Analysis method for combined suppression of cogging torque and suspension force pulsation in motor

Abstract

The invention discloses an analysis method for cogging torque and suspension force pulsation combined suppression in a bearingless permanent magnet slice motor, and the method comprises the steps: determining the magnetic field harmonic attributes of a rotor permanent magnet and a suspension magnetic field in an air gap after stator cogging modulation based on a magnetic field modulation effect; a cogging torque and suspension force pulsation generation mechanism is explained, and harmonic waves generating cogging torque (condition 1) and suspension force pulsation (condition 2) are determined based on the cogging torque and suspension force pulsation generation mechanism; harmonic waves meeting the conditions 1 and 2 at the same time are determined, and a coupling term is obtained. According to the method, guidance can be provided for optimization design of the high-performance bearingless permanent magnet slice motor, and the cogging torque or the suspension force pulsation of the motor is reduced through a method of reducing the number of coupling terms or the amplitude of the coupling terms.

Description

Technical Field

[0001] The invention relates to the field of bearingless motor body design, and mainly designs an analysis method for joint suppression of cogging torque and suspension force pulsation in a bearingless permanent magnet thin-film motor. Background Art

[0002] The stator and rotor of the bearingless permanent magnet thin-film motor are easy to isolate, the rotor has no contact with other parts, and the size is small. It has been successfully applied in medical equipment, semiconductor manufacturing and other fields that require ultra-pure transmission. The commonly used motor type for centrifugal blood pumps is the bearingless permanent magnet thin-film motor. This application scenario has very high requirements for the operating performance of the motor. Currently, almost all centrifugal blood pumps on the market are imported and expensive. Therefore, at a time when various infectious diseases are prevalent, it is of great significance to develop high-performance domestic bearingless permanent magnet thin-film motors.

[0003] Bearingless permanent magnet thin-film motors face two problems at the same time: cogging torque and suspension force pulsation. Existing studies have treated the two as two independent parts when suppressing them, without considering whether there is a coupling relationship between them. For bearingless permanent magnet thin-film motors, the cogging torque will cause the suspended rotor to vibrate during rotation while causing speed fluctuations, making the rotor suspension unstable, and this is more obvious at light loads or low speeds; and the suspension force pulsation has a more serious impact on the rotor suspension performance. If the pulsation is too large, it may even make the motor unable to operate. Therefore, it is necessary to study the coupling relationship between the cogging torque and the suspension force pulsation to provide a guiding ideology for the design of high-performance bearingless permanent magnet thin-film motors. Summary of the invention

[0004] Purpose of the invention: In view of the problems existing in the above-mentioned background technology, the present invention proposes a method for analyzing the joint suppression of cogging torque and suspension force pulsation in a bearingless permanent magnet thin-film motor, providing a guiding ideology for optimizing the design of the motor structure, and realizing the joint suppression of cogging torque and suspension force pulsation according to the coupling relationship, thereby developing a high-performance bearingless permanent magnet thin-film motor.

[0005] Technical conditions: To achieve the above purpose, the technical solution of the present invention is: a method for analyzing the combined suppression of cogging torque and suspension force pulsation in a bearingless permanent magnet thin-film motor, comprising:

[0006] Determine the magnetomotive force generated by the rotor permanent magnet, and its Fourier decomposition is:

[0007]

[0008] Where: j is a positive odd number; A j is the amplitude of the jth harmonic of the permanent magnet magnetic potential; p r is the number of pole pairs of the rotor permanent magnet and is defined as the fundamental pole pair number of harmonics generated by the rotor permanent magnet; Ω ris the mechanical angular velocity of the motor; θ is the position angle of the motor air gap circumference.

[0009] Determine the magnetomotive force generated by the suspension winding with three-phase sinusoidal current, and its Fourier decomposition is:

[0010]

[0011] Where: ω is the frequency of the three-phase sinusoidal current; the values ​​of m and n are related to the winding structure of the motor; F m With F n They represent the magnetic potential amplitude when the number of harmonic pole pairs of the winding magnetic potential is equal to m and n respectively.

