Specific Subharmonic Elimination Method for the Modulated Pole Structure Design of Bearingless Motors

Abstract

The present invention discloses a specific sub-harmonic elimination method for the design of a modulation pole structure of a bearingless motor. Determine the number of pole pairs of the rotor poles of the motor, the number of specific sub-harmonic orders of the rotor magnetomotive force to be eliminated, the number of specific sub-harmonics of the rotor magnetomotive force to be eliminated, and the number of segments of a complete rotor pole. Establish an expression for the amplitude of each harmonic of the radial magnetization intensity of the modulation pole for the bearingless motor, solve to obtain the mechanical angle distribution of the modulation pole structure, and establish a bearingless motor with a modulation pole structure based on the solved mechanical angle distribution of the modulation pole to achieve the purpose of eliminating specific sub-harmonics. The present invention eliminates specific sub-harmonics of the rotor magnetomotive force that cause torque and suspension force fluctuations in the bearingless motor to reduce torque and suspension force fluctuations, and can simultaneously reduce the torque and suspension force fluctuations of the bearingless permanent magnet synchronous motor, improving the smooth operation of the motor.

Description

Technical Field

[0001] The present invention belongs to a motor control processing method in the field of motor optimal design, and particularly provides a specific sub-harmonic elimination method for the design of a modulation pole structure of a bearingless motor. Background Art

[0002] A bearingless permanent magnet synchronous motor has two sets of windings nested in the stator slots. One is a torque winding that provides torque, and the other is a suspension force winding that provides suspension force. When a suitable current is passed through the suspension force winding, the air-gap magnetic field distribution of the motor will contain a bias component, thereby generating a suspension force that suspends the rotor, overcoming the bearing wear problem caused by mechanical bearings and eliminating the need for a lubrication device. It has been widely used in special application scenarios such as vacuum and ultra-clean environments.

[0003] The air-gap magnetic field of a bearingless motor is complex, and the existence of stator and rotor magnetomotive force harmonics will cause torque and suspension force fluctuations in the motor, resulting in vibration and noise of the motor and affecting the smooth operation of the motor. Since the rotor magnetomotive force and the stator magnetomotive force of a bearingless permanent magnet synchronous motor will interact to generate harmonics, it is particularly important to analyze the interaction between the stator and rotor magnetomotive forces, eliminate the magnetomotive force harmonics that cause torque and suspension force fluctuations, and reduce torque and suspension force fluctuations to improve the smooth operation of the motor.

[0004] The interaction between the harmonic components in the permanent magnetic field and the harmonic components in the stator winding magnetic field will not only generate torque fluctuations but also generate suspension force fluctuations that make the rotor suspension unstable. At the same time, the existence of cogging torque will also exacerbate the torque fluctuations of the motor. The existence of torque fluctuations and suspension force fluctuations will cause vibration and noise in the bearingless motor, making the motor unable to operate smoothly. Therefore, it is very important to reduce the torque fluctuations and suspension force fluctuations of the bearingless motor.

[0005] The pole modulation technology can modulate the rotor magnetomotive force, improve the rotor magnetic field distribution, cut slots on the surface of the surface-mounted permanent magnet motor, and make the surface of the permanent magnet into a sinusoidal pulse width modulation shape. As the carrier ratio increases, the back electromotive force harmonics are effectively reduced, and the utilization rate of the permanent magnet is improved. Although this structure has a certain optimization effect on torque, the optimization effect is not obvious, and due to the reduction of the permanent magnet usage, the torque density decreases. Therefore, the specific harmonic elimination method is applied to the design of the modulation pole structure of the bearingless motor. The pole structure designed based on the specific sub-harmonic elimination method can effectively eliminate specific sub-rotor magnetomotive force harmonics and effectively reduce the torque and suspension force fluctuation amounts of the corresponding orders, improving the smooth operation of the motor. Summary of the Invention

[0006] To solve the problems existing in the background art, the purpose of the present invention is to provide a specific subharmonic elimination method for the modulation pole structure design of a bearingless motor. By performing Fourier decomposition on the square wave waveform of the rotor magnetomotive force of the modulation poles with radial magnetization, the expressions for the amplitudes of each subharmonic are obtained, and a non-linear equation set regarding the optimal mechanical angles of each modulation pole is solved, so as to achieve the purpose of eliminating each subharmonic.

