-objective optimization of the motor with NSGA-II after the optimization objective and constraint adjustment were defined.The parameters before and after optimization are shown in Table 4.The no-load back EMF, radial air gap flux density curve and harmonic distribution of the motor before and after optimization are shown in Figure 17.It can be seen that the optimized no-load back EMF was higher, the curve was more sinusoidal, and the harmonic content was less.Similarly, the content of higher harmonics in the optimized radial air gap flux density was also reduced.The no-load back EMF, radial air gap flux density curve and harmonic distribution of the motor before and after optimization are shown in Figure 17.It can be seen that the optimized no-load back EMF was higher, the curve was more sinusoidal, and the harmonic content was less.Similarly, the content of higher harmonics in the optimized radial air gap flux density was also reduced.Figure 18 shows the comparison of load output torque and maximum output torque before and after motor optimization.From the diagram, it can be seen that after the motor reached the rated torque before and after optimization, the torque ripple after optimization was only 0.68%, which was 51.43% lower than that before optimization.In addition, the maximum output torque after optimization was 9.46 kNm, which was slightly lower than that before optimization, but the overload multiple was still far more than four times.Figure 18 shows the comparison of load output torque and maximum output torque before and after motor optimization.From the diagram, it can be seen that after the motor reached the rated torque before and after optimization, the torque ripple after optimization was only 0.68%, which was 51.43% lower than that before optimization.In addition, the maximum output torque after optimization was 9.46 kNm, which was slightly lower than that before optimization, but the overload multiple was still far more than four times.The summary and comparison of the results before optimization, optimization results and finite element calculation results of the motor are shown in Table 5.Through the comparison of various electromagnetic properties, it can be known that the accuracy of the surrogate model of LHS-Kriging fitting was good, and the error between the model prediction value and the finite element calculation result was within the acceptable range.In addition, after optimization design, the efficiency of the motor was slightly improved, the amount of the permanent magnet was reduced by 8.2%, and the torque ripple was reduced by 51.43%.

Experimental Verification
Based on the above analysis and optimization, a 37kW,160rpm prototype was fabricated, as shown in Figure 19.The summary and comparison of the results before optimization, optimization results and finite element calculation results of the motor are shown in Table 5.Through the comparison of various electromagnetic properties, it can be known that the accuracy of the surrogate model of LHS-Kriging fitting was good, and the error between the model prediction value and the finite element calculation result was within the acceptable range.In addition, after optimization design, the efficiency of the motor was slightly improved, the amount of the permanent magnet was reduced by 8.2%, and the torque ripple was reduced by 51.43%.

Experimental Verification
Based on the above analysis and optimization, a 37kW,160rpm prototype was fabricated, as shown in Figure 19.The summary and comparison of the results before optimization, optimization results and finite element calculation results of the motor are shown in Table 5.Through the comparison of various electromagnetic properties, it can be known that the accuracy of the surrogate model of LHS-Kriging fitting was good, and the error between the model prediction value and the finite element calculation result was within the acceptable range.In addition, after optimization design, the efficiency of the motor was slightly improved, the amount of the permanent magnet was reduced by 8.2%, and the torque ripple was reduced by 51.43%.

Experimental Verification
Based on the above analysis and optimization, a 37kW,160rpm prototype was fabricated, as shown in Figure 19.Under the rated load, the motor was tested for load.Figure 20 shows the calculated and measured line back EMF curves and current curves under rated load.The measured line back EMF was 338 V, which was slightly lower than the simulated 343 V.The two curves were in good agreement.In addition, the measured current was 70 A, and the simulated current was 68.8 A. The error between the calculated value and the measured value was within the acceptable range.The summary and comparison of simulation calculation, measured data and optimized prediction results are shown in Table 6.On the whole, the errors between these three values are acceptable, which further proves the good accuracy of the LHS-Kriging surrogate model.Under the rated load, the motor was tested for load.Figure 20 shows the calculated and measured line back EMF curves and current curves under rated load.The measured line back EMF was 338 V, which was slightly lower than the simulated 343 V.The two curves were in good agreement.In addition, the current was 70 A, and the simulated current was 68.8 A. The error between the calculated value and the measured value was within the acceptable range.The summary and comparison of simulation calculation, measured data and optimized prediction results are shown in Table 6.On the whole, the errors between these three values are acceptable, which further proves the good accuracy of the LHS-Kriging surrogate model.

