Magnetic steel pc value calculation method and system based on finite element calculation

Abstract

The application relates to the technical field of Nd-Fe-B profiled magnetic steel, in particular to a magnetic steel Pc value calculation method and system based on finite element calculation; in the application, a permanent magnet model is constructed, an external magnetic field is added, grid division is carried out, the torque borne by the magnetic steel under the action of the external magnetic field is calculated, the magnetic torque of the magnetic steel is calculated, and the Pc value is inversely deduced according to the magnetic torque; the method is not limited by the size and shape of the magnetic steel, and can accurately calculate the Pc value of the magnetic steel with any shape and size.

Description

Technical Field

[0001] This invention relates to the field of neodymium iron boron shaped magnets, and particularly to a method and system for calculating the Pc value of magnets based on finite element analysis. Background Technology

[0002] Neodymium iron boron (NdFeB) magnetic properties are relatively sensitive to temperature, and demagnetization is prone to occur at high temperatures. The high-temperature demagnetization of NdFeB is closely related to the Pc value of the magnet. The Pc value of NdFeB magnets is also called the shape factor, which is only related to the shape and size of the magnet.

[0003] Currently, only regular magnet shapes such as cubes, axial cylinders, radial cylinders, and axial rings can be calculated. However, many magnets in actual production are irregular in shape, and existing methods cannot calculate the accurate Pc value of irregular magnets. For example, the Pc value of irregular magnets calculated by using volume or area equivalence to regular shapes is inaccurate, making it impossible to accurately assess the high-temperature demagnetization performance of irregular magnets. This is especially important in motor applications where the requirements for high-temperature demagnetization of magnets are very strict. Therefore, accurate calculation of magnet Pc values ​​is crucial. Summary of the Invention

[0004] To overcome the aforementioned shortcomings, the purpose of this invention is to provide a method for calculating the Pc value of a magnet based on finite element analysis. This method involves constructing a permanent magnet model, adding an external magnetic field, performing mesh generation, calculating the torque experienced by the magnet under the action of the external magnetic field, thereby calculating the magnetic moment of the magnet, and then deducing the Pc value from the magnetic moment. Furthermore, a system for calculating the Pc value of a magnet based on finite element analysis is also provided.

[0005] The technical solution of this invention to solve its technical problem is:

[0006] The method for calculating the Pc value of magnets based on finite element analysis includes the following steps:

[0007] Step S1: Establish a permanent magnet model;

[0008] Step S2: Add an external magnetic field to the permanent magnet model and set the physical parameters of the permanent magnet;

[0009] Step S3: Mesh the permanent magnet model, add a solver, and calculate the torque experienced by the permanent magnet under the action of an external magnetic field;

[0010] Step S4: The magnetic moment of the magnet is derived and calculated through the torque, and then the Pc value of the magnet is obtained.

[0011] As an improvement of the present invention, in step S1, the geometric dimensions of the permanent magnet are input into the finite element software to construct a permanent magnet model.

[0012] As a further improvement of the present invention, in step S1, an air domain with a size one to five times that of the model is constructed within the permanent magnet model, and a layer of 1 mm to 5 mm is set as the boundary of the infinite element domain.

[0013] As a further improvement of the present invention, in step S2, the parameters of the external magnetic field are input into the finite element software, thereby adding an external magnetic field to the permanent magnet model.

[0014] As a further improvement of the present invention, in step S2, the remanence, restoring permeability and magnetization direction of the permanent magnet are input into the finite element software, the direction of the external magnetic field is at an angle to the magnetization direction of the permanent magnet, and the outermost layer of the permanent magnet model is set as the boundary of the infinite element domain and the torque calculation object is set.

[0015] As a further improvement of the present invention, in step S3, the permanent magnet model is meshed by using a physical field to control the mesh and setting an adaptive meshing.

[0016] As a further improvement of the present invention, in step S3, a steady-state solver is added to the permanent magnet model and the relative tolerance is set to 1e-6.

