Electromagnetic finite element calculation method for coupling orthotropic hysteresis model

Abstract

The invention relates to an electromagnetic finite element calculation method for coupling an orthotropic hysteresis model, which comprises the following steps of: establishing a finite element model of an analysis object, and determining a simulation time step length and a to-be-solved time step sequence; establishing an orthotropic dynamic Preisach hysteresis model based on an actually measured hysteresis loop and basic material parameters of the laminated core single sheets; based on an iterative algorithm and the Preisach hysteresis model, establishing a nonlinear system equation of the finite element model and an iterative equation of the nonlinear system equation; and at each time step to be solved, based on a Preisach hysteresis model and an iterative algorithm, solving a nonlinear system equation to obtain a time domain simulation result of the hysteresis finite element problem. According to the method, the defects of an existing electromagnetic finite element analysis technology in the aspects of hysteresis and anisotropy modeling are overcome, the calculation stability, efficiency, universality and the like are remarkably improved, and the urgent requirement of new-generation electrical equipment for the high-precision electromagnetic simulation technology can be met; the pharmaceutical composition has prominent substantive features and remarkable progress.

Description

Technical Field

[0001] This invention relates to the fields of magnetic material modeling and electromagnetic calculation technology, and in particular to an electromagnetic finite element calculation method for a coupled orthogonal anisotropic hysteresis model. Background Technology

[0002] In the field of electromagnetic design and performance analysis of electrical equipment, accurately determining the electromagnetic field distribution and evaluating key performance indicators are crucial for product design optimization, energy efficiency improvement, and reliability assessment. With the rapid development of computer technology and numerical simulation technology, electromagnetic numerical simulation technology based on the finite element method has become an indispensable core tool in the design of complex electromagnetic devices such as synchronous motors, asynchronous motors, transformers, and induction heating equipment. By discretizing a continuous domain into a finite number of elements and solving Maxwell's equations, the finite element method can obtain key parameters such as magnetic flux density, magnetic field strength, loss distribution, and electromagnetic force under different operating conditions. This provides engineers with intuitive and accurate design and analysis basis, thereby significantly shortening the design cycle, reducing the number of prototypes, and lowering R&D costs.

[0003] Currently, mainstream commercial electromagnetic finite element software generally uses single-value magnetization curves to describe the electromagnetic constitutive relationship of magnetic materials in practical engineering applications. This single-value magnetization characteristic assumes a single deterministic relationship between the magnetic flux density and magnetic field strength of the material, neglecting complex properties such as hysteresis, spatial anisotropy, and dynamic loss effects of magnetic materials. Although this simplification greatly reduces modeling complexity and improves computational efficiency, enabling the widespread adoption of numerical analysis in industrial design, its inherent limitations are becoming increasingly apparent in various applications involving high-precision electromagnetic simulation. On the one hand, this method cannot handle electromagnetic analysis problems with special equipment or high-precision requirements, such as torque analysis of hysteresis motors, residual magnetism assessment of transformers, or iron loss calculation under complex excitations. On the other hand, current national strategies and industrial upgrading place new demands on electrical equipment for high energy efficiency and high quality. Traditional methods are insufficient to support key indicators such as optimal material utilization and high-reliability equipment operation, necessitating the introduction of more accurate and efficient simulation technologies in the design phase.

[0004] Therefore, although existing commercial software and numerical simulation methods have played an irreplaceable role in general engineering design, they still suffer from insufficient accuracy, low computational efficiency, and poor iterative convergence when analyzing problems such as hysteresis, anisotropy, and dynamic losses. Based on this, developing a general computational method that can be stably and efficiently embedded into the finite element analysis framework and accurately describe the anisotropic hysteresis characteristics of materials has become an urgent technical requirement for improving the accuracy of electromagnetic structure design, optimizing the application of advanced materials, and realizing the development of high-quality electrical equipment. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide an electromagnetic finite element calculation method for a coupled orthogonal anisotropic hysteresis model.

