阅读说明：本技术 一种高机械鲁棒性磁场调制式辐向永磁电机及其多谐波优化设计方法 (High-mechanical robustness magnetic field modulation type radial permanent magnet motor and multi-harmonic optimization design method thereof ) 是由 陈前 廖继红 赵文祥 刘国海 徐高红 于 2021-06-23 设计创作，主要内容包括：本发明公开了一种高机械鲁棒性磁场调制式辐向永磁电机及其多谐波优化设计方法。为增强传统磁场调制式辐向永磁电机的转子机械鲁棒性,提出了一种具有倒T型永磁结构的磁场调制式辐向永磁电机。由于所提出的电机隶属多工作谐波的磁场调制电机,提出一种基于气隙谐波的多目标优化设计方法。具体实施过程包括：基于磁场调制原理,分析电机转矩产生机理,并推导出转矩和转矩脉动的公式。根据转矩和转矩脉动公式,分析气隙谐波对转矩和转矩脉动的贡献,并选定对影响较大的气隙谐波产生的转矩和转矩脉动为子目标。然后,采用响应面分析和多目标骨干粒子群算法结合来优化子目标,最终兼顾电机的转矩和转矩脉动优化。(The invention discloses a high-mechanical robustness magnetic field modulation type radial permanent magnet motor and a multi-harmonic optimization design method thereof. In order to enhance the mechanical robustness of a rotor of a traditional magnetic field modulation type radial permanent magnet motor, the magnetic field modulation type radial permanent magnet motor with the inverted T-shaped permanent magnet structure is provided. As the motor belongs to a magnetic field modulation motor with multiple working harmonics, a multi-objective optimization design method based on air gap harmonics is provided. The specific implementation process comprises the following steps: based on the magnetic field modulation principle, the motor torque generation mechanism is analyzed, and a formula of torque and torque ripple is deduced. The contribution of the air gap harmonics to the torque and torque ripple is analyzed according to a torque and torque ripple formula, and the torque and torque ripple generated on the air gap harmonics with larger influence is selected as a sub-target. And then, optimizing the sub-targets by combining response surface analysis and a multi-target backbone particle swarm algorithm, and finally considering the torque and torque ripple optimization of the motor.)

1. A magnetic field modulation type radial permanent magnet motor with high mechanical robustness is characterized by comprising a stator and a rotor module inside the stator; the rotor module of the motor comprises two rotor teeth and three permanent magnets, wherein the permanent magnets are inverted T-shaped and are formed by combining a radial permanent magnet and a Halbach permanent magnet array; the two permanent magnets at the lower end are magnetized in the radial direction, the magnetizing directions are opposite, the two permanent magnets are placed in a manner of being tightly attached to the radial permanent magnets, and the magnetic isolation bridges are arranged on the two sides; or clinging to the tooth wall of the rotor to ensure that the magnetism isolating bridge is in the middle, and the radial permanent magnet in the middle is magnetized tangentially; meanwhile, the self-shielding effect of the lower Halbach permanent magnet array is utilized, the permanent magnet field is prevented from being closed in the rotor, and the integrated processing of the rotor structure is realized.

2. The field modulated radial permanent magnet machine of claim 1, wherein the stator and rotor of the machine are salient pole structures, such that the permanent magnet field and the armature reaction field are modulated by the salient poles of the stator and rotor, thereby generating more operating harmonics.

3. A multi-harmonic optimization design method of a high-mechanical robustness magnetic field modulation type radial permanent magnet motor is characterized in that air gap harmonics are introduced into optimization of torque and torque pulsation, and the implementation steps are as follows:

step 1, analyzing the permanent magnet air gap flux density and the armature reaction air gap flux density of a target motor, and determining the harmonic order of the permanent magnet air gap flux density and the armature reaction air gap flux density and the corresponding rotating speed;

step 2, deriving an electromagnetic torque expression based on an air gap magnetic field modulation principle, and further deriving formulas of average torque and torque ripple;

step 3, analyzing the influence of air gap harmonics on the torque and the torque ripple according to a torque and torque ripple formula, and selecting average torque and torque ripple with larger influence as optimization sub-targets;

step 4, selecting key design parameters, and determining the range of the parameters by using finite element software;

step 5, analyzing the influence of the motor parameters on the sub-target by using a Taguchi sensitivity analysis method, and dividing the design parameters into two layers according to the sensitivity;

and 6, keeping the low-sensitivity parameters unchanged, and optimizing the high-sensitivity parameters by combining a response surface analysis method and a multi-target backbone particle swarm algorithm.

