Magnetic conductivity initial value prediction method for improving motor finite element analysis and calculation efficiency

Abstract

The invention discloses a magnetic conductivity initial value prediction method for improving motor finite element analysis and calculation efficiency, and belongs to the technical field of motor design and electromagnetic field numerical calculation. The problem of improving the solving speed of a motor finite element model is solved. The method comprises the steps of establishing a stator side equivalent magnetic circuit model; establishing a rotor side magnetic field distribution prediction model for predicting air gap magnetic field distribution under different rotor topological structures; constructing a rotor side equivalent magnetic circuit model based on air-gap magnetic field distribution under different rotor topological structures predicted by a rotor side magnetic field distribution prediction model, and then solving by combining the stator side equivalent magnetic circuit model and the obtained rotor side equivalent magnetic circuit model. And obtaining magnetic conductivity approximate distribution data of a motor iron core area as an initial value, substituting the initial value into the finite element model of the motor, and carrying out iterative solution to obtain a motor electromagnetic performance analysis result. The method effectively solves the problems that in traditional finite element analysis, due to blind setting of the initial magnetic conductivity, the number of non-linear iterations is large, and calculation time is long.

Description

Technical Field

[0001] This invention belongs to the field of motor design and electromagnetic field numerical calculation technology, specifically relating to a method for predicting the initial value of permeability to improve the calculation efficiency of finite element analysis of motors. Background Technology

[0002] With the rapid development of new energy vehicles, aerospace, and high-end industrial servo systems, extremely high demands are being placed on the power density and efficiency of permanent magnet synchronous motors (PMSMs). In the process of fine motor design, the finite element method has become an indispensable analysis tool due to its ability to accurately handle complex geometries and material nonlinear characteristics.

[0003] However, the finite element method faces significant challenges in computational efficiency, especially when dealing with the nonlinear saturation characteristics of ferromagnetic materials. To simulate the BH nonlinear relationship of core materials, finite element solvers typically employ the Newton-Raphson algorithm for iterative solutions. In traditional finite element analysis, the initial permeability is usually set to the vacuum permeability or a fixed constant. Because this initial value deviates significantly from the actual permeability distribution under the motor's operating conditions (especially under heavy load saturation), the solver often requires a large number of iterations to reach the convergence region, which greatly consumes computational resources and time. For design scenarios requiring large-scale multi-objective optimization, this time cost is unacceptable.

[0004] While existing technologies offer fast computational models based on analytical methods or simple equivalent magnetic circuit methods, analytical methods struggle to accurately describe stator slotting effects and core saturation. Traditional equivalent magnetic circuit models suffer from poor versatility when dealing with complex and varied rotor topologies (such as built-in "I"-shaped or built-in "V"-shaped rotors), resulting in high modeling difficulty and limited accuracy. Therefore, there is an urgent need for a method to accelerate finite element model solving that maintains the high accuracy of finite element methods while significantly improving convergence speed. Summary of the Invention

[0005] The problem this invention aims to solve is to improve the speed of solving finite element models of motors, and proposes a method for predicting the initial value of permeability to improve the calculation efficiency of finite element analysis of motors.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for predicting the initial value of magnetic permeability to improve the calculation efficiency of finite element analysis of electric motors includes the following steps:

[0008] S1. Establish the equivalent magnetic circuit model on the stator side;

[0009] S2. Establish a rotor-side magnetic field distribution prediction model to predict the air gap magnetic field distribution under different rotor topologies;

[0010] S3. Based on the air gap magnetic field distribution predicted by the rotor-side magnetic field distribution prediction model obtained in step S2, construct the rotor-side equivalent magnetic circuit model, and then solve the stator-side equivalent magnetic circuit model obtained in step S1 and the rotor-side equivalent magnetic circuit model to obtain the approximate distribution data of magnetic permeability in the motor core region.

[0011] S4. Substitute the approximate distribution data of magnetic permeability in the motor core region obtained in step S3 as the initial value into the finite element model of the motor for iterative solution to obtain the electromagnetic performance analysis results of the motor.

[0012] Furthermore, the specific implementation method of step S1 includes the following steps:

[0013] S1.1. Based on the air region of the stator slot equivalent with constant reluctance, the iron core region of the stator tooth and yoke equivalent with variable reluctance, and the excitation effect of the equivalent winding current of the magnetomotive force source, an equivalent magnetic circuit model with the stator slot and the corresponding region as the basic unit is constructed.