[0006] This invention is achieved through the following technical solution: An electromagnetic finite element method for calculating a coupled orthogonal anisotropic magnetic hysteresis model includes the following steps: S1. Establish a finite element model of the analysis object, which includes a three-dimensional laminated iron core, coils and air, and determine the simulation time step and the time step sequence to be solved; S2. Based on the measured hysteresis loops and basic material parameters of the laminated iron core, an orthogonal anisotropic dynamic Preisach hysteresis model is established. S3. Based on the iterative algorithm and the orthogonal anisotropic dynamic Preisach hysteresis model, establish the nonlinear system equations and iterative equations of the finite element model; S4. At each time step to be solved, based on the orthogonal anisotropic dynamic Preisach hysteresis model and iterative algorithm, the nonlinear system equations are solved to obtain the time-domain simulation results of the hysteresis finite element problem.

[0007] According to the above technical solution, preferably, step S1 includes: Determining the Cartesian coordinate system axis, axis, Axial direction; Establish a geometric model of the object under analysis, wherein the stacking direction of the laminated iron cores is parallel to... axis; The entire region is meshed, and the simulation time step is defined as a constant. The time step sequence to be solved Defined as ,in , This represents the total number of simulation time steps.

[0008] According to the above technical solution, preferably, in step S2, the measured hysteresis loop is along... The magnetic flux density amplitude of the sample obtained by directional cutting under 5Hz magnetization condition From 0.1T to A cluster of alternating hysteresis loops, among which... For materials Near-saturation magnetic flux density in the direction of Choose x and y.

[0009] According to the above technical solution, preferably, in step S2, the basic material parameters are the thickness h of a single lamination of the laminated core material and its electrical conductivity. and residual loss coefficient .

[0010] According to the above technical solution, preferably, in step S2, the expression of the orthogonal anisotropic dynamic Preisach hysteresis model is: , in, That is, the orthogonal anisotropic dynamic Preisach hysteresis model outputs a magnetic field strength vector; for The magnetic flux density vector at that moment; They are respectively At any given time, the magnetic flux density Directional components; Represent The Preisach hysteresis model in terms of direction, i.e., the mapping from magnetic flux density components to magnetic field strength components; superscript This is the matrix transpose symbol; make ,use This represents the Preisach hysteresis model in the d-direction, where d is taken as... Then its expression is: , in, The static magnetic field strength output representing the Preisach hysteresis model in the d-direction is a component of its total output; and That is, the two are the same mapping and are functionally equivalent; Represents the magnetic flux density vector B d-direction component; ; , This is a sign function; it returns 1 for a positive number, 0 for zero, and -1 for a negative number.

[0011] According to the above technical solution, preferably, in step S3, the nonlinear system equation of the finite element model can be expressed as: , in, Let be the field degree of freedom vector. Let Lagrange multiplier vectors be used. For load vector, Here is the nonlinear stiffness matrix of the system; The boundary constraints of the nonlinear system equations can be uniformly expressed as follows: ,in, For the constraint matrix, A constraint value vector; The nonlinear system equations actually discretize the vector magnetic potential field as follows: , in, for The j-th element, For grid nodes Finite element basis functions, This represents the total number of nodes in the finite element mesh.

[0012] According to the above technical solution, preferably, in step S3, the iterative algorithm is the Newton-Raphson method, and the iterative algorithm establishes the iterative equations of the nonlinear system of the finite element model for solving. The iterative equations of the finite element model are expressed as: .

[0013] in, The total unknown vector, ; This is the residual vector.

[0014] According to the above technical solution, preferably, in step S4, the Jacobian matrix of the iterative algorithm is calculated using a hybrid differential magnetoresistance calculation method. The calculation method, a hybrid differential magnetoresistive method, is executed in each iteration of each time step to be solved until the convergence criterion is met, thus obtaining a convergent solution to the total unknown vector of the nonlinear system equations. Alternatively, the convergent solution of the field degree-of-freedom vector can be obtained. ;according to The vector magnetic potential, magnetic flux density, and magnetic field strength distribution of each time step to be solved can be calculated, thus obtaining the time-domain simulation results of the finite element model.

[0015] The beneficial effects of this invention are: This invention introduces an orthogonal anisotropic dynamic Preisach hysteresis model, which comprehensively considers magnetic saturation, hysteresis, magnetic anisotropy and dynamic magnetization characteristics. It can realistically reflect the magnetic response behavior of iron core materials under complex magnetization paths. Combined with the hysteresis parameter identification method based on Everett function, the model has high accuracy, smoothness and good material applicability.