Conclusions
In this paper, four kinds of pole-slot ratio schemes were compared and the accuracies of six optimized surrogate models were analyzed for low-speed high-torque permanent magnet motors.The specific conclusions are summarized as follows:

•
The four pole-slot ratio schemes of 70P84S, 70P168S, 80P90S and 80P180S were compared.Since 70P84S and 80P90S are concentrated windings, the winding ends are shorter and the magnetic flux leakage is smaller, so the efficiency of the two is slightly higher and the power factor is also higher.However, the pole-slot ratio of the concentrated winding led to rich air gap harmonics, so the eddy current loss of the permanent magnet also increased significantly, and the torque ripple was also large.At the same time, the maximum output torque multiples of both were far less than four times.The power factor of the 80P180S motor was the highest, the torque ripple was 3.96%, and the maximum output torque multiple was slightly lower than four times.The efficiency of the 70P168 motor was slightly lower, and the power factor was much lower than the other three pole-slot ratios, but the minimum torque ripple was only 1.4%, and the maximum output torque multiple was far more than four times, reaching 4.48 times.

Conclusions
In this paper, four kinds of pole-slot ratio schemes were compared and the accuracies of six optimized surrogate models were analyzed for low-speed high-torque permanent magnet motors.The specific conclusions are summarized as follows: • The four pole-slot ratio schemes of 70P84S, 70P168S, 80P90S and 80P180S were compared.Since 70P84S and 80P90S are concentrated windings, the winding ends are shorter and the magnetic flux leakage is smaller, so the efficiency of the two is slightly higher and the power factor is also higher.However, the pole-slot ratio of the concentrated winding led to rich air gap harmonics, so the eddy current loss of the permanent magnet also increased significantly, and the torque ripple was also large.At the same time, the maximum output torque multiples of both were far less than four times.The power factor of the 80P180S motor was the highest, the torque ripple was 3.96%, and the maximum output torque multiple was slightly lower than four times.The efficiency of the 70P168 motor was slightly lower, and the power factor was much lower than the other three pole-slot ratios, but the minimum torque ripple was only 1.4%, and the maximum output torque multiple was far more than four times, reaching 4.48 times.

•
Six surrogate models were obtained by combining two sample point sampling methods (CCD, LHS) and three surrogate model fitting methods (GA, Kriging, ANN), and the accuracy of the six surrogate models was compared.It can be seen that the sample space obtained by CCD sampling was prone to normal concentration in distribution, and the samples sampled by LHS were evenly distributed in the sample space, which benefited from the hierarchical sampling strategy of LHS sampling.In addition, ANN required a large amount of sample data, which took a huge amount of calculation time, so the accuracy of the ANN fitting surrogate model was the worst, and the accuracy of the GA fitting surrogate model was worse than that of the Kriging fitting surrogate model.In summary, the LHS sampling method combined with the Kriging surrogate model fitting method was more suitable for motor optimization, and the finite element calculation results were very close to the optimization prediction results.