[0012] The Fourier decomposition of the air gap permeance function of the motor considering the slotting effect is:

[0013]

[0014] Where: i is 0 or a positive integer; P i represents the amplitude of the i-th air gap permeability harmonic; N s Indicates the number of stator teeth.

[0015] The permanent magnet magnetic flux density expression is obtained by multiplying the Fourier decomposition of the air gap permeability function of the motor considering the slot effect with the Fourier decomposition of the magnetomotive force generated by the rotor permanent magnet:

[0016]

[0017] The expression of suspension magnetic flux density is obtained by multiplying the Fourier decomposition of the air gap permeability function of the motor considering the slot effect with the Fourier decomposition of the magnetomotive force generated by the suspension winding:

[0018]

[0019] The mechanism of cogging torque generation is explained from the perspective of the interaction between two harmonics. The content is: the number of harmonic pole pairs of the modulated magnetic fields of the two permanent magnets is equal, but the electrical angular velocities are different.

[0020] The generation mechanism of suspension force pulsation is explained from the perspective of the interaction between the two harmonics. The content is: the modulated harmonic of a permanent magnet magnetic field and a harmonic of the suspension magnetic field differ by one pair of poles, and the electrical angular velocities are different.

[0021] It is determined that condition 1 is satisfied, that is, the interaction generates torque pulsation, thereby contributing to the permanent magnet magnetic field harmonics of part of the cogging torque.

[0022] Among them, condition 1 is:

[0023]

[0024] Where: i 1 with i2 is 0 or a positive odd number; j 1 With j 2 is a positive odd number. The pole pairs of the two permanent magnet harmonics are |j 1 p r ±i 1 N s | and |j 2 p r ±i 2 N s |.

[0025] Determine whether condition 2 is satisfied, that is, the interaction between the permanent magnet magnetic field harmonics and the suspension magnetic field harmonics generates the suspension force pulsation. Among them, condition 2 is:

[0026]

[0027] Where: k is 0 or a positive integer. The pole pair number of the permanent magnet magnetic field harmonic is |jp r ±iN s |; The pole pair number of the suspension magnetic field harmonic is |m(n)±kN s |.

[0028] Determine the permanent magnet magnetic field harmonics that satisfy both conditions 1 and 2, and obtain the coupling terms. The combination of conditions 1 and 2 can be summarized as:

[0029]

[0030] Where: p ct =|jp r ±iN s |, is the pole pair number of the coupling term permanent magnet magnetic field harmonic.

[0031] Beneficial effects:

[0032] The present invention proposes a method for analyzing the combined suppression of cogging torque and suspension force pulsation in a bearingless permanent magnet thin-film motor, establishes a unified function of suspension force pulsation and torque pulsation with respect to magnetic field and pole slot matching, and introduces a magnetic field modulation factor into the function, thereby overcoming the shortcomings of the traditional design method that can only suppress one type of pulsation alone and the pulsation model is inaccurate. It provides a guiding ideology for optimizing the design of the motor structure. The coupling relationship analyzed according to the proposed method can achieve the combined suppression of cogging torque and suspension force pulsation, thereby developing a high-performance bearingless permanent magnet thin-film motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart for analyzing the combined suppression of cogging torque and suspension force pulsation in a bearingless permanent magnet thin-film motor proposed by the present invention;

[0034] Figure 2This is a structural topology diagram of a bearingless permanent magnet thin-film motor with 12 stator teeth, 1 pair of rotor permanent magnets, and 2 pairs of suspended windings used in Example 1 of the present invention;

[0035] Figure 3 It is a star diagram of slot emf with 120 degree phase belt used for suspension winding;

[0036] Figure 4 It is the star diagram of slot emf with 60 degree phase belt used for suspension winding;

[0037] Figure 5 This is a simulation diagram of the radial suspension force of the motor when the suspension winding adopts a 120-degree phase belt;

[0038] Figure 6 This is a simulation diagram of the radial suspension force of the motor when the suspension winding uses a 60-degree phase belt. DETAILED DESCRIPTION

[0039] The present invention is further described below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] The present invention proposes a method for analyzing the combined suppression of cogging torque and suspension force pulsation in a bearingless permanent magnet thin-film motor. Figure 1 A flowchart of the method is shown in FIG.

