Design and calculation method for low torsional rigidity of permanent magnet coupler

Abstract

The invention discloses a low torsional rigidity design and calculation method for a permanent magnet coupling. According to the method, through the low-torsional-rigidity structural design, transmission of vibration from the driving end to the load end can be effectively reduced, the service life of shafting parts is prolonged, the transmission reliability is improved, and the high practical application value is achieved; besides, according to the magnetic circuit forming characteristics of the drum-type permanent magnet coupling, an equivalent magnetic circuit of the drum-type permanent magnet coupling is constructed based on an equivalent magnetic circuit method, the torque and rigidity analytic expression of the drum-type permanent magnet coupling is deduced by solving the magnetic circuit, and finite element calculation which is long in time consumption and complex in calculation does not need to be carried out. The method can provide important technical support for the initial stage of design, torsional rigidity prediction, vibration reduction and isolation effect evaluation and the like of the drum-type permanent magnet coupler, and has the advantages of simplicity in operation, high adaptability, short calculation time and the like in practical engineering application. The method is a calculation method with engineering practical application value.

Description

Technical Field

[0001] The invention belongs to the technical field of permanent magnet flexible vibration reduction and isolation transmission, and relates to a low dynamic torsional stiffness structural design of a cylindrical permanent magnet coupling and a torsional stiffness analytical calculation method. Background Art

[0002] Torsional vibration is a special vibration form of rotating mechanical shaft system, which is widely present in transmission systems such as automobiles, ships, aerospace, wind power generation, etc. It is one of the important reasons for the noise, fatigue and damage of shaft system parts. As a commonly used part in the transmission system, the coupling plays an important role in controlling the vibration transmission between the active end and the driven end. However, the traditional coupling belongs to the contact transmission, and it is inevitable that there are problems such as wear, fatigue damage, and direct vibration transmission. In recent years, with the development of permanent magnetic materials, permanent magnetic transmission devices represented by cylindrical permanent magnetic couplings have developed rapidly. With the characteristics of non-contact transmission, it can effectively reduce the vibration transmission from the drive end to the load end. However, the magnetic force generated by the permanent magnet is highly nonlinear. A small offset between the two magnets will cause a large change in the force. The traditional full-magnet configuration cylindrical permanent magnetic coupling has a large torsional stiffness during the shaft system startup phase, which will lead to insufficient absorption of the shaft system torsional vibration and impact load, aggravating the transmission of vibration from the drive end to the load end, and then accelerating the fatigue and damage of the shaft system components, affecting the life and reliability of the transmission shaft system. Therefore, the large torsional stiffness under the load starting condition is one of the important reasons why the vibration reduction and vibration absorption capacity of the traditional cylindrical permanent magnetic coupling cannot meet the design expectations. In addition, the current research on the transmission characteristics of cylindrical permanent magnetic couplings mainly relies on finite element simulation analysis. The calculation process is time-consuming, and there is a situation where the returned solution does not converge. The calculation accuracy is greatly affected by factors such as mesh division, boundary conditions, and simulation environment settings, making the structural parameter iteration of the cylindrical permanent magnetic coupling in the design phase difficult and the calculation time cost high. Therefore, proposing a structural design of low dynamic torsional stiffness of a cylindrical permanent magnet coupling under load starting conditions and a fast analytical prediction method of torsional stiffness are of great significance in guiding the initial design.