4. The multi-harmonic optimization design method of the high-mechanical-robustness magnetic field modulation type radial permanent magnet motor according to claim 3, characterized in that: the electromagnetic torque in the step 2 is generated by the combined action of the electric load and the magnetic load with the same harmonic order and corresponding same rotating speed, and is expressed by the following formula:

wherein D is_siIs the stator inner diameter l_stkIs the axial length of the motor, B_gvIs the magnetic load, i.e. the amplitude, K, of the v-th harmonic of the air-gap flux density of the permanent magnet_svIs the amplitude of the electrical load v-th harmonic,is the angle between the v-times magnetic load and the electrical load; therefore, it is necessary to analyze the air gap flux density generated by the permanent magnet and the air gap flux density generated by the armature reaction, respectively.

5. The multi-harmonic optimization design method of the high-mechanical-robustness magnetic field modulation type radial permanent magnet motor according to claim 3, characterized in that: in the step 1, the air gap flux density of the permanent magnet can be obtained by the product of magnetomotive force generated by the permanent magnet and magnetic conductance at the stator side, wherein the magnetomotive force generated by the permanent magnet can be expressed as:

wherein, F_RPMbAnd F_RPMnFourier coefficient of magnetomotive force generated by the permanent magnet, n is harmonic number of magnetomotive force generated by the permanent magnet, P_PMIs the pole pair number of the permanent magnet, theta is the phase angle, theta₀At an initial angle, ω_rIs the rotor angular velocity, t is time; the stator-side permeance can be expressed as follows:

wherein, Λ_s0，Λ_sbAnd Λ_skIs the Fourier coefficient of the stator-side permeance, k is the harmonic order of the stator-side permeance, P_sThe number of stator slots is; thus, the air gap flux density produced by a permanent magnet can be expressed as follows:

as can be seen from the above formula, the air gap flux density is composed of two harmonics, i.e., the rotating speed is omega_rN P of_PMSub-harmonics and speed of revolution nP_PMω_r/(nP_PM±kP_s) Is | nP_PM±kP_sThe sub-harmonic.

6. The multi-harmonic optimization design method of the high-mechanical-robustness magnetic field modulation type radial permanent magnet motor according to claim 3, characterized in that: the air gap magnetic density generated by the armature reaction in the step 1 can be obtained by the product of the magnetomotive force generated by the armature reaction and the magnetic conductance at the rotor side, wherein the air gap magnetomotive force generated by the armature reaction can be expressed as:

wherein N is_RCIs the number of turns of a phase winding, i is the harmonic number of the magnetomotive force generated by the armature reaction, theta is the phase angle, D_RiProducing magnetic motion for armature reactionFourier coefficient of potential, i_A,i_B,i_C,i_D,i_EThe current of A, B, C, D and E phases respectively;

when i is 5r, r is 1, 2.

When i-5 r-1, i-5 r-2, i-5 r-3, r-1, 2.

When i-5 r-4, r-1, 2,.,

wherein, I_RmaxIs the current amplitude, P_rThe number of the rotor pole pairs; the fourier expression for the rotor-side air-gap permeance is as follows:

wherein, Λ_Rr0,Λ_RrbAnd Λ_RrpThe Fourier coefficient of the rotor side air gap permeance is shown, and p is the harmonic number of the rotor side permeance; thus, the air gap flux density produced by the armature reaction can be expressed as follows:

when i is 5r, r is 1,2,.,

wherein, beta₁And beta₂Can be expressed as:

when i-5 r-4, r-1, 2,.,

wherein, beta₁And beta₂Can be expressed as:

therefore, based on the above formula of the air gap flux density generated by the armature reaction, the harmonic characteristic of the air gap flux density generated by the armature reaction can be obtained:

when i is 5r-4, r is 1,2, the rotation speed with the harmonic order of 2i-1 is (P)_rω_r/(2i-1)), harmonic order is (pP)_rThe rotational speed of +2i-1 is ((P +1) P)_rω_r/(pP_r+ (2i-1))), harmonic order | pP |)_rThe rotational speed of- (2i-1) | is ((P-1) P_rω_r/[pP_r-(2i-1)])；

When i is 5r, r is 1,2, the rotation speed with harmonic order 2i-1 is (-P)_rω_r/(2i-1)), the rotational speed at the harmonic order of (2i-1+ pPr) is ((P-1) P_rω_r/(pP_r+ (2i-1))), harmonic order | pP |)_rThe rotational speed of- (2i-1) | is ((P +1) P_rω_r/(pP_r-(2i-1)))。

7. The multi-harmonic optimization design method of the high-mechanical-robustness magnetic field modulation type radial permanent magnet motor according to claim 3, characterized in that: in step 2, the electromagnetic torque may be expressed as follows:

wherein e is_iAnd i_iThe subscript i is a, b, c, d, e; omega is the mechanical angular speed of the rotor; to calculate e_iIntroducing a winding function:

wherein N is_jNumber of turns of armature winding of the jth harmonic, P_aThe number of pole pairs of the armature winding is set; from this, the formula of a counter potential, the formula of electromagnetic torque, and the average torque T are derived_avgAnd torque ripple T_rippleThe formula (2).

