A design method for an axial passive magnetic bearing with damping effect

Abstract

The present invention discloses a design method for an axial passive magnetic bearing with damping effect, wherein the axial passive magnetic bearing comprises at least one repulsive permanent magnet group and one damping permanent magnet group, wherein the damping permanent magnet group comprises a damping permanent magnet and a damping conductor. The design method comprises: determining the structural dimensions of the damping permanent magnet according to the structural requirements of the axial passive magnetic bearing; determining the candidate thickness of the damping conductor based on the structural requirements of the axial passive magnetic bearing, the magnetization parameters of the damping permanent magnet group and the structural dimensions of the damping permanent magnet; verifying the equivalent damping coefficient of the axial passive magnetic bearing based on the candidate thickness; determining the candidate thickness as the target thickness of the damping conductor when the equivalent damping coefficient is verified to be qualified; and designing the structure of the axial passive magnetic bearing according to the target thickness of the damping conductor. The design method provided by the embodiment of the present invention greatly improves the design accuracy and effectively ensures the use safety of the axial passive magnetic bearing with damping effect.

Description

Technical Field

[0001] The invention relates to the technical field of magnetic bearings, and in particular to a design method for an axial passive magnetic bearing with damping effect. Background Art

[0002] Compared with air static pressure bearings and mechanical bearings, magnetic bearings can achieve non-contact suspension support, with advantages such as simple structure, low processing and manufacturing precision requirements, low vibration and noise, and strong environmental adaptability. They have become important components of precision positioning workbenches. Magnetic bearings achieve stable suspension of the rotor part by balancing the gravity of the rotor part and the magnetic force of the stator part.

[0003] Existing magnetic bearings can be divided into active magnetic bearings and passive magnetic bearings according to whether the magnetic force is controllable. Active magnetic bearings can actively control the bearing stiffness and damping effect by controlling the size and direction of the current in the coil winding. They have the functions of active vibration control and active vibration suppression, but they need to be installed with high-precision and high-quality displacement sensors, controllers and power amplifiers. The system is complex, the cost is high, and the reliability is low. Passive magnetic bearings do not need to be used with components such as sensors and controllers. They have the advantages of simple structure, low cost, low power consumption, and high system reliability. They can meet the requirements of contactless suspension support of rotating motion machinery. However, most of the current patent documents only propose the structure of passive magnetic bearings, and lack corresponding analysis and design models. Summary of the invention

[0004] In order to overcome the problems existing in the related art, the present invention provides a design method of an axial passive magnetic bearing with damping effect.

[0005] According to a first aspect of the present invention, a design method for an axial passive magnetic bearing with damping effect is provided, wherein the axial passive magnetic bearing comprises at least one repulsive permanent magnet group and one damping permanent magnet group, wherein the damping permanent magnet group comprises a damping permanent magnet and a damping conductor, and the design method comprises:

[0006] Determining the structural dimensions of the damping permanent magnet according to the structural requirements of the axial passive magnetic bearing;

[0007] Determining a candidate thickness of the damping conductor based on the structural requirements of the axial passive magnetic bearing, the magnetization parameters of the damping permanent magnet group, and the structural dimensions of the damping permanent magnet;

[0008] Based on the candidate thickness, verifying an equivalent damping coefficient of the axial passive magnetic bearing;

[0009] When the equivalent damping coefficient is verified to be qualified, determining the candidate thickness as the target thickness of the damping conductor;

[0010] The structure of the axial passive magnetic bearing is designed according to the target thickness of the damping conductor.

[0011] In some embodiments, determining the candidate thickness of the damping conductor based on the structural requirements of the axial passive magnetic bearing, the magnetization parameters of the damping permanent magnet group, and the structural dimensions of the damping permanent magnet includes:

[0012] Based on the structural requirements of the axial passive magnetic bearing, the magnetization parameters of the damping permanent magnet group and the structural dimensions of the damping permanent magnet, first configuration information is established, wherein the first configuration information includes a first parameter, the first parameter is used to represent the thickness of the damping conductor, and the first configuration information is used to characterize the relationship between the damping force of the damping permanent magnet group and the first parameter;

[0013] The first parameter is derived based on the first configuration information, and the first parameter when the derivative is zero is used as a candidate thickness of the damping conductor.

[0014] In some embodiments, the structural requirements of the axial passive magnetic bearing include: an air gap is provided between the stator and the rotor of the axial passive magnetic bearing, the damping permanent magnet and the damping conductor are respectively located on both sides of the air gap and are arranged opposite to each other, the damping conductor is cylindrical, and the damping permanent magnet is annular and surrounds the circumference of the axial passive magnetic bearing;

[0015] The magnetization parameters of the damping permanent magnet group include the magnetization intensity of the damping permanent magnet;

[0016] The structural dimensions of the damping permanent magnet include the inner diameter and the outer diameter of the damping permanent magnet.

[0017] In some embodiments, verifying the equivalent damping coefficient of the axial passive magnetic bearing based on the candidate thickness includes:

[0018] Determining the equivalent damping coefficient of the axial passive magnetic bearing according to the candidate thickness;

[0019] Performing modal analysis on the axial passive magnetic bearing to determine the axial resonant speed of the axial passive magnetic bearing;

[0020] Determining a target equivalent damping coefficient according to the axial resonant speed;

[0021] The equivalent damping coefficient is compared with the target equivalent damping coefficient. When the equivalent damping coefficient is greater than the target equivalent damping coefficient, the equivalent damping coefficient is verified to be qualified.

[0022] In some embodiments, the design method further includes:

[0023] When the equivalent damping coefficient fails to be verified, the structural size of the damping permanent magnet is re-determined and the corresponding candidate thickness is determined until the equivalent damping coefficient passes the verification.

[0024] In some embodiments, the design method further includes:

[0025] Determining first design parameters of the repulsive permanent magnet group based on the mechanical performance requirements of the axial passive magnetic bearing;

[0026] Based on the first design parameter, determining a target stiffness of the repulsive permanent magnet group;

[0027] Determining second design parameters of the repulsive permanent magnet group based on structural requirements, magnetization property requirements, and magnetization parameters of the repulsive permanent magnet group;

[0028] Based on the second design parameter, determining the bearing stiffness of each of the repulsive permanent magnet groups;

[0029] Determining the number of the repulsive permanent magnet groups according to the target stiffness and the bearing stiffness of each of the repulsive permanent magnet groups;

[0030] The structure of designing the axial passive magnetic bearing according to the target thickness of the damping conductor comprises:

[0031] The structure of the axial passive magnetic bearing is designed according to the target thickness of the damping conductor and the number of the repulsive permanent magnet groups.