[0016] In the finite element method (FEM) solution process, a hybrid differential magnetoresistive calculation method highly adapted to the Newton-Raphson algorithm is proposed. Through adaptive switching between time-difference and incremental-difference methods, it effectively balances computational efficiency and convergence stability, and eliminates the need for rigorous analytical derivatives, facilitating its extension to other hysteresis models. This method enables efficient and stable solutions to two-dimensional and three-dimensional electromagnetic finite element problems, significantly improving the efficiency and engineering applicability of electromagnetic simulation for electrical equipment.

[0017] In summary, this invention has made systematic improvements from multiple levels, including material constitutive modeling, numerical algorithm design, and finite element coupling solution mechanism. It not only effectively overcomes the shortcomings of existing electromagnetic finite element analysis technology in hysteresis and anisotropy modeling, but also achieves significant improvements in computational stability, efficiency, and versatility. It can meet the urgent needs of the new generation of electrical equipment for high-precision electromagnetic simulation technology, and has outstanding substantive features and significant progress. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the execution steps of an electromagnetic finite element calculation method for a coupled orthogonal anisotropic hysteresis model according to the present invention.

[0019] Figure 2 This is a finite element model diagram from Embodiment 2 of the present invention; wherein, Figure 2 (1) in the figure represents the overall geometric structure of the finite element model. Figure 2 (2) is a top view of the mesh division of the core domain and coil domain of the finite element model.

[0020] Figure 3 This is a simulation diagram of the hysteresis loop by the orthogonal anisotropic dynamic Preisach hysteresis model in Embodiment 2 of the present invention. Figure 3 In (1), the measured and simulated values ​​of the hysteresis loop of a single core piece in the x-direction are given. Figure 3 (2) represents the measured and simulated values ​​of the hysteresis loop of a single core piece in the y-direction.

[0021] Figure 4 This is a comparison chart of the solution efficiency of the hybrid differential magnetoresistance calculation method (the method of this invention) in Embodiment 2 of this invention and the traditional analytical method. Figure 4 (1) in the table compares the number of iterations required for each time step. Figure 4 (2) in the table compares the running time required for each time step.

[0022] Figure 5 This is a comparison chart of simulation results between the electromagnetic finite element calculation method (the method of this invention) of coupled orthogonal anisotropic magnetic hysteresis model in Embodiment 2 of this invention and the traditional analysis method. Figure 5 Figure (1) in the figure is a comparison of simulation and test results of the method of the present invention. Figure 5 (2) is a comparison chart of simulation and test results using the traditional analysis method.

[0023] Figure 6 In Embodiment 2 of this invention, the finite element calculation method described in this invention is applied to the core region under different excitation frequencies. Simulation results of the hysteresis loop at the point. Detailed Implementation

[0024] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and preferred embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0025] Example 1: As Figure 1 As shown, the present invention includes the following steps: S1. Establish a finite element model of the analysis object, which includes a three-dimensional laminated iron core, coils and air, and determine the simulation time step and the time step sequence to be solved.

[0026] When establishing a finite element model, the spatial axes of the Cartesian coordinate system are first determined. The direction is determined, and then a geometric model of the core, coils, and air domain is established based on this coordinate system. In particular, it is necessary to ensure that the stacking direction of the core laminations is parallel to the direction of the air. The axis is then used to mesh the entire region. The simulation time step is defined as a constant. The time-step sequence to be solved Defined as ,in , This represents the total number of simulation time steps.

[0027] S2. Based on the measured hysteresis loops and basic material parameters of the laminated iron core, an orthogonal anisotropic dynamic Preisach hysteresis model is established.

[0028] First, a single lamination of the stacked core refers to a single core material sample obtained by cutting along the spatial axis direction parallel to the spatial axis, based on the relative position of the spatial axis and the stacked core in the finite element model. Specifically, since the single core material sheet is relatively thin, cutting the sample along the z-axis of the spatial axis is not feasible; therefore, only two samples cut along the x-axis and y-axis directions need to be prepared.

[0029] Secondly, the measured hysteresis loop is along The magnetic flux density amplitude of the sample obtained by directional cutting under 5Hz magnetization condition From 0.1T to A cluster of alternating hysteresis loops (in 0.1T increments), also known as BH loops, in which... For materials Near-saturation magnetic flux density in the direction of Choose x and y.

[0030] Meanwhile, the basic material parameters are the thickness h of a single lamination of the laminated core material and its electrical conductivity. and residual loss coefficient The thickness of a single sheet was measured using a micrometer screw gauge, and the conductivity was obtained using the four-probe method. The residual loss coefficient... Obtained by the Bertotti loss separation method.

