Staggered self-centering hybrid magnetic thrust bearing structure and restoring force calculation method

Abstract

The invention belongs to the technical field of hybrid magnetic suspension bearings, and discloses a staggered self-centering hybrid magnetic thrust bearing structure and a restoring force calculation method. According to the staggered self-centering hybrid magnetic thrust bearing structure, a radial repulsive force ring is used for generating a restoring force which counteracts the unbalanced force of an axial repulsive force ring in the radial direction and the gravity of a rotor, and the stability of two offset freedom degrees in a radial plane of the rotor is maintained; the axial repulsive force rings are used for counteracting unbalanced loads of the radial repulsive force rings in the axial direction and external axial loads and maintaining the stability of the rotor in the axial direction; the axial electromagnetic bearing is used for counteracting the overturning moment of the rotor around the radial plane and maintaining the stability of the rotor around the transverse rotation freedom degree and the vertical rotation freedom degree. The restoring force calculation method does not need to depend on finite element simulation, is suitable for occasions where calculation resources are limited and parameters in the initial stage of design need to be rapidly iterated, and has good rapidity, practicability and convenience in actual engineering application.

Description

Technical Field

[0001] This invention belongs to the field of hybrid magnetic levitation bearing technology, and relates to a hybrid magnetic thrust bearing structure with misalignment and self-centering and a method for calculating restoring force. Background Technology

[0002] Hybrid magnetic thrust bearings are a combined magnetic levitation bearing system formed on the basis of active magnetic bearings, passive magnetic thrust bearings, and other auxiliary supports and stabilizing structures. They combine the advantages of active magnetic bearings (strong control capability and stable rotor levitation) with passive magnetic thrust bearings (strong residual magnetic field and high load-bearing capacity). This allows for smaller bearing sizes, material savings, and suitability for miniaturized and compact applications. Most existing hybrid magnetic thrust bearing designs use permanent magnets to provide a bias magnetic field and electromagnets to provide a control magnetic field to balance the load or external interference. In actual use, coupling often exists between the control magnetic field and the bias magnetic field, increasing coil power loss and heat generation, and there is a risk of demagnetization of the permanent magnets. Furthermore, in the design of hybrid magnetic thrust bearings, considering the axial thrust load requirements, the passive magnetic thrust bearing is designed with positive stiffness in the axial direction to generate a restoring force that counteracts external loads. However, according to Enshao's theorem, the magnetic force generated by the passive magnetic thrust bearing along the radial plane is inherently unstable. When the rotor experiences a slight radial displacement, the magnetic force generated by the permanent magnet will accelerate its slippage instead of restoring it to the center position. To achieve stable rotor levitation, the stability of the remaining degrees of freedom besides axial displacement and rotation must be considered. Currently, to achieve stability of the two degrees of freedom of rotor displacement along the radial plane, an additional radial electromagnetic bearing needs to be designed, increasing the design difficulty and structural complexity of hybrid magnetic thrust bearings. Therefore, proposing a hybrid magnetic thrust bearing structure design with radial misalignment self-centering function and its radial restoring force calculation method is of great significance.

[0003] To address the radial suspension problem of hybrid magnetic thrust bearings, Yang Jiafeng, Gong Gao, and Wu Rui proposed a five-degree-of-freedom suspension hybrid magnetic thrust bearing system in their patent "Five-Degree-of-Freedom Hybrid Magnetic Suspension Bearing, Motor and Control Method Thereof" (CN202310616587.8). This system utilizes permanent magnets to generate bias magnetic fields in the radial and axial air gaps between the rotor and stator, supplemented by a control magnetic field generated by control coils to achieve levitation. Its advantages include the ability to achieve multi-degree-of-freedom levitation, shortened shaft length, and improved shaft speed. However, the coupling relationship between the bias magnetic field generated by the permanent magnets and the control magnetic field generated by the coils in the proposed hybrid magnetic levitation bearing is complex, requiring various types of coils and placing high demands on the control system. To address the structural design issues of magnetic levitation thrust bearings, Zhu Longfei, Guo Zhenghua, Liu Kang, and others proposed an axial permanent magnet levitation thrust bearing composed of an easily detachable radial attractive magnetic ring and an axial repulsive magnetic ring in their patent "An Axial Permanent Magnet Levitation Thrust Permanent Magnet Bearing" (CN202411016278.8). Its advantage is that it can achieve high axial load levitation and reduce the difficulty of maintenance and repair. However, the magnetic levitation bearing structure proposed in the paper still requires an auxiliary bearing to maintain balance in the radial direction, and there is contact constraint in the rotor radial direction, which makes it impossible to achieve stable levitation.