8. The multi-harmonic optimization design method of the high-mechanical robustness magnetic field modulation type radial permanent magnet motor according to claim 7, characterized in that: slave torque ripple T_rippleThe formula (c) shows that the order n of the generated torque ripple is 5r ± 1,5r ± 3; meanwhile, torque harmonic analysis is carried out on the proposed motor, main torque ripple harmonic waves are found to be 2, 11 and 20 times, and n can be calculated to be 1,3,10,12,19 and 21, and all values of n in the torque ripple formula are met.

9. The multi-harmonic optimization design method of the high-mechanical-robustness magnetic field modulation type radial permanent magnet motor according to claim 3, characterized in that: in step 3, n is 1,3, k is 1,2,3 …, the calculated air gap magnetic densities causing the secondary torque ripple are 9, 13, 29, 49, 53, 71 times, the torque ripple generated by the air gap magnetic densities of 29 times can be found to be larger according to finite element analysis, and the torque generated by the air gap magnetic densities of 9 times and 11 times and the torque ripple generated by the air gap magnetic densities of 29 times can be used as optimization sub-targets in combination with the previous torque analysis.

10. The multi-harmonic optimization design method of the high-mechanical-robustness magnetic field modulation type radial permanent magnet motor according to claim 3, characterized in that: in the step 6, the low-sensitivity parameter is kept unchanged because the low-sensitivity parameter has little influence on the sub-target; the response surface analysis method is used for establishing a proxy model between design high-sensitivity parameters and sub-targets:

firstly, obtaining a combination of design parameters by adopting a BBD sampling design method, then, bringing sample points into Maxwell software to carry out parametric simulation, further obtaining sub-target values of each parameter combination, and then carrying out response surface analysis to obtain a function expression of high-sensitivity parameters and sub-targets;

then, the multi-objective backbone particle swarm algorithm is used for optimizing the proxy model, the function expression obtained by response surface analysis is substituted into a multi-objective backbone particle swarm algorithm program written by MATLAB, a pareto frontier chart combining two sub-targets can be obtained, and further the optimal sub-targets can be obtained.

Technical Field

The invention relates to design and optimization of magnetic field modulation type radial permanent magnets, in particular to a method for optimizing mechanical strength of a rotor and torque pulsation of a motor, and belongs to the technical field of motor manufacturing.

Background

In recent years, magnetic field modulation type permanent magnet motors play an important role in the fields of electric automobiles, aerospace, rail transit and the like, and the magnetic field modulation type permanent magnet motors have the following remarkable characteristics of high output torque, high efficiency, high power density and the like. The magnetic field modulation type permanent magnet motor adopts the magnetic material with high magnetic energy product to replace the traditional excitation winding, thereby not only eliminating the negative effect brought by the excitation winding, but also simplifying the mechanical structure of the motor, improving the operation reliability of the motor and correspondingly reducing the mechanical loss.

The stator permanent magnet type magnetic field modulation permanent magnet motor is paid much attention to due to the advantages of simple rotor structure, high mechanical strength, high efficiency, strong heat dissipation capacity and the like, but the permanent magnet and the armature winding are positioned in the stator slot, so that the area of the stator slot is reduced, the generation of electric load is further reduced, and the torque output capacity of the motor is reduced. Therefore, in order to fully utilize the rotor space, more and more researchers are dedicated to transferring the permanent magnets to the rotor, and a rotor permanent magnet type magnetic field modulation permanent magnet motor is proposed. The document CN104201852A proposes a winding complementary magnetic field modulation type permanent magnet motor, in which permanent magnets are transferred to a rotor, which increases the armature winding slot area and improves the space utilization rate of the rotor, and at the same time, the armature magnetic field and the permanent magnet magnetic field are separated, which relieves the magnetic saturation degree of the stator and improves the overload capability of the motor. However, the document CN104201852A proposes a winding complementary magnetic field modulation type permanent magnet motor having the following disadvantages: the magnetic adjusting air gap is arranged in the rotor module of the motor, so that the rotor structure is separated, and the mechanical strength of the rotor is lower; a rectangular magnetic adjusting block needs to be embedded in the magnetic adjusting air gap, the magnetic adjusting block moves in the magnetic adjusting air gap, a brush slip ring needs to be arranged on the side of the rotor to provide direct-current exciting current, and the brush slip ring is complex in structure and needs to be maintained regularly; the torque ripple of the motor is large.