[0007] The technical solution of the present invention is as follows:

[0008] S1: Determine the number of pole pairs P of the rotor poles of the motor according to the basic parameters of the designed bearingless motor. According to the number of specific subharmonic orders n of the rotor magnetomotive force that needs to be eliminated in the designed bearingless motor, determine the number N - 1 of specific subharmonics of the rotor magnetomotive force that needs to be eliminated, and then determine that the number of segments of a complete rotor pole is N; a complete rotor pole is divided into N sub-blocks, and each sub-block serves as a modulation pole;

[0009] S2: According to the specific subharmonic elimination method, establish the expressions for the amplitudes of each subharmonic of the radial magnetization intensity of the modulation poles for a bearingless motor with the number of rotor pole pairs P, the number of specific subharmonic orders n, the number N - 1 of specific subharmonics that need to be eliminated, and the number of segments N of a complete rotor pole.

[0010] S3: Solve to obtain the angular value distribution of the modulation poles according to the expressions for the amplitudes of each subharmonic of the radial magnetization intensity of the modulation poles.

[0011] S4: Manufacture a bearingless motor according to the obtained angular value distribution of the modulation poles to achieve the purpose of eliminating specific subharmonics.

[0012] In specific implementation, a simulation model of the bearingless motor with the modulation pole structure is also established according to the obtained angular value distribution of the modulation poles, and a comparative simulation verification is carried out with the simulation model of the original bearingless motor with a complete rotor pole structure (monolithic pole structure), and only judge whether the verification reaches the purpose of eliminating specific subharmonics.

[0013] The specific subharmonics are odd subharmonic orders, n = 1, 3, 5...

[0014] The rotor pole structure of the bearingless motor is a surface-mounted pole structure, and the present invention divides a complete rotor pole of the surface-mounted pole structure bearingless motor into N blocks to form a modulation pole structure.

[0015] The present invention obtains the expressions of the amplitudes of the harmonics of the radial magnetization intensity by performing Fourier decomposition on the square-wave waveform of the radial magnetization intensity of the modulated poles with radial magnetization, establishes a system of nonlinear equations regarding each switching angle, and then iteratively solves the system of nonlinear equations to obtain the mechanical angle of the modulated poles, thereby achieving the purpose of eliminating each harmonic.

[0016] The method first obtains the mechanical angle of the modulated pole structure after dividing a rotor pole into n pieces, and in the end, the modulated poles of the other several pieces are obtained by rotational replication, and each modulated pole is rotationally symmetric.

[0017] Step S2 described above includes the following steps:

[0018] S21: Express the rotor magnetomotive force of the modulated poles with radial magnetization in terms of the radial magnetization intensity, regard the waveform of the rotor magnetomotive force generated by each modulated pole with radial magnetization as a series of square-wave waveforms and then perform Fourier decomposition to obtain the expressions of the amplitudes of the harmonics of the radial magnetization intensity of the modulated poles:

[0019]

[0020] In the formula, n is the order of a specific harmonic, N is the number of segments of a complete rotor pole, M is the amplitude of the square wave, P is the number of rotor pole pairs of the motor, and α nseg is the nth seg mechanical angle of the modulated pole, and M rk are respectively the amplitudes of the kth harmonics of the radial magnetization intensity of the modulated poles, and n seg represents the (1, 2, 3... N)th mechanical angles of the modulated poles.