[0032] In some embodiments, there is a spherical shell-shaped air gap between the stator and the rotor of the axial passive magnetic bearing;

[0033] The magnetization property requirements of the repulsive permanent magnet groups include: the magnetization strengths of the repulsive permanent magnet groups are equal, so that the bearing stiffnesses of the repulsive permanent magnet groups are equal;

[0034] The determining the bearing stiffness of each of the repulsive permanent magnet groups based on the second design parameter comprises:

[0035] Establishing second configuration information, the second configuration information is used to characterize the integral unit of the axial load force of a single group of the repulsive permanent magnet group, the second configuration information includes a second parameter, and the second parameter is used to represent the axial displacement of the rotor;

[0036] Based on the second configuration information, third configuration information is determined, where the third configuration information is obtained by performing spherical area integration on the second configuration information, taking the derivative of the second parameter, and setting the second parameter to zero;

[0037] The bearing stiffness of a single group of the repulsive permanent magnet groups is determined according to the third configuration information.

[0038] In some embodiments, the structural requirements of the repulsive permanent magnet group include: the repulsive permanent magnet group is annular and surrounds the circumference of the damping permanent magnet group, each of the repulsive permanent magnet groups is arranged in sequence along the radial direction of the axial passive magnetic bearing, the repulsive permanent magnet group includes two sub-permanent magnet groups, the two sub-permanent magnet groups are respectively located on the stator and the rotor of the axial passive magnetic bearing and are arranged correspondingly, the sub-permanent magnet group includes a first permanent magnet and two second permanent magnets, the two second permanent magnets are respectively located on the radial sides of the first permanent magnet in the sub-permanent magnet group;

[0039] The magnetization property requirements of the repulsive permanent magnet group include: the magnetization direction of the first permanent magnet is parallel to the axial direction of the axial passive magnetic bearing, the magnetization direction of the second permanent magnet points to the N pole of the first permanent magnet in the sub-permanent magnet group, the magnetization direction of the first permanent magnet and the magnetization direction of the second permanent magnet form an angle, and in one of the repulsive permanent magnet groups, the magnetization strengths of the first permanent magnet and the second permanent magnet are equal;

[0040] The magnetization parameters of the repulsive permanent magnet group include the magnetization intensity of the first permanent magnet;

[0041] The second design parameters include the width of the spherical shell air gap and the reference radius and reference angle of the repulsive permanent magnet group.

[0042] In some embodiments, the first design parameter includes a maximum axial load force and a maximum allowable axial displacement;

[0043] The step of determining a target stiffness of the repulsive permanent magnet group based on the first design parameter includes:

[0044] Obtaining the deadweight of the rotor of the axial passive magnetic bearing and setting a safety factor;

[0045] A target stiffness of the axial passive magnetic bearing is determined based on the first design parameter, the deadweight of the rotor, and the safety factor.

[0046] According to a second aspect of the present invention, there is provided an axial passive magnetic bearing with damping effect, wherein the axial passive magnetic bearing is designed by using the design method described in any one of the above embodiments.

[0047] The beneficial effects of the present invention are:

[0048] In the design method provided by the present invention, the candidate thickness of the damping conductor is determined based on the requirements and parameters of multiple aspects of the axial passive magnetic bearing, and the equivalent damping coefficient of the candidate thickness is verified, thereby realizing the quantitative design of the axial passive magnetic bearing with damping effect, greatly improving the design accuracy, and effectively ensuring the safety of the use of the axial passive magnetic bearing. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0050] Figure 1 It is a schematic cross-sectional view of an axial passive magnetic bearing with damping effect according to an exemplary embodiment.

[0051] Figure 2 The figure is a flow chart of a method for designing an axial passive magnetic bearing with damping effect according to an exemplary embodiment.

[0052] Figure 3 FIG. 1 is a flowchart of step S120 according to an exemplary embodiment.

[0053] Figure 4 FIG. 1 is a flowchart of step S130 according to an exemplary embodiment.

[0054] Figure 5 The figure is a flow chart of a method for designing an axial passive magnetic bearing with damping effect according to another exemplary embodiment.

[0055] Figure 6 FIG. 4 is a flowchart of step S240 according to an exemplary embodiment.

[0056] Figure 7 FIG. 1 is a flowchart of step S220 according to an exemplary embodiment.

[0057] In the figure: 10-stator; 20-rotor; 30-air gap; 1-repulsive permanent magnet group; 1a-repulsive permanent magnet group one; 1b-repulsive permanent magnet group two; 11-sub permanent magnet group; 111-first permanent magnet; 112-second permanent magnet; 2-damping permanent magnet group; 201-damping permanent magnet; 202-damping conductor. DETAILED DESCRIPTION

[0058] like Figure 1As shown, the passive magnetic bearing generally includes a stator 10 and a rotor 20. Usually, permanent magnets (refer to the first permanent magnet 111 and the second permanent magnet 112) are respectively provided on the stator 10 and the rotor 20, and the stator 10 and the rotor 20 are axially spaced apart from each other in the magnetic bearing. Figure 1 The magnetization directions of the permanent magnets arranged opposite to each other in the y direction (as shown in the figure) are opposite, so that the permanent magnets on the stator 10 and the rotor 20 repel each other due to the magnetic field, and thus an air gap 30 is formed between the stator 10 and the rotor 20. In the working state of the passive magnetic bearing, the load and its own gravity on the rotor 20 are balanced with the repulsive force from the permanent magnets on the stator 10, and the rotor 20 can stably maintain a suspended state.

[0059] Continue to refer Figure 1 On the stator 10 and the rotor 20 of some passive magnetic bearings, damping permanent magnets 201 and damping conductors 202 are provided respectively. The damping permanent magnets 201 and the damping conductors 202 can provide a certain damping effect for the passive magnetic bearing. Specifically, when the rotor 20 is displaced and deflected, the damping conductor 202 will cut the magnetic field lines generated by the damping permanent magnets 201, and eddy currents will be excited in the damping conductor 202. These eddy currents will generate a magnetic field in the opposite direction to the original magnetic field, causing the rotor 20 to be subjected to a force in the opposite direction of its movement, so that the vibration generated by the passive magnetic bearing when subjected to external impact can be quickly weakened and eliminated, thereby avoiding the imbalance of the bearing and enhancing the resistance of the passive magnetic bearing to external interference.