The existing torque ripple weakening methods mainly comprise rotor oblique poles, optimized windings and virtual pole adding structures, the optimized methods can complicate the structure of the motor, and the torque ripple optimization principle is difficult to explain. Therefore, it is important to simplify the motor structure and optimize the torque ripple of the motor in principle from the torque ripple generation.

Disclosure of Invention

The invention aims to provide a magnetic field modulation type radial permanent magnet motor with high mechanical robustness and a multi-harmonic optimization design method thereof. On the basis of a high-mechanical robustness magnetic field modulation type radial permanent magnet motor, in order to improve the torque performance of the motor, a motor optimization design method of multi-air-gap harmonic waves is provided.

The technical scheme adopted by the invention is as follows: a magnetic field modulation type radial permanent magnet motor with high mechanical robustness comprises a stator and a rotor module inside the stator; the rotor module of the motor comprises two rotor teeth and three permanent magnets, wherein the permanent magnets are inverted T-shaped and are formed by combining a radial permanent magnet and a Halbach permanent magnet array; the two permanent magnets at the lower end are magnetized in the radial direction, the magnetizing directions are opposite, the two permanent magnets are placed in a manner of being tightly attached to the radial permanent magnets, and the magnetic isolation bridges are arranged on the two sides; or clinging to the tooth wall of the rotor to ensure that the magnetism isolating bridge is in the middle, and the radial permanent magnet in the middle is magnetized tangentially; meanwhile, the self-shielding effect of the lower Halbach permanent magnet array is utilized, the permanent magnet field is prevented from being closed in the rotor, and the integrated processing of the rotor structure is realized.

Furthermore, the stator and the rotor of the motor are both in a salient pole structure, so that the permanent magnetic field and the armature reaction magnetic field are both modulated by the salient poles of the stator and the rotor, and more working harmonics are generated.

A multi-harmonic optimization design method of a high-mechanical robustness magnetic field modulation type radial permanent magnet motor introduces air gap harmonics into optimization of torque and torque pulsation, and comprises the following implementation steps:

step 1, analyzing the permanent magnet air gap flux density and the armature reaction air gap flux density of a target motor, and determining the harmonic order of the permanent magnet air gap flux density and the armature reaction air gap flux density and the corresponding rotating speed;

step 2, deriving an electromagnetic torque expression based on an air gap magnetic field modulation principle, and further deriving formulas of average torque and torque ripple;

step 3, analyzing the influence of the air gap harmonic on the torque and the torque ripple according to an average torque and torque ripple formula, and selecting the torque and the torque ripple with larger influence as an optimization sub-target;

step 4, selecting key design parameters, and determining the range of the parameters by using finite element software;

step 5, analyzing the influence of the motor parameters on the sub-target by using a Taguchi sensitivity analysis method, and dividing the design parameters into two layers according to the sensitivity;

and 6, keeping the low-sensitivity parameters unchanged, and optimizing the high-sensitivity parameters by combining a response surface analysis method and a multi-target backbone particle swarm algorithm.

Further, the electromagnetic torque in step 2 is generated by the combined action of the electric load and the magnetic load with the same harmonic order and corresponding rotation speed, and is expressed by the following formula:

wherein D is_siIs the stator inner diameter l_stkIs the axial length of the motor, B_gvIs the magnetic load, i.e. the amplitude, K, of the v-th harmonic of the air-gap flux density of the permanent magnet_svIs the amplitude of the electrical load v-th harmonic,is the angle between the v-times magnetic load and the electrical load; therefore, it is necessary to analyze the air gap flux density generated by the permanent magnet and the air gap flux density generated by the armature reaction, respectively.