[0004] In summary, the proposed method for calculating the restoring force of a misaligned self-centering hybrid magnetic thrust bearing structure is of great significance for solving the problems of complex magnetic circuits and large coupling interference in existing radial suspension structures, as well as for guiding the design of radial suspension structures of hybrid magnetic thrust bearings and the rapid calculation of radial restoring force. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention presents a misaligned self-centering hybrid magnetic thrust bearing structure and a method for calculating restoring force. The aim is to achieve stability in all degrees of freedom except for rotor axial offset and rotational degrees of freedom by proposing a hybrid magnetic bearing structure combining a radial repulsion ring, an axial repulsion ring, and an axial electromagnetic bearing. Specifically, the radial repulsion ring generates an unbalanced force to counteract the slight radial offset of the axial repulsion ring and the restoring force of the rotor's gravity, maintaining stability in the two offset degrees of freedom of the rotor along the radial plane; the axial repulsion ring counteracts the unbalanced load along the axial direction of the radial repulsion ring and external axial loads, maintaining stability in the rotor's axial direction; the axial electromagnetic bearings, installed at both ends of the hybrid magnetic thrust bearing, avoid excessive magnetic circuit coupling with the permanent magnets, counteract the overturning moment of the rotor about the radial plane, maintain stability in the rotor's lateral and vertical rotational degrees of freedom, and assist in bearing some external loads, enhancing the load capacity of the hybrid magnetic thrust bearing. Furthermore, to achieve rapid iteration of the initial structural parameters of the radial and axial repulsion rings, an analytical calculation method for the radial restoring force is proposed, comprehensively considering the effects of radial unbalanced force and rotor gravity in the axial repulsion ring. This provides important technical support for the design of the structural parameters of the repulsion ring in a misaligned self-centering hybrid magnetic thrust bearing. This calculation method does not rely on finite element simulation and is suitable for situations with limited computational resources and where rapid iteration of initial design parameters is required. It demonstrates good speed, practicality, and convenience in practical engineering applications.