[0003] In order to study the transmission characteristics and structural optimization design of cylindrical permanent magnet couplings, Li Guangjun, Guo Heyi, Xu Lei and others, in the article "Magnetic Field Simulation Analysis and Structural Optimization Design of Cylindrical Permanent Magnet Couplings", aimed at the long-term safe and reliable operation of cylindrical permanent magnet couplings used in stirring devices, fully considered the actual operating conditions, established a three-dimensional magnetic field simulation model of the cylindrical permanent magnet coupling, analyzed the influence of various structural parameters on the magnetic torque, and carried out structural optimization design for the demagnetization failure problem of permanent magnets. However, the analysis process relied on finite element analysis, and did not give a specific analytical calculation method. In addition, the structural optimization object only focused on reducing the influence of temperature rise on the safe and reliable operation of the cylindrical permanent magnet coupling, and did not perform structural optimization on the torsional stiffness of the cylindrical permanent magnet coupling. In order to optimize the design of torsional stiffness of cylindrical permanent magnet coupling, Zheng Yisheng, Lu Guanglin, Zhang Xinong and others proposed a quasi-zero stiffness coupling composed of rubber and permanent magnet in the patent "A Quasi-Zero Stiffness Coupling" (CN201610032023.X). By selecting the geometric parameters of the inner and outer magnetic ring permanent magnets, the negative stiffness generated by the magnetic spring is close to the positive stiffness of the rubber bearing, so that the total stiffness reaches a quasi-zero state. In theory, this method can effectively reduce the torsional stiffness of the cylindrical permanent magnet coupling under load starting conditions. However, the combination of rubber and permanent magnet increases the complexity of the structure, and the design and selection of positive and negative stiffness are difficult. The specific selection method is not given in the article.

[0004] Therefore, a low dynamic torsional stiffness structural design and an analytical calculation method of torsional stiffness for a cylindrical permanent magnet coupling are proposed, which is of great significance to the design and research of cylindrical permanent magnet couplings. Summary of the invention

[0005] In order to make up for the defects of the prior art, the present invention invents a low dynamic torsional stiffness structural design and torsional stiffness analytical calculation method for a cylindrical permanent magnet coupling. The purpose is to optimize the structure of the existing cylindrical permanent magnet coupling to reduce the torsional stiffness in the startup phase and enhance the torsional vibration absorption capacity of the cylindrical permanent magnet coupling. In combination with the torque analytical calculation model established based on the equivalent magnetic circuit method, the torsional stiffness in the startup phase is calculated and evaluated, providing important technical support for the initial structural design of the cylindrical permanent magnet coupling, torsional stiffness calculation, and buffering vibration absorption, vibration reduction and isolation effect evaluation. The method has good practicality, operability and convenience in actual engineering applications.

[0006] The technical solution of the present invention:

[0007] A low torsional stiffness design and calculation method for a cylindrical permanent magnet coupling. The structural design method is characterized in that the area difference between the outer rotor permanent magnet 2 and the inner rotor permanent magnet 3 surfaces participating in the magnetic field coupling is utilized. When the inner rotor permanent magnet 3 moves within a small deflection angle range, the excess magnetic flux from the outer rotor permanent magnet 2 forms an auxiliary magnetic circuit through the convergence effect of the high magnetic permeability partition 4. Therefore, the magnetic flux of the main magnetic circuit passing through the inner rotor permanent magnet 3 remains almost unchanged. According to Lenz's law, the torque received by the inner rotor permanent magnet 2 remains almost unchanged under a small deflection angle, thereby realizing the "flexible" design of the cylindrical permanent magnet coupling in the startup phase and achieving the purpose of reducing the torsional stiffness. The torsional stiffness analytical calculation method is characterized in that, firstly, an equivalent magnetic circuit of any two adjacent pairs of magnetic poles is constructed based on the equivalent magnetic circuit method; secondly, the magnetic resistance and magnetic flux at each location are calculated according to the series-parallel relationship of the magnetic circuit; then, the total magnetic energy at the air gap between the two adjacent pairs of magnetic poles is calculated according to the electromagnetic field theory, and the torque analytical formula of the cylindrical permanent magnetic coupling is obtained by combining the principle of virtual work, and the torsional stiffness analytical formula is obtained after differentiation; finally, the deflection angle value is substituted to quantitatively evaluate the torque and torsional stiffness of the cylindrical permanent magnetic coupling under the starting working condition stage. The specific steps of the calculation method are as follows:

[0008] The first step is to determine the key structural parameters of the cylindrical permanent magnet coupling