Further, in step 1, the air gap flux density of the permanent magnet may be obtained by a product of a magnetomotive force generated by the permanent magnet and a stator-side flux guide, wherein the magnetomotive force generated by the permanent magnet may be expressed by fourier decomposition as:

wherein, F_RPMbAnd F_RPMnFourier coefficient of magnetomotive force generated by the permanent magnet, n is harmonic number of magnetomotive force generated by the permanent magnet, P_PMIs the pole pair number of the permanent magnet, theta is the phase angle, theta₀At an initial angle, ω_rIs the rotor angular velocity, t is time; the stator-side permeance can be expressed as follows:

wherein, Λ_s0，Λ_sbAnd Λ_skIs the Fourier coefficient of the stator-side permeance, k is the harmonic order of the stator-side permeance, P_sThe number of stator slots is; thus, the air gap flux density produced by a permanent magnet can be expressed as follows:

as can be seen from the above formula, the air gap flux density is composed of two harmonics, i.e., the rotating speed is omega_rN P of_PMSub-harmonics and speed of revolution nP_PMω_r/(nP_PM±kP_s) Is | nP_PM±kP_sThe sub-harmonic.

Further, the air gap flux density generated by the armature reaction in the step 1 can be obtained by the product of the magnetomotive force generated by the armature reaction and the magnetic conductance on the rotor side, wherein the air gap magnetomotive force generated by the armature reaction can be expressed by fourier decomposition as:

wherein N is_RCIs the number of turns of a phase winding, i is the harmonic number of the magnetomotive force generated by the armature reaction, theta is the phase angle, D_RiFourier coefficient, i, of the magnetomotive force generated for the armature reaction_A,i_B,i_C,i_D,i_EThe current of A, B, C, D and E phases respectively;

when i is 5r, r is 1, 2.

When i-5 r-1, i-5 r-2, i-5 r-3, r-1, 2.

When i-5 r-4, r-1, 2,.,

wherein, I_RmaxIs the current amplitude, P_rThe number of the rotor pole pairs; the fourier expression for the rotor-side air-gap permeance is as follows:

wherein, Λ_Rr0,Λ_RrbAnd Λ_RrpThe Fourier coefficient of the rotor side air gap permeance is shown, and p is the harmonic number of the rotor side permeance; thus, the air gap flux density produced by the armature reaction can be expressed as follows:

when i is 5r, r is 1,2,.,

wherein, beta₁And beta₂Can be expressed as:

when i-5 r-4, r-1, 2,.,

wherein, beta₁And beta₂Can be expressed as:

therefore, based on the above formula of the air gap flux density generated by the armature reaction, the harmonic characteristic of the air gap flux density generated by the armature reaction can be obtained:

when i is 5r-4, r is 1,2, the rotation speed with the harmonic order of 2i-1 is (P)_rω_r/(2i-1)), harmonic order is (pP)_rThe rotational speed of +2i-1 is ((P +1) P)_rω_r/(pP_r+ (2i-1))), harmonic order | pP |)_rThe rotational speed of- (2i-1) | is ((P-1) P_rω_r/[pP_r-(2i-1)])；

When i is 5r, r is 1,2, the rotation speed with harmonic order 2i-1 is (-P)_rω_r/(2i-1)), the rotational speed at the harmonic order of (2i-1+ pPr) is ((P-1) P_rω_r/(pP_r+ (2i-1))), harmonic order | pP |)_rThe rotational speed of- (2i-1) | is ((P +1) P_rω_r/(pP_r-(2i-1)))。

Further, in step 2, the electromagnetic torque may be expressed as follows:

wherein e is_iAnd i_iThe subscript i is a, b, c, d, e; omega is the mechanical angular speed of the rotor; to calculate e_iIntroducing a winding function:

wherein N is_jNumber of turns of armature winding of the jth harmonic, P_aThe number of pole pairs of the armature winding is set; therefore, the formula for the a-counter potential can be derived as follows:

wherein r is_gIs the air gap length, L_stkIs axial length, B_g(theta, t) is the air gap flux density generated by the permanent magnet, N_a(θ) is a phase winding function;

then, the electromagnetic torque equation can be derived as follows:

further, the average torque T can be obtained_avgAnd torque ripple T_rippleAre respectively expressed as follows:

further, the slave torque ripple T_rippleThe formula (c) shows that the order n of the generated torque ripple is 5r ± 1,5r ± 3; meanwhile, the torque harmonic analysis is carried out on the proposed motor, the main torque ripple harmonic is found to be 2, 11 and 20 times, and n can be calculated to be 1,3,10,12,19 and 21 and all satisfy the torque ripple formulaThe value of (1) is shown.

In step 3, in order to reduce the secondary torque ripple, n is 1,3, k is 1,2,3 …, the calculated air gap flux densities causing the secondary torque ripple are 9, 13, 29, 49, 53, 71 times, the torque ripple generated by the air gap flux density of 29 times can be found to be larger according to finite element analysis, and the torque generated by the air gap flux densities of 9 times and 11 times and the torque ripple generated by the air gap flux density of 29 times can be used as optimization sub-targets in combination with the previous torque analysis.