[0021] Step S3 described above includes the following steps:

[0022] S31: According to the expressions of the amplitudes of the harmonics of the radial magnetization intensity of the modulated poles, set the expressions of the amplitudes of the specific harmonics of the magnetization intensity of the specific harmonic orders to be eliminated (excluding the fundamental wave, n = 1) to 0, keep the amplitude of the fundamental wave of a complete rotor pole consistent with the amplitude of the fundamental wave of the modulated pole structure, and eliminating the specific harmonics of the magnetization intensity can eliminate the corresponding harmonics of the rotor magnetomotive force. The specific harmonic orders to be eliminated are n = 3, 5, 7..., that is, set the expressions of the amplitudes of the harmonics of the radial magnetization intensity of the modulated poles when n = 3, 5, 7... to 0, and then establish the following system of nonlinear equations:

[0023]

[0024] The present invention keeps the fundamental wave amplitude of a complete rotor magnetic pole consistent with that of the modulation magnetic pole structure, and a nonlinear equation set can be established by making the harmonic coefficients of each order be 0. This nonlinear equation set is a complex nonlinear transcendental equation. Solving the nonlinear equation set to obtain the mechanical angle of the modulation magnetic pole can eliminate specific harmonics.

[0025] S32: Randomly select the 2nd to Nth mechanical angles α2~α of the modulation magnetic pole N ;

[0026] S33: According to the 2nd to Nth mechanical angles α2~α of the current modulation magnetic pole N screen the initial mechanical angles α1~α of the modulation magnetic pole under one rotor magnetic pole N as follows:

[0027] Substitute the 2nd to Nth mechanical angles α2~α of the current modulation magnetic pole N into the nonlinear equation set in step S31 to solve for the corresponding mechanical angle α1 of the first modulation magnetic pole, and substitute the 2nd to Nth mechanical angles α2~α of the modulation magnetic pole N into the nonlinear equation set M rk and simultaneously establish the following objective function:

[0028] M rk →0

[0029] where →0 means approaching 0;

[0030] Then solve the objective function, continuously reduce the harmonic amplitudes of each order of the radial magnetization intensity to be eliminated to approach 0 until the 1st to Nth mechanical angles α1~α of the optimized modulation magnetic pole are screened out N ;

[0031] S34: Substitute the 1st to Nth mechanical angles α1~α of the modulation magnetic pole screened out in step S33 N into the nonlinear equation set established in step S31, set M rk to 0, and use the Newton iteration method to iteratively solve this nonlinear equation set to obtain the mechanical angle distribution of the optimal modulation magnetic pole structure. The mechanical angle distribution of the optimal modulation magnetic pole structure includes the 1st to Nth mechanical angles α1~α of the optimal modulation magnetic pole N ;

[0032] S35: The mechanical angle distribution of the optimal modulation magnetic pole structure obtained in step S34 is the mechanical angle in the first 1 / 4 cycle under one rotor magnetic pole. Calculate the mechanical angle in the latter 1 / 4 cycle symmetrically according to the mechanical angle in the first 1 / 4 cycle, so as to obtain the mechanical angle distribution of the modulation magnetic pole structure under one rotor magnetic pole.

[0033] The mechanical angle occupied by the modulation pole structure under one rotor pole is π / P. The mechanical angle in the first 1 / 4 cycle is symmetric with the mechanical angle in the last 1 / 4 cycle about the mechanical angle of π / 2P. Then, the mechanical angle in the last 1 / 4 cycle is calculated based on the symmetry of the mechanical angle in the first 1 / 4 cycle.

[0034] In step S32, the initial mechanical angle distribution is obtained in the following way:

[0035] For the 2nd to Nth initial mechanical angles α2~α of the modulation poles N , 10000 sets of N - 1 random numbers in the interval (0, 1) are selected. After sorting the N - 1 random numbers in ascending order, they are used as the coefficients c of the 2nd to Nth mechanical angles of the modulation poles nseg , and then the 2nd to Nth mechanical angles of the modulation poles are obtained according to the following formula:

[0036]

[0037] where represents the coefficient of the nth seg mechanical angle, represents the nth seg mechanical angle of the modulation pole;

[0038] For the first initial mechanical angle α1 of the modulation pole, it is obtained by separately solving the first equation established in step S31:

[0039]

[0040] where the modulation ratio m is taken as 1, α1 represents the first initial mechanical angle of the modulation pole, arccos is the inverse cosine function, N represents the number of segments of one rotor pole, and n seg represents the subscript of the mechanical angle of the modulation pole used to distinguish which mechanical angle it is. n seg only takes values of 2, 3…N, represents the nth seg mechanical angle of the modulation pole.

