A magnetic resistance composite permanent magnetic thrust bearing based on halbach array and a method for calculating magnetic force of non-equal-length annular magnetic group

Abstract

The application belongs to the technical field of magnetic thrust bearing vibration reduction and isolation, and provides a reluctance composite permanent magnetic thrust bearing based on a Halbach array and a non-equal-length annular magnetic group magnetic force calculation method. The stator adopts an annular magnetic group and damping ring alternately arranged configuration, the magnetic force generated by the interaction between the stator and the rotor annular magnetic group is used for non-contact bearing, and the damping ring cuts the magnetic induction lines to generate a damping effect when the annular rotor magnetic group generates axial movement, thereby inhibiting the vibration under the impact load and improving the vibration reduction effect; meanwhile, the Halbach array is used to effectively improve the unit volume bearing capacity and damping effect. In addition, the magnetic dipole moment method and the Monte Carlo method are used for non-equal-length complex magnetic body axial force calculation, the four-fold integral calculation problem is avoided, the calculation is simple, accurate, practical and has high engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of magnetic thrust bearing vibration reduction and isolation technology, and relates to a magnetic reluctance composite permanent magnet thrust bearing based on Halbach array and a magnetic force calculation method for non-equal length annular magnetic groups. Background Technology

[0002] Unmanned underwater vehicles, ships, and other underwater and surface equipment are core equipment for safeguarding my country's maritime rights and ensuring national defense security. The rapid development of modern science and technology has placed more stringent demands on the acoustic stealth performance of such equipment, and longitudinal vibration noise of the propulsion shaft is its main noise source, severely restricting its acoustic stealth performance. Permanent magnet thrust bearings utilize the non-contact transmission of magnetic force to significantly reduce longitudinal vibration noise of the propulsion shaft. Furthermore, a configuration employing alternating annular magnetic assemblies and damping rings can generate induced eddy currents during relative motion of the stator and rotor using changes in magnetic field lines, thereby producing eddy current damping forces that impede relative motion. This configuration can effectively suppress vibration under impact loads without adding mass or increasing stiffness, significantly improving vibration reduction performance. However, the alternating annular magnetic assemblies and damping rings configuration presents problems such as complex magnetic circuit analysis and severe magnetic field line distortion during relative motion of the stator and rotor, and the non-equal axial lengths of the annular magnetic assemblies between the stator and rotor make magnetic force calculation extremely difficult. Therefore, proposing a magnetic force calculation method for a magnetoresistive composite permanent magnet thrust bearing based on Halbach array and a non-uniform length annular magnetic group is of great significance for improving load-bearing and damping effects, further reducing vibration and noise under impact loads, and guiding the optimized design of permanent magnet thrust bearings.

[0003] Regarding magnetic reluctance composite magnetic bearings, Jiang Shuyun proposed in his patent "A Permanent Magnet Bearing with High Load Capacity and Damping Performance" (CN102003462B) that both the stator and rotor adopt an alternating arrangement of annular magnetic groups and damping rings, with the annular magnetic groups of the stator and rotor axially opposite to the damping rings. Although this can balance load-bearing and damping effects, the negative stiffness configuration makes it prone to collision and adsorption when subjected to axial force, resulting in a highly unstable structure. Regarding the magnetic force calculation method for non-uniform length magnets, Yang Li of Xi'an University of Technology used the magnetic charge method and virtual displacement method to calculate the magnetic force in his 2016 master's thesis "Study on Axial Magnetic Force of Halbach Permanent Magnet Bearing Composed of Permanent Magnet Rings with Different Rectangular Cross Sections". Although it can obtain the axial magnetic force of complex non-uniform length magnet arrays within a certain error range, the magnetic force calculation formula is extremely complex and difficult to apply to engineering practice.

[0004] Therefore, proposing a magnetic force calculation method for a magnetoresistive composite permanent magnet thrust bearing based on Halbach array and a non-uniform length annular magnetic group is of great significance for improving the longitudinal vibration reduction performance and magnetic circuit structure design of magnetic thrust bearings. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention presents a magnetic reluctance composite permanent magnet thrust bearing based on a Halbach array and a magnetic force calculation method for non-uniform length annular magnetic arrays. The aim is to employ a configuration where the bearing stator uses alternating annular magnetic arrays and damping rings, allowing the thrust bearing to meet both load-bearing and damping requirements. The Halbach magnetic array structure enhances the load-bearing and damping effect per unit volume, and the magnetic dipole moment method and Monte Carlo method are used for rapid magnetic force calculation of complex non-uniform length magnetic arrays. This magnetic bearing has a compact structure, reducing bearing stiffness and increasing damping effect while maintaining load-bearing capacity, thereby improving the longitudinal vibration reduction performance of the magnetic bearing. Furthermore, the calculation method is widely adaptable and can be used for magnetic force calculations with different magnetization methods and different annular magnetic array structures. In engineering applications, it is simple to operate, accurate in calculation, and highly practical.