[0006] The technical solution of this invention: A misaligned self-centering hybrid magnetic thrust bearing structure is assembled from a radial repulsion ring, an axial repulsion ring, and an axial electromagnetic bearing. The radial repulsion ring generates a restoring force to resist the radial offset of the rotor, maintaining the stability of the rotor's movement along the radial plane. The axial repulsion ring bears the external axial load and maintains the axial stability of the rotor. The axial electromagnetic bearings at both ends of the bearing assist in maintaining the stability of the rotor's rotation around the radial plane, offsetting the unbalanced overturning moment and part of the external axial load on the rotor. The misaligned self-centering hybrid magnetic thrust bearing structure includes a mounting shaft, bearing cover, protective bearing, round nut, conductor disc, end cover, stator core, axial coil, threaded sleeve, rotor radial magnet disc, rotor radial repulsion ring, stator radial repulsion ring, stator radial magnet disc, stator spacer, rotor axial magnet disc, rotor axial repulsion ring, stator axial repulsion ring, stator axial magnet disc, positioning bar, flat key, stator cylinder, and axial displacement sensor. During assembly, the rotor axial repulsion ring and stator axial repulsion ring are axially embedded in the annular grooves of the rotor axial magnet disk and stator axial magnet disk, respectively; the rotor radial repulsion ring and stator radial repulsion ring are radially embedded in the annular grooves of the rotor radial magnet disk and stator radial magnet disk, respectively; the axial electromagnetic bearing consists of a conductor disk, a stator core, an axial coil, and axial displacement sensors. Four axial displacement sensors, evenly arranged along the circumference of the stator core, detect the axial clearance between the stator core and the conductor disk, thereby obtaining the rotor winding... XY The real-time position of the plane; applied along the circumference of the stator core by four axial coils evenly arranged to a conductor disk mounted on the mounting shaft. X, +X, -Y, +Y The electromagnetic attraction from four directions, through the cooperation of two sets of axial electromagnetic bearings symmetrically arranged at both ends, generates resistance to the rotor's rotation. XY The resistive torque of planar overturning enables the rotor to rotate... XY Stability of planar rotation; The rotor axial magnet disk is circumferentially positioned on the mounting shaft via a flat key, and axial preload and positioning of the rotor axial magnet disk, rotor radial magnet disk, and conductor disk are achieved via round nuts. The stator axial magnet disk, stator spacer ring, and stator radial magnet disk are circumferentially positioned with the stator cylinder via positioning strips, and axial positioning and preload are achieved via threaded sleeves. The stator core is interference-fitted onto the inner stop of the end cover and fixed to the shaft end of the stator cylinder via the outer stop on the end cover. The protective bearing is embedded in the side annular groove of the end cover and axially positioned and preloaded via the bearing cover to prevent direct contact between the rotor and stator. Through the above structural design, the rotor of the hybrid magnetic thrust bearing can achieve misalignment self-centering and stable levitation in all directions. Its advantages are that the radial levitation of the rotor relies only on the repulsive force generated by the permanent magnet ring, the structure is simple, and no additional control system is required.

[0007] A method for calculating the restoring force of a misaligned self-centering hybrid magnetic thrust bearing structure is proposed. First, the key parameters of the misaligned self-centering hybrid magnetic thrust bearing are determined. Second, an analytical model of the radial restoring force of a single-sided radial repulsion ring is constructed, and the formula for calculating the restoring force is obtained. Third, an analytical model of the radial unbalanced force of a single-sided axial repulsion ring is constructed, and the formula for calculating the unbalanced force is obtained. Then, the formula for calculating the effective radial restoring force of the rotor on one side is obtained. Finally, the effective radial restoring force under the maximum rotor offset is obtained, and the load-bearing safety factor is calculated. This method comprehensively considers the influence of the radial unbalanced force of the axial repulsion ring and the rotor's gravity on the radial restoring force, enabling rapid calculation of the radial restoring force of the supporting rotor. In practical engineering applications, it has advantages such as low computational load and convenient operation.