[0031] Furthermore, the expression for the orthogonal anisotropic dynamic Preisach hysteresis model is as follows: , in, That is, the orthogonal anisotropic dynamic Preisach hysteresis model outputs a magnetic field strength vector; for The magnetic flux density vector at that moment; They are respectively At any given time, the magnetic flux density Directional components; Represent The Preisach hysteresis model in terms of direction, i.e., the mapping from magnetic flux density components to magnetic field strength components; superscript This is the matrix transpose symbol; make ,Right now and For the same mapping relationship, when the input quantities are exactly the same, The reason is that the magnetic field vector of the laminated iron core is basically parallel to the laminated plane, and Since directional magnetic properties are difficult to measure and simulate, material properties in the y-direction are used as an approximation.

[0032] use This represents the Preisach hysteresis model in the d-direction, where d is taken as... Then its expression is: , in, The static magnetic field strength output representing the Preisach hysteresis model in the d-direction is a component of its total output; and That is, the two are the same mapping and are functionally equivalent; Represents the magnetic flux density vector B d-direction component; ; , This is a sign function; it returns 1 for a positive number, 0 for zero, and -1 for a negative number.

[0033] The mapping relationship represented is based on the Everett binary function in the d direction. and global magnetization function Established. Specifically, , The equals sign indicates that both sides of the equation have the same mapping and are functionally equivalent. Therefore, it is only necessary to identify the function. and This application provides a precise , The identification method should be noted that the following steps are based on... For example, direction ( Pick A unified description will be provided. In actual implementation, when... When choosing x or y, the processing is completely independent, and the parameters involved are not shared between them.

[0034] according to A cluster of alternating hysteresis loops in the directional sample, assuming their total number is... Extract the ascending branch of each cyclic line, and then... The mapping from magnetic flux density to magnetic field strength on a branch is denoted as the branch function. Among them, subscript The code for the loop .

[0035] make For the first The magnetic flux density amplitude of the loop, for each branch function In its domain The samples are taken in ascending order and at uniform intervals according to magnetic flux density. ( The )th sampling point (including endpoints). Let the be the . The first ascending branch sampling points The magnetic flux density at is The corresponding magnetic field strength is:

[0036] For each fixed sampling point number Construct the interpolation node set and function value set as follows:

[0037]

[0038] By performing piecewise cubic interpolation on the two point sets mentioned above, a cluster dependent on the sampling point index is obtained. The interpolation function is denoted as . That is, to form a function set:

[0039] This function set satisfies:

[0040] In the interval Internal extraction ( Take an odd number of equally spaced points, denoted as:

[0041] For each Substitute it into all The function yields the set of magnetic field strength points:

[0042] And construct the corresponding magnetic flux density auxiliary point set:

[0043] Using the aforementioned magnetic flux density auxiliary point set as interpolation nodes and the magnetic field strength point set as function values, an interpolation function is constructed through linear interpolation. Its domain is .

[0044] For all By performing the above process, a set of numbers is obtained. The set of interpolation functions:

[0045] This function set will be used directly. The identification process.

[0046] To construct a bivariate function First, determine its two-dimensional interpolation grid node set, and define the grid node index as: .

[0047] make Then the grid node set is:

[0048] On this grid, The node function values ​​are defined by the following piecewise functions:

[0049] in, Belongs to the function set mentioned above .

[0050] Based on the interpolation grid nodes and their corresponding function values, a continuous bivariate function can be constructed using the bilinear interpolation method. Its domain is .

[0051] The binary function This is solely for simulating the hysteresis characteristics of the core material. To describe the saturation magnetization of this material outside the hysteresis region, this application establishes a global magnetization function. :

[0052]

[0053] in, For the core material to be fully saturated with magnetic flux density, ; It is the vacuum magnetoresistance; Here, it is a formal argument of the function and has no special meaning. The fitting parameters are defined as follows:

[0054] In actual calculations, It can take tiny values, such as 0.001, to replace limit calculations.

[0055] This completes the function. The identification can also yield the function. .

[0056] Subsequently, this application also provides an efficient The output value calculation method should be noted as follows: For example, direction ( Pick A unified description will be provided. In actual implementation, when... Pick or At that time, the processing steps are completely independent, and the parameters involved are not shared between them. In particular, due to the characteristics of the core material... direction and The equivalence of directions makes .