[0006] The technical solution of the present invention: A Halbach array-based reluctance composite permanent magnet thrust bearing is disclosed. First, the rotor back iron and the shaft are coaxially connected via a flat key, with the right end face of the rotor back iron coinciding with the wedge-shaped end face of the shaft, thus completing the installation and axial positioning of the rotor back iron. Second, the annular rotor magnet assembly is alternately embedded into the rotor back iron in a magnetization sequence of radial inward, tangential counterclockwise, radial outward, and tangential clockwise, completing the installation of the permanent magnet thrust bearing rotor module. Finally, the rotor end cover is fixed to the inner rotor back iron with bolts, completing the magnetization of the annular rotor. The axial positioning of the assembly is then performed. Next, the stator damping ring and annular stator magnetic assembly are embedded into the stator in an alternating arrangement to complete the stator module installation. The magnetization method of the annular stator magnetic assembly is the same as that of the annular rotor magnetic assembly. The stator end cover is fixed to the stator back iron with bolts, completing the axial positioning of the damping ring and magnetic assembly in the stator back iron. Simultaneously, the alignment between the rotor and stator is adjusted using adjusting screws. Finally, the shaft connecting flange is bolted to the shaft, enabling the thrust bearing to achieve a transmission connection with external components. This invention features a compact structure. It can significantly increase the air gap magnetic flux density between the stator and rotor using the Halbach array annular magnetic assembly, improving axial load capacity. Furthermore, when the magnetic thrust bearing is subjected to axial thrust, the damping ring and magnetic assembly cut magnetic field lines, generating eddy currents, which in turn form eddy current damping force, reducing the vibration of the magnetic thrust bearing under impact loads. This invention possesses high practicality and engineering application value.

[0007] A magnetic reluctance composite permanent magnet thrust bearing based on a Halbach array includes a shaft connecting flange 1, a first connecting bolt 2, a shaft 3, a rotor end cover 4, a stator end cover 5, a stator radially inward magnetizing assembly 6, a stator tangentially counterclockwise magnetizing assembly 7, a stator radially outward magnetizing assembly 8, a stator tangentially clockwise magnetizing assembly 9, a damping ring 10, a flat key 11, a rotor radially inward magnetizing assembly 12, a rotor tangentially counterclockwise magnetizing assembly 13, a rotor radially outward magnetizing assembly 14, a rotor tangentially clockwise magnetizing assembly 15, a stator back iron 16, a rotor back iron 17, a second connecting bolt 18, a third connecting bolt 19, an adjusting screw 20, and a stator magnet array guide pin 21.

[0008] The rotor back iron 17 and the rotating shaft 3 are coaxially connected by a flat key 11, and the right end face of the rotor back iron 17 coincides with the wedge-shaped end face of the rotating shaft 3, completing the installation and axial positioning of the rotor back iron 17; the rotor magnet array consists of 9 independent annular rotor magnet groups, each annular rotor magnet group including 3 rotor radially inward magnet groups 12, 2 rotor tangentially counterclockwise magnet groups 13, 2 rotor radially outward magnet groups 14, and 2 rotor tangentially clockwise magnet groups 15, the annular rotor magnet groups are arranged according to... The rotor radially inward magnetizing group 12, the rotor tangential counterclockwise magnetizing group 13, the rotor radially outward magnetizing group 14, and the rotor tangential clockwise magnetizing group 15 are arranged in sequence and installed on the rotor back iron 17. The rotor end cover 4 is fixed to the rotor back iron 17 by the second connecting bolt 18, thus completing the installation of the rotor and the axial positioning of the rotor magnet array. The stator magnet array consists of 9 independent annular stator magnet groups, each annular stator magnet group including 3 stator radially inward magnetizing groups 6, 2, and 3. There are 7 stator tangential counterclockwise magnetizing groups, 8 stator radially outward magnetizing groups, and 9 stator tangential clockwise magnetizing groups. The annular stator magnetic groups are arranged in the following order: damping ring 10, stator radially inward magnetizing group 6, damping ring 10, stator tangential counterclockwise magnetizing group 7, damping ring 10, stator radially outward magnetizing group 8, damping ring 10, stator tangential clockwise magnetizing group 9, and damping ring 10. This ensures that the annular rotor magnetic groups and the annular stator magnetic groups maintain the same magnetizing method. The stator is axially aligned and fixed inside the stator back iron 16 by the stator magnet array guide pin 21. Then, the stator end cover 5 is fixed to the stator back iron 16 by the third connecting bolt 19. The centering adjustment between the stator and the rotor is completed by adjusting the screw 20, thus completing the installation of the stator, the axial limit of the stator magnet array and the centering adjustment between the stator and the rotor. The rotating shaft connecting flange 1 is connected to the rotating shaft 3 by the first connecting bolt 2, so that the magnetic reluctance composite permanent magnet thrust bearing can achieve the transmission connection with the external components.

