A magnetostrictive loop simulation method based on microscopic statistical J-A model

Abstract

A magnetostrictive loop simulation method based on microstatistical J-A model, aiming at solving the problems of existing magnetostrictive simulation method, such as complex operation, more parameters to be solved, and ignoring the influence of magnetic hysteresis effect and loss, the method comprises the following steps: first, based on the principle of microstatistical magnetic moment, a magnetic moment angle distribution probability function is proposed; second, the magnetization intensity expression obtained by discrete summation of the probability distribution function is introduced into the traditional inverse J-A model to simulate the influence of the magnetic field on the magnetic properties; then, the non-magnetic hysteresis magnetization function is corrected and the magnetostrictive model based on the magnetic moment deformation is introduced; next, the magnetostrictive model is dynamically expanded to include eddy current loss and residual loss; finally, the microstatistical magnetostrictive model considering the magnetic hysteresis effect is constructed combined with the irreversible magnetization component; the model has strong physical significance, can be applied to finite element numerical calculation, accurately estimates the core vibration, is suitable for the optimization of core design of electrical equipment such as motors and transformers, and has important practical value.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of magnetostriction hysteresis loop calculation, and particularly relates to a magnetostriction hysteresis loop simulation method based on a microscopic statistical J-A model. BACKGROUND

[0002] Soft magnetic materials are widely used in electrical equipment such as motors and transformers due to their low loss and high permeability. During operation, the core material in the magnetization process will produce a magnetostriction effect, resulting in device vibration and noise pollution. Magnetostriction is a physical phenomenon in which the size or shape of a soft magnetic material changes under the action of a magnetic field. This change in turn causes mechanical vibration, which is one of the main causes of electrical equipment vibration and noise.

[0003] Currently, the magnetostriction simulation methods for soft magnetic materials mostly use phenomenological models. Although phenomenological models have strong mathematical significance, their distribution functions are difficult to determine in practical applications, and the calculation process is complex, making it difficult to quickly reflect the magnetostriction characteristics of soft magnetic materials. In addition, some scholars have proposed a magnetostriction model based on magnetic domain theory, which takes into account the microscopic magnetization mechanism of soft magnetic materials. However, the model has many parameters to be solved, and to a large extent, it depends on the accuracy of experimental data, which limits its application range to some extent.

[0004] More importantly, some existing magnetostriction simulation methods often ignore the hysteresis effect of magnetostriction relative magnetic flux density and magnetic field strength, i.e., the magnetic hysteresis effect. Magnetic hysteresis is a nonlinear, hysteresis relationship between the magnetization state and the magnetic field strength of magnetic materials under the action of a magnetic field, and is one of the important characteristics of magnetic materials. Ignoring the magnetic hysteresis effect will result in a large deviation between the simulation results and the actual situation, making it impossible to accurately estimate the vibration of the core.

[0005] In addition, some models also ignore the impact of loss on the magnetic hysteresis effect during simulation. The total magnetic hysteresis loss of soft magnetic materials is mainly composed of static magnetic hysteresis loss, eddy current loss and residual loss. These losses have an important influence on the magnetic properties and magnetostriction characteristics of the material. Ignoring the loss factor will make the simulation results unable to truly reflect the dynamic response characteristics of the material under the action of a magnetic field.

[0006] In summary, the existing technology has many shortcomings in simulating the magnetostriction characteristics of soft magnetic materials. Therefore, it is necessary to develop a more accurate and efficient magnetostriction hysteresis loop simulation method for soft magnetic materials based on the microscopic statistical J-A hysteresis model and dynamic expansion, in order to better meet the needs of electrical equipment core design optimization. SUMMARY

[0007] The technical problem solved by the present application is to provide a magnetostriction hysteresis loop simulation method based on a microscopic statistical J-A model, to solve the technical problems of inaccurate simulation method, unclear physical meaning and complex operation in the field of magnetostriction hysteresis loop calculation, especially in the aspect of simulating the magnetostriction characteristics of soft magnetic materials under the action of a magnetic field, the existing technology mostly adopts phenomenological models or magnetostriction models based on magnetic domain theory, but these models have the limitations of difficulty in determining the distribution function, complex operation, too many parameters to be solved, and ignoring the influence of magnetic hysteresis effect and loss.