[0060] In the past, the design of passive magnetic bearings with damping function often adopted empirical values, and roughly estimated the relevant design parameter values ​​according to the actual use of the magnetic bearings. However, this design method is qualitative design. On the one hand, the design accuracy is low, and it is difficult to ensure a good match with the usage scenario. On the other hand, the reliability is poor, and it is easy to have abnormal conditions and even cause safety accidents.

[0061] In order to solve the problems existing in the related art, an embodiment of the present invention provides a design method for an axial passive magnetic bearing with damping effect, wherein the axial passive magnetic bearing includes at least one repulsive permanent magnet group and a damping permanent magnet group, and the damping permanent magnet group includes a damping permanent magnet and a damping conductor. The design method includes: determining the structural dimensions of the damping permanent magnet according to the structural requirements of the axial passive magnetic bearing; determining the candidate thickness of the damping conductor based on the structural requirements of the axial passive magnetic bearing, the magnetization parameters of the damping permanent magnet group and the structural dimensions of the damping permanent magnet; verifying the equivalent damping coefficient of the axial passive magnetic bearing based on the candidate thickness; when the equivalent damping coefficient is verified to be qualified, determining the candidate thickness as the target thickness of the damping conductor; and designing the structure of the axial passive magnetic bearing according to the target thickness of the damping conductor. In the design method provided by the embodiment of the present invention, the candidate thickness of the damping conductor is determined based on the requirements and parameters of the axial passive magnetic bearing in multiple aspects, and the equivalent damping coefficient is verified for the candidate thickness, thereby realizing the quantitative design of the axial passive magnetic bearing with damping effect, greatly improving the design accuracy, and effectively ensuring the safety of the use of the axial passive magnetic bearing.

[0062] The technical scheme in the embodiment of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiment of the present invention. Obviously, the described embodiment is only a part of the embodiment of the present invention, not all of the embodiments. Based on the embodiment of the present invention, all other embodiments obtained by those skilled in the art without creative work belong to the protection scope of the present invention.

[0063] like Figure 2 As shown, this embodiment provides a design method for an axial passive magnetic bearing with a damping effect. The designed axial passive magnetic bearing includes at least one repulsive permanent magnet group (refer to Figure 1 The repulsive permanent magnet group 1) and a damping permanent magnet group (reference Figure 1 The design method of the damping permanent magnet group 2 shown in FIG. 2 specifically includes the following steps:

[0064] Step S110: Determine the structural dimensions of the damping permanent magnet according to the structural requirements of the axial passive magnetic bearing.

[0065] like Figure 1 As shown, when the axial passive magnetic bearing includes both the repulsive permanent magnet group 1 and the damping permanent magnet group 2, the structural dimensions of the repulsive permanent magnet group 1 and the damping permanent magnet group 2 need to be coordinated. In one example, the damping permanent magnet group 2 can be arranged on the radial inner side of the repulsive permanent magnet group 1 (refer to Figure 1 ), so that when the number of repulsive permanent magnet groups 1 is not determined, sufficient design space can be reserved for the repulsive permanent magnet groups 1. Of course, the damping permanent magnet group 2 can also be arranged radially outside the repulsive permanent magnet group 1 or at other positions, and there is no limitation on this.

[0066] The damping permanent magnet 201 is used to provide a bias magnetic field for generating eddy currents for the damping conductor 202. According to the structural requirements of the axial passive magnetic bearing, the structural dimensions of the damping permanent magnet 201 in the damping permanent magnet group 2 are first preset, and a group of more suitable values ​​are selected. If it is found in the subsequent design steps that the preset structural dimensions cannot meet the design requirements, the structural dimensions of the damping permanent magnet 201 can be adjusted at any time. When presetting the structural dimensions, the values ​​that are convenient for the subsequent design steps or the processing and manufacturing of the bearing can be preferentially selected, for example, the damping permanent magnet 201 of the existing specifications can be selected.

[0067] Step S120: Determine candidate thicknesses of the damping conductor based on structural requirements of the axial passive magnetic bearing, magnetization parameters of the damping permanent magnet group, and structural dimensions of the damping permanent magnet.

[0068] As mentioned above, the damping permanent magnet group 2 suppresses the displacement deflection of the rotor 20 by generating eddy currents in the damping conductor 202, and in the damping conductor 202, the thickness thereof directly affects the intensity and distribution of the eddy currents. In theory, the thicker the damping conductor 202 is, the more eddy currents it can accommodate, and the more significant the damping effect of the damping permanent magnet group 2 is. However, when the thickness of the damping conductor 202 is too large, the dynamic performance of the axial passive magnetic bearing will be seriously affected. Therefore, the overall design of the magnetic bearing can be comprehensively considered to determine a more suitable candidate thickness of the damping conductor 202. In one example, based on the structural requirements of the axial passive magnetic bearing, the magnetization parameters of the damping permanent magnet group 2 and the structural dimensions of the damping permanent magnet 201, configuration information can be established to characterize the relationship between the damping force of the damping permanent magnet group 2 and the thickness of the damping conductor 202, and the thickness when the damping force is maximum is selected as the candidate thickness of the damping conductor 202, wherein the configuration information can be obtained, for example, by deducing through physical formulas, or by other methods such as software simulation, without limitation.

[0069] Step S130: verifying the equivalent damping coefficient of the axial passive magnetic bearing based on the candidate thickness.

[0070] The equivalent damping coefficient determines the speed at which the magnetic bearing returns to the equilibrium state, is an indicator for measuring the energy dissipation capacity of the magnetic bearing, and is directly related to the operating stability of the magnetic bearing and its resistance to external interference. Therefore, after determining the candidate thickness of the damping conductor 202, the equivalent damping coefficient of the axial passive magnetic bearing needs to be verified based on the candidate thickness to determine whether the damping permanent magnet group 2 under the candidate thickness can ensure the stable operation of the magnetic bearing. The verification method of the equivalent damping coefficient can, for example, first obtain a critical value as the target equivalent damping coefficient, and then judge whether the equivalent damping coefficient under the current candidate thickness is qualified by comparing the numerical values, or directly substitute the equivalent damping coefficient under the current candidate thickness for verification, such as inputting its numerical value into the software for model simulation.