[0009] A method for calculating the magnetic force of non-uniform length toroidal magnetic arrays is presented. This method ignores curvature effects, equating the toroidal magnetic array to a rectangular magnet. A magnetic force calculation model for a single toroidal stator and rotor magnetic array is established using the magnetic dipole moment method. Considering the difficulty of calculating the quadruple integral, the Monte Carlo method is used to simplify the quadruple integral, significantly reducing the complexity of the magnetic force calculation model. Finally, the magnetic forces of different toroidal magnetic arrays are superimposed to obtain the total axial force. This method can perform magnetic force calculations on toroidal magnetic arrays with different magnetization methods and rectangular cross-sections. The calculation method is fast, accurate, widely applicable, and has high practical value.

[0010] The specific steps are as follows: The first step is to determine the key structural parameters of the reluctance composite permanent magnet thrust bearing; Key structural parameters of reluctance composite permanent magnet thrust bearings include the remanence of the annular rotor magnetic assembly. B r1 Residual magnetism of the toroidal stator magnet group B r2 Inner diameter of the annular rotor magnetic assembly R 1. Outer diameter of the annular rotor magnetic assembly R 2. Axial length of the annular rotor magnetic assembly a 0. Radial thickness of the annular rotor magnetic assembly b 0. Axial movement of the annular rotor magnetic assembly dz, Air gap between the annular rotor magnetic assembly and the annular stator magnetic assembly h、 Axial length of the single damping ring 10 in a single pair of annular rotor magnetic assemblies and annular stator magnetic assemblies c 0. Inner diameter of the ring stator magnetic assembly R 3. Outer diameter of the ring stator magnetic assembly R 4. Axial length of the annular stator magnetic assembly d 0. Radial thickness of the annular stator magnetic assembly e 0. Equivalent rotor magnetic strip n Number of stator magnetic strips after equivalent n Magnetization direction matrix of the annular rotor magnetic assembly β 1. Magnetization direction matrix of the ring stator magnet assembly β 2 、 Monte Carlo sampling points N Curvature correction factor k ; The second step is to convert a single pair of annular rotor magnetic groups and annular stator magnetic groups into magnetic force calculation models of magnets of equal height, and to establish a magnetic force calculation method for a single pair of non-equal length annular magnetic groups. First, take any annular rotor magnetic assembly and an annular stator magnetic assembly, both of which are equivalent to rectangular magnetic strips of equal height. Determine the height of the rotor and stator magnetic strips after the equivalent configuration: (1) In the formula, LThis refers to the equivalent heights of the rotor and stator magnetic strips; Determine the equivalent cross-sectional areas of the rotor and stator magnetic strips: (2) In the formula, S 1 represents the cross-sectional area of ​​the equivalent rotor magnetic strip. S 2 represents the cross-sectional area of ​​the equivalent stator magnetic strip; Secondly, randomly select one sampling point from each of the equivalent rotor and stator magnetic strips, and calculate the angle between the direction of the line connecting the two sampling points and the horizontal direction. θ Distance between two sampling points r 12 : (3) In the formula, z 1 represents the x-coordinate of the sampling point in the equivalent rotor magnetic strip. y 1 represents the ordinate of the sampling point in the equivalent rotor magnetic strip, z 2 represents the x-coordinate of the sampling point in the equivalent stator magnetic strip. y 2 represents the ordinate of the sampling point in the equivalent stator magnetic strip; Subsequently, the magnetic field strength at the sampling points in the equivalent rotor magnetic strip was determined. : (4) In the formula, The magnetic field strength at the sampling point in the rotor magnetic strip after the equivalent operation. dH r1 The magnetic field strength at the sampling point in the equivalent rotor magnetic strip. The component along the direction of the line connecting two sampling points in the equivalent rotor magnetic strip and the equivalent stator magnetic strip; dH θ1 The magnetic field strength at the sampling point in the equivalent rotor magnetic strip. The component of the direction of the line connecting two sampling points in the vertically equivalent rotor magnetic strip and the vertically equivalent stator magnetic strip; J 1 represents the equivalent rotor magnetic stripe polarization intensity mode, the magnitude of which is equal to the remanence of the annular rotor magnetic assembly. B r1 ; β 11 The angle between the magnetization direction of the rotor magnetic strip and the horizontal direction after the equivalent