[0008] To solve the above technical problems, the technical scheme adopted by the present application is as follows: a magnetostriction hysteresis loop simulation method based on a microscopic statistical J-A model, comprising the following steps:

[0009] Step 1: Based on the principle of microscopic magnetic moment statistics, an improved Boltzmann function is proposed to represent the magnetic moment angle distribution probability, and the magnetization intensity expression is obtained by discrete summation of the probability distribution function;

[0010] Step 2: Introduce the magnetization intensity expression obtained in Step 1 into the traditional inverse J-A model to simulate the influence of the magnetic field on the magnetic properties;

[0011] Step 3: Modify and calculate the traditional non-magnetic hysteresis function expression, and introduce it into the magnetostriction model based on the magnetic moment deformation;

[0012] Step 4: Dynamically extend the magnetostriction model, and incorporate the influence of eddy current loss and residual loss on the magnetic properties, and modify the effective magnetic field intensity expression;

[0013] Step 5: Combine the irreversible magnetization component to construct a microscopic statistical magnetostriction model considering the magnetic hysteresis effect.

[0014] In the preferred scheme, the specific steps of Step 1 are as follows: the macroscopic magnetic properties and magnetostriction properties are characterized by the magnetic moment angle probability distribution function and the saturation magnetization direction related deformation, the local free energy of the magnetic moment is including Zeeman energy and magnetic crystal anisotropy energy , and the magnetic moment angle probability distribution function considering the magnetic field is defined using the improved function , and the specific expression is as follows:

[0015] (1)

[0016] (2)

[0017] (3)

[0018] (4)

[0019] wherein, and correspond to external magnetic field and saturation magnetization, respectively; , , are the magnetic field strength H in 、 、 directional cosine of the direction of is the vacuum permeability; , , are the magnetization in 、 、 directional cosine of the direction of and are the magnetic crystal anisotropy constants; denotes the normalized function of the magnetic field; is a parameter related to the initial magnetic susceptibility of the material; is the angle between the atomic magnetic moment and the direction of the magnetic field.

[0020] In the preferred embodiment, the magnetization of Step 1 is in the probability distribution function After the definition, the magnetization under the magnetic field is obtained by three-dimensional integration The analytical expression is as follows:

[0021] (5)

[0022] wherein, is the angle between the magnetization direction of the magnetic moment and the magnetostriction measurement direction; is the angle between the projection of the magnetization direction of the magnetic moment on the plane and the direction.

[0023] In the preferred embodiment, the specific steps of Step 2 are to replace the non-hysteresis magnetization expression in the inverse J-A hysteresis model with a magnetization expression calculated based on the probability function of the angle distribution of the magnetic moment, and the effective magnetic field strength is modified according to the influence of the magnetic field on the magnetic properties, and the expression is as follows:

[0024] (6)

[0025] wherein, denotes the non-hysteresis magnetization; denotes the effective magnetic field strength.

[0026] In the preferred embodiment, the specific step of Step 3 is that the magnetostriction strain is calculated according to the deformation related to the direction of the saturation magnetic moment, and the modified non-hysteresis magnetization function The magnetic field intensity H and the single-valued magnetization intensity are iteratively solved to obtain the fitting relationship of , wherein represents the domain wall interaction coefficient; represents the coupling coefficient; and further obtaining the expression of the magnetostriction strain of the soft magnetic material, which is specifically as follows:

[0027] (7)

[0028] In the formula, represents the magnetostriction strain of the soft magnetic material; represents the saturation magnetostriction; represents the length of the atomic structure after deformation; represents the length of the initial atomic structure; represents the applied magnetic field.

[0029] In the preferred embodiment, in Step 4, the effective magnetic field intensity is modified to increase the counter field related to the eddy current loss and the residual loss, and the eddy current loss field and the residual loss field are calculated according to the loss separation theory, which is specifically as follows:

[0030] (8)

[0031] In the formula, is the effective magnetic field intensity considering the dynamics; is the eddy current loss field intensity; is the residual loss field intensity; is the direction coefficient related to the direction of ; is the thickness of the soft magnetic material; is the dimensionless coefficient; is the cross-sectional area of the material lamination; is a statistical parameter representing the local magnetic field distribution of the magnet; is the electrical conductivity of the soft magnetic material, is the magnetic flux density.

