A method for modeling and solving equivalent magnetic network of planar induction motor

Abstract

The application relates to an equivalent magnetic network modeling and solving method for a planar induction motor, which comprises the following steps: dividing an electromagnetic field solving area of the planar induction motor; given size structure parameters and input parameters of the planar induction motor, establishing an axial flux three-dimensional cylindrical coordinate system; establishing a preliminary magnetic network model, determining grid node position angle information, and performing numerical solving of cross magnetic conductance units; adaptively connecting dynamic nodes of air gaps according to position angle information of air gap layer connecting nodes; based on a B-H curve of nonlinear ferromagnetic materials, performing cubic spline interpolation solving of permeability of the nonlinear magnetic conductance units, and performing iterative solving through a relaxation coefficient method; and after the iteration is completed, air gap magnetic density solving is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of motor modeling and electromagnetic field solving, and particularly relates to an equivalent magnetic network modeling and solving method of a planar induction motor. BACKGROUND

[0002] With the development of deep space exploration missions, large deployable mechanisms are more widely used in spacecraft. In order to meet the stress-free assembly and performance testing, the inclination may tilt when the ground microgravity simulation test is carried out due to environmental factors. With the continuous development of motor technology, the working scene of the motor is also changing. The planar induction motor can generate a horizontal traveling wave magnetic field and can generate a planar electromagnetic force to compensate for the gravity component when tilted.

[0003] With the continuous development of computer technology, numerical methods represented by the finite element method have been widely used in the initial design stage of the motor and the field of electromagnetic field solving, but they also have the problems of long calculation time and large memory consumption. In contrast, the equivalent magnetic network method can better balance the requirements of solving accuracy and calculation time. In the traditional equivalent magnetic network modeling and solving process, the modeling and solving of the air gap part is a key research direction. The air gap part is connected by single radial magnetic conductance at first, but this method has the disadvantage of not being able to simulate the tangential component, and the magnetic conductance connection is suddenly changed, which affects the solving of the electromagnetic field. In view of the deflection problem of the magnetic force line in the air gap area, the concept of cross magnetic conductance is proposed. This modeling method can realize the solving of the magnetic field in two directions, but the connection between the cross magnetic conductance and the upper node is still in the form of direct connection, which has the problem of sudden change of the magnetic conductance connection state. In the context of dynamic changes of the magnetic network nodes, in view of the sudden change of the magnetic conductance connection in the traditional way, the linkage between the air gap nodes and the core nodes is mostly in the form of single-direction magnetic conductance unit connected by Ostovic empirical coefficient. Although the single-direction magnetic conductance connection has the advantage of convenient solving, it cannot handle the deflection problem of the magnetic force line in the connection layer.

[0004] In view of the above, an equivalent magnetic network method is proposed, which can accurately and effectively solve the air gap magnetic field and predict the performance of the motor, and is particularly important in the process of motor design research. SUMMARY

[0005] The application discloses an equivalent magnetic network modeling and solving method of a planar induction motor, which can accurately solve the air gap magnetic field of the planar induction motor and predict the performance of the motor, and effectively shorten the calculation time in the motor analysis and design stage. The technical scheme is as follows:

[0006] An equivalent magnetic network modeling and solving method for a planar induction motor, characterized in that it comprises the following steps:

[0007] Step 1: divide the electromagnetic field solving region of planar induction motor;

[0008] Step 2: given the size and structure parameters of planar induction motor and input parameters, establish the axial flux three-dimensional cylindrical coordinate system;

[0009] Step 3: establish the preliminary magnetic network model, determine the grid node position angle information, and perform numerical solving of the cross magnetic conductance unit;

[0010] Step 4: according to the position angle information of the air gap layer connecting nodes, adaptively connect the air gap dynamic nodes, as follows:

[0011] According to the position angle information of the air gap region connecting nodes of the preliminary magnetic network model, taking the node axis angle difference of each magnetic conductance unit as the basis, the position information between nodes is divided into coincidence, intersection and separation. According to the position relationship, the air gap dynamic node layer is obtained, the adjacent node layers are adaptively connected, and the equivalent magnetic network model construction is completed;

[0012] When the node angle of the primary side and the air gap layer changes, the number of nodes and the value of the magnetic conductance unit dynamically change. The node axis angle difference of the magnetic conductance unit is represented as follows:

[0013] γ pg =θ p -θ g

[0014] In the formula, θ p is the primary side position angle, and θ g is the air gap position angle;