[0057] To achieve efficient computation, this application creates a space with a size of... dynamic arrays Used to record key magnetization trajectory points. It is a variable whose value is determined by each time step. The input determines the outcome. Each column is shaped like , represents a magnetic flux density-magnetic field strength pair. It is updated at each time step and then passed to the next time step for consideration. The output depends on the current and historical inputs.

[0058] Based on the function , and dynamic arrays ,propose The calculation method is as follows: In the initial state, set Input Output ,initialization .

[0059] At any time Let the input be , Output calculation and The update is performed according to the following branch steps: Branch 1: Calculation of Saturated Region If satisfied Then, the saturation region calculation is performed: remember .

[0060] make ;Will Updated to .

[0061] The calculation is complete; proceed to the next moment.

[0062] Branch 2: Hysteresis Region Calculation If the saturation region calculation is not triggered, then the following hysteresis region calculation is performed: Compare current input Input from the previous moment : Branch 2.1: If ,but . No change. Calculation complete, proceed to the next time step.

[0063] Branch 2.2: If ,judge Whether it is valid, among which express The first element in the first row and first column.

[0064] Branch 2.2.1: If so, then let ;Will Updated to The calculation is complete; proceed to the next moment.

[0065] Branch 2.2.2: If not, determine the reference point according to the following steps. and : exist ( Find the last one greater than in the first row. The element is denoted as .

[0066] like If it exists, then for middle The next adjacent element; like If it does not exist, then .

[0067] remember for ( (second row) in Elements in the same column.

[0068] Calculation output: .

[0069] renew Remove All columns following the current column (excluding the current column itself), then... Add a new column at the end .

[0070] The calculation is complete; proceed to the next moment.

[0071] Branch 2.3: If ,judge Whether it is valid or not.

[0072] Branch 2.3.1: If so, then let ;Will Updated to The calculation is complete; proceed to the next moment.

[0073] Branch 2.3.2: If not, determine the reference point according to the following steps. and : exist Find the last one less than The element, whose value is denoted as _. .

[0074] like If it exists, then for middle The next adjacent element; like If it does not exist, then .

[0075] remember for Zhongyu Elements in the same column.

[0076] Calculation output: .

[0077] renew Remove All columns following the current column (excluding the current column itself), then... Add a new column at the end .

[0078] The calculation is complete; proceed to the next moment.

[0079] Thus, the orthogonal anisotropic dynamic Preisach hysteresis model can be established, and its output value can be determined according to... The expression is evaluated.

[0080] S3. Based on the iterative algorithm and the orthogonal anisotropic dynamic Preisach hysteresis model, establish the nonlinear system equations and iterative equations of the finite element model.

[0081] The equations of a nonlinear system in a finite element model can be expressed in matrix form: , This system is based on Maxwell's equations and uses vector magnetic potential. The field quantities to be solved are obtained by spatial discretization of the finite element model using the Galerkin method.

[0082] in, Let be the field degree of freedom vector. Let Lagrange multiplier vectors be used. For load vector, Here is the nonlinear stiffness matrix of the system; the boundary constraints of the nonlinear system equations can be uniformly expressed as: ,in, For the constraint matrix, This is the constraint value vector.

[0083] The nonlinear system equations actually discretize the vector magnetic potential field as follows: , in, for The j-th element, For grid nodes Finite element basis functions, This represents the total number of nodes in the finite element mesh.

[0084] Meanwhile, the iterative algorithm used in this application is the Newton-Raphson method. The iterative algorithm establishes the iterative equations of the nonlinear system of the finite element model for solving. First, the above matrix-form nonlinear system equations are rewritten into residual-form nonlinear equations:

[0085] in, The total unknown vector, ; residual vector Defined as:

[0086] Among them, the nonlinear response vector elements (No. (number of elements) is:

[0087] In addition, load vector elements for:

[0088] In the above two equations, For grid nodes Finite element basis functions, For the finite element solution domain; magnetic field strength ,in , This represents the Preisach hysteresis model described in step S2; Let be the source current density of the finite element model.

[0089] Based on the aforementioned nonlinear equations in residual form, the Newton-Raphson iterative equations for the finite element model are established as follows:

[0090] in, Represents the number of iterations. Represents the iterative increment of the solution. For the Jacobian matrix:

[0091] Among them, the tangent stiffness matrix elements The calculation is as follows:

[0092] In the formula, For the differential magnetoresistivity tensor of the material, the iron core region Based on the Preisach hysteresis model The calculation method is detailed in step S4. For areas outside the core region, Degenerate into a scalar .