[0071] Step S140: When the equivalent damping coefficient is verified to be qualified, the candidate thickness is determined as the target thickness of the damping conductor.

[0072] When the equivalent damping coefficient is verified to be qualified, it indicates that the damping permanent magnet group 2 under the candidate thickness has the ability to ensure the stable operation of the magnetic bearing, so the candidate thickness can be used as the target thickness of the damping conductor 202 .

[0073] Step S300: designing the structure of the axial passive magnetic bearing according to the target thickness of the damping conductor.

[0074] In this design method, the candidate thickness of the damping conductor is determined based on the requirements and parameters of the axial passive magnetic bearing in many aspects, and the equivalent damping coefficient of the candidate thickness is verified. According to the determined target thickness of the damping conductor, the structure of the axial passive magnetic bearing can be designed more accurately, and the quantitative design of the axial passive magnetic bearing with damping effect is realized, which greatly improves the design accuracy and effectively ensures the safety of the axial passive magnetic bearing.

[0075] In one embodiment, if Figure 3 As shown, step S120 specifically includes the following steps:

[0076] Step S121: Based on the structural requirements of the axial passive magnetic bearing, the magnetization parameters of the damping permanent magnet group and the structural dimensions of the damping permanent magnet, establish first configuration information, the first configuration information including a first parameter, the first parameter is used to represent the thickness of the damping conductor, and the first configuration information is used to characterize the relationship between the damping force of the damping permanent magnet group and the first parameter.

[0077] In this step, the first configuration information can be obtained by deducing relevant physical formulas (described in detail later), and of course, it can also be established by other methods, which is not limited.

[0078] Step S122: Deriving the first parameter based on the first configuration information, and taking the first parameter when the derivative is zero as a candidate thickness of the damping conductor.

[0079] In the damping permanent magnet group 2, as the thickness of the damping conductor 202 gradually increases, the damping force of the damping permanent magnet group 2 first increases and then gradually decreases, so there is a thickness value of the damping conductor 202 that makes the damping force of the damping permanent magnet group 2 reach the maximum. In this regard, first configuration information can be established to represent the relationship between the damping force of the damping permanent magnet group 2 and the thickness of the damping conductor 202, and then the thickness of the damping conductor 202 is derived in the first configuration information. When the derivative is zero, the damping force of the damping permanent magnet group 2 reaches the maximum, and the thickness value of the damping conductor 202 corresponding to this time can be used as the candidate thickness of the damping conductor 202.

[0080] In one embodiment, if Figure 1 As shown, the structural requirements of the axial passive magnetic bearing include: an air gap 30 is provided between the stator 10 and the rotor 20 of the axial passive magnetic bearing, the damping permanent magnet 201 and the damping conductor 202 are respectively located on both sides of the air gap 30 and are arranged opposite to each other, the damping conductor 202 is cylindrical, and the damping permanent magnet 201 is annular and surrounds the circumference of the axial passive magnetic bearing. The magnetization parameters of the damping permanent magnet group 2 include the magnetization intensity of the damping permanent magnet 201. The structural dimensions of the damping permanent magnet 201 include the inner diameter and the outer diameter of the damping permanent magnet 201.

[0081] At this time, the first configuration information can be established according to the virtual displacement principle. According to the virtual displacement principle, the derivative of the magnetic field energy at the air gap 30 in the axial displacement is the damping force, so the expression of the magnetic field energy at the air gap 30 can be first determined to establish the first configuration information. The expression of the magnetic field energy at the air gap 30 is shown as follows:

[0082]

[0083] Where W is the magnetic field energy at the air gap, R ci and R co are the inner diameter and outer diameter of the damping permanent magnet 201, δ is the thickness of the air gap, h sl is the thickness of the damping conductor 202 (i.e., the first parameter), z is the axial displacement of the rotor 20, and B cz is the main magnetic field strength of the damping permanent magnet 201, B czlou is the leakage magnetic field strength of the damping permanent magnet 201, μ0 is the vacuum magnetic permeability (μ0=4π×10 -7 H / m).

[0084] Among them, B cz and B czlou Can be determined by the following formula:

[0085]

[0086] In the formula, B r1 is the magnetization intensity of the damping permanent magnet 201 .

[0087] In the expression of the magnetic field energy W at the air gap, the axial displacement z of the rotor 20 is derived to obtain the first configuration information as shown in the following formula:

[0088]

[0089] In the formula, F d is the damping force of the damping permanent magnet group.

[0090] Therefore, by solving the following differential equation, the candidate thickness of the damping conductor 202 can be obtained:

[0091]

[0092] In one embodiment, if Figure 4 As shown, step S130 specifically includes the following steps:

[0093] Step S131: Determine the equivalent damping coefficient of the axial passive magnetic bearing according to the candidate thickness.

[0094] Assume that the relationship between the displacement s and time t generated by the rotor axial vibration is expressed as:

[0095]

[0096] in, is the maximum displacement caused by axial vibration, is the angular frequency of vibration.

[0097] Then the speed v generated by the rotor axial vibration is:

[0098]

[0099] According to the law of conservation of energy, the eddy current loss consumed by the rotor is the mechanical energy of vibration W. d , whose expression is:

[0100]

[0101] Assume that the equivalent damping coefficient is C d , then the mechanical energy W d It can also be expressed as:

[0102]

[0103] in, is the maximum displacement caused by axial vibration, is the speed generated by axial vibration.

[0104] From this we can get the equivalent damping coefficient C d for:

[0105]

[0106] Step S132: performing modal analysis on the axial passive magnetic bearing to determine the axial resonant speed of the axial passive magnetic bearing.

[0107] The purpose of setting the damping permanent magnet group 2 is to suppress the axial vibration of the rotor part. Therefore, the thickness h of the damping conductor 202 can be set to slPerform modal analysis on the axial passive magnetic bearing of the candidate thickness and obtain the axial vibration frequency n of the rotor part under this condition. z , used to verify the thickness h of the damping conductor 202 sl When the thickness is a candidate, whether the damping effect of the damping permanent magnet group 2 can meet the axial vibration frequency requirement. The modal analysis of the axial passive magnetic bearing can be implemented by software simulation and other methods, which is not limited in this embodiment.

[0108] Step S133: Determine a target equivalent damping coefficient according to the axial resonance speed.