[0041] Embodiment 1

[0042] This embodiment adopts the following bearingless permanent magnet thin-film motor structure: 12 stator teeth, 1 pair of rotor permanent magnets, and 2 pairs of suspension windings, but the suspension winding structure is not determined. The motor topology is shown in the figure below. Figure 2 shown.

[0043] The rotor permanent magnet adopts parallel magnetization, and the Fourier decomposition formula of the magnetomotive force generated by the permanent magnet can be obtained as follows:

[0044]

[0045] Where: j is a positive odd number; A j is the amplitude of the jth harmonic of the permanent magnet magnetic potential; p r Ω is the number of pole pairs of the rotor permanent magnet and is defined as the fundamental wave pole pair number of harmonics generated by the rotor permanent magnet. In this embodiment, it is 1; r is the mechanical angular velocity of the motor; θ is the position angle of the motor air gap circumference.

[0046] The Fourier decomposition of the magnetomotive force generated by the suspension winding with three-phase sinusoidal current is:

[0047]

[0048] Where: ω is the frequency of the three-phase sinusoidal current; the values ​​of m and n are related to the winding structure of the motor; F m With F n They represent the magnetic potential amplitude when the number of harmonic pole pairs of the winding magnetic potential is equal to m and n respectively.

[0049] The Fourier decomposition of the air gap permeance function of the motor considering the slotting effect is:

[0050]

[0051] Where: i is 0 or a positive integer; P i represents the amplitude of the i-th air gap permeability harmonic; N s Indicates the number of stator teeth, which is 12 in this embodiment.

[0052] The permanent magnet magnetic flux density expression is obtained by multiplying the Fourier decomposition of the air gap permeability function of the motor considering the slot effect with the Fourier decomposition of the magnetomotive force generated by the rotor permanent magnet:

[0053]

[0054] The above formula can be used to obtain the harmonic properties of the permanent magnet magnetic field actually existing in the air gap after stator tooth modulation, as shown in Table 1.

[0055] Table 1

[0056]

[0057] The expression of suspension magnetic flux density is obtained by multiplying the Fourier decomposition of the air gap permeability function of the motor considering the slot effect with the Fourier decomposition of the magnetomotive force generated by the suspension winding:

[0058]

[0059] The above formula can be used to obtain the harmonic properties of the suspension magnetic field actually existing in the air gap after stator tooth modulation, as shown in Table 2. a is the number of pole pairs of the suspension winding, which is 2 in this embodiment.

[0060] Table 2

[0061]

[0062] The mechanism of cogging torque generation is explained from the perspective of the interaction between two harmonics. The content is: the number of harmonic pole pairs of the magnetic fields of the two permanent magnets after modulation is equal, but the electrical angular velocities are different.

[0063] The generation mechanism of suspension force pulsation is explained from the perspective of the interaction between the two harmonics. The content is: the radial suspension force F in the x-axis and y-axis directions of the motor rotor x With F y The formula is:

[0064]

[0065] From the above F x With F y It can be concluded from the formula that if the modulated permanent magnet magnetic field harmonic differs from the suspension magnetic field harmonic by one pole pair and their electrical angular velocities are different, the interaction between the two can generate suspension force pulsations.

[0066] It is determined that condition 1 is satisfied, that is, the interaction generates torque pulsation, thereby contributing to the permanent magnet magnetic field harmonics of part of the cogging torque.

[0067] Among them, condition 1 is:

[0068]

[0069] Where: i 1 with i 2 is 0 or a positive odd number; j 1 With j 2 is a positive odd number. The pole pairs of the two permanent magnet harmonics are |j 1 p r ±i 1 N s | and |j 2 p r ±i 2 N s |.