[0008] The steps are as follows: The first step is to determine the key parameters of the misaligned self-centering hybrid magnetic thrust bearing; First, determine the structural parameters of the rotor radial repulsion ring and the stator radial repulsion ring: the inner radius of the stator radial repulsion ring is... R1. The outer radius of the rotor radial repulsion ring is R 2. The axial lengths of both the rotor radial repulsion ring and the stator radial repulsion ring are... L The radial thickness of both the rotor radial repulsion ring and the stator radial repulsion ring is H Then, the structural parameters of the rotor axial repulsion ring and the stator axial repulsion ring are determined: the outer radii of both the rotor axial repulsion ring and the stator axial repulsion ring are... r 1. The inner radius is... r 2. The axial length is all l The axial distance between the rotor radial repulsion ring and the stator radial repulsion ring is s Finally, the rotor's own weight is G The radial clearance at the bearing protection point is g The residual magnetism of the rotor radial repulsion ring, stator radial repulsion ring, rotor axial repulsion ring, and stator axial repulsion ring is all... B r Both relative permeability are μ r ; The second step is to construct an analytical model of the radial restoring force of a single-sided radial repulsion ring and obtain the formula for calculating the restoring force. First, define the intermediate function. f ( θ )as follows: (1) In the formula: δ 0 is the nominal air gap thickness, and δ 0= R 1- R 2. α Let be the section modulus of the rotor radial repulsion ring and the stator radial repulsion ring, and , μ r =1.05、 e For the rotor radial repulsion ring edge + X Directional offset; θ The circumferential position angle is initially equal to + X Directions coincide; Secondly, obtain the total magnetic energy of the air gap as a function of the offset. e Analytical expression of change W m ( e )as follows: (2) In the formula: R avg Let be the average radius of the rotor radial repulsion ring and the stator radial repulsion ring, and ; μ 0 is the permeability of free space, and μ 0=4 π ×10 -7 H / m; Then, for the analytical expression W m ( e The Taylor expansion is performed, and the calculation formula is as follows: (3) In the formula: W 0 represents the zero eccentric potential energy constant term, and ; ; W 2 is a linear stiffness term, and ; ; O ( e 3 ) represents a higher-order infinitesimal term; Finally, the radial restoring force as a function of the offset is obtained using the virtual displacement method. e Analytical expression of change f 1( e )as follows: (4) The third step is to construct an analytical model of radial unbalanced force of a single-sided axial repulsion ring and obtain the calculation formula for the unbalanced force. First, obtain the analytical expression for the radial distance between corresponding points of the rotor axial repulsion ring and the stator axial repulsion ring. δ ( θ )as follows: (5) In the formula: s The axial clearance between the rotor axial repulsion ring and the stator axial repulsion ring; It is the eccentric direction angle, and ; Then, it is assumed that all magnetic field energy is concentrated at the average radius of the rotor axial repulsion ring and the stator axial repulsion ring. r avg On the cylindrical surface, the analytical formula for the total magnetic energy of the air gap is... W n ( e )as follows: (6) In the formula: r avg Let be the average radius of the rotor axial repulsion ring and the stator axial repulsion ring, and ; β The leakage flux coefficient ranges from 0.1 to 0.3. Finally, the radial unbalanced force as a function of the offset is obtained using the virtual displacement method. e Analytical expression of changef 2( e )as follows: (7) Step 4: Obtain the calculation formula for the effective radial restoring force on one side of the rotor; Effective radial restoring force on one side of the rotor f m ( e )as follows: (8) Step 5: Obtain the effective radial restoring force under the maximum rotor offset and calculate the load-bearing safety factor; Due to the radial constraint of the protected bearing, the maximum radial offset of the rotor is the radial clearance at the protected bearing. e = g Substitute radial effective restoring force f m ( e The effective radial restoring force under the maximum rotor offset was calculated. F r The load-bearing safety factor is calculated by combining the rotor's own weight. S The calculation formula is as follows: (9) This completes the calculation of the restoring force of the misaligned self-centering hybrid magnetic thrust bearing structure.

[0009] The beneficial effects of this invention are that it proposes a misaligned self-centering hybrid magnetic thrust bearing, which is assembled from a radial repulsion ring, an axial repulsion ring, and an axial electromagnetic bearing. The radial repulsion ring generates a restoring force to resist the radial offset of the rotor, maintaining the stability of the rotor's movement along the radial plane. The structure is simple and requires no additional control system. The axial repulsion ring bears the external axial load and maintains the axial stability of the rotor, with high load-bearing capacity and no need for power supply. The axial electromagnetic bearings at both ends of the bearing assist in maintaining the stability of the rotor's rotation around the radial plane, offsetting the unbalanced overturning moment and part of the external axial load on the rotor. It provides good real-time position control performance for the rotor, helping to enhance the rotor's ability to resist changes in external load and achieve stable levitation in all directions. Furthermore, based on the structural characteristics of the proposed misaligned self-centering hybrid magnetic thrust bearing, an analytical calculation method for the radial restoring force is proposed, comprehensively considering the radial unbalanced force of the axial repulsion ring and the rotor's gravity. This method enables rapid calculation of the radial restoring force supporting the rotor, offering advantages such as low computational load and convenient operation in practical engineering applications. It provides important technical support for the initial rapid design iteration of the radial restoring force of the misaligned self-centering hybrid magnetic thrust bearing. Attached Figure Description