[0017] As a further improvement of the present invention, in step S3, the torque of the permanent magnet under the action of the external magnetic field is obtained by solving Maxwell's equations. During the calculation process, if the tolerance requirement of 1e-6 is not met, the mesh will be automatically re-divided until the tolerance requirement is met, and the calculation will stop.

[0018] As a further improvement of the present invention, in step S4, after obtaining the magnetic moment of the magnet, the Pc value of the magnet is deduced.

[0019] A system for calculating the Pc value of magnetic steel based on finite element method, comprising:

[0020] The geometry building block is used to create permanent magnet models;

[0021] The physics module is used to input the physical parameters of the permanent magnet into the permanent magnet model and add an external magnetic field;

[0022] The finite element calculation module is used to mesh the permanent magnet model and calculate the torque experienced by the permanent magnet under the action of an external magnetic field.

[0023] The data processing module is used to derive and calculate the magnetic moment of the magnet from the torque, and then obtain the Pc value of the magnet.

[0024] In this invention, a permanent magnet model is constructed, and physical parameters of the permanent magnet and an external magnetic field are set within the permanent magnet model. The permanent magnet model is then meshed, and the torque experienced by the magnet under the action of the external magnetic field is calculated, thereby obtaining the magnetic moment of the magnet. The Pc value is then derived from the magnetic moment. The method of this invention is not limited by the size and shape of the magnet and can accurately calculate the Pc value of magnets of any shape and size. Attached Figure Description

[0025] For ease of explanation, the present invention will be described in detail below with reference to the preferred embodiments and accompanying drawings.

[0026] Figure 1 This is a flowchart of the method steps of the present invention;

[0027] Figure 2 Line graph showing the demagnetization of neodymium iron boron magnets and the Pc value;

[0028] Figure 3 This is a schematic diagram of adding an external magnetic field to the permanent magnet model of the present invention;

[0029] Figure 4 This is a schematic diagram of the mesh after adaptive encryption in Example 1;

[0030] Figure 5 This is a schematic diagram showing the calculation results output of Example 1;

[0031] Figure 6 This is a schematic diagram of the mesh after adaptive encryption in Example 2;

[0032] Figure 7 This is a schematic diagram of the calculation results output in Example 2. Detailed Implementation

[0033] 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 embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0034] The high-temperature demagnetization of neodymium iron boron magnets is significantly related to the Pc value of the magnet, and the mechanism is as follows: Figure 2 As shown, the Pc line is a straight line passing through the origin in the second quadrant. The absolute value of the slope is the Pc value of the magnet. If the Pc line is above the high temperature inflection point, such as P1, the magnet will not lose its magnetic properties after passing through the high temperature and returning to the normal temperature. If the Pc line is below the high temperature inflection point, such as P2, the magnet will lose its magnetic properties after passing through the high temperature and returning to the normal temperature, and it will not be able to recover its performance before the high temperature.

[0035] like Figures 1 to 7 As shown, the method for calculating the Pc value of a magnet based on finite element analysis according to the present invention includes the following steps:

[0036] Step S1: Establish a permanent magnet model;

[0037] Step S2: Add an external magnetic field to the permanent magnet model and set the physical parameters of the permanent magnet;

[0038] Step S3: Mesh the permanent magnet model, add a solver, and calculate the torque experienced by the permanent magnet under the action of an external magnetic field;

[0039] Step S4: The magnetic moment of the magnet is derived and calculated through the torque, and then the Pc value of the magnet is obtained.

[0040] Finite element method (FE) calculations divide the solution domain into many interconnected finite element units, establish the connections between the units through boundary conditions, and solve the system of equations to obtain the results. The finite element method not only has high computational accuracy but can also adapt to various complex shapes.

[0041] The Pc value of neodymium iron boron magnets is also called the form factor, which is only related to the shape and size of the magnet.