[0093] The iterative algorithm repeatedly updates the algorithm according to the aforementioned Newton-Raphson iterative equation until the convergence criterion is met, thus obtaining the desired result. The convergent solution.

[0094] S4. At each time step to be solved, based on the orthogonal anisotropic dynamic Preisach hysteresis model and iterative algorithm, the nonlinear system equations are solved to obtain the time-domain simulation results of the hysteresis finite element problem.

[0095] In this application, a hybrid differential magnetoresistance calculation method is used for the Jacobian matrix in the iterative algorithm. The calculation is performed, where the hybrid differential magnetoresistive calculation method is executed in each iteration of each time step to be solved. Specifically, for time... (At the k-th time step), the aforementioned Newton-Raphson iterative equation can be written as:

[0096] Among them, the Jacobian matrix and tangent stiffness matrix elements for:

[0097]

[0098] For ease of explanation, the formula will be... Abbreviated as ;make express The quantity in the value is the value of the nth iteration at step k, and so on. express The quantity in the first The convergence value of the time step, the same applies below.

[0099] Iron Heart Area The differential magnetoresistance is determined by the aforementioned calculation method, which is performed according to the following steps: set up ,Right now Let them be a pair of diagonal tensors. The main diagonal elements are collectively denoted as , in .

[0100] In particular, , .

[0101] Branch 1: If , , This is the differential magnetoresistive tensor used during the convergence of the previous time step.

[0102] Branch 2: If , set up ( ) is a relatively small value, typically 0.01.

[0103] Execution Step The In the next iteration, let (especially) The historical input sequence (partially) is as follows: ,Right now and all time steps prior to it Convergence value; corresponding time series: Based on this state ,Will The calculation is as follows: Branch 2.1: If ,

[0104] in, The output is calculated according to the method described in step S2; specifically, it should be... Considered Input at any moment.

[0105] Branch 2.2: If ,

[0106] in, , , ; The output is calculated according to the method described in step S2; specifically, it should be... , Considered separately , Input the time interval and calculate in chronological order. The output of .

[0107] Branch 3: If ,

[0108] In actual calculations, It can take tiny values, such as 0.001, to replace limit calculations.

[0109] Thus, the Iron Heart area This can be determined. Branches 2.1 and 2.2 are respectively called the time-difference method and the incremental difference method, which constitute the main body of the hybrid differential magnetoresistive calculation method. This method can prioritize shortening the calculation time when the iteration increment is small, and prioritize ensuring convergence performance when the iteration increment is large.

[0110] Furthermore, as described in step S3, for other areas outside the core region, Constant as a scalar .

[0111] The hybrid differential magnetoresistance calculation method is executed in each iteration of each time step to be solved until the convergence criterion is met, thus obtaining the convergent solution of the total unknown vector of the nonlinear system equation. Alternatively, the convergent solution of the field degree-of-freedom vector can be obtained. ;according to The vector magnetic potential, magnetic flux density, and magnetic field strength distribution of each time step to be solved can be calculated, thus obtaining the time-domain simulation results of the finite element model.

[0112] Example 2: To verify the method proposed in this example, a system was established as follows: Figure 2 The finite element baseline model shown is proposed by the International Electromagnetic Computation Association and named TEAM P32 (Testing Electromagnetic Analysis Methods Problem 32), specifically designed to evaluate numerical simulation methods for anisotropic hysteresis. The model structure includes a three-pillar laminated iron core and two excitation coils, each excited by an AC voltage source with a 90° phase difference. Under a 10Hz periodic time-varying excitation, a rotating magnetic field is generated in the T-connected region of the laminated iron core. The local magnetic flux density waveform in this region can be measured by the core-wound induction coils. By comparing the consistency between the actual measured waveform and the simulated waveform, the effectiveness of the numerical calculation method described in this invention can be evaluated.

[0113] right Figure 2 The finite element model shown was subjected to time-step simulation with a time step size of 1.25e-3 s. A total of 2 cycles were solved, resulting in 161 time steps (including time 0). The excitation coil was set as a current-type coil, and the current waveform was obtained from measured data.