[0109] The expression of the target equivalent damping coefficient is shown as follows:

[0110]

[0111] In the formula, C d0 is the target equivalent damping coefficient, λ d is the logarithmic attenuation rate (usually in the range of 0.7 to 1) required for damping the permanent magnet group 2 , and m is the deadweight of the rotor 20 .

[0112] Step S134: comparing the equivalent damping coefficient with the target equivalent damping coefficient. When the equivalent damping coefficient is greater than the target equivalent damping coefficient, the equivalent damping coefficient is verified to be qualified.

[0113] When C d Greater than C d0 It indicates that the damping permanent magnet group 2 can effectively suppress the axial vibration of the rotor part, has the ability to ensure the stable operation of the magnetic bearing, and the equivalent damping coefficient is verified to be qualified.

[0114] In one embodiment, the design method further specifically includes the following steps:

[0115] Step S150: When the equivalent damping coefficient verification fails, the structural dimensions of the damping permanent magnet are re-determined and the corresponding candidate thickness is determined until the equivalent damping coefficient verification passes.

[0116] The failure of the equivalent damping coefficient verification indicates that the damping permanent magnet group 2 is difficult to effectively suppress the axial vibration of the rotor part at this time, and the current candidate thickness of the damping conductor 202 cannot meet the design requirements. Therefore, it is possible to return to step S110, adjust the structural dimensions of the damping permanent magnet 201, redetermine its structural dimension value, and then redetermine the corresponding candidate thickness, and perform the equivalent damping coefficient verification again until the equivalent damping coefficient verification is qualified.

[0117] In one embodiment, if Figure 1As shown, in addition to the damping permanent magnet group 2, the axial passive magnetic bearing also includes at least one repulsive permanent magnet group 1. As mentioned above, the repulsive permanent magnet group 1 provides an axial load force for the axial passive magnetic bearing through the mutual repulsion of the magnetic field, so that the rotor 20 can maintain a stable suspension state, so the repulsive permanent magnet group 1 also needs to be designed. Figure 5 As shown, the design method further specifically includes the following steps:

[0118] Step S210: Determine the first design parameter of the repulsive permanent magnet group based on the mechanical performance requirements of the axial passive magnetic bearing.

[0119] The requirements for mechanical properties of axial passive magnetic bearings vary depending on factors such as the location, purpose, and use environment. Therefore, when designing axial passive magnetic bearings, the requirements for mechanical properties (such as axial load and operating stability) can be determined first, and then the value of the first design parameter (such as maximum axial load and maximum allowable axial displacement) can be determined based on the mechanical performance requirements. The standard for determining the value of the first design parameter can be set according to actual conditions and is not limited here. For example, for the maximum axial load, 1.5-2.0 times the commonly used axial load of the axial passive magnetic bearing in the actual working environment can be set as its maximum axial load. For the maximum allowable axial displacement, for example, the displacement critical value of the unbalanced rotor 20 and the maximum allowable displacement fluctuation value of the rotating part of the equipment connected to the rotor 20 can be comprehensively considered, and 0.7-0.8 times the minimum of the two can be taken.

[0120] Step S220: Determine the target stiffness of the repulsive permanent magnet group based on the first design parameter.

[0121] Stiffness refers to the elastic properties of the bearing, which can reflect the ability of the bearing to resist deformation. The greater the stiffness, the smaller the deformation of the bearing when it is under load. Normally, the bearing is used to achieve movement between the components connected to the stator 10 and the components connected to the rotor 20. Therefore, the higher the stiffness of the bearing, the less likely the movement between the two parts will be disturbed by the outside world, thereby better ensuring the normal operation of the mechanical equipment. Based on the first design parameter, the target stiffness of the repulsive permanent magnet group 1 can be obtained, which can ensure that the axial passive magnetic bearing can meet its mechanical performance requirements and has good operating stability. The target stiffness can be derived or characterized according to the operational relationship between it and the first design parameter (described in detail later), or it can also be simulated using relevant software to output a target stiffness value based on the first design parameter.

[0122] Step S230: Determine the second design parameters of the repulsive permanent magnet group based on the structural requirements, magnetization property requirements and magnetization parameters of the repulsive permanent magnet group.

[0123] The space used for bearing installation and operation in mechanical equipment is often limited, so the value of the second design parameter of the axial passive magnetic bearing (such as the relevant structural dimensions of the repulsive permanent magnet group) can be determined first. In one example, the second design parameter may include the radius, radial thickness, and thickness of the bearing air gap of the permanent magnet in the repulsive permanent magnet group 1. The value of the determined second design parameter can make the size of the magnetic bearing less than or equal to its spatial size, so that the repulsive permanent magnet group 1 can meet the spatial limitations of the axial passive magnetic bearing. The specific value of the second design parameter can be set according to actual conditions. For example, when determining the radial thickness of the permanent magnet, the radial thickness of the permanent magnet of the existing specifications can be preferentially selected to facilitate subsequent bearing processing and manufacturing.

[0124] Step S240: Determine the bearing stiffness of each repulsive permanent magnet group based on the second design parameter.

[0125] As mentioned above, the repulsive permanent magnet groups 1 on the stator 10 and the rotor 20 of the magnetic bearing repel each other and thus provide load capacity for the magnetic bearing. Therefore, the bearing stiffness of each repulsive permanent magnet group 1 can be determined to ensure that the load capacity provided by the repulsive permanent magnet group 1 can meet the needs of the axial passive magnetic bearing. After determining the value of the second design parameter, the bearing stiffness of each repulsive permanent magnet group 1 in the axial passive magnetic bearing can be obtained based on the second design parameter, and the sum of the bearing stiffness of each repulsive permanent magnet group 1 is the stiffness that the repulsive permanent magnet group 1 in the axial passive magnetic bearing can provide. The method for determining the bearing stiffness of the repulsive permanent magnet group 1 can refer to the target stiffness of the aforementioned axial passive magnetic bearing, and can be obtained by means of an operational relationship with the second design parameter (described in detail later) or software simulation.

[0126] Step S250: Determine the number of repulsive permanent magnet groups according to the target stiffness and the bearing stiffness of each repulsive permanent magnet group.

[0127] When determining the number of repulsive permanent magnet groups 1, a larger number of groups can be appropriately selected so that the sum of the bearing stiffness of each repulsive permanent magnet group 1 is greater than the target stiffness of the axial passive magnetic bearing, ensuring that the stiffness provided by the repulsive permanent magnet group 1 can always meet the target stiffness requirements.