[0015] According to the air gap adaptive mode, the magnetic conductance unit is calculated as follows:

[0016]

[0017] In the formula, G zpg is the normal magnetic conductance unit under the air gap adaptive mode, G tpg is the tangential magnetic conductance unit under the air gap adaptive mode, and θ pg is represented as:

[0018]

[0019] Step 5: based on the B-H curve of nonlinear ferromagnetic material, the magnetic permeability of the nonlinear magnetic conductance unit is solved by cubic spline interpolation, and the iteration is solved by relaxation coefficient method;

[0020] Step 6: after the iteration is completed, the air gap magnetic density is solved

[0021] After meeting the convergence condition, store the calculation results at the current position, and enter the next position iteration until all position moment solving is completed, and the air gap magnetic density is solved.

[0022] Further, in step 1, the divided planar induction motor electromagnetic field solving region includes: yoke, tooth, slot, tooth top, pole shoe, slot opening, air gap and cast iron plate.

[0023] Further, in step 2, the established axial flux three-dimensional cylindrical coordinate system is: the origin is the center point of the ring structure of the planar induction motor, and the coordinate system coordinate values are (θ, r, z), wherein r is the horizontal distance of the moving point to the cylindrical axis, θ is the azimuth angle of the moving point to the reference direction with the same radius r direction passing through the horizontal plane, and z is the vertical distance of the moving point to the horizontal plane where the origin is located.

[0024] Further, the method of step 3 is as follows:

[0025] 1) Tooth magnetic potential calculation

[0026] Given the current excitation, the slot current value and tooth magnetic potential are calculated in sequence according to the energization mode:

[0027]

[0028] In the formula, Q is the number of primary side slots, N a is the number of turns of a single tooth, F sj is the equivalent magnetic motive force source on the jth tooth, I sj is the equivalent current in the jth slot, that is, the sum of positive and negative currents in the slot;

[0029] 2) Magnetic conductance unit solving

[0030] According to the magnetic flux direction and the material characteristics flowing through, the magnetic field is analyzed by dividing the ring, and the solving region is expanded along the radial direction;

[0031] According to whether the solving region is a linear region, the properties of the magnetic conductance unit are set to be nonlinear or linear on each ring surface, considering the distribution of magnetic lines in the planar induction motor, the cross magnetic conductance unit containing tangential and normal magnetic conductance is selected for solving, and the normal magnetic conductance G z and the tangential magnetic conductance G t The expressions are as follows:

[0032]

[0033] In the formula, μ is the magnetic permeability, θ is the angle corresponding to the magnetic conductance unit, R is the radius corresponding to the magnetic conductance unit in each ring cross section, L is the length of the magnetic conductance unit in the radial direction, and h is the height of the magnetic conductance unit.

[0034] 3) Magnetic flux source calculation:

[0035] φ=G·F

[0036] Φ is the magnetic flux source placed in the tooth part, G is the magnetic conductance of the tooth part, and F is the magnetic potential of the tooth part;

[0037] 4) Connection of the magnetic network model:

[0038] The connection of the nonlinear magnetic conductance unit, the linear magnetic conductance unit and the magnetic flux source completes the preliminary magnetic network model building, and the grid node position angle information is determined according to the number of magnetic conductance units in each region and the corresponding angle.

[0039] Further, the split ring analysis magnetic field mode is based on the following assumptions:

[0040] a) The current excitation given by the motor is uniformly distributed in the slot, and it is considered that only axial magnetic flux and circumferential magnetic flux exist in the magnetic circuit of the motor, and the radial magnetic flux is ignored;

[0041] b) The magnetic field only exists in the annular analysis region, and the end effect of the magnetic field is ignored;

[0042] c) When dynamic alternating current is passed, the eddy current generated in the ferromagnetic material is ignored.