•
Low-speed and high-torque permanent magnet motors are mostly used in coal mining, transportation and other industries.At present, the low-speed high-torque permanent magnet motor is still a hot research topic.We believe that ultra-low-speed permanent magnet direct-drive motors and industrial and mining low-speed high-torque permanent magnet motors will have a broader prospect in the future.Ultra-low-speed permanent magnet direct drive can reduce the cooperation of low-speed motor in the first stage deceleration mechanism, giving full play to the advantages of direct drive motors.In addition, low-speed and high-torque permanent magnet direct-drive motors have been successfully applied in the fields of wind power generation and new energy vehicles.However, low-speed and high-torque permanent magnet motors for industrial and mining still need more research, which should mainly focus on exploring the relationship between the pole-slot ratio, winding form, and high starting torque and high overload capacity.In summary, we believe that ultra-lowspeed permanent magnet direct-drive motors and high-performance industrial and mining low-speed high-torque permanent magnet motors have greater development prospects.
The design difficulty of a low-speed high-torque permanent magnet motor lies in the selection of the pole-slot ratio scheme and the optimization design of the motor.In this paper, four representative pole-slot ratio schemes were comprehensively compared.In addition, two sample point sampling methods and three surrogate model fitting methods were combined to obtain six surrogate models.The accuracy of the surrogate model was analyzed, and the most suitable surrogate model establishment method was obtained by comparison.The work performed in this paper provides a certain reference value for the selection of a pole-slot ratio scheme and the optimization design of a low-speed high-torque permanent magnet motor.

Figure 2 .
Figure 2. The no-load back EMF curves and harmonic distribution diagrams of four pole-slot ratio motors.(a) No-load back EMF curves.(b) Harmonic distribution.

Figure 3 .
Figure 3.The no-load radial air gap flux density curves and harmonic distribution of four pole-slot ratio motors.(a) No-load radial air gap flux density curves.(b) Harmonic distribution.

Figure 2 .
Figure 2. The no-load back EMF curves and harmonic distribution diagrams of four pole-slot ratio motors.(a) No-load back EMF curves.(b) Harmonic distribution.

Figure 2 .
Figure 2. The no-load back EMF curves and harmonic distribution diagrams of four pole-slot ratio motors.(a) No-load back EMF curves.(b) Harmonic distribution.

Figure 3 .
Figure 3.The no-load radial air gap flux density curves and harmonic distribution of four pole-slot ratio motors.(a) No-load radial air gap flux density curves.(b) Harmonic distribution.

Figure 3 .
Figure 3.The no-load radial air gap flux density curves and harmonic distribution of four pole-slot ratio motors.(a) No-load radial air gap flux density curves.(b) Harmonic distribution.

Figure 5 .
Figure 5.The output torque and maximum torque curves of four pole-slot ratio motors.(a) Output torque curves.(b) Maximum torque curves.

Figure 5 .
Figure 5.The output torque and maximum torque curves of four pole-slot ratio motors.(a) Output torque curves.(b) Maximum torque curves.Figure 5.The output torque and maximum torque curves of four pole-slot ratio motors.(a) Output torque curves.(b) Maximum torque curves.

Figure 5 .
Figure 5.The output torque and maximum torque curves of four pole-slot ratio motors.(a) Output torque curves.(b) Maximum torque curves.Figure 5.The output torque and maximum torque curves of four pole-slot ratio motors.(a) Output torque curves.(b) Maximum torque curves.

Figure 6 .
Figure 6.Performance of four pole-slot ratio motors.(a) Efficiency and Power factor.(b) motor loss.

Figure 6 .
Figure 6.Performance of four pole-slot ratio motors.(a) Efficiency and Power factor.(b) motor loss.

Figure 7 .
Figure 7.The cross section of the stator and rotor unit motor of 70P168S motor.

Figure 8 .
Figure 8. Influence of tooth width on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and core loss.

Figure 7 .
Figure 7.The cross section of the stator and rotor unit motor of 70P168S motor.

Figure 7 .
Figure 7.The cross section of the stator and rotor unit motor of 70P168S motor.

Figure 8 .
Figure 8. Influence of tooth width on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and core loss.

Figure 8 .
Figure 8. Influence of tooth width on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and core loss.

Figure 9 .
Figure 9. Influence of slot opening on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and core loss.

Figure 10 .
Figure 10.Influence of pole-pitch ratios of magnets on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and solid loss.

Figure 9 .
Figure 9. Influence of slot opening on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and core loss.

Figure 9 .
Figure 9. Influence of slot opening on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and core loss.

Figure 10 .
Figure 10.Influence of pole-pitch ratios of magnets on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and solid loss.

Figure 10 .
Figure 10.Influence of pole-pitch ratios of magnets on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and solid loss.