operation; Next, the equivalent stator magnetic stripe magnetic polarization intensity vector is... The decomposition is performed along the lines parallel and perpendicular to the lines connecting the two sampling points in the equivalent rotor and stator magnetic strips, respectively: (5) In the formula, This is the equivalent stator magnetic stripe magnetic polarization intensity vector, the magnitude of which is equal to the remanence of the toroidal stator magnetic array. B r2 The direction is parallel to the magnetization direction of the equivalent stator magnetic strip; This represents the equivalent stator magnetic stripe polarization intensity mode. β 21 The angle between the magnetization direction of the stator magnetic strip and the horizontal direction after the equivalent operation; Then, the static magnetic energy between the rotor and stator magnetic bars after the equivalent calculation is performed. W : (6) Finally, regarding static magnetic energy W Regarding axial differentiation, calculate the equivalent axial force between a single pair of rotor and stator magnetic strips. F z : (7) Step 3: Calculate the total axial force of the reluctance composite permanent magnet thrust bearing; First, determine the horizontal and vertical coordinates of each sampling point inside the equivalent rotor magnetic strip and each sampling point inside the equivalent stator magnetic strip: (7) In the formula, z 1ik For the first i The first equivalent rotor magnetic strip inside k The x-coordinate of each sampling point; y 1ik For the first i The first equivalent rotor magnetic strip inside k The ordinate of each sampling point; z 2jk For the first j The first equivalent stator magnetic strip inside k The x-coordinate of each sampling point; y 2jk For the first j The first equivalent stator magnetic strip inside k The ordinate of each sampling point; u 1ik , u 2ik , u 1jk , And they are independent of each other. i, j ∈[1,2 … n]、 k ∈[1,2 … N]; Next, substitute the above formula into the second step to solve for the angle between the direction of the line connecting the two sampling points and the horizontal direction. θ Distance between two sampling points r12 In the formula, the angle between the line connecting any two sampling points in the rotor magnetic strip and the stator magnetic strip after any equivalent transformation and the horizontal direction is obtained. θ ijk Distance between two sampling points r ijk ; (8) Finally, the axial force between the equivalent rotor magnetic strip and the equivalent stator magnetic strip, calculated in the second step, will be used as the basis for further calculation. F z Discretize the formula and calculate the total axial force when the axial displacement of the rotor magnetic strip is dz after the equivalent process. F z,total : (9) In the formula, F z,total The total axial force. β 1i For the first i The magnetization direction of the equivalent rotor magnetic strips β 2j For the first j The magnetization direction of the equivalent stator magnetic strip.

[0011] The beneficial effects of this invention are as follows: This invention proposes a magnetic reluctance composite permanent magnet thrust bearing based on a Halbach array. The structure employs an alternating arrangement of annular magnetic groups and damping rings in the stator, while the rotor consists entirely of annular magnetic groups. This configuration allows the magnetic thrust bearing to meet load-bearing requirements while also considering damping characteristics, thereby reducing vibration under impact loads. Furthermore, the use of Halbach arrays in both the inner and outer annular magnetic groups further enhances load-bearing and damping effects. Simultaneously, the magnetic force calculation method for non-uniform length annular magnetic groups proposed in this invention equates the annular magnetic group to rectangular magnetic strips, reducing computational complexity. The magnetic dipole moment method can be used to calculate the magnetic force of inner and outer annular magnetic groups with arbitrary magnetization directions and axial lengths. In addition, the Monte Carlo method is combined to transform the integral form of the magnetic force calculation formula into a discrete form, avoiding the complexity of quadruple integral calculations. In engineering applications, this invention features simple calculation, strong practicality, and wide applicability. Attached Figure Description

[0012] Figure 1 This is an assembly diagram of a magnetoresistive composite permanent magnet thrust bearing based on a Halbach array; Figure 2 yes Figure 1 Middle YZ A sectional view of a plane; Figure 3 Flowchart of the magnetic force calculation method for non-equal length ring magnetic fields; Figure 4 This is a schematic diagram of the stator and rotor annular magnetic assemblies being equivalent to rectangular permanent magnets of equal length. Figure 5 It is a magnetic force calculation model for a single pair of non-equal length ring magnetic groups.