[0043] Further, the method of step 5 is:

[0044] 1) Based on the node current method, the magnetic conductance, magnetic potential and magnetic flux matrix equations are established:

[0045]

[0046] In the formula, in the sub-magnetic conductance matrix G ii , the diagonal elements represent the self-magnetic conductance of each node in the i-th layer, and the non-diagonal elements represent the negative value of the mutual magnetic conductance between each node in the i-th layer; the sub-magnetic conductance matrix G ij represents the negative value of the mutual magnetic conductance between each node in the i-th layer and each node in the j-th layer, the sub-column vector F i T is the magnetic potential of each node in the i-th layer, and the sub-column vector Φ i T is the equivalent magnetic flux source of each node in the i-th layer;

[0047] 2) The equation is solved to obtain the node magnetic potential, and the magnetic potential difference of the nonlinear type magnetic conductance unit is calculated according to the node magnetic potential, and the unit magnetic field strength is solved;

[0048] 3) Based on the given B-H curve of the ferromagnetic material, the method of cubic spline interpolation is used to solve the unit magnetic induction intensity of the nonlinear type, and the unit permeability is further obtained;

[0049] 4) The permeability is iterated by using the relaxation coefficient method until the error requirement is met, and the expression is as follows:

[0050] μ k+1 = αμ k +(1-α)μk-1

[0051] In the formula, μ k+1 is the material permeability obtained by relaxation iteration, k is the current iteration number, and a is a relaxation coefficient, 0 < a < 1.

[0052] The beneficial effects of the present application are:

[0053] First, the equivalent magnetic network modeling and solving method of the planar induction motor of the present application is based on magnetic circuit analysis of the motor, and compared with the finite element method, the calculation resource occupation and solving time are greatly reduced, and the analysis efficiency is effectively improved in the motor design optimization stage.

[0054] Second, compared with the existing equivalent magnetic network modeling, the equivalent magnetic network modeling and solving method of the planar induction motor of the present application uses a single-direction permeability in the air gap and the core connecting layer, and the present application considers the deflection of the magnetic force line in the air gap and the core connecting layer. When the network model is established, the adaptive cross connecting permeability is used, which can effectively solve the axial and tangential components of the connecting layer air gap magnetic density, and achieve better solving accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 is a schematic diagram of a planar induction motor model;

[0056] Figure 2 is a distribution diagram of a planar induction motor solving region;

[0057] Figure 3 is a radial ring cross-section expansion diagram;

[0058] Figure 4 is a planar induction motor magnetic network model diagram;

[0059] Figure 5 is a permeability unit schematic diagram;

[0060] Figure 6 is an adaptive cross permeability nonlinear variation and node connection process schematic diagram;

[0061] Figure 7 is a magnetic network model node schematic diagram;

[0062] Figure 8 is a magnetic network iteration schematic diagram;

[0063] Figure 9 is a comparison diagram of the calculated air gap magnetic density and the finite element method analysis result. DETAILED DESCRIPTION

[0064] The following examples enable a person skilled in the art to more fully understand the present application, but do not limit the present application in any way.

[0065] The application provides an equivalent magnetic network modeling and solving method for a planar induction motor, comprising equivalent magnetic network modeling based on an adaptive air gap connection layer equivalent magnetic path method, and iterative solving of two parts. Wherein, the equivalent magnetic network model of the planar induction motor includes four parts of a primary side core part permeance, a secondary side cast iron plate permeance, a slot area air permeance and an air gap permeance. After the equivalent magnetic network model is established, the permeability of the ferromagnetic material is solved by cubic spline interpolation according to the B-H curve of the ferromagnetic material, and the permeability of the nonlinear ferromagnetic material region is iteratively solved in a relaxation iteration mode. Thus, the planar induction motor magnetic field analysis based on the equivalent magnetic network is realized, and the calculation result has good consistency with the finite element result.

[0066] Figure 1 The topological structure diagram of the planar induction motor which is the research object of the embodiment of the application is shown in the figure. The motor system is composed of an air floating bearing shell, porous graphite, a core, a winding and a magnetically conductive and electrically conductive cast iron plate. The core is a half-closed parallel slot structure, including a yoke part, a tooth part, a slot part and the like. The motor is a 12-slot motor, and the winding is wound in the tooth part in the form of concentrated winding. The parameters of the planar induction motor in the embodiment of the application are shown in Table 1.

[0067] Table 1 Parameters of the planar induction motor in the embodiment of the application

[0068]

[0069]

[0070] In the background of the ring analysis shown in the figure, the electromagnetic field solving region is divided into nine parts: a primary side yoke part, a primary side tooth part, a primary side slot part, a primary side tooth top, a primary side pole shoe, a primary side slot opening, an air gap and a cast iron plate, as shown in the figure. Figure 1 On the basis of the topological structure diagram of the embodiment of the application shown in the figure, the application divides the motor structure according to the motor topological structure and the material characteristics of each part.