[0114] A test platform for this model was constructed, in which the core material was composed of five stacked 0.35mm thick silicon steel sheets. This material has an electrical conductivity of 1.695e6 S / m and a residual loss coefficient of 0.2291. Each excitation coil consists of 90 turns. It is made of copper wire.

[0115] function , During the identification process, for The relevant parameter selection and calculation results are shown in Table 1: Table 1. Parameter selection and calculation results in the hysteresis model identification process. ; To verify the accuracy of the hysteresis model described in this invention in characterizing the core material, its simulation results are presented below. Figure 3 .in, x , y The measured data for each direction are obtained from single samples cut along the corresponding direction. Each figure shows the simulation results of hysteresis loops with the same amplitude at two frequency points. The hysteresis loops shown were not involved in the model identification process. The results demonstrate the accuracy of the hysteresis model in simulating the static and dynamic hysteresis loops of the core material.

[0116] To verify the beneficial effects of the hybrid differential magnetoresistive calculation method described in this invention, its computational efficiency is compared with that of the traditional analytical method. The traditional method calls [the method name] in each iteration of each time step. or The analytical expression of the differential magnetoresistance tensor is derived and the calculation of the differential magnetoresistance tensor is completed. Compared with the method of the present invention, this results in a significant redundant computational overhead and poor versatility. Figure 4 The diagram illustrates the number of iterations and runtime for each time step in the entire solution process for both methods. It can be observed that the convergence capabilities of the two methods are similar, meaning the required number of iterations almost overlaps; however, the method described in this invention significantly reduces the total time consumption by employing an efficient time-difference method to calculate the differential reluctance in intervals with small iteration increments. Specifically, in plotting… Figure 4 In (2), the running time is defined as: (total simulation time / total number of iterations) × number of iterations at that time step.

[0117] To verify the beneficial effects of the finite element method for the coupled hysteresis model described in this invention, its simulation results are compared with those of traditional analysis methods. Traditional methods use isotropic single-valued magnetization curves to characterize the magnetic properties of the iron core, which are characterized by fast calculation speed and ease of implementation. However, as... Figure 5 As shown, the simulation results of the magnetic flux density trajectory in the test area of ​​the benchmark model differ between the two methods. The degree of agreement between the proposed method and the measured values ​​is significantly higher than that of the traditional method, which proves the effectiveness and necessity of the method proposed in this invention.

[0118] To verify that the finite element method for the coupled hysteresis model described in this invention can reflect the dynamic response of the core material at different frequencies, the simulation current frequency was changed sequentially to 100Hz, 400Hz, and 800Hz, and the core column of the iron core was examined. The variation of the hysteresis loop at a given point at various frequencies is presented in [the diagram / image]. Figure 6It can be observed that the area enclosed by the loop increases with increasing frequency. This is because the hysteresis model described in this invention takes into account eddy current losses and abnormal losses. Therefore, within a certain frequency band, eddy current-related terms can be ignored in the finite element master equation (especially when using a 2D finite element model to simulate laminated iron cores), and the dynamic magnetic field and loss distribution in the iron core can be simulated using the hysteresis model and finite element calculation method described in this invention.

[0119] In summary, this invention addresses the prominent technical shortcomings of traditional finite element methods, such as insufficient modeling accuracy of magnetic materials, poor stability in solving hysteresis problems, and difficulty in balancing computational efficiency and versatility. It provides an electromagnetic finite element calculation method with coupled orthogonal anisotropic hysteresis models. Systematic improvements have been made at multiple levels, including material constitutive modeling, numerical algorithm design, and finite element coupling solution mechanisms. This method not only effectively overcomes the deficiencies of existing electromagnetic finite element analysis techniques in hysteresis and anisotropic modeling but also achieves significant improvements in computational stability, efficiency, and versatility. It can meet the urgent needs of next-generation electrical equipment for high-precision electromagnetic simulation technology, demonstrating outstanding substantive features and significant progress.

[0120] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. An electromagnetic finite element calculation method for a coupled orthogonal anisotropic magnetic hysteresis model, characterized in that, Includes the following steps: S1. Establish a finite element model of the analysis object, which includes a three-dimensional laminated iron core, coils and air, and determine the simulation time step and the time step sequence to be solved; S2. Based on the measured hysteresis loops and basic material parameters of the laminated iron core, an orthogonal anisotropic dynamic Preisach hysteresis model is established. S3. Based on the iterative algorithm and the orthogonal anisotropic dynamic Preisach hysteresis model, establish the nonlinear system equations and iterative equations of the finite element model; S4. At each time step to be solved, based on the orthogonal anisotropic dynamic Preisach hysteresis model and iterative algorithm, the nonlinear system equations are solved to obtain the time-domain simulation results of the hysteresis finite element problem.