[0041] The mechanical angles of the modulation poles under one rotor pole satisfy the ascending sorting relationship:

[0042]

[0043] In the present invention, a complete rotor magnetic pole is divided into N pieces to form a modulation magnetic pole structure. Specifically, by establishing an expression for the amplitude of each harmonic of the radial magnetization intensity of the modulation magnetic pole, keeping the fundamental wave amplitude of a complete rotor magnetic pole consistent with the fundamental wave amplitude of the modulation magnetic pole structure, a non-linear equation set is established with a specific harmonic coefficient being 0. Through Newton iteration, each optimal mechanical angle of the modulation magnetic pole is solved, and an electric machine model is established for simulation analysis. The modulation magnetic pole structure designed by using the specific harmonic elimination method can eliminate specific harmonics in the rotor magnetomotive force.

[0044] The beneficial effects of the present invention are as follows:

[0045] The present invention eliminates the harmonics of the rotor magnetomotive force that cause torque and suspension force fluctuations in a bearingless motor to reduce torque and suspension force fluctuations.

[0046] The bearingless motor designed by applying the method of the present invention can reduce the torque and suspension force fluctuations of a bearingless permanent magnet synchronous motor simultaneously, and improve the operation stability of the motor. Brief Description of the Drawings

[0047] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments:

[0048] Figure 1 It is a schematic diagram of the modulation magnetic pole structure;

[0049] Figure 2 It is a schematic diagram of the simulation model of the bearingless motor with the modulation magnetic pole structure;

[0050] Figure 3 It is a schematic diagram of the simulation model of the bearingless motor with a complete rotor magnetic pole structure;

[0051] Figure 4 It is a comparison diagram of the amplitudes of each harmonic of the radial magnetization intensity;

[0052] Figure 5 It is a comparison diagram of the torque waveforms and a comparison diagram of the torque fluctuation distributions;

[0053] Figure 6 It is a comparison diagram of the suspension force waveforms and a comparison diagram of the suspension force fluctuation distributions. Specific Embodiments

[0054] The present invention will be further described below in conjunction with the drawings and specific embodiments.

[0055] The specific implementation of the embodiment of the present invention is as follows:

[0056] Below, taking a 24-slot motor as an example, the pole numbers of the torque winding and the suspension winding are p a = 2, p sTaking the motor with =1 as an example, the implementation mode of the present invention will be described in detail. The parameters of the motor are shown in Table 1.

[0057] Table 1 Parameters of Bearingless Permanent Magnet Synchronous Motor

[0058]

[0059]

[0060] (1) According to the basic parameters of the bearingless motor in Table 1, the rotor pole pair number of the motor is determined to be P = 2; the specific harmonic orders of the rotor magnetomotive force that need to be eliminated are n = 3, 5, 11, 13, 23, 25. Therefore, the number of specific harmonics of the rotor magnetomotive force that need to be eliminated is N - 1 = 6, and the number of permanent magnet blocks per pole is N = 7. The distribution of modulation poles under one rotor pole is as Figure 1 shown.