[0071] According to the topological structure of the embodiment of the application shown in the figure, the application adopts a ring analysis mode in the motor analysis process, and the radial ring cross section development diagram is shown in the figure. Figure 1 Figure 2

[0072] In the background of the ring analysis shown in the figure, the electromagnetic field solving region is divided into nine parts: a primary side yoke part, a primary side tooth part, a primary side slot part, a primary side tooth top, a primary side pole shoe, a primary side slot opening, an air gap and a cast iron plate, as shown in the figure. Figure 2 Figure 3

[0073] ​​​​Based on the magnetic field distribution characteristics of planar induction motor, the axial flux three-dimensional cylindrical coordinate system is established, the origin is the center point of the ring structure of planar induction motor, the coordinate value of the coordinate system is (θ, r, z), where r is the horizontal distance from the moving point to the cylindrical axis, θ is the azimuth angle of the moving point to the reference direction with the same radius r direction on the horizontal plane, z is the vertical distance from the moving point to the horizontal plane where the origin is located, and the size and structure parameters of the planar induction motor are given.

[0074] According to the magnetic flux direction and the material characteristics flowing through the material, considering the different area magnetic flux distribution density, nonlinear magnetic conductance, linear magnetic conductance unit is set respectively and the number of magnetic conductance unit is given;

[0075] The magnetic flux source can be written as:

[0076] φ=G·F

[0077] In the formula, Φ is the magnetic flux source placed in the tooth part, G is the tooth magnetic conductance, and F is the tooth magnetic potential.

[0078] Given the current excitation, the slot current value and tooth magnetic potential are calculated in turn according to the energization mode:

[0079]

[0080] In the formula, Q is the number of primary side slots, N a is the number of turns of the coil on a single tooth, F sj is the equivalent magnetic motive force source on the jth tooth, I sj is the equivalent current in the jth slot, that is, the sum of positive and negative currents in the slot.

[0081] Figure 4 It is a magnetic network model diagram of planar induction motor. As shown in the figure, the nonlinear magnetic conductance unit, the linear magnetic conductance unit and the magnetic flux source are connected to preliminarily establish the magnetic network model, the grid node position information is determined according to the number of magnetic conductance unit in each area, and the value of the magnetic conductance unit is solved.

[0082] Figure 5 It is a schematic diagram of magnetic conductance unit. The expression is as follows:

[0083]

[0084] In the formula, μ is the magnetic permeability, θ is the corresponding angle of the magnetic conductance unit, R is the corresponding radius of the magnetic conductance unit, L is the length of the magnetic unit in the radial direction, and h is the height of the magnetic unit.

[0085] According to the node position angle information of the magnetic network model connected with the air gap area, the node position information between nodes is obtained as shown in Figure 6 , which is divided into coincidence, intersection and separation, and the air gap dynamic node layer is obtained according to the position relationship.

[0086] The air gap dynamic node layer is established on the basis of the change of the node angle of the primary side and the air gap layer, the number of nodes and the value of the magnetic conductance unit dynamically change, and the node angle information difference can be represented as follows:

[0087] γ pg = θ p - θ g

[0088] In the formula, θ p is the node position angle of the primary side, and θ g is the node position angle of the air gap.

[0089] Under the energized background, the magnetic lines of force will deflect at the connection between the nonlinear ferromagnetic material and the air gap, so the adaptive air gap magnetic conductance adopts the form of a cross magnetic conductance, and the calculation is as follows:

[0090]

[0091] In the formula, θpg can be represented as:

[0092]

[0093] The adaptive connection adjacent node layers complete the construction of the magnetic network model, and a schematic diagram of the magnetic network model nodes is shown in Figure 7 .

[0094] Thus, the establishment of the equivalent magnetic network model of the planar induction motor in the entire embodiment is completed, and based on the node current method, the magnetic conductance, magnetic potential, and magnetic flux matrix equations are established:

[0095]

[0096] In the formula, in the sub-magnetic conductance matrix G ii , the diagonal elements represent the self-magnetic conductance of each node in the i-th layer, and the non-diagonal elements represent the negative value of the mutual magnetic conductance between each node in the i-th layer. The sub-magnetic conductance matrix G ij represents the negative value of the mutual magnetic conductance between each node in the i-th layer and each node in the j-th layer, the sub-column vector F i T is the magnetic potential of each node in the i-th layer, and the sub-column vector Ф i T is the equivalent magnetic flux source of each node in the i-th layer.