[0014] The permeability of the constant reluctance is set to the permeability of vacuum, while the permeability of the variable reluctance is calculated based on the magnetic flux density in the region and the magnetization curve of the core material.

[0015] The constant reluctance R of the equivalent magnetic circuit model on the stator side Const Variable reluctance R Var The formula for calculating the magnetomotive force source F is as follows:

[0016]

[0017]

[0018]

[0019] Where μ0 is the free permeability, μ Var denoted as ρ, where ρ is the permeability of the variable reluctance, l is the equivalent region length, A is the equivalent region cross-sectional area, N is the number of turns in the winding, and i is the winding current.

[0020] S1.2. Based on the periodic symmetry of the motor stator geometry, an equivalent magnetic circuit model for the stator side is established using the stator slots and corresponding regions obtained in step S1 as the basic units. The magnetic circuit structure of each stator slot unit in the equivalent magnetic circuit model for the stator side remains consistent.

[0021] Furthermore, the specific implementation method of step S2 includes the following steps:

[0022] S2.1. Determine key design parameters based on the rotor topology, including permanent magnet dimensions, pole arc coefficient, and magnetic bridge width;

[0023] S2.2. Conduct sample collection, and obtain the key design parameter combination covering the design space through Latin hypercube sampling, including rotor design parameters and position angle parameters;

[0024] S2.3. Use the finite element analysis method to solve in batches the magnetic flux density data of different positions on the inner surface of the equivalent stator core under the combination of key design parameters obtained in step S2.2;

[0025] S2.4. Using rotor design parameters and position angle parameters as input data, and magnetic flux density data at different positions on the inner circular surface of the equivalent stator core under the corresponding position angle parameters as output data, a training dataset for the rotor side magnetic field distribution prediction model is established.

[0026] S2.5. Train a random forest regression model based on the training dataset to obtain a rotor-side magnetic field distribution prediction model, which is used to predict the air gap magnetic field distribution under different rotor topologies.

[0027] Furthermore, the specific implementation method of step S2.3 includes the following steps:

[0028] S2.3.1. Geometric model construction: Draw the rotor geometric model based on the rotor design parameters;

[0029] S2.3.2. Material property definition, assigning corresponding electromagnetic characteristic parameters to different components, including magnetization curve data of core material, magnetization direction of permanent magnet and remanence parameters;

[0030] S2.3.3. The boundary conditions are set to have a magnetic field in the radial direction only on the inner circular surface of the equivalent stator core;

[0031] S2.3.4. Model mesh generation: The geometric model is discretized into finite elements using the finite element method;

[0032] S2.3.5. Model Solving: The static magnetic field analysis mode is used to solve the model and obtain the magnetic flux density data at different positions on the inner circular surface of the equivalent stator core.

[0033] Furthermore, the specific implementation method of step S3 includes the following steps:

[0034] S3.1. Establish a rotor equivalent magnetic circuit model that matches the stator-side equivalent magnetic circuit structure. Based on the stator-side magnetic circuit division structure, divide the air gap region into several sector regions and perform equivalent transformations using constant reluctance and magnetomotive force sources respectively.

[0035] The invariant reluctance of the rotor equivalent magnetic circuit model simulates the influence of the air gap region and the permanent magnet region on the magnetic field flow. The resistance value R is used to represent the invariant reluctance of the sector region corresponding to the central angle θ.r (θ) is calculated based on the geometric parameters of the air gap and permanent magnet, and its expression is as follows:

[0036]

[0037] Where g is the air gap thickness, r si L is the inner radius of the stator. ef h is the axial length of the motor. m,i l m,i Let μ0 and μ be the thickness and width of the i-th permanent magnet, respectively. m These are the permeability of vacuum and the permeability of permanent magnets, respectively.

[0038] Magnetomotive force source F in the rotor equivalent magnetic circuit model r (θ) simulates the excitation effect of a permanent magnet rotor, used as an equivalent magnetomotive force source for a sector region with a central angle of θ. The calculation method is as follows:

[0039]

[0040] Among them, B r (ω) is the magnetic flux density at position ω on the inner circle of the stator, calculated based on the rotor-side magnetic field distribution prediction model in step S2. To calculate the magnetic flux of the equivalent sector region using the discrete integration method;

[0041] S3.2. Connect the stator-side equivalent magnetic circuit model and the rotor-side equivalent magnetic circuit model to merge them into a complete motor equivalent magnetic circuit model;

[0042] S3.3. Solve the complete equivalent magnetic circuit model of the motor obtained in step S3.2 through iterative calculation to obtain the approximate distribution data of magnetic permeability in the motor core region.