[0010] Figure 1 This is an assembly drawing of a misaligned self-centering hybrid magnetic thrust bearing; Figure 2 yes Figure 1 Middle YZ A sectional view of a plane; Figure 3 yes Figure 2 Schematic diagram of the rotor assembly; Figure 4 for Figure 2 A schematic diagram of real-time rotor position control via a central axial electromagnetic bearing; Figure 5 for Figure 2 Schematic diagram of the analytical model of the radial restoring force generated by a single-sided radial repulsion ring; Figure 6 for Figure 2 Schematic diagram of the analytical model of radial unbalanced force generated by a single-sided axial repulsion ring; Figure 7 A flowchart of a method for calculating the radial restoring force of a misaligned self-centering hybrid magnetic thrust bearing; In the diagram: 1-Mounting shaft, 2-Bearing cover, 3-Protective bearing, 4-Round nut, 5-Conductor disc, 6-End cover, 7-Stator core, 8-Axial coil, 9-Threaded sleeve, 10-Rotor radial magnet disc, 11-Rotor radial repulsion ring, 12-Stator radial repulsion ring, 13-Stator radial magnet disc, 14-Stator spacer, 15-Rotor axial magnet disc, 16-Rotor axial repulsion ring, 17-Stator axial repulsion ring, 18-Stator axial magnet disc, 19-Positioning bar, 20-Flat key, 21-Stator cylinder, 22-Axial displacement sensor. Detailed Implementation

[0011] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0012] This implementation case uses a misaligned self-centering hybrid magnetic thrust bearing with an axial rated load of 300N for analytical calculation of radial restoring force. The specific steps are as follows: The first step is to determine the key parameters of the misaligned self-centering hybrid magnetic thrust bearing; Figure 2 A type of misaligned self-centering hybrid magnetic thrust bearing along YZ A sectional view of the plane, wherein the inner radius of the stator radial repulsion ring 12 is... R 1 = 0.032m, the outer radius of the rotor radial repulsion ring 11 is R 2 = 0.0312m, axial length is L =0.012m, radial thickness is H =0.008m; the outer radii of the rotor axial repulsion ring 16 and the stator axial repulsion ring 17 are r1 = 0.0365m, inner radius is r 2 = 0.0245m, axial length is l =0.006m, axial spacing is s =0.001m; Rotor's own weight G =15N; Protects the radial clearance at 3 points on the bearing. g =0.0005m; Residual magnetism of rotor radial repulsion ring 11, stator radial repulsion ring 12, rotor axial repulsion ring 16 and stator axial repulsion ring 17 B r =1.41T, permeability μ r =1.05; The second step is to construct an analytical model of the radial restoring force of a single-sided radial repulsion ring and obtain the formula for calculating the restoring force. Substituting the known parameters into equations (1) to (4), we can see that... δ 0 = 0.0008m α =0.192、 R avg =0.0316m W 0 = 0.947 J W 1=0、 W 2 = -82049.616 N / m W 3=0, f ( θ The analytical expression is as follows: W m ( e The analytical expression is as follows: W m ( e The Taylor expansion of the analytical expression is as follows: f 1( e The analytical expression is as follows: The third step is to construct an analytical model of radial unbalanced force of a single-sided axial repulsion ring and obtain the calculation formula for the unbalanced force. Substituting the known parameters into equations (5) to (7), we can see that... r avg =0.0305m β =0.2, δ ( θ The analytical expression is as follows: W n ( e The analytical expression is as follows: f 2( e The analytical expression is as follows: Step 4: Obtain the calculation formula for the effective radial restoring force on one side of the rotor; Will f 1( e )and f 2( e Substituting into equation (8), we get, f m ( e The analytical expression is as follows: Step 5: Obtain the effective radial restoring force under the maximum rotor offset and calculate the load-bearing safety factor; Due to the radial constraint of the protected bearing, the maximum radial displacement of the rotor is equal to the clearance of the protected bearing. e = g Substituting 0.0005m into equation (9), the radial restoring force under the maximum rotor offset can be obtained. F r =20.976N, substituting into equation (10) yields the bearing safety factor. S =1.4. The calculation is now complete.