[0097] The equation is solved to obtain the node magnetic potential, and the magnetic potential difference of the magnetic conductance unit is calculated according to the node magnetic potential, and the unit magnetic field strength is solved;

[0098] Figure 8 is a schematic diagram of the magnetic network iteration. The steps of the magnetic network iteration in the embodiment are as follows:

[0099] Step 1: The planar induction motor used in the example of the application is parameterized and set.

[0100] Step 2: According to the topology structure of the example of the application, the iteration at time t and radius r is carried out respectively in the iterative process of the step method in use.

[0101] Step 3: According to the grid node position information, the position relationship between nodes is determined.

[0102] Step 4: According to the position relationship between nodes, the air gap nodes are adaptively connected.

[0103] Step 5: The magnetic network equation is solved to obtain the magnetic field strength H of each node unit.

[0104] Step 6: According to the B-H curve of the nonlinear ferromagnetic material, the cubic spline interpolation is used to solve the magnetic induction intensity B and permeability μ of the node unit. k .

[0105] Step 7: The relaxation coefficient method is used to iteratively solve the permeability until the error requirement is met, and the expression is as follows:

[0106] μ k+1 = αμ k +(1-α)μ k-1

[0107] In the formula, μ k+1 is the material permeability obtained by relaxation iteration, k is the current iteration number, and α is the relaxation coefficient, 0<α<1.

[0108] Step 8: After meeting the convergence condition, the calculation results at the current position are stored, and the next position iteration is entered until all position time solving is completed, the node values are stored, and the air gap magnetic flux density solving is realized.

[0109] Figure 9 The figure is a comparison between the air gap magnetic flux density calculated by the application and the finite element method analysis result. The air gap magnetic flux density waveforms obtained by the two methods have high consistency, indicating that the equivalent magnetic network solving method based on adaptive connection of air gap dynamic nodes has high calculation accuracy and can be expected to become an effective alternative to the finite element method in the analysis process.

[0110] Based on the equivalent magnetic network solving method, the application proposes a cross permeability unit dynamic connection magnetic network modeling idea to solve the problem that the single radial permeability obtained from the empirical formula cannot accurately reflect the magnetic line deflection in the traditional equivalent magnetic network, and realizes the calculation of the electromagnetic performance of the air gap magnetic flux density axial component of the planar induction motor.

[0111] The above are only preferred embodiments of the present application, and the protection scope of the present application is not limited to the above-mentioned embodiments. Any technical scheme falling within the concept of the present application shall fall within the protection scope of the present application. It should be noted that, for ordinary skilled in the art, some improvements and refinements without departing from the principles of the present application shall be considered as the protection scope of the present application.

Claims

1. A method for modeling and solving an equivalent magnetic network for a planar induction motor, characterized in that: The following steps are involved: Step 1: Divide the electromagnetic field solution area of ​​the planar induction motor; Step 2: Given the size, structure and input parameters of the planar induction motor, establish a three-dimensional cylindrical coordinate system for the axial flux; Step 3: Establish a preliminary magnetic network model, determine the grid node position angle information, and perform numerical solution of the cross-permeability unit; Step 4: Adaptively connect the air gap dynamic nodes based on the position angle information of the air gap layer connection nodes. The method is as follows: Based on the position angle information of the nodes connected to the air gap area in the preliminary magnetic network model, and taking the angle difference of the axis of each magnetic permeability unit node as the judgment basis, the position information between nodes is divided into overlap, intersection, and separation. According to the position relationship, the air gap dynamic node layer is obtained, and the adjacent node layers are adaptively connected to complete the construction of the equivalent magnetic network model. When the angle between the primary side and the air gap layer node changes, the number of nodes and the value of the magnetic permeability unit are dynamically transformed. The angle difference between the axis of the magnetic permeability unit node is expressed as follows: c pg =θ p -θg g Where θ p is the primary side position angle, θ g is the air gap position angle; The magnetic permeability unit is calculated according to the air gap adaptive mode as follows: Where R is the radius of the magnetic permeability unit in each ring section, L is the length of the magnetic permeability unit in the radial direction, h is the height of the magnetic permeability unit, G zpg is the normal permeability unit in the air gap adaptive mode, G tpg is the tangential permeability unit in the air gap adaptive mode, θ pg Expressed as: Step 5: Based on the BH curve of the nonlinear ferromagnetic material, the permeability of the nonlinear magnetic permeability unit is solved by cubic spline interpolation and iteratively solved by the relaxation coefficient method; Step 6: After the iteration is completed, the air gap magnetic flux density is solved After the convergence conditions are met, the calculation results at the current position are stored and the next position iteration is entered until all position moments are solved to achieve the air gap magnetic density solution.