[0042] In this invention, by constructing a permanent magnet model and adding an external magnetic field, meshing is performed, and the torque experienced by the magnet under the action of the external magnetic field is calculated, thereby calculating the magnetic moment of the magnet, and then the Pc value is derived from the magnetic moment.

[0043] In step S1, the geometric dimensions of the permanent magnet are input into the finite element software to construct a permanent magnet model. Within the permanent magnet model, an air domain with a size one to five times that of the model is constructed, and a layer of 1 mm to 5 mm is set as the boundary of the infinite element domain.

[0044] In step S2, the parameters of the external magnetic field are input into the finite element software, thereby adding an external magnetic field to the permanent magnet model; the remanence, restoring permeability, and magnetization direction of the permanent magnet are input into the finite element software, the direction of the external magnetic field is at an angle to the magnetization direction of the permanent magnet, the outermost layer of the permanent magnet model is set as the boundary of the infinite element domain and the torque calculation object is set.

[0045] In step S3, the permanent magnet model is meshed by using a physical field-controlled mesh and setting an adaptive mesh. A steady-state solver is added to the permanent magnet model and the relative tolerance is set to 1e-6. The torque on the permanent magnet under the action of an external magnetic field is obtained by solving Maxwell's equations. During the calculation, if the tolerance requirement of 1e-6 is not met, the mesh will be automatically re-meshed until the tolerance requirement is met, and then the calculation will stop.

[0046] In step S4, after obtaining the magnetic moment of the magnet, the Pc value of the magnet is derived; specifically, the input expression... Where L is torque, M mLet be the magnetic moment of the magnet, θ be the angle between the direction of the magnetic moment (magnetization direction) and the direction of the external magnetic field, and H1 be the external magnetic field. Then input the expression: V is the volume of the magnet. To restore permeability, The calculated Pc is the remanence.

[0047] This invention provides a system for calculating the Pc value of magnetic steel based on finite element method, comprising:

[0048] The geometry building block is used to create permanent magnet models;

[0049] The physics module is used to input the physical parameters of the permanent magnet into the permanent magnet model and add an external magnetic field;

[0050] The finite element calculation module is used to mesh the permanent magnet model and calculate the torque experienced by the permanent magnet under the action of an external magnetic field.

[0051] The data processing module is used to derive and calculate the magnetic moment M of the magnet from the torque L. m Then, the Pc value of the magnet is obtained.

[0052] Specifically, the geometry construction module inputs the geometric shape and dimensions of the permanent magnet into the Comsol finite element software. Its shape and dimensions are unrestricted, and its volume is V. It also constructs an air domain with a size of 1-5 times that of the model and sets a layer of 1-5 mm as the boundary of the infinite element domain.

[0053] The physics module adds the mfnc physics field to the Comsol finite element software, which includes the remanence (Br) and restoring permeability of the permanent magnet. The magnetization direction and external magnetic field H1 parameters are input into the Comsol finite element software. The external magnetic field direction is at an angle of θ° to the magnetization direction of the permanent magnet. The outermost layer of the permanent magnet model is set as the boundary of the infinite element domain, and the torque calculation object is set.

[0054] The finite element calculation module meshes the permanent magnet model, uses physical field control to control the mesh and sets adaptive meshing, adds a steady-state solver and sets the relative tolerance to 1e-6 to ensure high accuracy of the results, and obtains the torque L of the permanent magnet under the action of an external magnetic field by solving Maxwell's equations. If the tolerance requirement is not met, the mesh will be automatically re-generated until the tolerance requirement is met and the calculation stops.

[0055] Data processing module, input expression Where L is torque, M m Let be the magnetic moment of the magnet, θ be the angle between the direction of the magnetic moment (magnetization direction) and the direction of the external magnetic field, and H1 be the external magnetic field. Then input the expression: V is the volume of the magnet. To restore permeability, The calculated Pc is the remanence.