[0128] At this time, step S300 specifically includes the following steps:

[0129] Step S301: designing the structure of the axial passive magnetic bearing according to the target thickness of the damping conductor and the number of repulsive permanent magnet groups.

[0130] In one embodiment, if Figure 1As shown, the opposite end surfaces on the stator 10 and the rotor 20 are both spherical surfaces, and the spherical surface on the stator 10 coincides with the spherical surface on the rotor 20, so that a spherical shell-shaped air gap 30 is provided between the stator 10 and the rotor 20 of the axial passive magnetic bearing. The spherical surface on the stator 10 can be an outward convex spherical surface, and the spherical surface on the rotor 20 corresponds to an inward concave spherical surface (refer to Figure 1 ), of course, the spherical surface on the stator 10 can also be a concave spherical surface, in which case the spherical surface on the rotor 20 corresponds to a convex spherical surface (not shown in the drawings), and this embodiment does not limit this. Since the centers of the two spherical surfaces coincide, when the rotor 20 is angularly deflected during rotation, the direction of the repulsive force on the rotor 20 is always along its axial direction and passes through the center of the spherical surface, so that the spherical shell air gap 30 can be kept uniform, thereby eliminating the torsional moment and improving the suspension accuracy of the magnetic bearing. In addition, the relative magnetic pole area of ​​the magnetic bearing can be significantly increased, thereby improving the bearing stiffness and bearing capacity.

[0131] At the same time, the magnetization property requirements of the repulsive permanent magnet group 1 specifically include: the axial passive magnetic bearing includes a plurality of repulsive permanent magnet groups 1 (reference Figure 1 As shown in the figure, the magnetization intensity and radial thickness of each repulsive permanent magnet group 1 are equal. According to the calculation formula of the stiffness of the permanent magnet, the bearing stiffness of each repulsive permanent magnet group 1 is equal, so only the bearing stiffness of a single repulsive permanent magnet group 1 can be calculated, so as to greatly reduce the amount of calculation and simplify the design process.

[0132] At this time, if Figure 6 As shown, step S240 specifically includes the following steps:

[0133] Step S241: establishing second configuration information, the second configuration information is used to characterize the integral unit of the axial load force of a single group of repulsive permanent magnets, the second configuration information includes a second parameter, and the second parameter is used to represent the axial displacement of the rotor.

[0134] Since the repulsive permanent magnet group 1 is arranged radially outside the damping permanent magnet group 2 and is in a circular ring shape on the spherical surface, the various physical property parameters of the repulsive permanent magnet group 1 can be expressed in integral form. Among them, the second configuration information can be first established to characterize the integral unit of the axial load force of the single repulsive permanent magnet group 1. The second configuration information can be derived from the relevant physical formula (described in detail later), and of course it can also be established in other ways, which is not limited.

[0135] Step S242: Based on the second configuration information, determine the third configuration information, where the third configuration information is obtained by performing spherical area integration on the second configuration information, derivatizing the second parameter, and setting the second parameter to zero.

[0136] Based on the second configuration information, the spherical area is integrated to obtain the axial load force of the single repulsive permanent magnet group 1. As mentioned above, the bearing stiffness can reflect the ability of the bearing to resist deformation, which can be expressed by the ratio between the load and the displacement. Therefore, the second parameter is further differentiated and the second parameter is set to zero (that is, the axial displacement of the rotor 20 is zero) to obtain the third configuration information, which can be used to characterize the bearing stiffness of the repulsive permanent magnet group 1.

[0137] Step S243: Determine the bearing stiffness of the single repulsive permanent magnet group according to the third configuration information.

[0138] According to the obtained third configuration information, by numerically substituting or transforming the third configuration information, the value or expression of the bearing stiffness of a single repulsive permanent magnet group 1 can be determined, and then the sum of the bearing stiffnesses of each repulsive permanent magnet group 1 can be determined.

[0139] In one embodiment, if Figure 1 As shown, the structural requirements of the repulsive permanent magnet group 1 include: the repulsive permanent magnet group 1 is annular and surrounds the circumference of the damping permanent magnet group 2, and each repulsive permanent magnet group 1 is along the radial direction of the axial passive magnetic bearing ( Figure 1 The repulsive permanent magnet group 1 includes two sub-permanent magnet groups 11, which are respectively located on the stator 10 and the rotor 20 of the axial passive magnetic bearing and are arranged correspondingly. The sub-permanent magnet group 11 includes a first permanent magnet 111 and two second permanent magnets 112, and the two second permanent magnets 112 are respectively located on both sides of the radial direction of the first permanent magnet 111 in the sub-permanent magnet group 11. The magnetization property requirements of the repulsive permanent magnet group 1 include: the magnetization direction of the first permanent magnet 111 is parallel to the axial direction of the axial passive magnetic bearing ( Figure 1 The magnetization direction of the second permanent magnet 112 points to the N pole of the first permanent magnet 111 in the sub-permanent magnet group 11, and an angle is formed between the magnetization direction of the first permanent magnet 111 and the magnetization direction of the second permanent magnet 112. In a repulsive permanent magnet group 1, the magnetization strengths of the first permanent magnet 111 and the second permanent magnet 112 are equal. The magnetization parameters of the repulsive permanent magnet group 1 include the magnetization strength of the first permanent magnet 111.

[0140] A first permanent magnet 111 and a second permanent magnet 112 are arranged in the sub-permanent magnet group 11 to form a Halbach array structure together. On the one hand, it can effectively improve the air gap magnetic field fluctuation of the magnetic bearing caused by the splicing of permanent magnets, improve the uniformity of the air gap magnetic density, and thus improve the suspension accuracy of the magnetic bearing. On the other hand, it can also enable the stator 10 and the rotor 20 to produce a strong magnetic concentration effect, which can significantly enhance the air gap magnetic field strength, further improve the bearing capacity and stiffness of the magnetic bearing, and achieve the technical effect of both high suspension accuracy and high bearing stiffness.