Further, in the step 6, since the sub-target is influenced by the low-sensitivity parameter to a small extent, the low-sensitivity parameter is kept unchanged; the response surface analysis method is used for establishing a proxy model between design high-sensitivity parameters and sub-targets:

firstly, obtaining a combination of design parameters by adopting a BBD sampling design method, then, bringing sample points into Maxwell software to carry out parametric simulation, further obtaining sub-target values of each parameter combination, and then carrying out response surface analysis to obtain a function expression of high-sensitivity parameters and sub-targets;

then, the multi-objective backbone particle swarm algorithm is used for optimizing the proxy model, the function expression obtained by response surface analysis is substituted into a multi-objective backbone particle swarm algorithm program written by MATLAB, a pareto frontier chart combining two sub-targets can be obtained, and further the optimal sub-targets can be obtained.

The beneficial effects obtained by the invention are as follows:

1. compared with the traditional magnetic field modulation type radial permanent magnet motor which needs a non-conductor support part and a rotor separation type, the motor provided by the invention utilizes the magnetic field self-shielding effect of the Halbach permanent magnet array at the lower end, avoids the permanent magnet field from being closed in the rotor, realizes the integrated processing of the rotor, and improves the mechanical robustness of the rotor of the motor.

2. The T-shaped permanent magnet array provided by the invention has various construction modes, can be used for placing the radial permanent magnet and the Halbach permanent magnet together, can also be isolated by the isolation bridge, and has flexibility.

3. The air slots are arranged among the permanent magnetic poles on the rotor, so that the weight of the rotor is reduced, and the dynamic response capability of the motor is improved.

4. Based on the magnetic field modulation principle, the motor disclosed by the invention has multiple working harmonics, and the main component sources of the torque and the torque ripple are obtained, so that the overall torque performance can be improved only by optimizing the main torque and the torque ripple in the optimization process.

5. The motor optimization method based on the air gap harmonic wave can analyze the output torque of the motor and the torque ripple generation principle, and can reveal the reason of torque ripple reduction.

6. The response surface analysis is adopted to establish a proxy model of the design parameters and the sub-targets, the relation between all the design parameters and the sub-targets can be considered, and the simulation time is reduced.

Drawings

Fig. 1 is a topological structure of a magnetic field modulation type radial permanent magnet motor with high mechanical robustness.

Fig. 2 is a flow chart of the optimal design of the air gap harmonic-based high-mechanical robustness magnetic field modulation type radial permanent magnet motor.

Fig. 3 is a magnetomotive force-flux guide model generated by a permanent magnet: (a) magnetomotive force generated by the permanent magnet; (b) the stator-side flux guide.

Fig. 4 is an armature reaction magnetomotive force-flux guide model: (a) magnetomotive force generated by armature reaction; (b) the rotor side flux guide.

FIG. 5 is a graph of the contribution of air gap flux density to torque.

Fig. 6 is a parameter model diagram of a high mechanical robustness magnetic field modulation type radial permanent magnet motor.

Fig. 7 is a pareto frontier map after optimization.

FIG. 8 is a comparison of sub-goals before and after optimization: (a) torque; (b) the torque is pulsated.

Fig. 9 is a torque performance comparison of the motor before and after optimization.

FIG. 10 is a comparison of cogging torque before and after optimization.

Detailed Description

The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

Fig. 1 shows a high mechanical robustness magnetic field modulated radial permanent magnet motor provided by the present invention, a rotor module of the motor includes two rotor teeth and three permanent magnets, wherein the permanent magnet structure is an inverted T-shape and can be regarded as a combination of a radial permanent magnet and a Halbach permanent magnet array; the two permanent magnets at the lower end are magnetized in opposite radial directions, the two permanent magnets can be placed close to the radial permanent magnets, the magnetic isolation bridges are arranged at two sides, and can also be close to the tooth walls of the rotor, so that the magnetic isolation bridges are arranged in the middle, and the radial permanent magnets in the middle are magnetized in a tangential direction; meanwhile, the self-shielding effect of the lower Halbach permanent magnet array is utilized, the permanent magnet field is prevented from being closed in the rotor, and the integrated processing of the rotor structure is realized.

Furthermore, the stator and the rotor of the motor are both in a salient pole structure, so that the permanent magnetic field and the armature reaction magnetic field are both modulated by the salient poles of the stator and the rotor, and more working harmonics are generated.