[0043] Furthermore, in step S4, the initial value file of the approximate distribution data of the magnetic permeability of the motor core region obtained in step S3 is substituted into the finite element mesh element to set the starting iteration point for the nonlinear solution of the finite element model.

[0044] The beneficial effects of this invention are:

[0045] The present invention provides a method for predicting the initial value of magnetic permeability to improve the computational efficiency of finite element analysis of motors. This method significantly improves computational efficiency by using a hybrid model (equivalent magnetic circuit + surrogate model) with low computational cost to pre-obtain a magnetic permeability distribution close to the true solution, replacing the blind initial value setting in traditional finite element analysis and greatly reducing the number of calculations required for nonlinear iterative convergence.

[0046] The present invention provides a method for predicting the initial value of permeability to improve the calculation efficiency of finite element analysis of motors. This method is highly versatile. It uses a data-driven surrogate model on the rotor side, which avoids the shortcomings of traditional analytical methods that are difficult to adapt to complex and variable rotor topologies (such as built-in "I" type, built-in "V" type, etc.).

[0047] The present invention provides a method for predicting the initial value of magnetic permeability to improve the calculation efficiency of finite element analysis of motors, while ensuring no loss of accuracy. The present invention does not sacrifice mesh density for speed, but rather optimizes the convergence starting point of the algorithm to achieve rapid solution while ensuring high accuracy of finite element analysis. Attached Figure Description

[0048] Figure 1 This is a flowchart of a method for predicting the initial value of magnetic permeability to improve the calculation efficiency of finite element analysis of motors, as described in this invention.

[0049] Figure 2 This is a schematic diagram of the cross-sectional structure of a 10-pole, 12-slot permanent magnet synchronous motor in an embodiment of the present invention;

[0050] Figure 3 This is a diagram of the equivalent magnetic circuit topology of the stator side of the motor under unit slot pitch in an embodiment of the present invention, showing the node connection relationship of the teeth, yoke, and leakage magnetic path;

[0051] Figure 4 This is a schematic diagram illustrating the process of establishing a surrogate model for predicting the rotor-side magnetic field distribution in an embodiment of the present invention.

[0052] Figure 5 This is a diagram of the equivalent magnetic circuit topology of the motor per unit slot pitch in an embodiment of the present invention.

[0053] Figure 6 This is a schematic diagram of the iterative solution process for the equivalent magnetic circuit model of the motor in an embodiment of the present invention. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.

[0055] Therefore, the following detailed description of specific embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.

[0056] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with accompanying drawings. Figure 1 - Appendix Figure 6 Detailed explanation is as follows:

[0057] Example 1:

[0058] A method for predicting the initial value of magnetic permeability to improve the calculation efficiency of finite element analysis of electric motors includes the following steps:

[0059] S1. Establish the equivalent magnetic circuit model on the stator side;

[0060] Furthermore, the specific implementation method of step S1 includes the following steps:

[0061] S1.1. Based on the air region of the stator slot equivalent with constant reluctance, the iron core region of the stator tooth and yoke equivalent with variable reluctance, and the excitation effect of the equivalent winding current of the magnetomotive force source, an equivalent magnetic circuit model with the stator slot and the corresponding region as the basic unit is constructed.

[0062] The permeability of the constant reluctance is set to the permeability of vacuum, while the permeability of the variable reluctance is calculated based on the magnetic flux density in the region and the magnetization curve of the core material.

[0063] The constant reluctance R of the equivalent magnetic circuit model on the stator side Const Variable reluctance R Var The formula for calculating the magnetomotive force source F is as follows:

[0064]

[0065]

[0066]

[0067] Where μ0 is the free permeability, μ Var denoted as ρ, where ρ is the permeability of the variable reluctance, l is the equivalent region length, A is the equivalent region cross-sectional area, N is the number of turns in the winding, and i is the winding current.

[0068] S1.2. Based on the periodic symmetry of the motor stator geometry, an equivalent magnetic circuit model for the stator side is established using the stator slots and corresponding regions obtained in step S1 as the basic units. The magnetic circuit structure of each stator slot unit in the equivalent magnetic circuit model for the stator side remains consistent.