[0013] In the diagram: 1-Shaft connecting flange, 2-First connecting bolt, 3-Shaft, 4-Rotor end cover, 5-Stator end cover, 6-Stator radial inward magnetization assembly, 7-Stator tangential counterclockwise magnetization assembly, 8-Stator radial outward magnetization assembly, 9-Stator tangential clockwise magnetization assembly, 10-Damping ring, 11-Flat key, 12-Rotor radial inward magnetization assembly, 13-Rotor tangential counterclockwise magnetization assembly, 14-Rotor radial outward magnetization assembly, 15-Rotor tangential clockwise magnetization assembly, 16-Stator back iron, 17-Rotor back iron, 18-Second connecting bolt, 19-Third connecting bolt, 20-Adjusting screw, 21-Stator magnet array guide pin. Detailed Implementation

[0014] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0015] Example A magnetic reluctance composite permanent magnet thrust bearing based on a Halbach array was selected, which includes four magnetization methods and has nine rotor magnet arrays and nine stator magnet arrays.

[0016] like Figures 1-2 As shown, the installation steps for the reluctance composite permanent magnet thrust bearing based on the Halbach array are as follows: First, the rotor back iron 17 and the rotating shaft 3 are coaxially connected by a flat key 11, and the right end face of the rotor back iron 17 coincides with the wedge-shaped end face of the rotating shaft 3, completing the installation and axial positioning of the rotor back iron 17; the rotor magnet array consists of 9 independent annular rotor magnet groups, each annular rotor magnet group including 3 rotor radially inward magnet groups 12, 2 rotor tangentially counterclockwise magnet groups 13, 2 rotor radially outward magnet groups 14, and 2 rotor tangentially clockwise magnet groups 15, the annular rotor magnets The magnetic array is arranged in the following order: rotor radially inward magnetizing group 12, rotor tangential counterclockwise magnetizing group 13, rotor radially outward magnetizing group 14, and rotor tangential clockwise magnetizing group 15. It is installed on the rotor back iron 17, and the rotor end cover 4 is fixed to the rotor back iron 17 by the second connecting bolt 18, thus completing the rotor installation and axial positioning of the rotor magnet array. The stator magnet array consists of 9 independent annular stator magnetic groups, each annular stator magnetic group including 3 stator radially inward magnetizing groups 6. The annular stator magnetic groups consist of 7 (two stator tangential counterclockwise magnetization groups), 8 (two stator radially outward magnetization groups), and 9 (two stator tangential clockwise magnetization groups). The annular stator magnetic groups are arranged in the following order: damping ring 10, stator radially inward magnetization group 6, damping ring 10, stator tangential counterclockwise magnetization group 7, damping ring 10, stator radially outward magnetization group 8, damping ring 10, stator tangential clockwise magnetization group 9, and damping ring 10. This arrangement ensures that the annular rotor magnetic groups maintain the same magnetization method as the annular stator magnetic groups. The stator is axially aligned and fixed inside the stator back iron 16 by the stator magnet array guide pin 21. Then, the stator end cover 5 is fixed to the stator back iron 16 by the third connecting bolt 19. The centering adjustment between the stator and the rotor is completed by adjusting the screw 20, thus completing the installation of the stator, the axial limit of the stator magnet array and the centering adjustment between the stator and the rotor. The rotating shaft connecting flange 1 is connected to the rotating shaft 3 by the first connecting bolt 2, so that the magnetic reluctance composite permanent magnet thrust bearing can achieve the transmission connection with the external components.

[0017] At this point, the installation of a magnetoresistive composite permanent magnet thrust bearing based on a Halbach array is complete.