On the basis of a high-mechanical robustness magnetic field modulation type radial permanent magnet motor, a multi-air-gap harmonic optimization method is provided, the optimization process is shown in fig. 2, and the specific implementation steps are as follows:

step 1, analyzing the permanent magnet air gap flux density and the armature reaction air gap flux density of the target motor, and determining the harmonic order of the permanent magnet air gap flux density and the armature reaction air gap flux density and the corresponding rotating speed.

The electromagnetic torque may be generated by the combined action of electrical and magnetic loads having the same harmonic order and corresponding rotational speed, and is formulated as follows:

wherein D is_siIs the stator inner diameter l_stkIs the axial length of the motor, B_gvIs the magnetic load, i.e. the amplitude, K, of the v-th harmonic of the magnetic flux density of the permanent magnet air gap_svIs the amplitude of the electrical load v-th harmonic,is the angle between the v magnetic and electrical loads. Therefore, in order to analyze the torque generation mechanism of the motor, the target motor needs to be subjected to the analysis of the air gap flux density generated by the permanent magnet and the armature reaction air gap flux density;

further, the air gap flux density generated by the permanent magnet can be obtained by the product of the magnetomotive force generated by the permanent magnet and the stator-side flux guide, as shown in fig. 3, the magnetomotive force generated by the permanent magnet and the stator-side flux guide are distributed, and therefore, the air gap magnetomotive force generated by the permanent magnet can be expressed by fourier decomposition as:

wherein, F_RPMbAnd F_RPMnFourier coefficient of magnetomotive force generated by the permanent magnet, n is harmonic number of magnetomotive force generated by the permanent magnet, P_PMIs the pole pair number of the permanent magnet, theta is the phase angle, theta₀At an initial angle, ω_rIs the rotor angular velocity and t is time. The fourier decomposition of the stator-side permeance can be expressed as follows:

wherein, Λ_s0，Λ_sbAnd Λ_skIs the Fourier coefficient of the stator-side permeance, k is the harmonic order of the stator-side permeance, P_sThe number of stator slots. Thus, the air gap flux density produced by a permanent magnet can be expressed as follows:

from this formula, it can be seen that the air gap flux density generated by the permanent magnet consists of two harmonics, nP_PMSub-harmonic sum | nP_PM±kP_sThe sub-harmonic, air gap flux density harmonic and corresponding rotational speed are as follows:

further, the air gap flux density generated by the armature reaction can be obtained by multiplying the magnetomotive force generated by the armature reaction and the rotor-side flux guide, and the magnetomotive force generated by the armature reaction and the rotor-side flux guide are distributed as shown in fig. 4. The air gap magnetomotive force generated by the armature reaction can be expressed by fourier decomposition as:

wherein N is_RCIs the number of turns of a phase winding, i is the harmonic number of the magnetomotive force generated by the armature reaction, theta is the phase angle, D_RiFourier coefficient, i, of the magnetomotive force generated for the armature reaction_A,i_B,i_C,i_D,i_EThe current of A, B, C, D and E phases respectively;

when i is 5r, r is 1, 2.

When i-5 r-1, i-5 r-2, i-5 r-3, r-1, 2.

When i-5 r-4, r-1, 2,.,

wherein, I_RmaxIs the current amplitude, P_rIs the number of pole pairs, omega, of the rotor_rIs the rotor angular velocity; the fourier expression for the rotor-side air-gap permeance is as follows:

wherein, Λ_Rr0,Λ_RrbAnd Λ_RrpFourier coefficient of rotor-side air gap permeance, and p is harmonic number of rotor-side permeance，P_rIs the number of pole pairs, θ, of the rotor₀At an initial angle, ω_rIs the rotor angular velocity and t is time. Thus, the air gap flux density produced by the armature reaction can be expressed as follows:

when i is 5r, r is 1,2,.,

wherein, beta₁And beta₂Can be expressed as:

when i-5 r-4, r-1, 2,.,

wherein, beta₁And beta₂Can be expressed as:

therefore, based on the above formula of the air gap flux density generated by the armature reaction, the harmonic characteristic of the air gap flux density generated by the armature reaction can be obtained:

when in useWherein r is an even number;

when i is equal to 5r,wherein r is an odd number.

Thus the armature is reversedThe number of air gap flux density harmonics to be generated can also be determined by | nP_PM±kP_sFor the 20-slot 11-pole motor designed by the invention, based on the maxwell stress-strain method, the electromagnetic torque harmonic contribution proportion shown in fig. 5 can be obtained, and further the main working harmonics of the air-gap flux density generated by the permanent magnet and the armature reaction are 9, 11 and 31.