[0056] This invention generates an external magnetic field in finite element software. Figure 3 As shown, the torque on the magnet in the external magnetic field is calculated, the magnetic moment is deduced, and then Pc is deduced. This method is not limited by the shape and size of the magnet and can obtain an accurate Pc value. The technical route of this invention is as follows: establish a permanent magnet model - set material parameters - add an external magnetic field - set the object to calculate the torque - mesh generation - set the solver - run the calculation - view the torque results - calculate the magnetic moment - calculate the Pc value.

[0057] The present invention provides the following embodiments:

[0058] Example 1:

[0059] Step 1: Create a permanent magnet model D17.02x2.3 in the COMSOL geometry module, with a volume V=523.2832mm. 3 Construct an air domain, 1-5 times the diameter in size, and set an outer layer of 1-5 mm;

[0060] Step 2: Add the MFNC physics interface, set the permanent magnet performance parameters: remanence Br: 1.38T, and recovery permeability. :1.05; The magnetization direction is 2.3, and the outer layer is defined as the boundary of an infinite elemental domain;

[0061] Step 3: Add an external magnetic field to the mfnc physical field, such that the external magnetic field H1 = 1,000,000 A / m, and its direction is 90° to the magnetization direction of the magnet.

[0062] Step 4: Add torque calculation in the MFNC physics field, and select the magnet as the calculation object;

[0063] Step 5: Mesh the permanent magnet model, using a physics-controlled mesh and setting it to a high-precision adaptive mesh. The adaptively refined mesh is shown below. Figure 4 As shown;

[0064] Step 6: Add a Stationary Solver and set the relative tolerance to 1e-6;

[0065] Step 7: Perform finite element analysis;

[0066] Step 8: Enter the expression in the software parameter definition. and The calculation results are as follows Figure 5 As shown, the Pc obtained by finite element calculation in Example 1 is 0.30419.

[0067] Since the magnet in Example 1 has a regular shape, we performed conventional theoretical calculations, specifically, based on the theoretical formula. D is the diameter and L is the thickness. The calculated Pc = 0.3046. It can be seen that the magnet in Example 1 is a regular shape. The theoretical calculation result Pc obtained after theoretical calculation is 0.3046. This theoretical calculation result Pc = 0.3046 is very close to the Pc of 0.30419 obtained by finite element calculation in Example 1.

[0068] In this embodiment, the measured magnetic moment of the uncoated black sheet is 6.952E-7Wb.m, and Pc=0.2907, which is very close to the Pc of 0.30419 obtained by finite element calculation in embodiment one.

[0069] It can be seen that the method in Example 1 can calculate the Pc value of a regular-shaped magnet. The calculated result is very close to the theoretical calculation result and also very close to the measured result, indicating that the method in Example 1 has high accuracy in calculating the Pc value of a regular-shaped magnet.

[0070] Example 2:

[0071] Step 1: Create an irregular permanent magnet model in the COMSOL geometry module, with a volume V = 681.0733 mm². 3 Construct an air domain, 1-5 times the diameter in size, and set an outer layer of 1-5 mm;

[0072] Step 2: Add the MFNC physics interface, set the permanent magnet performance parameters: remanence Br: 1.4T, and recovery permeability. 1.04; The magnetization direction is the thickness direction, and the outer layer is defined as the boundary of an infinite element field.

[0073] Step 3: Add an external magnetic field to the mfnc physical field, such that the external magnetic field H1 = 500000 A / m, and the direction is 45° with the magnetization direction of the magnet.

[0074] Step 4: Add torque calculation in the MFNC physics field, and select the magnet as the calculation object;

[0075] Step 5: Mesh the model, using physics-controlled meshing and setting it to a high-precision adaptive mesh. The adaptively refined mesh is shown below. Figure 6 As shown;

[0076] Step 6: Add a Stationary Solver and set the relative tolerance to 1e-6;

[0077] Step 7: Perform finite element analysis;

[0078] Step 8: Enter the expression in the software parameter definition. and The calculation results are as follows Figure 7 As shown, the finite element calculation yielded a result of Pc = 0.32562;

[0079] In Example 2, the measured magnetic moment of the uncoated black sheet was 9.252E-7Wb.m, and Pc=0.3076, which is very close to the Pc=0.32562 obtained by finite element calculation using the method in Example 2. This indicates that the accuracy of the Pc value calculated by the method in Example 2 for irregularly shaped magnets is also very high.