[0032] In the preferred embodiment, the specific step of Step 5 is that the influence of the irreversible magnetization component on the hysteresis effect between the magnetostriction and the magnetic flux density is considered, and the expression of the magnetostriction loop simulation method is constructed by introducing the undetermined coefficient and the shape coefficient which varies with the material type, and the expression is as follows:

[0033] (9)

[0034] wherein, is the dynamic magnetization; is the non-magnetizable intensity; is the undetermined coefficient; is the shape coefficient varying with the material type; is the pinning parameter; is the domain wall bending parameter; is the coefficient introduced to prevent the appearance of non-physical explanations; is the coupling coefficient.

[0035] The magnetostriction hysteresis loop simulation method based on the micro-statistical J-A model has the following beneficial effects:

[0036] 1. The magnetostriction hysteresis loop simulation method based on the micro-statistical J-A model solves the problems of inaccurate simulation method, unclear physical meaning and complex operation in the field of magnetostriction hysteresis loop calculation, overcomes the limitations of the existing technology that mainly adopts phenomenological models or magnetostriction models based on magnetic domain theory, and effectively improves the simulation accuracy and physical meaning by proposing a new method.

[0037] 2. The magnetostriction hysteresis loop simulation method based on the micro-statistical J-A model proposes a new magnetic moment angle probability distribution function, which can more accurately describe the distribution and change of the magnetic moment under the action of the magnetic field, and this innovation makes the understanding of the magnetic moment angle distribution more in-depth, providing a solid foundation for the subsequent calculation of magnetization and magnetostriction.

[0038] 3. The magnetostriction hysteresis loop simulation method based on the micro-statistical J-A model combines the micro-statistical construction model with the traditional inverse J-A magnetic hysteresis model to form an improved magnetic hysteresis model with both magnetic hysteresis effect and physical meaning, and by introducing the micro-statistical principle, the model enhances the physical meaning while maintaining mathematical simplicity, improving the simulation accuracy.

[0039] 4. The magnetostriction hysteresis loop simulation method based on the micro-statistical J-A model dynamically extends the magnetostriction model and incorporates the influence of eddy current loss and residual loss on magnetic properties, which makes the model more accurately simulate the dynamic characteristics in the actual magnetization process, improving the practicality and accuracy of the model.

[0040] 5. The magnetostriction hysteresis loop simulation method based on the micro-statistical J-A model combines irreversible magnetization components to construct a micro-statistical magnetostriction model considering magnetic hysteresis effect, which can more accurately simulate the magnetic hysteresis relationship between magnetostriction and magnetic flux density, providing a powerful tool for the estimation and optimization design of the magnetostriction effect of the core material in electrical equipment.

[0041] 6、The model established by the application has strong physical meaning, can more deeply reveal the magnetostrictive characteristics of soft magnetic materials under the action of a magnetic field, has a hysteresis effect, can more accurately simulate the hysteresis phenomenon in the actual magnetization process, and improves the accuracy and practicability of simulation;

[0042] 7、The method of the application can be applied to the simulation of magnetostrictive characteristics of soft magnetic materials, and provides strong support for research in related fields, and is particularly suitable for predicting and optimizing the design of the magnetostrictive effect of core materials in electrical equipment, and helps to improve the performance and reliability of electrical equipment;

[0043] 8、The application provides a magnetostrictive hysteresis loop simulation method based on a micro-statistical J-A model, which improves the accuracy and practicability of simulation by introducing a probability distribution function, combining micro-statistics to construct a model and a traditional inverse J-A hysteresis model, performing dynamic expansion, and considering irreversible magnetization components;

[0044] 9、The method of the application has broad application prospects in the design optimization of core materials of electrical equipment, the prediction of magnetostrictive effects, and the research of magnetostrictive characteristics of soft magnetic materials, and as related technologies continue to develop, the method of the application is expected to provide stronger support for research and application in related fields. BRIEF DESCRIPTION OF DRAWINGS

[0045] The application will be further described below in combination with the drawings and implementation examples:

[0046] Figure 1 The simulation flowchart of the method of the application is shown in the figure;