[0009] Assume that the thickness of the outer rotor back iron 1 and the inner rotor back iron 5 is sufficient and the magnetic leakage is negligible; first determine the key structural parameters of the cylindrical permanent magnet coupling; among them, the thickness of the outer rotor permanent magnet 2 and the inner rotor permanent magnet 3 are both h1, the length is l, and the coercive force is H c , the number of magnetic pole pairs is p; the outer radius of the outer rotor permanent magnet 2 is R1, the outer radius of the inner rotor permanent magnet 3 is R2, the thickness of the outer rotor back iron 1 and the inner rotor back iron 5 are both h2, the central angle of the high magnetic permeability partition 4 is α0, and the thickness of the air gap between the inner and outer rotors is a g , and the outer rotor permanent magnet 2 and the inner rotor permanent magnet 3 are evenly distributed along the circumferential direction, the N pole and the S pole are evenly arranged alternately, and the relative deflection angle of the inner and outer rotors along the axis during the load starting stage is θ;

[0010] The second step is to construct the equivalent magnetic circuit of any two adjacent pairs of magnetic poles based on the equivalent magnetic circuit method.

[0011] According to the structural symmetry, any two adjacent pairs of magnetic poles are selected to construct the equivalent magnetic circuit of the cylindrical permanent magnetic coupling, and the following assumptions are made: ① The magnetic circuit is divided into several sections, each of which has the same cross-sectional area and the same magnetic medium; ② The magnetic field intensity in each section of the magnetic circuit is the same everywhere, and the direction is consistent with the magnetic circuit path; ③ The magnetic flux is evenly distributed on each cross section of the magnetic circuit; ④ Ignore the leakage magnetic flux at the air gap, etc., assume that the magnetic circuit is an ideal magnetic circuit, do not consider saturation, and set the magnetic permeability of the ferromagnetic material to a constant value;

[0012] Step 3: According to the series-parallel relationship of each magnetic resistance, calculate the magnetic resistance and magnetic flux at each point in the magnetic circuit

[0013] First, the magnetic resistance and magnetic flux of the outer rotor permanent magnet 2 are calculated as follows:

[0014]

[0015] In the formula, R pm1 is the reluctance of the outer rotor permanent magnet, H -1 ; μ0 is the vacuum permeability, and μ0=4π×10 -7 H / m; μ pm is the relative magnetic permeability of the permanent magnet, and μ pm =1.05;Φ pm1 is the magnetic flux of the outer rotor permanent magnet, Wb;

[0016] Secondly, the magnetic resistance and magnetic flux of the inner rotor permanent magnet 3 are calculated as follows:

[0017]

[0018] In the formula, R pm2 is the reluctance of the inner rotor permanent magnet, H -1 ; Φ pm2 is the magnetic flux of the inner rotor permanent magnet, Wb;

[0019] Then, the magnetic resistance of the high magnetic permeability separator 4 is calculated as follows:

[0020]

[0021] In the formula, R y is the magnetic reluctance of the high permeability separator, H -1 ;μ iron is the relative magnetic permeability of the separator, and μ iron =4000;

[0022] Finally, the magnetic resistance and magnetic flux at the air gap are calculated as follows:

[0023]

[0024] Where A(θ) is the flux equivalent area of ​​the air gap between the inner and outer rotors, m 2 ; R g is the air gap reluctance, H -1 ;μ air is the relative magnetic permeability of air, and μ air =1; R / / For R y and R pm2 The parallel magnetic resistance, H -1 ; Φ g is the magnetic flux at the air gap between two adjacent pairs of magnetic poles, Wb; K fK is the back ferromagnetic resistance effect coefficient, which is generally 1 to 1.2, and is taken as 1.1 here; I is the magnetic flux leakage coefficient, without considering the influence of magnetic flux leakage, and is taken as 1 here;

[0025] Step 4: Based on the electromagnetic field theory, calculate the total magnetic energy at the air gap between two adjacent pairs of magnetic poles, and combine it with the principle of virtual work to obtain the torque analytical formula of the cylindrical permanent magnetic coupling after correction. After differentiation, obtain the torsional stiffness analytical formula