[0069] S2. Establish a rotor-side magnetic field distribution prediction model to predict the air gap magnetic field distribution under different rotor topologies;

[0070] Furthermore, the specific implementation method of step S2 includes the following steps:

[0071] S2.1. Determine key design parameters based on rotor topology, including permanent magnet dimensions, pole arc coefficient, and magnetic bridge width (for built-in rotors).

[0072] S2.2. Conduct sample collection, and obtain the key design parameter combination covering the design space through Latin hypercube sampling, including rotor design parameters and position angle parameters;

[0073] S2.3. Use the finite element analysis method to solve in batches the magnetic flux density data of different positions on the inner surface of the equivalent stator core under the combination of key design parameters obtained in step S2.2;

[0074] Furthermore, the specific implementation method of step S2.3 includes the following steps:

[0075] S2.3.1. Geometric model construction: Draw the rotor geometric model based on the rotor design parameters;

[0076] S2.3.2. Material property definition, assigning corresponding electromagnetic characteristic parameters to different components, including magnetization curve data of core material, magnetization direction of permanent magnet and remanence parameters;

[0077] S2.3.3. The boundary conditions are set to have a magnetic field in the radial direction only on the inner circular surface of the equivalent stator core;

[0078] S2.3.4. Model mesh generation: The geometric model is discretized into finite elements using the finite element method;

[0079] S2.3.5. Model Solving: The static magnetic field analysis mode is used to solve the model and obtain the magnetic flux density data at different positions on the inner circular surface of the equivalent stator core.

[0080] S2.4. Using rotor design parameters and position angle parameters as input data, and magnetic flux density data at different positions on the inner circular surface of the equivalent stator core under the corresponding position angle parameters as output data, a training dataset for the rotor side magnetic field distribution prediction model is established.

[0081] S2.5. Train a random forest regression model based on the training dataset to obtain a rotor-side magnetic field distribution prediction model, which is used to predict the air gap magnetic field distribution under different rotor topologies.

[0082] S3. Based on the air gap magnetic field distribution predicted by the rotor-side magnetic field distribution prediction model obtained in step S2, construct the rotor-side equivalent magnetic circuit model, and then solve the stator-side equivalent magnetic circuit model obtained in step S1 and the rotor-side equivalent magnetic circuit model to obtain the approximate distribution data of magnetic permeability in the motor core region.

[0083] Furthermore, the specific implementation method of step S3 includes the following steps:

[0084] S3.1. Establish a rotor equivalent magnetic circuit model that matches the stator-side equivalent magnetic circuit structure. Based on the stator-side magnetic circuit division structure, divide the air gap region into several sector regions and perform equivalent transformations using constant reluctance and magnetomotive force sources respectively.

[0085] The invariant reluctance of the rotor equivalent magnetic circuit model simulates the influence of the air gap region and the permanent magnet region on the magnetic field flow. The resistance value R is used to represent the invariant reluctance of the sector region corresponding to the central angle θ. r (θ) is calculated based on the geometric parameters of the air gap and permanent magnet, and its expression is as follows:

[0086]

[0087] Where g is the air gap thickness, r si L is the inner radius of the stator. ef h is the axial length of the motor. m,i l m,i Let μ0 and μ be the thickness and width of the i-th permanent magnet, respectively. m These are the permeability of vacuum and the permeability of permanent magnets, respectively.

[0088] Magnetomotive force source F in the rotor equivalent magnetic circuit model r (θ) simulates the excitation effect of a permanent magnet rotor, used as an equivalent magnetomotive force source for a sector region with a central angle of θ. The calculation method is as follows:

[0089]

[0090] Among them, B r (ω) is the magnetic flux density at position ω on the inner circle of the stator, calculated based on the rotor-side magnetic field distribution prediction model in step S2. To calculate the magnetic flux of the equivalent sector region using the discrete integration method;

[0091] S3.2. Connect the stator-side equivalent magnetic circuit model and the rotor-side equivalent magnetic circuit model to merge them into a complete motor equivalent magnetic circuit model;

[0092] S3.3. Solve the complete equivalent magnetic circuit model of the motor obtained in step S3.2 through iterative calculation to obtain the approximate distribution data of magnetic permeability in the motor core region.

[0093] S4. Substitute the approximate distribution data of magnetic permeability in the motor core region obtained in step S3 as the initial value into the finite element model of the motor for iterative solution to obtain the electromagnetic performance analysis results of the motor.