[0047] Figure 2 The isotropic unit atomic structure of the application is shown in the figure;

[0048] Figure 3 The figure shows the comparison between the simulation value and the experimental value of the hysteresis model under a magnetic flux density of 1.2T when the excitation frequency is 50Hz;

[0049] Figure 4 The figure shows the comparison between the simulation value and the experimental value of the magnetostrictive model under a magnetic flux density of 1.2T when the excitation frequency is 50Hz. DETAILED DESCRIPTION

[0050] The technical solutions in the application will be further described below in combination with the drawings and examples:

[0051] Example 1

[0052] The following is a specific embodiment of a magnetostriction hysteresis loop simulation method based on a microscopic statistical J-A model according to the present application. Through detailed steps and parameter settings, a professional in the same technical field can successfully reproduce the technical solution of the present application according to this description.

[0053] As shown in Figure 1 , a magnetostriction hysteresis loop simulation method based on a microscopic statistical J-A model includes the following steps:

[0054] Step 1: Based on the principle of microscopic magnetic moment statistics, a new Boltzmann function is proposed to represent the probability distribution of the angle of the magnetic moment. The magnetization expression is obtained by discrete summation of the probability distribution function;

[0055] Step 2: The magnetization expression obtained by discrete summation of the probability distribution function is introduced into the traditional inverse J-A model to simulate the effect of the magnetic field on the magnetic properties;

[0056] Step 3: The traditional non-hysteresis magnetization function expression is modified and calculated, and introduced into the magnetostriction model based on the deformation of the magnetic moment;

[0057] Step 4: The magnetostriction model is dynamically extended to include the effects of eddy current loss and residual loss on magnetic properties, and the effective magnetic field strength expression is modified;

[0058] Step 5: Combine the irreversible magnetization component to build a microscopic statistical magnetostriction model considering hysteresis effect.

[0059] In this embodiment, the specific implementation steps and principles of calculating the magnetization based on the magnetic moment angle probability function in step 1 are as follows:

[0060] Soft magnetic materials will spontaneously magnetize in a free state, and the magnetic moment will be randomly distributed. When an external magnetic field is applied, the atomic magnetic moments inside the material will gradually align in the same direction, creating a local magnetic moment ordered region. The macroscopic magnetic properties and magnetostriction properties are characterized by the magnetic moment angle probability distribution function and the saturation magnetization direction related deformation.

[0061] When the atomic magnetic moments inside the material are affected by the magnetic field, the local free energy of the magnetic moment is summarized as the Zeeman energy and the magnetic crystal anisotropy energy , The influence of the external magnetic field on the equilibrium state is introduced, and the expression is as follows:

[0062] (1)

[0063] In the formula, is the vacuum permeability, and H / m;

[0064] is the magnetocrystalline anisotropy energy, which is derived from the interaction between the electron spin and the orbital motion in the material, and makes the magnetic moments align along the easy magnetization direction when a magnetic field is applied. The expression is as follows:

[0065] (2)

[0066] In the formula, and is the magnetocrystalline anisotropy constant. When the soft magnetic material has macroscopic isotropy, then ;

[0067] At this time, the local free energy of the magnetic moment can be expressed as:

[0068] (3)

[0070] By using the improved Boltzmann function definition to consider the magnetic moment angle probability distribution function of the magnetic field, the probability function can be expressed as:

[0071] (10)

[0072] In order to simplify the calculation, we assume that the probability of the magnetic moment distribution in each direction is the same, and the average operation is performed on the magnetic moment angle distribution, and the probability distribution function is obtained as:

[0073] (4)

[0074] In the formula, is the angle between the projection of the magnetic moment magnetization direction in the plane and the direction, as shown in Figure 4 .

[0075] In order to solve the normalized function of the magnetic field, the three-dimensional integral of the magnetic moment angle distribution probability function is performed, and the value is assigned to 1:

[0076] (11)

[0077] By calculating , it is expressed as:

[0078] (12)

[0079] At this time, the proportion of the energy contribution of each magnetic moment magnetization to the magnetization of the unit magnetic moment can be expressed as:

[0080] (13)

[0081] After the new probability function is defined, the magnetization under the magnetic field is solved by three-dimensional integration The analytical expression is:

[0082] (5);

[0083] In the formula, is the angle between the projection of the magnetization direction of the magnetic moment in the YZ plane and the Z direction, as shown in Figure 2 .