[0026] First, the total magnetic energy at the air gap between two adjacent pairs of magnetic poles is calculated according to the electromagnetic field theory. The formula is as follows:

[0027]

[0028] Where W g is the total magnetic energy in the air gap between two adjacent pairs of magnetic poles, J; Λ g is the magnetic permeability at the air gap between two adjacent pairs of magnetic poles, H;

[0029] Then, combined with the principle of virtual work, the torque of the cylindrical permanent magnet coupling is calculated as follows:

[0030]

[0031] Where, T(θ) is the torque of the cylindrical permanent magnet coupling, N·m; dW g , dθ are W g , the differential corresponding to θ;

[0032] Finally, the torque analytical formula of the cylindrical permanent magnet coupling is derived to calculate the torsional stiffness. The formula is as follows:

[0033]

[0034] Where K(θ) is the torsional stiffness of the cylindrical permanent magnetic coupling, N·m / deg; dT(θ) is the differential of T(θ);

[0035] Step 5: Substitute the deflection angle value to calculate the torque and torsional stiffness of the cylindrical permanent magnet coupling.

[0036] Substituting the relative deflection angle θ of the inner and outer rotors along the axis during the load-starting stage of the cylindrical permanent magnet coupling into the analytical formulas of T(θ) and K(θ), the torque T and torsional stiffness K of the cylindrical permanent magnet coupling under the starting condition can be obtained. The calculation is now complete.

[0037] The beneficial effect of the present invention is that the calculation method does not require time-consuming and complex finite element calculations. It only needs to construct an equivalent magnetic circuit according to the magnetic circuit formation characteristics of the cylindrical permanent magnet coupling, and perform analytical calculations on its torque and torsional stiffness according to the principle of virtual work, thereby achieving quantitative analysis of the torsional stiffness of the cylindrical permanent magnet coupling in the startup phase and effective evaluation of the vibration reduction and isolation effect. It has the advantages of simple operation and short calculation time in practical engineering applications. In addition, through the low dynamic torsional stiffness structural design of the cylindrical permanent magnet coupling, its absorption capacity for torsional vibration can be enhanced, effectively reducing the transmission of vibration from the drive end to the load end, and improving the service life and transmission reliability of shaft system components, and has high practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic diagram of the structure of a low torsional stiffness cylindrical permanent magnet coupling. In the figure: 1-outer rotor back iron, 2-outer rotor permanent magnet, 3-inner rotor permanent magnet, 4-high magnetic permeability partition, 5-inner rotor back iron; h1-permanent magnet thickness, h2-back iron thickness, R1-outer rotor permanent magnet outer diameter, R2-inner rotor permanent magnet outer diameter, a g - air gap thickness, p-number of magnetic pole pairs, θ-relative deflection angle of inner and outer rotors along the axis, α0-center angle of high magnetic permeability partition; main magnetic circuit-magnetic flux loop formed by permanent magnets, auxiliary magnetic circuit-magnetic flux loop formed by permanent magnets and high magnetic permeability partitions;

[0039] Figure 2 It is a flow chart of the analytical calculation method of the stiffness of a low torsional stiffness cylindrical permanent magnetic coupling;

[0040] Figure 3 It is an equivalent magnetic circuit of any two adjacent pairs of magnetic poles of a low torsional stiffness cylindrical permanent magnetic coupling, where (a) is the equivalent magnetic circuit formed by two adjacent pairs of magnetic poles, and (b) is a simplified magnetic circuit; in the figure: R pm1 is the reluctance of the outer rotor permanent magnet, Φ pm1 is the magnetic flux of the outer rotor permanent magnet, R pm2 is the reluctance of the inner rotor permanent magnet, Φ pm2 is the magnetic flux of the inner rotor permanent magnet, R i1 is the outer rotor back iron reluctance, R i2 is the inner rotor back iron magnetic resistance, R y is the magnetic resistance of the high magnetic permeability separator, R g is the air gap reluctance, Φ g is the magnetic flux at the air gap between two adjacent pairs of magnetic poles, R / / For R y and R pm2 The parallel magnetic resistance, K f is the back ferromagnetic resistance coefficient. DETAILED DESCRIPTION

[0041] The implementation examples of the present invention are further described below in conjunction with the accompanying drawings and technical solutions.