[0094] Furthermore, in step S4, the initial value file of the approximate distribution data of the magnetic permeability of the motor core region obtained in step S3 is substituted into the finite element mesh element to set the starting iteration point of the nonlinear solver of the finite element model.

[0095] Furthermore, in step S4, although the equivalent magnetic circuit model and the surrogate model have certain simplification errors, the calculated magnetic permeability distribution trend is highly consistent with the real physical field. This data is extracted and formatted into an initial value file that can be recognized by the finite element software. This initial value file is substituted into the finite element mesh element to set the starting iteration point for the nonlinear solution of the finite element model, thereby reducing the number of iteration calculations required for the finite element solution to reach convergence.

[0096] The following is a practical application example of this embodiment:

[0097] Step S1: Establish the equivalent magnetic circuit model on the stator side.

[0098] by Figure 2 The 10-pole, 12-slot permanent magnet synchronous motor shown is the object of analysis. Considering the periodic symmetry of the motor, a stator slot pitch (30-degree mechanical angle) is selected as the basic unit. The equivalent magnetic circuit topology of the stator side under a unit slot pitch is shown in the figure below. Figure 3 As shown, the equivalent magnetic circuit model divides the stator physical region into: the stator yoke, the stator tooth body, the stator tooth tip, and the slot leakage magnetic region. Variable reluctance is used in the equivalent flux linkage model to simulate the core material. The variable reluctance R of the equivalent stator tooth body region is used as an example. tooth For example, the formula for calculating its resistance is:

[0099]

[0100] Among them, l tooth A is the average length of the tooth region. tooth μ is the average cross-sectional area of ​​the tooth region. tooth The permeability of the tooth region is obtained by interpolating the magnetization curve of the core material based on the magnetic flux density of the tooth region.

[0101] In the equivalent flux linkage model, the variable reluctance is used to simulate air or non-magnetic regions (such as the winding space within the slot and slot leakage flux), and its permeability is constant at the free permeability μ0. The constant reluctance R of the equivalent stator slot region is used as the simulating factor. slot For example, the formula for calculating its resistance is:

[0102]

[0103] Among them, l slot A is the average length of the groove region. slot denoted as the average cross-sectional area of ​​the groove region, and μ0 as the vacuum permeability.

[0104] Magnetomotive force source F in the equivalent flux linkage model coil The formula for calculating the value of the excitation effect used to simulate the winding current is as follows:

[0105]

[0106] Where N is the number of turns in the winding, i phase This represents the instantaneous value of the phase current at the current moment.

[0107] Each stator tooth root node of the motor is connected to the adjacent tooth root node through the yoke magnetic reluctance, and each stator tooth tip node is connected to the adjacent tooth tip node through the slot magnetic reluctance.

[0108] Step S2: Establish a surrogate model for predicting the rotor-side magnetic field distribution. The model establishment process is as follows: Figure 4 As shown.

[0109] For the built-in "I"-shaped rotor topology in this embodiment, the traditional magnetic circuit method is difficult to consider the influence of complex geometric structures such as magnetic isolation bridges on the rotor magnetic field distribution. Therefore, a data-driven surrogate model based on random forest is used to predict the rotor magnetic field distribution. The specific implementation steps are as follows:

[0110] Step S21: Determine key design parameters based on rotor topology. By analyzing the geometric characteristics of the built-in "I"-shaped rotor topology in this embodiment, four key design parameters are specifically selected: permanent magnet width l m Permanent magnet thickness h m Magnetic bridge width l bridge Polar arc coefficient α p .

[0111] Step S22: Sample collection is performed by obtaining a series of design parameter combinations covering the design space through Latin hypercube sampling. In this embodiment, the Latin hypercube sampling algorithm is used to extract 500 sample points within the aforementioned four-dimensional key parameter design space. Latin hypercube sampling ensures a uniform distribution of samples within the design space, avoids the clustering phenomenon of traditional random sampling, and improves the generalization ability of the surrogate model.

[0112] Step S23: The rotor air gap magnetic field distribution characteristics under the aforementioned design parameter combination are solved in batches using the finite element method. In this embodiment, the script interface of electromagnetic simulation finite element software such as Ansys Maxwell or Flux is used to automatically batch process and solve the 500 sets of collected sample points. The specific modeling and solution methods are as follows:

[0113] Step S231: Geometric model construction, draw the rotor geometric model according to the rotor design parameters;

[0114] Step S232: Material property definition, assigning corresponding electromagnetic characteristic parameters to different components, the core of which includes: magnetization curve data of iron core material, magnetization direction of permanent magnet and remanence parameters, etc.