[0061] (2) For a bearingless motor with a rotor pole pair number of P = 2, specific harmonic orders of n = 3, 5, 11, 13, 23, 25 that need to be eliminated, a number of specific harmonics of N - 1 = 6 that need to be eliminated, and a number of blocks per complete rotor pole of N = 7, establish an expression for the amplitude of each harmonic of the radial magnetization intensity of the modulation poles. Perform Fourier decomposition on the square wave waveform of the radial magnetization intensity of the radially magnetized modulation poles. The expression for the amplitude of each harmonic of the radial magnetization intensity of the modulation poles:

[0062]

[0063] (3) According to the expression (1) for the amplitude of each harmonic of the radial magnetization intensity, solve for the optimal mechanical angle of the modulation poles.

[0064] According to the expression for the amplitude of each harmonic of the radial magnetization intensity of the modulation poles, excluding the fundamental wave (n = 1), set the expressions for the amplitudes of the harmonics of n = 3, 5, 11, 13, 23, 25 that need to be eliminated as M r6 , M r10 , M r22 , M r26 , M r46 , M r50 to 0. Keep the fundamental wave amplitude of a complete rotor pole consistent with the fundamental wave amplitude M r1 of the modulation pole structure, and establish the following non - linear equations by setting the coefficients of each harmonic to 0:

[0065]

[0066] For the 2nd to 7th initial mechanical angles α2 to α7 of the modulation poles, 10,000 groups of 6 random numbers between the intervals (0, 1) are randomly selected. After sorting the 6 random numbers in ascending order, they are used as the coefficients c of the 2nd to 7th mechanical angles of the modulation poles nseg Then, the 2nd to 7th mechanical angles of the modulation poles can be obtained by the following formula:

[0067]

[0068] Wherein, represents the coefficient of the n seg (2, 3... 7)th mechanical angle, represents the n seg (2, 3... 7)th mechanical angle of the modulation pole, n seg represents the subscript of the mechanical angle of the modulation pole for distinguishing which angle it is. In formula (5), n seg only takes 2, 3... 7.

[0069] Separate and solve the first equation in formula (2) to obtain the first initial mechanical angle α1 of the modulation pole. The first mechanical angle value α1 is as shown in formula (4)

[0070]

[0071] Wherein, the modulation ratio m takes 1, α1 represents the first initial mechanical angle of the modulation pole, N represents the number of segments of a rotor pole, n seg represents the subscript of the mechanical angle of the modulation pole for distinguishing which angle it is, represents the n seg th mechanical angle of the modulation pole.

[0072] Substitute the 2nd to 7th initial mechanical angles α2 to α7 of the modulation pole into formula (3), and the corresponding α1 can be solved

[0073] Substitute the 10,000 groups of α2 to α7 obtained from formula (3) into the non-linear equation system M r6 , M r10 , M r22 , M r26 , M r46 , M r50 Let:

[0074]

[0075] Wherein, →0 means approaching 0;

[0076] Continuously narrow down M r6 , M r10 , Mr22 , M r26 , M r46 , M r50 The value of M is adjusted to be closer to 0 until a set of initial mechanical angles α1~α7 of the modulation magnetic poles are selected, as shown in Table 2.

[0077] During the entire solution process of the mechanical angle of the modulation magnetic pole structure, the following constraints must be satisfied:

[0078] The mechanical angles α1~α7 of the modulation magnetic poles under one rotor magnetic pole satisfy an increasing sorting relationship:

[0079] α1<α2<…<α7 (6)

[0080] Table 2 Selection of initial mechanical angle values

[0081]

[0082] Substitute the set of initial mechanical angles α1~α7 of the modulation magnetic pole structure in Table (2) into (2) to establish the nonlinear equation system (5). Let M r6 , M r10 , M r22 , M r26 , M r46 , M r50 all be 0, and use the Newton iteration method (the fsolve function in Matlab) to solve the nonlinear equation system (5). When the program converges, the mechanical angle distribution α1~α7 of the optimal modulation magnetic pole structure can be iteratively obtained, as shown in Table 3.

[0083]

[0084] Among them, α1~α7 represent a set of initial mechanical angles of the modulation magnetic pole structure, and M r6 , M r10 , M r22 , M r26 , M r46 , M r50 represent the harmonic amplitudes of the specific sub-harmonic orders n = 3, 5, 11, 13, 23, 25 of the rotor magnetomotive force that need to be eliminated.