[0042] This implementation case uses a cylindrical permanent magnet coupling with a rated power of 1.26kW and 18 pairs of magnetic poles to perform analytical calculation of the torsional stiffness during the startup phase.

[0043] Figure 1 The structure diagram of a low torsional stiffness cylindrical permanent magnet coupling is shown in FIG. 1 , wherein the outer rotor permanent magnet 2 and the inner rotor permanent magnet 3 of the cylindrical permanent magnet coupling have a thickness of h1 = 8 mm, a length of l = 50 mm, and a coercive force of H c =907000A / m, number of magnetic pole pairs p = 18 pairs, outer radius of outer rotor permanent magnet 2 R1 = 52mm, outer radius of inner rotor permanent magnet 3 R2 = 41mm, thickness of outer rotor back iron 1 and inner rotor back iron 5 h2 = 8mm, central angle of high magnetic permeability partition 4 α0 = 4deg, thickness of air gap between inner and outer rotors a g =3mm, during the load starting phase, the relative deflection angle of the inner and outer rotors along the axis is θ=1deg.

[0044] Figure 2 This is a flow chart of the analytical calculation method for the stiffness of a low torsional stiffness cylindrical permanent magnetic coupling. The specific calculation steps are as follows:

[0045] The first step is to determine the key structural parameters of the cylindrical permanent magnet coupling

[0046] First, the key structural parameters of the cylindrical permanent magnet coupling are determined. The thickness of the outer rotor permanent magnet 2 and the inner rotor permanent magnet 3 of the cylindrical permanent magnet coupling is h1=8mm, the length is l=50mm, and the coercive force is H c =907000A / m, number of magnetic pole pairs p = 18 pairs, outer radius of outer rotor permanent magnet 2 R1 = 52mm, outer radius of inner rotor permanent magnet 3 R2 = 41mm, thickness of outer rotor back iron 1 and inner rotor back iron 5 h2 = 8mm, central angle of high magnetic permeability partition 4 α0 = 4deg, thickness of air gap between inner and outer rotors a g =3mm, during the load starting stage, the relative deflection angle of the inner and outer rotors along the axis is θ=1deg;

[0047] The second step is to construct the equivalent magnetic circuit of any two adjacent pairs of magnetic poles based on the equivalent magnetic circuit method.

[0048] Figure 3 It is an equivalent magnetic circuit of any two adjacent pairs of magnetic poles of a low torsional stiffness cylindrical permanent magnetic coupling, where (a) is the equivalent magnetic circuit formed by two adjacent pairs of magnetic poles, and (b) is a simplified magnetic circuit;

[0049] Step 3: According to the series-parallel relationship of each magnetic resistance, calculate the magnetic resistance and magnetic flux at each point in the magnetic circuit

[0050] Substituting the known key parameters into equations (1) to (9), we can obtain the reluctance of the outer rotor permanent magnet R pm1 =7.254×10 6 H -1 、Outer rotor permanent magnet magnetic flux Φ pm1 =1.029×10 -3 Wb, inner rotor permanent magnet reluctance R pm2 =1.178×10 7 H -1 、Inner rotor permanent magnet magnetic flux Φ pm2 =6.335×10 -4 Wb, high magnetic permeability separator magnetic resistance R y =9.521×10 3 H -1 , R y and R pm2 The parallel magnetic resistance R / / =9.513×10 3 H -1 , the analytical formula of the magnetic flux equivalent area A(θ) of the air gap between the inner and outer rotors is:

[0051]

[0052] Air gap reluctance R g The analytical formula is:

[0053]

[0054] Magnetic flux Φ at the air gap between two adjacent pairs of magnetic poles g The analytical formula is:

[0055]