[0115] Step S233: Set boundary conditions, ignore the slotted structure of the stator core, and treat the stator core as an equivalent ring structure with infinite permeability. At this time, only the radial magnetic field exists on the inner circular surface of the equivalent stator core.

[0116] Step S234: Model mesh generation, using the finite element method to discretize the geometric model into finite elements;

[0117] Step S235: Model Solving. The static magnetic field analysis mode is used to solve the model, obtaining magnetic flux density data at different positions on the inner circle of the equivalent stator core. Since the magnetic flux density distribution has periodic symmetry, only data for one pole distance range (0-36 degrees) needs to be recorded.

[0118] Step S24: Using the rotor design parameters and position angle parameters as input parameters, and the equivalent magnetic flux density of the inner surface of the stator core at the corresponding position angle as the output parameter, a training dataset for the rotor magnetic field distribution characteristic prediction model is established. In this embodiment, based on each set of design parameter sample points, a uniformly distributed position angle within a pole pitch range (0-36 degrees) is collected as input parameters. Each set of design parameter sample points corresponds to 60 position angle parameter sample points, so the final training dataset for the rotor magnetic field distribution characteristic prediction model contains 3000 sample points.

[0119] Step S25: Construct a random forest regression model based on the training dataset as a surrogate model for predicting the rotor magnetic field distribution characteristics. The model input is the rotor design parameters (permanent magnet width l). m Permanent magnet thickness h m Magnetic bridge width l bridge Polar arc coefficient α p The model output is the magnetic flux density B on the inner circle of the equivalent stator core at the corresponding position angle, along with the position angle parameter ω. r (ω).

[0120] Step S3: Solve the stator-side equivalent magnetic circuit model and the rotor-side magnetic field distribution prediction proxy model together to obtain the approximate distribution data of magnetic permeability in the motor core region.

[0121] Step S3: Solve the stator-side equivalent magnetic circuit model and the rotor-side magnetic field distribution prediction proxy model together to obtain the approximate distribution data of magnetic permeability in the motor core region.

[0122] The specific implementation steps are as follows:

[0123] Step S31: Establish a rotor equivalent magnetic circuit model that matches the stator-side equivalent magnetic circuit structure. This model divides the air gap region into several sector regions based on the stator-side magnetic circuit division structure. Equivalent regions are represented by constant reluctance and magnetomotive force sources. The constant reluctance simulates the influence of the air gap region and the permanent magnet region on the magnetic field flow. The constant reluctance used to represent the sector region corresponding to the central angle θ has a resistance value R. r (θ) is calculated based on the geometric parameters of the air gap and permanent magnet, and the expression is as follows:

[0124]

[0125] Where g is the air gap thickness, r si L is the inner radius of the stator. ef h is the axial length of the motor. m,i l m,i Let μ0 and μ be the thickness and width of the i-th permanent magnet, respectively. m These are the permeability of vacuum and the permeability of the permanent magnet, respectively, and θ is the fillet corresponding to the equivalent sector region of the magnetoresistive field.

[0126] A magnetomotive force source simulates the excitation effect of a permanent magnet rotor. The magnetomotive force source, with a value F, is used to simulate the equivalent sector region with a central angle of θ. r The calculation method for (θ) is as follows:

[0127]

[0128] Where, r si L is the inner radius of the stator. ef Let B be the axial length of the motor, θ be the fillet radius corresponding to the equivalent sector region of the reluctance, and B be the radius of the motor. r (ω) represents the magnetic flux density at position ω on the inner circle of the stator, calculated based on the rotor magnetic field prediction model described in step S2. The magnetic flux of the equivalent sector region is calculated using the discrete integration method.

[0129] Step S32: Connect the stator-side equivalent magnetic circuit model and the rotor-side equivalent magnetic circuit model to merge them into a complete motor equivalent magnetic circuit model, as shown below. Figure 5 As shown.

[0130] Step S33: Solve the equivalent magnetic circuit model of the motor through iterative calculation. Figure 6 A schematic diagram of the iterative solution process for the equivalent magnetic circuit model is shown.