[0085] Table 3 Optimal mechanical angle values

[0086]

[0087] The mechanical angle distribution of the optimal modulation pole structure obtained by iterative solution is the mechanical angle of the first 1 / 4 cycle under one rotor pole. The mechanical angle occupied by the permanent magnet under one pole is π / 2. The angle of the first 1 / 4 cycle and the switching angle in the latter 1 / 4 cycle are symmetric about the mechanical angle of π / 4. Thus, the angle of the latter 1 / 4 cycle under one pole can be symmetrically calculated, and the mechanical angle distribution of the modulation pole structure under one rotor pole is obtained, as shown in Table 3.

[0088] According to Table 3, a bearingless motor simulation model of the modulation pole structure (as Figure 2 shown) is established and compared with the simulation model of a bearingless motor with the original complete rotor pole structure (monolithic pole structure) (as Figure 3 shown) for verification. As Figure 4 shown, the 3rd, 11th, 13th, 23rd, etc. harmonics of the rotor magnetomotive force of the bearingless motor with the modulation pole structure are effectively eliminated. At the same time, the 7th and 9th harmonics are reduced. The 5th and 25th harmonics of the rotor magnetomotive force are slightly increased compared with the monolithic structure, but can be ignored. As Figure 5 shown, the average torque of the monolithic pole structure is 5.172 Nm, and the torque ripple is 16.49%. After specific harmonic elimination, the average torque of the bearingless motor with the modulation pole structure is 5.15 Nm, and the torque ripple drops to 7.93%. The torque ripple is reduced by 51.91% compared with the original structure. As Figure 6 shown, the average suspension force of the monolithic pole structure is 306.91 N, and the suspension force ripple is 2.74%. After specific harmonic elimination, the average suspension force of the bearingless motor with the modulation pole structure is 304.15 N, and the suspension force ripple is 1.01%. Compared with the monolithic pole structure, the suspension force ripple is reduced by 63.14%. After verification, the specific harmonic elimination method for the design of the modulation pole structure of the bearingless motor can effectively eliminate specific rotor magnetomotive force harmonics and reduce torque and suspension force ripples, improving the running stability of the motor.

[0089] The above embodiments are only used to illustrate the technical concept and features of the present invention, and the purpose is to enable those who are familiar with this technology to understand the content of the present invention and implement it accordingly, and it cannot be used to limit the protection scope of the present invention. All equivalent changes or modifications made according to the spirit and essence of the present invention should be covered within the protection scope of the present invention.