And 2, deriving a formula of torque and torque ripple based on an air gap magnetic field modulation principle. The electromagnetic torque can be expressed as follows:

wherein e is_iAnd i_iThe winding counter potential and phase current, respectively, and omega is the rotor mechanical angular velocity. To calculate e_iIntroducing a winding function:

wherein N is_jNumber of turns of armature winding of the jth harmonic, P_aThe number of pole pairs of the armature winding. Therefore, the formula for the a-counter potential can be derived as follows:

wherein r is_gIs the air gap length, L_stkAxial length, B_g(theta, t) generating air gap flux density for the permanent magnet; then, the electromagnetic torque equation can be derived as follows:

then, the average torque T_avgAnd torque ripple T_rippleCan be expressed as follows:

further, from the torque ripple formula, n which generates the torque ripple is 5r ± 1,5r ± 3; meanwhile, torque harmonic analysis is carried out on the proposed motor, main torque ripple harmonic waves are found to be 2, 11 and 20 times, and n can be calculated to be 1,3,10,12,19 and 21, and all values of n in the torque ripple formula are met.

And 3, analyzing the influence of the air gap harmonic on the torque and the torque ripple according to a torque and torque ripple formula. The torque and torque ripple that affect more are selected to optimize the sub-goals.

In order to reduce the secondary torque ripple, n is 1,3, k is 1,2,3 …, the calculated air gap flux density causing the secondary torque ripple is 9, 13, 29, 49, 53, 71 times, the torque ripple generated by the air gap flux density of 29 times can be found to be larger according to finite element analysis, and the torque generated by the air gap flux density of 9 times and 11 times and the torque ripple generated by the air gap flux density of 29 times can be taken as optimization sub-targets in combination with the previous torque analysis.

And 4, selecting key design parameters, and determining the parameter range by using finite element analysis software.

The design parameter model selected by the invention is shown in FIG. 6, and the initial values and the variation ranges of the design parameters obtained according to finite element analysis are as follows:

and 5, analyzing the influence of the motor parameters on the sub-target by using a Taguchi sensitivity analysis method, and dividing the design parameters into two layers according to the sensitivity.

Firstly, a seven-parameter three-level orthogonal table L is established for seven parameters₂₇(3⁷) The design parameters and corresponding horizontal numbers are as follows, where L represents the code of the orthogonal table, 27 represents the number of rows of the orthogonal table, 3 represents the horizontal number, and 7 represents 7 parameters;

then obtaining response values of 27 parameter combinations through finite element simulation; finally, the degree of influence of each parameter level on the target is calculated, variance analysis is carried out on the response value of each parameter level to obtain the sensitivity value of each parameter, the parameters can be divided into two layers according to the value of comprehensive sensitivity, and the result is as follows:

and 6, keeping the low-sensitivity parameters unchanged, and optimizing the high-sensitivity parameters by combining a response surface analysis method and a multi-target backbone particle swarm algorithm.

And the low-sensitivity parameters have small influence on the sub-target, so that the low-sensitivity parameters are kept unchanged, and the high-sensitivity design parameters are optimized. In order to reduce the simulation times, a proxy model between the sub-targets and the design variables is established by adopting a response surface analysis method. And then, optimizing the proxy model by adopting a multi-objective backbone particle swarm algorithm. The optimization results are shown in FIG. 7 as a Pareto chart. In order to more intuitively see the change conditions of the design parameters and the sub-targets before and after optimization, the comparison between the design parameters and the targets before and after optimization is listed:

after optimization, the sub-target changes are shown in FIG. 8, and the final torque waveform comparison is shown in FIG. 9, where it can be seen that after optimization, the output torque is increased from 6.78Nm to 7.77Nm, and the torque ripple is reduced from 7% to 3.1%. As can be seen from fig. 8 and 9, the proposed optimization design method based on air gap harmonics is effective.

Comparing the cogging torque of the motors before and after the optimization as shown in fig. 10, it can be seen that the cogging torque was reduced after the optimization from the first 309.1mNm to 264.4mNm, indicating that the proposed optimization method is effective.

In conclusion, the invention discloses a magnetic field modulation type radial permanent magnet motor with high mechanical robustness and a multi-harmonic optimization design method thereof. On the basis of a high-mechanical robustness magnetic field modulation type radial permanent magnet motor, the aim of optimizing torque and torque pulsation is achieved by introducing air gap harmonic waves as a bridge for connecting a motor structure with an optimization target.

In the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.