[0131] At the start of the solution process, the permeability of the variable reluctance in this embodiment model is initialized to 5000μ0. The iterative solution process is as follows: First, the magnetic circuit equations of the model are constructed according to Kirchhoff's circuit laws, and their expressions are as follows:

[0132]

[0133] in, Let F be the magnetic flux vector, F be the magnetomotive force vector, and R be the magnetoresistance matrix.

[0134] The magnetic flux of each magnetic circuit is obtained by solving the magnetic circuit equations, corresponding to the magnetic flux in each equivalent region. The expression for calculating the magnetic flux density B in each region inside the iron core is as follows:

[0135]

[0136] in, Let A be the magnetic flux within the equivalent region, and let A be the cross-sectional area of ​​the equivalent region.

[0137] Based on this magnetic flux density value, the BH curve of the core material is retrieved, and the permeability data of each region inside the core is updated for the next iteration of calculation. The expression is as follows:

[0138]

[0139] Where n is the number of iterations. α is the permeability lookup function, and α is the relaxation factor (0 < α < 1) used to prevent oscillations.

[0140] Repeat the above iterative calculation process until the error between two consecutive iterations is less than the set residual threshold. Then, determine that the model has converged and output the magnetic permeability distribution data at this point.

[0141] Step S4: Substitute the approximate magnetic permeability distribution data as initial values ​​into the finite element model of the motor for iterative solution.

[0142] In this embodiment, the initial relative permeability of all finite element mesh elements in the equivalent region of the stator tooth body in the spatially corresponding equivalent magnetic circuit model is assigned the convergent permeability of the magnetic reluctance corresponding to the region in the equivalent magnetic circuit model. The stator yoke and tooth tip regions are treated in the same way.

[0143] Although the equivalent magnetic circuit model and the surrogate model have certain simplification errors, the magnetic permeability distribution trend obtained by them is highly consistent with the real physical field. This data is extracted and formatted into an initial value file that can be recognized by the finite element software. This initial value file is substituted into the finite element mesh element to set the starting iteration point for the nonlinear solution of the finite element model, thereby reducing the number of iteration calculations required for the finite element solution to reach convergence, and achieving a significant improvement in computational efficiency while ensuring accuracy.

[0144] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0145] Although this application has been described above with reference to specific embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of this application. In particular, as long as there is no structural conflict, the features in the specific embodiments disclosed in this application can be combined with each other in any way. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, this application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A method for predicting the initial value of magnetic permeability to improve the calculation efficiency of finite element analysis of electric motors, characterized in that, Includes the following steps: S1. Establish the equivalent magnetic circuit model on the stator side; S2. Establish a rotor-side magnetic field distribution prediction model to predict the air gap magnetic field distribution under different rotor topologies; S3. Based on the air gap magnetic field distribution predicted by the rotor-side magnetic field distribution prediction model obtained in step S2, construct the rotor-side equivalent magnetic circuit model, and then solve the stator-side equivalent magnetic circuit model obtained in step S1 and the rotor-side equivalent magnetic circuit model to obtain the approximate distribution data of magnetic permeability in the motor core region. S4. Substitute the approximate distribution data of magnetic permeability in the motor core region obtained in step S3 as the initial value into the finite element model of the motor for iterative solution to obtain the electromagnetic performance analysis results of the motor.

2. The method for predicting the initial value of magnetic permeability to improve the calculation efficiency of finite element analysis of motors according to claim 1, characterized in that, The specific implementation method of step S1 includes the following steps: S1.

1. Based on the air region of the stator slot equivalent with constant reluctance, the iron core region of the stator tooth and yoke equivalent with variable reluctance, and the excitation effect of the equivalent winding current of the magnetomotive force source, an equivalent magnetic circuit model with the stator slot and the corresponding region as the basic unit is constructed. The permeability of the constant reluctance is set to the permeability of vacuum, while the permeability of the variable reluctance is calculated based on the magnetic flux density in the region and the magnetization curve of the core material. The constant reluctance R of the equivalent magnetic circuit model on the stator side Const Variable reluctance R Var The formula for calculating the magnetomotive force source F is as follows: Where μ0 is the free permeability, μ Var denoted as ρ, where ρ is the permeability of the variable reluctance, l is the equivalent region length, A is the equivalent region cross-sectional area, N is the number of turns in the winding, and i is the winding current. S1.