Claims

1. A specific sub - harmonic elimination method for the modulation pole structure design of a bearingless motor, characterized in that, The method comprises the following steps: S1: Determine the number of pole pairs P of the rotor poles of the motor according to the basic parameters of the designed bearingless motor. According to the number of specific harmonics n of the rotor magnetomotive force to be eliminated by the designed bearingless motor, determine the number N - 1 of specific harmonics of the rotor magnetomotive force to be eliminated, and further determine that the number of segments of a complete rotor pole is N; a complete rotor pole is divided into N sub - segments, and each sub - segment serves as a modulation pole; S2: Establish an expression for the amplitude of each harmonic of the radial magnetization intensity of the modulation poles of the bearingless motor according to the specific harmonic elimination method; S3: Solve to obtain the angular value distribution of the modulation poles according to the expression for the amplitude of each harmonic of the radial magnetization intensity of the modulation poles; S4: Manufacture the bearingless motor according to the obtained angular value distribution of the modulation poles to achieve the purpose of eliminating specific harmonics; The step S2 comprises the following steps: S21: Express the rotor magnetomotive force of the modulation poles magnetized radially in terms of the radial magnetization intensity. Regard the rotor magnetomotive force waveforms generated by each modulation pole magnetized radially as a series of square - wave waveforms and then perform Fourier decomposition to obtain an expression for the amplitude of each harmonic of the radial magnetization intensity of the modulation poles: where n is the order of a specific harmonic, N is the number of segments of a complete rotor pole, M is the amplitude of the square wave, P is the number of rotor pole pairs of the motor, and α nseg is the n seg th mechanical angle of the modulation pole, and M rk are the amplitudes of the kth harmonics of the radial magnetization intensity of the modulation pole, respectively, and n seg represents the (1, 2, 3…N)th mechanical angle of the modulation pole; The step S3 comprises the following steps: S31: According to the expression for the amplitude of each harmonic of the radial magnetization intensity of the modulation poles, set the expression for the amplitude of the specific harmonic of the magnetization intensity of the specific harmonic order to be eliminated except for the fundamental wave to 0, and keep the fundamental - wave amplitude of a complete rotor pole consistent with the fundamental - wave amplitude of the modulation - pole structure, and then establish the following non - linear equations: S32: Randomly select the 2nd to Nth mechanical angles α2 to α of the modulation magnetic poles N ; S33: According to the second to the Nth mechanical angles α2 to α of the current modulation magnetic pole N screen the initial mechanical angles α1 to α of the modulation magnetic pole under one rotor magnetic pole N as follows: Substitute the second to the Nth mechanical angles α2 to α of the current modulation magnetic pole N into the non-linear equations in step S31 to solve for the corresponding mechanical angle α1 of the first modulation magnetic pole, and substitute the mechanical angles α2 to α of the second to the Nth modulation magnetic poles N into the non-linear equations M rk to simultaneously establish the following objective function: M rk →0 where, →0 means approaching 0; Then, solve the objective function, continuously reduce the amplitudes of each harmonic of the radial magnetization intensity to be eliminated to approach 0 until the 1st to Nth mechanical angles α1~α of the optimized modulation poles are obtained by screening. N ; S34: The mechanical angles α1 to α of the 1st to Nth modulated magnetic poles selected in step S33 N are then substituted into the non-linear equations established in step S31. Set M rk to 0, and use the Newton iteration method to iteratively solve this non-linear equation system to obtain the mechanical angle distribution of the optimal modulated magnetic pole structure; S35: The mechanical - angle distribution of the optimal modulation - pole structure obtained in step S34 is the mechanical angle of the first 1 / 4 cycle under a rotor pole. Calculate the mechanical angle of the latter 1 / 4 cycle symmetrically according to the mechanical angle of the first 1 / 4 cycle; In the step S32, the initial mechanical - angle distribution is obtained in the following manner: For the 2nd to Nth initial mechanical angles α2 to α of the modulation magnetic poles N , 10,000 groups of N - 1 random numbers between the intervals (0, 1) are selected. After the N - 1 random numbers are sorted in ascending order, they are used as the coefficients c of the 2nd to Nth mechanical angles of the modulation magnetic poles nseg , and then the 2nd to Nth mechanical angles of the modulation magnetic poles are obtained according to the following formula: Among them, represents the coefficient of the n seg th mechanical angle, represents the n seg th mechanical angle of the modulation magnetic pole; For the first initial mechanical angle α1 of the modulation poles, it is obtained by separately solving the first equation established in step S31; Among them, the modulation ratio m is taken as 1, α1 represents the first initial mechanical angle of the modulation magnetic pole, arccos is the inverse cosine function, N represents the number of segments of a rotor magnetic pole, and n seg represents the mechanical angle of the modulation magnetic pole as the subscript of which represents the nth seg mechanical angle of the modulation magnetic pole.

2. The specific sub - harmonic elimination method for the modulation pole structure design of a bearingless motor according to claim 1, characterized in that: The rotor - pole structure of the bearingless motor is a surface - mounted pole structure.

3. The specific sub - harmonic elimination method for the modulation pole structure design of a bearingless motor according to claim 1, characterized in that: The mechanical angle of the modulation magnetic pole under a rotor magnetic pole satisfies an increasing sorting relationship:

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