2. The method for modeling and solving the equivalent magnetic network of a planar induction motor according to claim 1, characterized in that: In step 1, the divided planar induction motor electromagnetic field solution area includes: yoke, tooth, slot, tooth top, pole shoe, slot, air gap and cast iron plate.

3. The method for modeling and solving the equivalent magnetic network of a planar induction motor according to claim 1, wherein: In step 2, the established axial flux three-dimensional cylindrical coordinate system is as follows: the origin is the center point of the planar induction motor ring structure, and the coordinates of the coordinate system are (θ, r, z), where r is the horizontal distance from the moving point to the cylindrical axis, θ is the azimuth angle from the moving point to the reference direction in the same radius r direction on the horizontal plane, and z is the vertical distance from the moving point to the horizontal plane where the origin is located.

4. The method for modeling and solving the equivalent magnetic network of a planar induction motor according to claim 1, wherein: The method for step 3 is as follows: 1) Calculation of tooth magnetic potential Given current excitation, calculate the slot current value and tooth magnetic potential in sequence according to the power-on method: Where, Q is the number of primary side slots, N is a is the number of coil turns on a single tooth, F sj is the equivalent magnetomotive force source on the jth tooth, I sj is the equivalent current in the jth slot, that is, the sum of the positive and negative currents in the slot; 2) Solving the magnetic permeability unit According to the direction of magnetic flux and the characteristics of the material flowing through it, the magnetic field is analyzed by ring division, and the solution area is expanded along the radial direction; According to whether the solution area is a linear area, the property of the magnetic permeability unit is set to nonlinear or linear on each annular surface. Considering the distribution of magnetic lines of force in the planar induction motor, a cross magnetic permeability unit including tangential and normal magnetic permeabilities is selected for solution. The normal magnetic permeability G z and tangential permeability G t The expression is as follows: Where μ is the magnetic permeability, θ is the angle corresponding to the magnetic permeability unit; 3) Calculation of magnetic flux source: φ=G·F Ф is the magnetic flux source placed on the tooth, G is the tooth magnetic permeance, and F is the tooth magnetic potential; 4) Connecting magnetic network model: Connect the nonlinear magnetic permeability unit, linear magnetic permeability unit, and magnetic flux source to complete the construction of the preliminary magnetic network model. According to the number of magnetic permeability units in each area and the corresponding angle, determine the grid node position angle information.

5. The method for modeling and solving the equivalent magnetic network of a planar induction motor according to claim 4, characterized in that: The above-mentioned ring-by-ring magnetic field analysis method is based on the following assumptions: a) The current excitation given by the motor is evenly distributed in the slot. It is assumed that only axial flux and circumferential flux exist in the motor magnetic circuit, and radial flux is ignored. b) The magnetic field exists only in the annular analysis area, and the end effects of the magnetic field are ignored; c) When dynamic alternating current is applied, eddy currents generated in ferromagnetic materials are ignored.

6. The method for modeling and solving the equivalent magnetic network of a planar induction motor according to claim 4, characterized in that: The method for step 5 is: 1) Based on the node current method, the magnetic permeance, magnetic potential, and magnetic flux matrix equations are established: In the formula, in the sub-permeability matrix G ii In the matrix, the diagonal elements represent the self-permeance of each node in the i-th layer, and the off-diagonal elements represent the negative value of the mutual permeance between the nodes in the i-th layer; the sub-permeance matrix G ij Represents the negative value of the mutual magnetic permeability between the nodes in the i-th layer and the nodes in the j-th layer, and the sub-column vector F i T is the magnetic potential of each node in the i-th layer, and the sub-column vector Φ i T is the equivalent magnetic flux source of each node in the i-th layer; 2) Solve the equation to obtain the magnetic potential of each node, calculate the magnetic potential difference of the nonlinear magnetic permeability unit based on the node magnetic potential, and solve to obtain the unit magnetic field strength; 3) Based on the BH curve of the given ferromagnetic material, the cubic spline interpolation method is used to solve the nonlinear unit magnetic induction intensity, and further obtain the unit magnetic permeability; 4) The relaxation coefficient method is used to iterate the magnetic permeability until the error requirement is met. The expression is as follows: m k+1 =am k +(1-a)m k-1 Where μ k+1 is the material permeability obtained by relaxation iteration, k is the current iteration number, α is the relaxation coefficient, 0<α<1.

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