[0018] like Figures 3-5 As shown, the specific steps of a method for calculating the magnetic force of a non-uniform length toroidal magnetic array are as follows: The first step is to determine the key structural parameters of the reluctance composite permanent magnet thrust bearing; The residual magnetism of the annular rotor magnetic assembly is B r1 =1.4T, stator magnet remanence is B r2 =1.4T, inner diameter of the annular rotor magnetic assembly is R 1=50mm, outer diameter of the annular rotor magnetic assembly is R 2=55mm, axial length of the annular rotor magnetic assembly is a0=10mm, radial thickness of the annular rotor magnetic assembly is b 0=5mm, axial movement of the annular rotor magnetic assembly is dz =5mm 、 The air gap between the annular rotor magnetic assembly and the annular stator magnetic assembly is h =2mm 、 The axial length of a single damping ring in a single pair of annular rotor magnetic assemblies and annular stator magnetic assemblies is c 0=2.5mm, inner diameter of the ring stator magnetic assembly is R 3=57mm, outer diameter of the annular stator magnetic assembly is R 4=62mm, axial length of the annular stator magnetic assembly is d 0=5mm, radial thickness of the annular stator magnetic assembly is e 0=5mm, the equivalent number of rotor magnetic strips and the equivalent number of stator magnetic strips are n =9. The magnetization direction matrix of the annular rotor magnetic assembly is: β 1 = [270°0°90°180°270°0°90°180°270°], the magnetization direction matrix of the ring stator magnetic assembly is... β 2 = [270°180°90°0°270°180°90°0°270°] 、 The number of sampling points in Monte Carlo is N =10 7 The curvature correction factor is k =0.95; The second step is to convert a single pair of annular rotor magnetic groups and annular stator magnetic groups into magnetic force calculation models of magnets of equal height, and to establish a magnetic force calculation method for a single pair of non-equal length annular magnetic groups. From equation (2), the equivalent heights of the rotor and stator magnetic strips can be obtained as follows: L =351.9mm, the equivalent cross-sectional area of ​​the rotor magnetic strip is S 1=50mm 2 The equivalent cross-sectional area of ​​the stator magnetic strip is S 2=25mm 2 The method for calculating the magnetic force of a single pair of non-equal-length magnets is as follows: in, J 1= J 2= B r =1.4T, ; Step 3: Calculate the total axial force of the reluctance composite permanent magnet thrust bearing; First, select one sampling point in each of the equivalent rotor and stator magnetic strips, and calculate the axial force between the two points as an example: Pick i =j =1, u 1ik = u 2ik = u 1jk = u 2jk =0.5, from equation (8) we can get z 11k =10mm y 11k =2.5mm z 21k =5mm y 21k =9.5mm, and the angle between the line connecting the two sampling points and the horizontal direction can be obtained from equation (9). θ 11k = -54.5°, distance between two sampling points r 11k =8.6mm, from equation (10), the axial force between the two sampling points when the axial displacement of the two sampling points is dz=5mm can be obtained. F z，11k =328.7N; Secondly, considering the large number of sampling points, it is necessary to use the mathematical calculation tool MATLAB to calculate the total axial force when the axial displacement of the inner magnet is dz=5mm. F z,total =3449.1N; At this point, the magnetic force calculation for the non-uniform length toroidal magnetic array is complete.

[0019] This novel permanent magnet thrust bearing adopts a configuration in which damping rings and annular magnetic groups are arranged alternately in the stator section. It can achieve non-contact transmission by utilizing the magnetic force between the stator and rotor magnets, and can also generate a damping effect by utilizing the eddy current effect. This further improves the vibration reduction performance of the permanent magnet thrust bearing under impact load and increases the space utilization rate of the magnetic bearing. This structural innovation changes the traditional configuration of permanent magnet thrust bearings and provides new ideas for vibration reduction design of permanent magnet thrust bearings.

[0020] This calculation method equates the toroidal magnetic assembly to a rectangular magnetic strip, reducing computational complexity from a structural perspective. Furthermore, it utilizes the magnetic dipole moment method to calculate the magnetic force of inner and outer toroidal magnetic assemblies with arbitrary magnetization directions and axial lengths. In addition, it combines the Monte Carlo method to transform the integral form of the magnetic force calculation formula into a discrete form, avoiding the complexity of quadruple integral calculations. In engineering applications, it features simple calculation, strong practicality, and wide applicability.