[0070] In this embodiment, after stator tooth modulation, the number of permanent magnet magnetic field harmonic pole pairs is an odd number such as 1, 3, 5, and each harmonic is composed of multiple harmonics with different electrical angular velocities. Therefore, according to Condition 1, each permanent magnet magnetic field harmonic will contribute a part of the cogging torque.

[0071] Determine whether condition 2 is satisfied, that is, the interaction between the permanent magnet magnetic field harmonics and the suspension magnetic field harmonics generates the suspension force pulsation. Among them, condition 2 is:

[0072]

[0073] Where: k is 0 or a positive integer. The pole pair number of the permanent magnet magnetic field harmonic is |jp r ±iN s |; The pole pair number of the suspension magnetic field harmonic is |m(n)±kN s |.

[0074] In this embodiment, if the suspension winding adopts a three-phase 120-degree phase belt, its slot electromotive force star diagram is as follows: Figure 3 As shown, at this time, the value of m can be 2, 8, 14, etc., and the value of n can be 4, 10, 16, etc. If the suspension winding adopts a three-phase 60-degree phase belt, its slot electromotive force star diagram is as follows Figure 4 As shown, at this time, the value of m can be 2, 14, 26, etc., and the value of n can be 10, 22, 34, etc.

[0075] From condition 2, the two magnetic field harmonics that produce suspension force pulsation under the three-phase 120-degree phase band can be listed in Table 3.

[0076] Table 3

[0077]

[0078] Similarly, the two magnetic field harmonics that produce suspension force pulsation under the three-phase 60-degree phase band can be listed as Table 4.

[0079] Table 4

[0080]

[0081] Determine the permanent magnet magnetic field harmonics that satisfy both conditions 1 and 2, and obtain the coupling term. Among them, the combination of conditions 1 and 2 can be written as:

[0082]

[0083] Where: p ct =|jp r ±iN s |, is the pole pair number of the coupling term permanent magnet magnetic field harmonic.

[0084] According to the above formula, the coupling term of the cogging torque and the suspension force pulsation under the three-phase 120-degree phase belt is the permanent magnet magnetic field harmonic with pole pairs equal to 1, 3, 5, 7, 9, etc.; and the coupling term of the cogging torque and the suspension force pulsation under the three-phase 60-degree phase belt is the permanent magnet magnetic field harmonic with pole pairs equal to 1, 3, 9, 11, etc. It is easy to obtain that the coupling relationship is weaker under the three-phase 60-degree phase belt, so the suspension force pulsation is smaller. Figure 5 and Figure 6 The radial suspension force pulsation simulation diagrams of the motor with a three-phase 120-degree belt structure and a three-phase 60-degree belt structure are shown respectively. It can be seen that the radial suspension force pulsation when the suspension winding adopts a three-phase 60-degree belt structure is only 59% of that of the three-phase 120-degree belt structure.

[0085] In summary, it can be seen that in this embodiment, when the motor structure is determined, that is, the tooth slot torque is fixed, through the coupling analysis method proposed in the present invention, a reasonable motor design can be applied to reduce the number of coupling terms, thereby reducing the suspension force pulsation of the bearingless permanent magnet thin-film motor and improving the motor operation performance.

[0086] The above are only preferred specific implementation methods of the present application, but the protection scope of the present application is not limited thereto. It should be pointed out that any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed in the present application should be covered within the protection scope of the present application.

Claims

1. An analytical method for combined suppression of cogging torque and suspension force pulsation in a motor, characterized in that: The steps include: Based on the magnetic field modulation effect, the magnetic field harmonic properties of the rotor permanent magnet and the suspension magnetic field in the air gap after stator slot modulation are determined; The generation mechanism of cogging torque and suspension force pulsation is determined based on the interaction angle between the two harmonics; Determine the harmonics that produce the cogging torque (condition 1) and the suspension force pulsation (condition 2); The permanent magnet magnetic field harmonics that satisfy both conditions 1 and 2 are determined to obtain the coupling terms.