[0013] This calculation method comprehensively considers the effects of the radial unbalanced force of the axial repulsion ring and the rotor gravity, and can realize the rapid calculation of the radial restoring force of the supporting rotor. In practical engineering applications, it has the advantages of small calculation amount and convenient operation, and provides important technical support for the initial rapid design iteration of the radial restoring force of misaligned self-centering hybrid magnetic thrust bearings.

Claims

1. A misaligned self-centering hybrid magnetic thrust bearing structure, characterized in that, The misaligned self-centering hybrid magnetic thrust bearing structure includes a mounting shaft (1), a bearing cover (2), a protective bearing (3), a round nut (4), a conductor disc (5), an end cover (6), a stator core (7), an axial coil (8), a threaded sleeve (9), a rotor radial magnet disc (10), a rotor radial repulsion ring (11), a stator radial repulsion ring (12), a stator radial magnet disc (13), a stator spacer (14), a rotor axial magnet disc (15), a rotor axial repulsion ring (16), a stator axial repulsion ring (17), a stator axial magnet disc (18), a positioning bar (19), a flat key (20), a stator cylinder (21), and an axial displacement sensor (22). The rotor axial repulsion ring (16) and the stator axial repulsion ring (17) are axially embedded in the annular grooves of the rotor axial magnet disk (15) and the stator axial magnet disk (18), respectively; the rotor radial repulsion ring (11) and the stator radial repulsion ring (12) are radially embedded in the annular grooves of the rotor radial magnet disk (10) and the stator radial magnet disk (13), respectively; the axial electromagnetic bearing consists of a conductor disk (5), a stator core (7), an axial coil (8), and an axial displacement sensor (22). Four axial displacement sensors (22) evenly arranged along the circumference of the stator core (7) detect the axial gap between the stator core (7) and the conductor disk (5), thereby obtaining the rotor winding... XY The real-time position of the plane; applied along the circumference of the stator core (7) by four axial coils (8) evenly arranged to the conductor disk (5) mounted on the mounting shaft (1). X, +X, -Y, +Y The electromagnetic attraction from four directions, through the cooperation of two sets of axial electromagnetic bearings symmetrically arranged at both ends, generates resistance to the rotor's rotation. XY The resistive torque of planar overturning enables the rotor to rotate... XY Stability of planar rotation; The rotor axial magnet disk (15) is circumferentially positioned on the mounting shaft (1) by a flat key (20), and the rotor axial magnet disk (15), rotor radial magnet disk (10), and conductor disk (5) are axially preloaded and positioned by a round nut (4); the stator axial magnet disk (18), stator spacer (14), and stator radial magnet disk (13) are circumferentially positioned with the stator cylinder (21) by a positioning strip (19), and are axially positioned and preloaded by a threaded sleeve (9); the stator core (7) is interference-fitted onto the inner stop of the end cover (6), and is fixed to the shaft end of the stator cylinder (21) by the outer stop on the end cover (6); the protective bearing (3) is embedded in the side annular groove of the end cover (6), and is axially positioned and preloaded by the bearing cover (2) to prevent the rotor from directly contacting the stator.

2. A method for calculating the restoring force of a misaligned self-centering hybrid magnetic thrust bearing structure, characterized in that, The steps are as follows: The first step is to determine the key parameters of the misaligned self-centering hybrid magnetic thrust bearing; The second step is to construct an analytical model of the radial restoring force of a single-sided radial repulsion ring and obtain the formula for calculating the restoring force. The third step is to construct an analytical model of radial unbalanced force of a single-sided axial repulsion ring and obtain the calculation formula for the unbalanced force. Step 4: Obtain the calculation formula for the effective radial restoring force on one side of the rotor; Step 5: Obtain the effective radial restoring force under the maximum rotor offset and calculate the load safety factor.