[0080] Through Examples 1 and 2, it can be seen that the magnetic Pc value calculation method based on finite element calculation of the present invention can not only calculate the Pc value of magnetic steel of arbitrary shape, but also calculate the Pc value with high accuracy.

[0081] This invention can accurately calculate the Pc value of magnets of arbitrary shapes and accurately evaluate the high-temperature demagnetization performance of irregularly shaped magnets. The calculation results of the method of this invention are basically consistent with the measured results. The method of this invention for calculating the Pc value of irregularly shaped magnets is convenient to operate, can quickly obtain results, and has very high calculation accuracy.

[0082] The embodiments of the present invention are implemented based on Comsol software. The present invention can also be implemented using other finite element software, such as ANSYS Maxwell and JMAG.

[0083] The embodiments of the present invention are mainly aimed at neodymium iron boron magnets, but the present invention is not limited to neodymium iron boron magnets. The method of the present invention is also applicable to samarium cobalt, ferrite, and AlNiCo, and can also calculate the Pc value of samarium cobalt, ferrite, and AlNiCo.

[0084] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the magnetic steel Pc value based on finite element calculation, characterized in that, Includes the following steps: Step S1: Input the geometric shape and dimensions of the permanent magnet into the finite element software to construct a permanent magnet model. In the permanent magnet model, construct an air domain with a size one to five times that of the model and set a layer of 1 mm to 5 mm as the boundary of the infinite element domain. Step S2: Add an external magnetic field to the permanent magnet model and set the physical parameters of the permanent magnet. The parameters of the external magnetic field are input into the finite element software to add an external magnetic field to the permanent magnet model. Step S3: Use a physics-controlled mesh and set an adaptive mesh to mesh the permanent magnet model. Add a steady-state solver to the permanent magnet model and set the relative tolerance to 1e-6. Solve Maxwell's equations to obtain the torque on the permanent magnet under the action of an external magnetic field. If the tolerance requirement of 1e-6 is not met during the calculation, the mesh will be automatically re-meshed until the tolerance requirement is met, and then the calculation will stop. Step S4: Calculate the magnetic moment of the magnet by using the torque, and then deduce the Pc value of the magnet. Enter the expression: ， where L is the moment, M m is the magnetic moment of the magnet, θ is the angle between the magnetic moment direction and the external magnetic field direction, H1 is the external magnetic field, Enter the expression again: ， where V is the volume of the magnet steel, is the magnetic permeability, is the remanence, Pc calculated.

2. The method of claim 1, wherein the method is based on a finite element calculation. In step S2, the remanence, restoring permeability, and magnetization direction of the permanent magnet are input into the finite element software. The direction of the external magnetic field is at an angle to the magnetization direction of the permanent magnet. The outermost layer of the permanent magnet model is set as the boundary of the infinite element domain and the torque calculation object is set.

3. A system for calculating the magnetic steel Pc value based on finite element calculation, characterized by, include: The geometry building block is used to create permanent magnet models; The physics module is used to input the physical parameters of the permanent magnet into the permanent magnet model and add an external magnetic field; The finite element calculation module is used to mesh the permanent magnet model and calculate the torque experienced by the permanent magnet under the action of an external magnetic field. The data processing module is used to derive and calculate the magnetic moment of the magnet from the torque, and then obtain the Pc value of the magnet. The input expression is: ， where L is the moment, M m is the magnetic moment of the magnet, θ is the angle between the magnetic moment direction and the external magnetic field direction, H1 is the external magnetic field, Enter the expression again: ， where V is the volume of the magnet steel, is the remanence, Pc, calculated. is the remanence, Pc, calculated.

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