2. The electromagnetic finite element calculation method for a coupled orthogonal anisotropic magnetic hysteresis model according to claim 1, characterized in that, Step S1 includes: Determining the Cartesian coordinate system axis, axis, Axial direction; Establish a geometric model of the object under analysis, wherein the stacking direction of the laminated iron cores is parallel to... axis; The entire region is meshed, and the simulation time step is defined as a constant. The time step sequence to be solved Defined as ,in , This represents the total number of simulation time steps.

3. The electromagnetic finite element calculation method for a coupled orthogonal anisotropic magnetic hysteresis model according to claim 1, characterized in that, In step S2, the measured hysteresis loop is along... The magnetic flux density amplitude of the sample obtained by directional cutting under 5Hz magnetization condition From 0.1T to A cluster of alternating hysteresis loops, among which, For materials Near-saturation magnetic flux density in the direction of Choose x and y.

4. The electromagnetic finite element calculation method for a coupled orthogonal anisotropic magnetic hysteresis model according to claim 3, characterized in that, In step S2, the basic material parameters are the thickness h of a single lamination of the laminated core material and its electrical conductivity. and residual loss coefficient .

5. The electromagnetic finite element calculation method for a coupled orthogonal anisotropic hysteresis model according to claim 4, characterized in that, In step S2, the expression for the orthogonal anisotropic dynamic Preisach hysteresis model is: ， in, That is, the orthogonal anisotropic dynamic Preisach hysteresis model outputs a magnetic field strength vector; for The magnetic flux density vector at that moment; They are respectively At any given time, the magnetic flux density Directional components; Represent The Preisach hysteresis model in terms of direction, i.e., the mapping from magnetic flux density components to magnetic field strength components; superscript This is the matrix transpose symbol; make ,use This represents the Preisach hysteresis model in the d-direction, where d is taken as... Then its expression is: ， in, The static magnetic field strength output representing the Preisach hysteresis model in the d-direction is a component of its total output; and That is, the two are the same mapping and are functionally equivalent; Represents the magnetic flux density vector B d-direction component; ; , This is a sign function; it returns 1 for a positive number, 0 for zero, and -1 for a negative number.

6. The electromagnetic finite element calculation method for a coupled orthogonal anisotropic magnetic hysteresis model according to any one of claims 1-5, characterized in that, In step S3, the nonlinear system equations of the finite element model can be expressed as: ， in, Let be the field degree of freedom vector. Let Lagrange multiplier vectors be used. For load vector, Here is the nonlinear stiffness matrix of the system; The boundary constraints of the nonlinear system equations can be uniformly expressed as follows: ,in, For the constraint matrix, A constraint value vector; The nonlinear system equations actually discretize the vector magnetic potential field as follows: ， in, for The j-th element, For grid nodes Finite element basis functions, This represents the total number of nodes in the finite element mesh.

7. The electromagnetic finite element calculation method for a coupled orthogonal anisotropic hysteresis model according to claim 6, characterized in that, In step S3, the iterative algorithm is the Newton-Raphson method. This iterative algorithm establishes the iterative equations of the nonlinear system of the finite element model for solution. The iterative equations of the finite element model are expressed as: , in, The total unknown vector, ; This is the residual vector.

8. The electromagnetic finite element calculation method for a coupled orthogonal anisotropic magnetic hysteresis model according to claim 7, characterized in that, In step S4, the Jacobian matrix of the iterative algorithm is calculated using a hybrid differential magnetoresistance calculation method. calculate.

9. The electromagnetic finite element calculation method for a coupled orthogonal anisotropic magnetic hysteresis model according to claim 8, characterized in that, In step S4, the hybrid differential magnetoresistance calculation method is executed in each iteration of each time step to be solved until the convergence criterion is met, thus obtaining the convergent solution of the total unknown vector of the nonlinear system equation. The convergent solution of the field degree-of-freedom vector can also be obtained. ; according to The vector magnetic potential, magnetic flux density, and magnetic field strength distribution of each time step to be solved can be calculated, thus obtaining the time-domain simulation results of the finite element model.

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