[0056] Step 4: Based on the electromagnetic field theory, calculate the total magnetic energy at the air gap between two adjacent pairs of magnetic poles, and combine it with the principle of virtual work to obtain the torque analytical formula of the cylindrical permanent magnetic coupling after correction. After differentiation, obtain the torsional stiffness analytical formula

[0057] First, Φ g and R g Substituting into formula (10), we can get the total magnetic energy W between the air gaps of two adjacent pairs of magnetic poles: g The analytical formula is:

[0058]

[0059] To facilitate subsequent derivation, W is g The analytical expression is fitted with a polynomial within the range of 0 to 2 degrees, and W can be obtained. g The analytical formula after fitting is:

[0060] W g=-2.073×10 -5 θ 4 -2.914×10 -5 θ 3 +0.001764θ 2 -7.076×10 -6 θ+0.06302;

[0061] Then, combined with the principle of virtual work, the torque analytical formula of the cylindrical permanent magnet coupling is calculated by formula (11):

[0062]

[0063] Finally, the torque analytical formula of the cylindrical permanent magnet coupling is derived, and the torsional stiffness analytical formula is obtained as follows:

[0064]

[0065] Step 5: Substitute the deflection angle value to calculate the torque and torsional stiffness of the cylindrical permanent magnet coupling.

[0066] Substituting the relative deflection angle θ=1deg of the inner and outer rotors along the axis during the load starting stage of the cylindrical permanent magnet coupling into the analytical expressions of T(θ) and K(θ), we can obtain the torque T=3.46N·m and the torsional stiffness K=3.20N·m / deg during the starting stage of the cylindrical permanent magnet coupling. The calculation is now completed.

[0067] This method fully considers the problem of insufficient torsional vibration absorption capacity of the cylindrical permanent magnet coupling due to the large dynamic torsional stiffness under load starting conditions in actual applications. Through the design of low torsional stiffness structure, the transmission of vibration from the drive end to the load end can be effectively reduced, the service life of the shaft system components and the reliability of the transmission can be improved, and it has high practical application value. In addition, according to the magnetic circuit formation characteristics of the cylindrical permanent magnet coupling, the equivalent magnetic circuit of the cylindrical permanent magnet coupling is constructed based on the equivalent magnetic circuit method. The torque and stiffness analytical expressions of the cylindrical permanent magnet coupling are derived by solving the magnetic circuit. Without the need for time-consuming and complex finite element calculations, the torque and torsional stiffness of the cylindrical permanent magnet coupling in the starting stage can be quantitatively analyzed. It can provide important technical support for the initial design of the cylindrical permanent magnet coupling, torsional stiffness prediction and vibration reduction and isolation effect evaluation. In actual engineering applications, it has the advantages of simple operation, strong adaptability and short calculation time. It is a calculation method with practical engineering application value.