3. The method for calculating the restoring force of the misaligned self-centering hybrid magnetic thrust bearing structure according to claim 2, characterized in that, The key parameters for determining the misaligned self-centering hybrid magnetic thrust bearing include: First, determine the structural parameters of the rotor radial repulsion ring (11) and the stator radial repulsion ring (12): the inner radius of the stator radial repulsion ring (12) is... R 1. The outer radius of the rotor radial repulsion ring (11) is R 2. The axial lengths of the rotor radial repulsion ring (11) and the stator radial repulsion ring (12) are both L The radial thickness of both the rotor radial repulsion ring (11) and the stator radial repulsion ring (12) is H Then, the structural parameters of the rotor axial repulsion ring (16) and the stator axial repulsion ring (17) are determined: the outer radii of the rotor axial repulsion ring (16) and the stator axial repulsion ring (17) are both r 1. The inner radius is... r 2. The axial length is all l The axial distance between the rotor radial repulsion ring (11) and the stator radial repulsion ring (12) is s Finally, the rotor's own weight is G The radial clearance at the protective bearing (3) is g The residual magnetism of the rotor radial repulsion ring (11), stator radial repulsion ring (12), rotor axial repulsion ring (16), and stator axial repulsion ring (17) is all... B r Both relative permeability are μ r .

4. The method for calculating the restoring force of the misaligned self-centering hybrid magnetic thrust bearing structure according to claim 3, characterized in that, The specific implementation process of the second step is as follows: First, define the intermediate function. f ( θ )as follows: In the formula: δ 0 is the nominal air gap thickness, and δ 0= R 1- R 2. α Let be the section modulus of the rotor radial repulsion ring (11) and the stator radial repulsion ring (12), and , μ r =1.05、 e For the rotor radial repulsion ring (11) along + X Directional offset; θ The circumferential position angle is initially equal to + X Directions coincide; Secondly, obtain the total magnetic energy of the air gap as a function of the offset. e Analytical expression of change W m ( e )as follows: In the formula: R avg Let be the average radius of the rotor radial repulsion ring (11) and the stator radial repulsion ring (12), and ; μ 0 is the free permeability, and μ 0=4 π ×10 -7 H / m; Then, for the analytical expression W m ( e The Taylor expansion is performed, and the calculation formula is as follows: In the formula: W 0 represents the zero eccentric potential energy constant term, and ; ; W 2 is a linear stiffness term, and ; ; O ( e 3 ) represents a higher-order infinitesimal term; Finally, the radial restoring force as a function of the offset is obtained using the virtual displacement method. e Analytical expression of change f 1( e )as follows: 。 5. The method for calculating the restoring force of the misaligned self-centering hybrid magnetic thrust bearing structure according to claim 4, characterized in that, The specific implementation process of the third step is as follows: First, obtain the analytical expression for the radial distance between corresponding points of the rotor axial repulsion ring (16) and the stator axial repulsion ring (17). δ ( θ )as follows: In the formula: s The axial clearance between the rotor axial repulsion ring (16) and the stator axial repulsion ring (17); It is the eccentric direction angle, and ; Then, it is assumed that all the magnetic field energy is concentrated in the average radius of the rotor axial repulsion ring (16) and the stator axial repulsion ring (17). r avg On the cylindrical surface, the analytical formula for the total magnetic energy of the air gap is... W n ( e )as follows: In the formula: r avg Let be the average radius of the rotor axial repulsion ring (16) and the stator axial repulsion ring (17), and ; β The leakage flux coefficient ranges from 0.1 to 0.

3. Finally, the radial unbalanced force as a function of the offset is obtained using the virtual displacement method. e Analytical expression of change f 2( e )as follows: 。 6. The method for calculating the restoring force of the misaligned self-centering hybrid magnetic thrust bearing structure according to claim 5, characterized in that, The specific implementation process of the fourth step is as follows: Effective radial restoring force on one side of the rotor f m ( e )as follows: 。 7. The method for calculating the restoring force of the misaligned self-centering hybrid magnetic thrust bearing structure according to claim 6, characterized in that, The specific implementation process of step five is as follows: Due to the radial constraint of the protective bearing (3), the maximum radial offset of the rotor is the radial clearance at the protective bearing (3). e = g Substitute radial effective restoring force f m ( e The effective radial restoring force under the maximum rotor offset was calculated. F r The load-bearing safety factor is calculated by combining the rotor's own weight. S The calculation formula is as follows: This completes the calculation of the restoring force of the misaligned self-centering hybrid magnetic thrust bearing structure.

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