[0141] According to magnetostatics theory, the surface magnetic charge density of the first permanent magnet 111 and the second permanent magnet 112 at the spherical shell air gap 30 can be expressed based on the magnetization intensity of the first permanent magnet 111, so as to establish the first configuration information. The expressions are shown in the following formulas:

[0142]

[0143]

[0144] In the formula, σ * c is the surface magnetic charge density of the first permanent magnet 111, M is the magnetization intensity, σ * s is the surface magnetic charge density of the second permanent magnet 112, and α is the angle between the normal direction of the end face of the permanent magnet ring and the magnetization direction.

[0145] The second design parameters include the width of the spherical shell air gap 30 and the reference radius and reference angle of the repulsive permanent magnet group 1. The reference radius of the repulsive permanent magnet group 1 is the radius of the permanent magnet group located at the radially outermost side of the axial passive magnetic bearing (reference Figure 1 The outer diameter of the repulsive permanent magnet group 1b) shown in the figure, the reference angle can be approximately regarded as the average value of the angle formed by the intersection of the inner diameter and outer diameter of each repulsive permanent magnet group 1 and the spherical surface at the center of the spherical surface. The second configuration information established based on the above second design parameters can represent the integral unit of the axial load force of a single group of repulsive permanent magnet groups 1. At this time, the second configuration information can be shown as follows:

[0146]

[0147] Where, df z is the integral of the axial load force of a single group of repulsive permanent magnets, σ * cup and σ * cdown are the surface magnetic charge density of the first permanent magnet 111 on the spherical surface of the stator 10 and the rotor 20, σ * sup and σ * sdown are the surface magnetic charge density of the second permanent magnet 112 on the spherical surface of the stator 10 and the rotor 20, respectively; θ is the spatial angle between the magnetic charges of any two points on the spherical surface of the permanent magnet 112 on the stator 10 and the rotor 20; ds up and ds down They are the spherical surface area integrals on the spherical surfaces of the stator 10 and the rotor 20 respectively.

[0148] Among them, ds up and ds down Can be determined by the following formula:

[0149]

[0150]

[0151] In the formula, R up and R down are the reference radius of the repulsive permanent magnet group 1 on the spherical surface of the stator 10 and the rotor 20, θ up and θ down are the reference angles of the repulsive permanent magnet group 1 on the spherical surfaces of the stator 10 and the rotor 20 respectively.

[0152] By integrating the spherical area based on the second configuration information, the axial load force of the single repulsive permanent magnet group 1 can be obtained, and its expression is as follows:

[0153] In the formula, f z is the axial load force of the single repulsive permanent magnet group 1.

[0154]

[0155] Continue to derive the second parameter and set the second parameter (z) to zero to obtain the third configuration information shown below to represent the bearing stiffness K of the repulsive permanent magnet group 1: b :

[0156]

[0157] In one embodiment, the first design parameters include a maximum axial load force and a maximum allowable axial displacement. The target stiffness of the axial passive magnetic bearing can be obtained based on the first design parameters. The target stiffness can ensure that the axial passive magnetic bearing can meet its mechanical performance requirements and have good operating stability.

[0158] like Figure 7 As shown, step S220 specifically includes the following steps:

[0159] Step S221: Obtain the deadweight of the rotor of the axial passive magnetic bearing and set the safety factor.

[0160] Since the axial passive magnetic bearing is usually placed vertically, the gravity of its moving part is in the same direction as the axial load, and the load force required is the superposition of gravity and axial load. Therefore, when designing the axial passive magnetic bearing, it is also necessary to obtain the deadweight of the rotor 20. In addition, in order to ensure that the bearing can be stably and reliably suspended in the axial direction, a certain safety factor can be set additionally based on the superposition of gravity and axial load.

[0161] Step S222: Determine the target stiffness of the axial passive magnetic bearing based on the first design parameter, the deadweight of the rotor and the safety factor.

[0162] The calculation formula for the target stiffness of the axial passive magnetic bearing is shown below:

[0163]

[0164] In the formula, k sc is the safety factor (can be between 2 and 3), F w is the maximum axial load force, m is the deadweight of the rotor 20, g is the gravitational acceleration, △z max is the maximum allowable axial displacement.

[0165] When the bearing stiffness K of each repulsive permanent magnet group 1 b When they are equal, the target stiffness K of the axial passive magnetic bearing can be calculated a and the bearing stiffness K of the single repulsive permanent magnet group 1 b The multiple relationship of , determines the number N of the repulsive permanent magnet group 1. The number N of the repulsive permanent magnet group 1 can be determined by the following formula:

[0166]

[0167] It can be understood that the parameter values ​​in the above design method can refer to the structural values ​​of the existing passive magnetic bearing, and on this basis, the above design method can be used for calculation to obtain a suitable size result (target thickness of the damping conductor 202) to meet the requirements of design accuracy and safety of use.

[0168] like Figure 1 As shown, this embodiment provides an axial passive magnetic bearing with damping effect, which can be designed using the design method in any of the above embodiments. During the design process, the candidate thickness of the damping conductor is determined based on the requirements and parameters of the axial passive magnetic bearing in multiple aspects, and the equivalent damping coefficient of the candidate thickness is verified, thereby realizing the quantitative design of the axial passive magnetic bearing with damping effect. The axial passive magnetic bearing with damping effect provided in this embodiment has high design accuracy and can effectively ensure the safety of the use of the axial passive magnetic bearing.

[0169] The contents described in the embodiments of this specification are merely an enumeration of implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms described in the embodiments. The protection scope of the present invention also includes equivalent technical means that can be thought of by those skilled in the art based on the inventive concept.