Claims

1. A method for calculating the magnetic force of a non-uniform length annular magnetic assembly in a reluctance composite permanent magnet thrust bearing, characterized in that, The steps are as follows: The first step is to determine the key structural parameters of the reluctance composite permanent magnet thrust bearing; The magnetic reluctance composite permanent magnet thrust bearing includes a shaft connecting flange (1), a first connecting bolt (2), a shaft (3), a rotor end cover (4), a stator end cover (5), a stator radially inward magnetizing assembly (6), a stator tangentially counterclockwise magnetizing assembly (7), a stator radially outward magnetizing assembly (8), a stator tangentially clockwise magnetizing assembly (9), a damping ring (10), a flat key (11), a rotor radially inward magnetizing assembly (12), a rotor tangentially counterclockwise magnetizing assembly (13), a rotor radially outward magnetizing assembly (14), a rotor tangentially clockwise magnetizing assembly (15), a stator back iron (16), a rotor back iron (17), a second connecting bolt (18), a third connecting bolt (19), an adjusting screw (20), and a stator magnet array guide pin (21). The rotor back iron (17) and the rotating shaft (3) are coaxially connected by a flat key (11), and the right end face of the rotor back iron (17) coincides with the wedge-shaped end face of the rotating shaft (3), thus completing the installation and axial positioning of the rotor back iron (17). The rotor magnet array consists of 9 independent annular rotor magnet groups. Each annular rotor magnet group includes 3 rotor radially inward magnet groups (12), 2 rotor tangential counterclockwise magnet groups (13), 2 rotor radially outward magnet groups (14), and 2 rotor tangential clockwise magnet groups (15). The annular rotor magnet groups are magnetized radially inward according to the rotor radially inward magnetization. The magnetic array is arranged in sequence as follows: magnetic array (12), rotor tangential counterclockwise magnetization array (13), rotor radial outward magnetization array (14), and rotor tangential clockwise magnetization array (15). It is installed on the rotor back iron (17), and the rotor end cover (4) is fixed to the rotor back iron (17) by the second connecting bolt (18), thus completing the installation of the rotor and the axial positioning of the rotor magnet array. The stator magnet array consists of 9 independent annular stator magnetic arrays. Each annular stator magnetic array includes 3 stator radial inward magnetization arrays (6) and 2 stator tangential counterclockwise magnetization arrays (7). Two stator radially outward magnetizing groups (8) and two stator tangentially clockwise magnetizing groups (9) are arranged in the following order: damping ring (10), stator radially inward magnetizing group (6), damping ring (10), stator tangentially counterclockwise magnetizing group (7), damping ring (10), stator radially outward magnetizing group (8), damping ring (10), stator tangentially clockwise magnetizing group (9), damping ring (10). This ensures that the annular rotor magnetizing group and the magnetizing groups with the same magnetizing method in the annular stator magnetizing group are axially aligned and guided by stator magnet array guide pins. (21) Fix it inside the stator back iron (16), and then fix the stator end cover (5) on the stator back iron (16) by the third connecting bolt (19); complete the centering adjustment between the stator and the rotor by adjusting the screw (20), and complete the installation of the stator, the axial limit of the stator magnet array and the centering adjustment between the stator and the rotor; the rotating shaft connecting flange (1) and the rotating shaft (3) are connected by the first connecting bolt (2), so that the magnetic reluctance composite permanent magnet thrust bearing can realize the transmission connection with the external components; the key structural parameters of the magnetic reluctance composite permanent magnet thrust bearing include the residual magnetism of the annular rotor magnetic group. B r1 Residual magnetism of the toroidal stator magnet group B r2 Inner diameter of the annular rotor magnetic assembly R 1. Outer diameter of the annular rotor magnetic assembly R 2. Axial length of the annular rotor magnetic assembly a 0. Radial thickness of the annular rotor magnetic assembly b 0. Axial movement of the annular rotor magnetic assembly dz、 Air gap between the annular rotor magnetic assembly and the annular stator magnetic assembly h、 Axial length of the single damping ring (10) in a single pair of annular rotor magnetic assemblies and annular stator magnetic assemblies c 0. Inner diameter of the ring stator magnetic assembly R 3. Outer diameter of the ring stator magnetic assembly R 4. Axial length of the annular stator magnetic assembly d 0. Radial thickness of the annular stator magnetic assembly e 0. Equivalent rotor magnetic strip n Number of stator magnetic strips after equivalent n Magnetization direction matrix of the annular rotor magnetic assembly β 1. Magnetization direction matrix of the ring stator magnet assembly β 2 、 Monte Carlo sampling points N Curvature correction factor k ; The second step is to convert a single pair of annular rotor magnetic groups and annular stator magnetic groups into magnetic force calculation models of magnets of equal height, and to establish a magnetic force calculation