2. Based on the periodic symmetry of the motor stator geometry, an equivalent magnetic circuit model for the stator side is established using the stator slots and corresponding regions obtained in step S1 as the basic units. The magnetic circuit structure of each stator slot unit in the equivalent magnetic circuit model for the stator side remains consistent.

3. The method for predicting the initial value of magnetic permeability to improve the calculation efficiency of finite element analysis of motors according to claim 2, characterized in that, The specific implementation method of step S2 includes the following steps: S2.

1. Determine key design parameters based on the rotor topology, including permanent magnet dimensions, pole arc coefficient, and magnetic bridge width; S2.

2. Conduct sample collection, and obtain the key design parameter combination covering the design space through Latin hypercube sampling, including rotor design parameters and position angle parameters; S2.

3. Use the finite element analysis method to solve in batches the magnetic flux density data of different positions on the inner surface of the equivalent stator core under the combination of key design parameters obtained in step S2.2; S2.

4. Using rotor design parameters and position angle parameters as input data, and magnetic flux density data at different positions on the inner circular surface of the equivalent stator core under the corresponding position angle parameters as output data, a training dataset for the rotor side magnetic field distribution prediction model is established. S2.

5. Train a random forest regression model based on the training dataset to obtain a rotor-side magnetic field distribution prediction model, which is used to predict the air gap magnetic field distribution under different rotor topologies.

4. The method for predicting the initial value of magnetic permeability for improving the calculation efficiency of finite element analysis of motors according to claim 3, characterized in that, The specific implementation method of step S2.3 includes the following steps: S2.3.

1. Geometric model construction: Draw the rotor geometric model based on the rotor design parameters; S2.3.

2. Material property definition, assigning corresponding electromagnetic characteristic parameters to different components, including magnetization curve data of core material, magnetization direction of permanent magnet and remanence parameters; S2.3.

3. The boundary conditions are set to have a magnetic field in the radial direction only on the inner circular surface of the equivalent stator core; S2.3.

4. Model mesh generation: The geometric model is discretized into finite elements using the finite element method; S2.3.

5. Model Solving: The static magnetic field analysis mode is used to solve the model and obtain the magnetic flux density data at different positions on the inner circular surface of the equivalent stator core.

5. The method for predicting the initial value of magnetic permeability to improve the calculation efficiency of finite element analysis of motors according to claim 4, characterized in that, The specific implementation method of step S3 includes the following steps: S3.

1. Establish a rotor equivalent magnetic circuit model that matches the stator-side equivalent magnetic circuit structure. Based on the stator-side magnetic circuit division structure, divide the air gap region into several sector regions and perform equivalent transformations using constant reluctance and magnetomotive force sources respectively. The invariant reluctance of the rotor equivalent magnetic circuit model simulates the influence of the air gap region and the permanent magnet region on the magnetic field flow. The resistance value R is used to represent the invariant reluctance of the sector region corresponding to the central angle θ. r (θ) is calculated based on the geometric parameters of the air gap and permanent magnet, and its expression is as follows: Where g is the air gap thickness, r si L is the inner radius of the stator. ef h is the axial length of the motor. m,i l m,i Let μ0 and μ be the thickness and width of the i-th permanent magnet, respectively. m These are the permeability of vacuum and the permeability of permanent magnets, respectively. Magnetomotive force source F in the rotor equivalent magnetic circuit model r (θ) simulates the excitation effect of a permanent magnet rotor, used as an equivalent magnetomotive force source for a sector region with a central angle of θ. The calculation method is as follows: Among them, B r (ω) represents the magnetic flux density at position ω on the inner circle of the stator, calculated based on the rotor-side magnetic field distribution prediction model in step S2. To calculate the magnetic flux of the equivalent sector region using the discrete integration method; S3.

2. Connect the stator-side equivalent magnetic circuit model and the rotor-side equivalent magnetic circuit model to merge them into a complete motor equivalent magnetic circuit model; S3.

3. Solve the complete equivalent magnetic circuit model of the motor obtained in step S3.2 through iterative calculation to obtain the approximate distribution data of magnetic permeability in the motor core region.

6. The method for predicting the initial value of magnetic permeability to improve the calculation efficiency of finite element analysis of motors according to claim 5, characterized in that, In step S4, the initial value file of the approximate distribution data of the magnetic permeability of the motor core region obtained in step S3 is substituted into the finite element mesh element to set the starting iteration point for the nonlinear solution of the finite element model.

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