Claims

1. A design and calculation method for low torsional stiffness of a permanent magnet coupling, characterized in that: Here are the steps: The first step is to determine the key structural parameters of the cylindrical permanent magnet coupling Assume that the thickness of the outer rotor back iron (1) and the inner rotor back iron (5) is sufficient and the magnetic leakage is negligible; determine the key structural parameters of the cylindrical permanent magnet coupling; among which, the thickness of the outer rotor permanent magnet (2) and the inner rotor permanent magnet (3) are both h1, the length is l, and the coercive force is H c , the number of magnetic pole pairs is p; the outer radius of the outer rotor permanent magnet (2) is R1, the outer radius of the inner rotor permanent magnet (3) is R2, the thickness of the outer rotor back iron (1) and the inner rotor back iron (5) are both h2, the central angle of the high magnetic permeability partition (4) is α0, and the thickness of the air gap between the inner and outer rotors is a g , and the outer rotor permanent magnet (2) and the inner rotor permanent magnet (3) are evenly distributed in the circumferential direction, the N poles and the S poles are evenly arranged alternately, and the inner and outer rotors are deflected relative to each other along the axis by an angle of θ during the load starting stage; The second step is to construct the equivalent magnetic circuit of any two adjacent pairs of magnetic poles based on the equivalent magnetic circuit method. According to the structural symmetry, any two adjacent pairs of magnetic poles are selected to construct the equivalent magnetic circuit of the cylindrical permanent magnetic coupling, and the following assumptions are made: ① The magnetic circuit is divided into several sections, each of which has the same cross-sectional area and the same magnetic medium; ② The magnetic field intensity in each section of the magnetic circuit is the same everywhere, and the direction is consistent with the magnetic circuit path; ③ The magnetic flux is evenly distributed on each cross section of the magnetic circuit; ④ Ignore the leakage magnetic flux at the air gap, etc., assume that the magnetic circuit is an ideal magnetic circuit, do not consider saturation, and set the magnetic permeability of the ferromagnetic material to a constant value; Step 3: According to the series-parallel relationship of each magnetic resistance, calculate the magnetic resistance and magnetic flux at each point in the magnetic circuit First, the magnetic resistance and magnetic flux of the outer rotor permanent magnet (2) are calculated as follows: In the formula, R pm1 is the reluctance of the outer rotor permanent magnet, H -1 ; μ0 is the vacuum permeability, and μ0=4π×10 -7 H / m; μ pm is the relative magnetic permeability of the permanent magnet, and μ pm =1.05;Φ pm1 is the magnetic flux of the outer rotor permanent magnet, Wb; Secondly, the magnetic resistance and magnetic flux of the inner rotor permanent magnet (3) are calculated as follows: In the formula, R pm2 is the reluctance of the inner rotor permanent magnet, H -1 ; Φ pm2 is the magnetic flux of the inner rotor permanent magnet, Wb; Then, the magnetic reluctance of the high magnetic permeability separator (4) is calculated as follows: In the formula, R y is the magnetic resistance of the high permeability separator, H -1 ;μ iron is the relative magnetic permeability of the separator, and μ iron =4000; Finally, the magnetic resistance and magnetic flux at the air gap are calculated as follows: Where A(θ) is the flux equivalent area of ​​the air gap between the inner and outer rotors, m 2 ; R g is the air gap reluctance, H -1 ;μ air is the relative magnetic permeability of air, and μ air =1; R / / For R y and R pm2 The parallel magnetic resistance, H -1 ; Φ g is the magnetic flux at the air gap between two adjacent pairs of magnetic poles, Wb; K f K is the back ferromagnetic resistance effect coefficient, which is generally 1 to 1.2, and is taken as 1.1 here; I is the magnetic flux leakage coefficient, without considering the influence of magnetic flux leakage, and is taken as 1 here; Step 4: According to the electromagnetic field theory, calculate the total magnetic energy at the air gap between two adjacent pairs of magnetic poles, and combine it with the principle of virtual work to correct the torque analytical formula of the cylindrical permanent magnet coupling. After differentiation, get the torsional stiffness analytical formula. First, calculate the total magnetic energy at the air gap between two adjacent pairs of magnetic poles according to the electromagnetic field theory. The formula is as follows: Where W g is the total magnetic energy in the air gap between two adjacent pairs of magnetic poles, J; Λ g is the magnetic permeability at the air gap between two adjacent pairs of magnetic poles, H; Then, combined with the principle of virtual work, the torque of the cylindrical permanent magnet coupling is calculated as follows: Where, T(θ) is the torque of the cylindrical permanent magnet coupling, N·m; dW g , dθ are W g , the differential corresponding to θ; finally, the analytical formula of the torque of the cylindrical permanent magnet coupling is derived to calculate the torsional stiffness. The formula is as follows: Where K(θ) is the torsional stiffness of the cylindrical permanent magnetic coupling, N·m / deg; dT(θ) is the differential of T(θ); Step 5: Substitute the deflection angle value to calculate the torque and torsional stiffness of the cylindrical permanent magnet coupling. Substitute the relative deflection angle θ of the inner and outer rotors along the axis during the load-starting stage of the cylindrical permanent magnet coupling into the analytical formulas of T(θ) and K(θ) respectively, and obtain the torque T and torsional stiffness K of the cylindrical permanent magnet coupling under the starting condition. The calculation is now completed.

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