Figure 9 .
Figure 9. Influence of slot opening on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and core loss.

Figure 10 .
Figure 10.Influence of pole-pitch ratios of magnets on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and solid loss.

Figure 11 .
Figure 11.Influence of permanent magnet thickness on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and solid loss.

Figure 11 .
Figure 11.Influence of permanent magnet thickness on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and solid loss.

Figure 12 .
Figure 12.Influence of length of air gap on electromagnetic performance.(a) Torque ripple.(b) Core loss.(c) Solid loss.

Figure 12 .
Figure 12.Influence of length of air gap on electromagnetic performance.(a) Torque ripple.(b) Core loss.(c) Solid loss.

Figure 11 .
Figure 11.Influence of permanent magnet thickness on electromagnetic performance.(a) No-load back EMF and power factor.(b) Torque and torque ripple.(c) Efficiency and solid loss.

Figure 12 .
Figure 12.Influence of length of air gap on electromagnetic performance.(a) Torque ripple.(b) Core loss.(c) Solid loss.

Figure 14 .
Figure 14.Sensitivity values of structural optimization parameters.

Figure 14 .
Figure 14.Sensitivity values of structural optimization parameters.
Appl.Sci.2024,14,  x FOR PEERREVIEW  12 of 19    surrogate model is a non-parametric model, while CCD and Kriging are based on the data distribution characteristics of using the minimum sample space instead of the overall space, and the obtained sampling space has obvious Monte Carlo simulation characteristics.Finally, from the perspective of the fitting accuracy of the surrogate model, the LHS-Kriging fitting surrogate model was selected for the next multi-objective optimization.

Figure 17 .
Figure 17.The no-load back EMF and air gap radial flux density curves and corresponding harmonic distribution before and after motor optimization.(a) Curve of no-load back EMF.(b) Harmonic distribution of no-load back EMF.(c) Curve of radial air gap flux density.(d) Harmonic distribution of radial air-gap flux density.

Figure 17 .
Figure 17.The no-load back EMF and air gap radial flux density curves and corresponding harmonic distribution before and after motor optimization.(a) Curve of no-load back EMF.(b) Harmonic distribution of no-load back EMF.(c) Curve of radial air gap flux density.(d) Harmonic distribution of radial air-gap flux density.

Figure 18 .
Figure 18.Comparison of output torque and maximum torque before and after motor optimization.(a) Curve of output torque.(b) Curve of maximum output torque.

Figure 18 .
Figure 18.Comparison of output torque and maximum torque before and after motor optimization.(a) Curve of output torque.(b) Curve of maximum output torque.

Figure 18 .
Figure 18.Comparison of output torque and maximum torque before and after motor optimization.(a) Curve of output torque.(b) Curve of maximum output torque.

Figure 20 .
Figure 20.Test data and calculation data curve under rated load.(a) Line back EMF curves.(b) Rated current curves.

Figure 20 .
Figure 20.Test data and calculation data curve under rated load.(a) Line back EMF curves.(b) Rated current curves.

Table 1 .
Main data and performance requirements of low-speed high-torque motor.

Table 1 .
Main data and performance requirements of low-speed high-torque motor.

Table 2 .
Electromagnetic performance of four pole-slot ratio motors.

Table 2 .
Electromagnetic performance of four pole-slot ratio motors.

Table 3 .
The optimization parameters of the motor and the range of parameter variation.

Table 3 .
The optimization parameters of the motor and the range of parameter variation.

Table 4 .
Comparison of parameters before and after motor optimization.

Table 4 .
Comparison of parameters before and after motor optimization.

Table 5 .
The summary and comparison of the results before optimization, optimization results and finite element calculation results of the motor.

Table 5 .
The summary and comparison of the results before optimization, optimization results and finite element calculation results of the motor.

Table 5 .
The summary and comparison of the results before optimization, optimization results and finite element calculation results of the motor.

Table 6 .
Summary and comparison of simulation calculation and measured data.

Table 6 .
Summary and comparison of simulation calculation and measured data.