method for a single pair of non-equal length annular magnetic groups. First, take any annular rotor magnetic assembly and an annular stator magnetic assembly, both of which are equivalent to rectangular magnetic strips of equal height. Determine the height of the rotor and stator magnetic strips after the equivalent configuration: In the formula, L This refers to the equivalent heights of the rotor and stator magnetic strips; Determine the equivalent cross-sectional areas of the rotor and stator magnetic strips: In the formula, S 1 represents the cross-sectional area of ​​the equivalent rotor magnetic strip. S 2 represents the cross-sectional area of ​​the equivalent stator magnetic strip; Secondly, randomly select one sampling point from each of the equivalent rotor and stator magnetic strips, and calculate the angle between the direction of the line connecting the two sampling points and the horizontal direction. θ Distance between two sampling points r 12 : In the formula, z 1 represents the x-coordinate of the sampling point in the equivalent rotor magnetic strip. y 1 represents the ordinate of the sampling point in the equivalent rotor magnetic strip, z 2 represents the x-coordinate of the sampling point in the equivalent stator magnetic strip. y 2 represents the ordinate of the sampling point in the equivalent stator magnetic strip; Subsequently, the magnetic field strength at the sampling points in the equivalent rotor magnetic strip was determined. : In the formula, The magnetic field strength at the sampling point in the rotor magnetic strip after the equivalent operation. dH r1 The magnetic field strength at the sampling point in the equivalent rotor magnetic strip. The component along the direction of the line connecting two sampling points in the equivalent rotor magnetic strip and the equivalent stator magnetic strip; dH θ1 The magnetic field strength at the sampling point in the equivalent rotor magnetic strip. The component of the direction of the line connecting two sampling points in the vertically equivalent rotor magnetic strip and the vertically equivalent stator magnetic strip; J 1 represents the equivalent rotor magnetic stripe polarization intensity mode, the magnitude of which is equal to the remanence of the annular rotor magnetic assembly. B r1 ; β 11 The angle between the magnetization direction of the rotor magnetic strip and the horizontal direction after the equivalent operation; Next, the equivalent stator magnetic stripe magnetic polarization intensity vector is... The decomposition is performed along the lines parallel and perpendicular to the lines connecting the two sampling points in the equivalent rotor and stator magnetic strips, respectively: In the formula, This is the equivalent stator magnetic stripe magnetic polarization intensity vector, the magnitude of which is equal to the remanence of the toroidal stator magnetic array. B r2 The direction is parallel to the magnetization direction of the equivalent stator magnetic strip; This represents the equivalent stator magnetic stripe polarization intensity mode. β 21 The angle between the magnetization direction of the stator magnetic strip and the horizontal direction after the equivalent operation; Then, the static magnetic energy between the rotor and stator magnetic bars after the equivalent calculation is performed. W : Finally, regarding static magnetic energy W Regarding axial differentiation, calculate the equivalent axial force between a single pair of rotor and stator magnetic strips. F z : Step 3: Calculate the total axial force of the reluctance composite permanent magnet thrust bearing; First, determine the horizontal and vertical coordinates of each sampling point inside the equivalent rotor magnetic strip and each sampling point inside the equivalent stator magnetic strip: In the formula, z 1ik For the first i The first equivalent rotor magnetic strip inside k The x-coordinate of each sampling point; y 1ik For the first i The first equivalent rotor magnetic strip inside k The ordinate of each sampling point; z 2jk For the first j The first equivalent stator magnetic strip inside k The x-coordinate of each sampling point; y 2jk For the first j The first equivalent stator magnetic strip inside k The ordinate of each sampling point; u 1ik , u 2ik , u 1jk , And they are independent of each other. i, j ∈[1,2 … n]、 k ∈[1,2 … N]; Next, substitute the above formula into the second step to solve for the angle between the direction of the line connecting the two sampling points and the horizontal direction. θ Distance between two sampling points r 12 In the formula, the angle between the line connecting any two sampling points in the rotor magnetic strip and the stator magnetic strip after any equivalent transformation and the horizontal direction is obtained. θ ijk Distance between two sampling points r ijk ; Finally, the axial force between the equivalent rotor magnetic strip and the equivalent stator magnetic strip, calculated in the second step, will be used as the basis for further calculation. F z Discretize the formula and calculate the total axial force when the axial displacement of the rotor magnetic strip is dz after the equivalent process. F z,total : In the formula, F z,total The total axial force. β 1i For the first i The magnetization direction of the equivalent rotor magnetic strips β 2j For the first j The magnetization direction of the equivalent stator magnetic strip.

Images