2. The analysis method for combined suppression of cogging torque and suspension force pulsation in a motor according to claim 1, characterized in that: The process of obtaining the harmonic properties of the rotor permanent magnet magnetic field actually existing in the air gap under stator slot modulation includes: determining the magnetomotive force generated by the permanent magnet; Fourier decomposing the magnetomotive force; introducing the air gap permeability function considering the slotting effect; Fourier decomposing the air gap permeability function; multiplying the Fourier decomposition of the permanent magnet magnetomotive force with the Fourier decomposition of the air gap permeability function to obtain the modulated permanent magnet air gap flux density expression; and obtaining the harmonic properties of the modulated permanent magnet.

3. The analysis method for combined suppression of cogging torque and suspension force pulsation in a motor according to claim 1, characterized in that: The process of obtaining the harmonic properties of the suspension magnetic field actually existing in the air gap under stator slot modulation includes: determining the magnetomotive force generated by the suspension winding into which a symmetrical sinusoidal current is passed; Fourier decomposing the magnetomotive force; multiplying the Fourier decomposition of the suspension magnetomotive force with the Fourier decomposition of the air gap magnetic permeability function to obtain the modulated suspension air gap magnetic flux density expression; and obtaining the harmonic properties of the modulated suspension magnetic field.

4. The analysis method for combined suppression of cogging torque and suspension force pulsation in a motor according to claim 1, characterized in that: The mechanism of the cogging torque is determined from the perspective of the interaction between the two harmonics: after modulation, the harmonic pole pairs of the two permanent magnets are equal and the electrical angular velocities of rotation are different, and the interaction between the two produces torque pulsation.

5. The analysis method for combined suppression of cogging torque and suspension force pulsation in a bearingless permanent magnet thin-film motor according to claim 1, characterized in that: The generation mechanism of suspension force pulsation is determined according to the angle of interaction between the two harmonics: after modulation, a permanent magnet magnetic field harmonic and a suspension magnetic field harmonic differ by one pole and have different electrical angular velocities of rotation, and the two interact with each other to generate suspension force pulsation.

6. The analysis method for combined suppression of cogging torque and suspension force pulsation in a motor according to claim 1, characterized in that: Condition 1 is: Where: p1 and p2 are the pole pairs of the magnetic field harmonics of the two permanent magnets; p r is the number of pole pairs of the rotor permanent magnet; Ω r is the mechanical angular velocity of the motor rotor; i1 and i2 are 0 or positive odd numbers; j1 and j2 are positive odd numbers; N s is the number of stator teeth; sgn is the sign function.

7. The method for analyzing the combined suppression of cogging torque and suspension force pulsation in a motor according to claim 6, characterized in that: The number of magnetic field pole pairs of one permanent magnet is p1=|j1p r ±i1N s |, the number of magnetic field poles of another permanent magnet p2=|j2p r ±i2N s |.

8. The analysis method for combined suppression of cogging torque and suspension force pulsation in a motor according to claim 1, characterized in that: Condition 2 is: Where: p3 is the pole pair number of the harmonic magnetic field of a permanent magnet; p4 is the pole pair number of the harmonic magnetic field of a suspension; j is a positive odd number; i is 0 or a positive integer; m and n are positive integers, and their specific values ​​are related to the winding structure; ω is the frequency of the three-phase sinusoidal current passed into the suspension winding; k is 0 or a positive integer; p a is the number of pole pairs of the suspension winding; p r is the number of pole pairs of the rotor permanent magnet; Ω r is the mechanical angular velocity of the motor rotor; N s is the number of stator teeth; sgn is the sign function.

9. The method for analyzing the combined suppression of cogging torque and suspension force pulsation in a motor according to claim 8, characterized in that: The number of pole pairs of the permanent magnet magnetic field harmonics p3=|jp r ±iN s |, suspension magnetic field harmonic pole pair number p4=|m(n)±kN s |.

10. The method for analyzing the combined suppression of cogging torque and suspension force pulsation in a motor according to claim 8, characterized in that: The permanent magnet magnetic field harmonics that satisfy both conditions 1 and 2, that is, the coupling term between the two is: the pole pair number p ct =|jp r ±iN s |The permanent magnet magnetic field harmonics, and satisfy:

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