Claims

1. A design method for an axial passive magnetic bearing with damping effect, characterized in that: The axial passive magnetic bearing comprises at least one repulsive permanent magnet group (1) and a damping permanent magnet group (2), the damping permanent magnet group (2) comprising a damping permanent magnet (201) and a damping conductor (202), and the design method comprises: Determining the structural dimensions of the damping permanent magnet (201) according to the structural requirements of the axial passive magnetic bearing; Determining a candidate thickness of the damping conductor (202) based on the structural requirements of the axial passive magnetic bearing, the magnetization parameters of the damping permanent magnet group (2) and the structural dimensions of the damping permanent magnet (201); Based on the candidate thickness, verifying an equivalent damping coefficient of the axial passive magnetic bearing; When the equivalent damping coefficient is verified to be qualified, determining the candidate thickness as the target thickness of the damping conductor (202); Designing the structure of the axial passive magnetic bearing according to the target thickness of the damping conductor (202); Wherein, determining the candidate thickness of the damping conductor (202) based on the structural requirements of the axial passive magnetic bearing, the magnetization parameters of the damping permanent magnet group (2) and the structural dimensions of the damping permanent magnet (201) comprises: Based on the structural requirements of the axial passive magnetic bearing, the magnetization parameters of the damping permanent magnet group (2) and the structural dimensions of the damping permanent magnet (201), first configuration information is established, the first configuration information comprising a first parameter, the first parameter being used to represent the thickness of the damping conductor (202), the first configuration information being used to characterize the relationship between the damping force of the damping permanent magnet group (2) and the first parameter; Derivative the first parameter based on the first configuration information, and use the first parameter when the derivative is zero as a candidate thickness of the damping conductor (202); The verifying the equivalent damping coefficient of the axial passive magnetic bearing based on the candidate thickness includes: Determining the equivalent damping coefficient of the axial passive magnetic bearing according to the candidate thickness; Performing modal analysis on the axial passive magnetic bearing to determine the axial resonant speed of the axial passive magnetic bearing; Determining a target equivalent damping coefficient according to the axial resonant speed; The equivalent damping coefficient is compared with the target equivalent damping coefficient. When the equivalent damping coefficient is greater than the target equivalent damping coefficient, the equivalent damping coefficient is verified to be qualified.

2. The design method according to claim 1, characterized in that: The structural requirements of the axial passive magnetic bearing include: an air gap (30) is provided between the stator (10) and the rotor (20) of the axial passive magnetic bearing; the damping permanent magnet (201) and the damping conductor (202) are respectively located on both sides of the air gap (30) and are arranged opposite to each other; the damping conductor (202) is cylindrical; and the damping permanent magnet (201) is annular and surrounds the circumference of the axial passive magnetic bearing; The magnetization parameters of the damping permanent magnet group (2) include the magnetization intensity of the damping permanent magnet (201); The structural dimensions of the damping permanent magnet (201) include an inner diameter and an outer diameter of the damping permanent magnet (201).

3. The design method according to claim 1, characterized in that: The design method further comprises: When the equivalent damping coefficient fails to be verified, the structural dimensions of the damping permanent magnet (201) are re-determined and the corresponding candidate thickness is determined until the equivalent damping coefficient passes the verification.

4. The design method according to claim 1, characterized in that: The design method further comprises: Based on the mechanical performance requirements of the axial passive magnetic bearing, determining the first design parameters of the repulsive permanent magnet group (1); wherein the first design parameters include the maximum axial load force and the maximum allowable axial displacement; Based on the first design parameter, a target stiffness of the repulsive permanent magnet group (1) is determined; wherein, based on the first design parameter, determining the target stiffness of the repulsive permanent magnet group (1) comprises: obtaining the deadweight of the rotor (20) of the axial passive magnetic bearing and setting a safety factor; based on the first design parameter, the deadweight of the rotor (20) and the safety factor, determining the target stiffness of the axial passive magnetic bearing; Based on the structural requirements, magnetization property requirements and magnetization parameters of the repulsive permanent magnet group (1), a second design parameter of the repulsive permanent magnet group (1) is determined; wherein a spherical shell air gap (30) is provided between the stator (10) and the rotor (20) of the axial passive magnetic bearing; the magnetization property requirements of the repulsive permanent magnet group (1) include: the magnetization intensity of each of the repulsive permanent magnet groups (1) is equal, so that the bearing stiffness of each of the repulsive permanent magnet groups (1) is equal; the second design parameter includes the width of the spherical shell air gap (30) and the reference radius and reference angle of the repulsive permanent magnet group (1); Based on the second design parameter, the bearing stiffness of each repulsive permanent magnet group (1) is determined; wherein, based on the second design parameter, the bearing stiffness of each repulsive permanent magnet group (1) is determined, comprising: establishing second configuration information, the second configuration information being used to characterize an integral unit of the axial load force of a single group of the repulsive permanent magnet group (1), the second configuration information comprising a second parameter, the second parameter being used to represent the axial displacement of the rotor (20); based on the second configuration information, determining third configuration information, the third configuration information being obtained by performing spherical area integration on the second configuration information, then taking the derivative of the second parameter, and setting the second parameter to zero; and determining the bearing stiffness of the single group of the repulsive permanent magnet group (1) according to the third configuration information; The number of the repulsive permanent magnet groups (1) is determined according to the target stiffness and the bearing stiffness of each of the repulsive permanent magnet groups (1); wherein when the bearing stiffness of each of the repulsive permanent magnet groups (1) is equal, the repulsive permanent magnet group (1) comprises: Among them, K a is the target stiffness, K b is the bearing stiffness of a single repulsive permanent magnet group, N is the number of repulsive permanent magnet groups; The structure of the axial passive magnetic bearing is designed according to the target thickness of the damping conductor (202), comprising: The structure of the axial passive magnetic bearing is designed according to the target thickness of the damping conductor (202) and the number of the repulsive permanent magnet groups (1).

5. The design method according to claim 4, characterized in that: The structural requirements of the repulsive permanent magnet group (1) include: the repulsive permanent magnet group (1) is annular and surrounds the circumference of the damping permanent magnet group (2); each of the repulsive permanent magnet groups (1) is arranged in sequence along the radial direction of the axial passive magnetic bearing; the repulsive permanent magnet group (1) includes two sub-permanent magnet groups (11); the two sub-permanent magnet groups (11) are respectively located on the stator (10) and the rotor (20) of the axial passive magnetic bearing and are arranged correspondingly; the sub-permanent magnet group (11) includes a first permanent magnet (111) and two second permanent magnets (112); the two second permanent magnets (112) are respectively located on radial sides of the first permanent magnet (111) in the sub-permanent magnet group (11); The magnetization property requirements of the repulsive permanent magnet group (1) include: the magnetization direction of the first permanent magnet (111) is parallel to the axial direction of the axial passive magnetic bearing, the magnetization direction of the second permanent magnet (112) points to the N pole of the first permanent magnet (111) in the sub-permanent magnet group (11), an angle is formed between the magnetization direction of the first permanent magnet (111) and the magnetization direction of the second permanent magnet (112), and in one of the repulsive permanent magnet groups (1), the magnetization intensities of the first permanent magnet (111) and the second permanent magnet (112) are equal; The magnetization parameters of the repulsive permanent magnet group (1) include the magnetization intensity of the first permanent magnet (111).

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