[0084] Further, the specific implementation steps and principles of step 2 for simulating the effect of the magnetic field on the magnetic properties in combination with the traditional inverse J-A model are as follows:

[0085] The micro-statistical construction model is combined with the traditional inverse J-A hysteresis model to simulate the effect of the magnetic field on the magnetic properties. The traditional J-A model is a hysteresis model that considers the physical motion of the domain wall surface, is suitable for isotropic materials, and has relatively simple parameter solving. We replace the non-hysteresis magnetization expression in the inverse J-A hysteresis model with the magnetization expression calculated based on the probability function of the magnetic moment angle distribution, and modify the magnetic field strength to the effective magnetic field strength , so that the improved hysteresis model can produce hysteresis effect and has physical meaning. The expression of the proposed micro-statistical J-A hysteresis model is:

[0086] (6).

[0087] Further, the specific implementation steps and principles of step 3 for introducing the magnetostriction model and modifying the non-hysteresis magnetization function are as follows:

[0088] The magnetostriction strain is calculated according to the deformation related to the saturation magnetization direction, and the length of the initial atomic result can be represented in discrete or integral form:

[0089] (14)

[0090] In the formula, represents the deformation variable; represents the probability distribution function.

[0091] After the magnetic field is applied, the angular distribution probability changes, and the changed atomic length is represented as:

[0092] (15)

[0093] In order to reflect the mutual dependence of magnetostriction and magnetization of soft magnetic materials during the magnetization process, we use the modified non-hysteresis magnetization function to the magnetic field strength H and the single-valued magnetization strength The iterative solution is performed to obtain the fitting relationship of wherein, represents the magnetic domain wall interaction coefficient; represents the coupling coefficient; and the magnetostrictive strain of the soft magnetic material may be represented as:

[0094] (7).

[0095] Further, the specific implementation steps and principles of the step 4 of dynamically expanding the magnetostrictive model and considering the loss effect are as follows:

[0096] The total magnetic hysteresis loss of the soft magnetic material is mainly composed of static hysteresis loss , eddy current loss and residual loss :

[0097] (16)

[0098] wherein, the eddy current loss is related to the thickness and electrical conductivity of the soft magnetic material, and the residual loss is related to the microstructure, physical properties and external working conditions of the soft magnetic material and various other factors; then the static hysteresis loss, the eddy current loss and the residual loss are respectively:

[0099] (17)

[0100] (18)

[0101] (19)

[0102] In the formula, is a dimensionless coefficient, taking a value of 0.1356; is a magnetization period; is a magnetic flux density.

[0103] In order to further generalize the static inverse J-A model to a dynamic model, we correct the effective field based on the loss separation theory proposed by Bertotti, and add two inverse fields related to the eddy current and residual loss, so that the expression of the effective magnetic field is corrected as:

[0104] (8)

[0105] In the formula, is a direction coefficient related to the direction of , equal to 1 or -1.

[0106] Further, the step 5 constructs the specific implementation steps and principles of the microstatistical magnetostrictive model considering the hysteresis effect are:

[0107] Because the soft magnetic material is affected by the magnetic field, the magnetostriction and the magnetic flux density also have hysteresis effect, and the hysteresis phenomenon of magnetostriction is caused by the existence of The component is the result of the pinning effect hindering the magnetization process corresponding to the external magnetic field, so when constructing the magnetostriction loop simulation model, the influence of the irreversible magnetization component needs to be considered, and the expression of the magnetostriction loop simulation method based on the microstatistical J-A model provided by the application is:

[0108] (9).

[0109] Example 2

[0110] In another preferred embodiment, based on example 1, the specific implementation method and steps of the magnetostriction loop simulation method based on the microstatistical J-A model of the application are described in detail in combination with the drawings.

[0111] As shown in the accompanying Figure 1 To realize the simulation of the magnetostriction loop of the soft magnetic material, the method provided by the application includes the following steps as shown in the simulation flowchart:

[0112] Step 1: Based on the magnetic moment angle distribution probability function, the magnetization intensity of the soft magnetic material under the action of the magnetic field is obtained The analytical expression is:

[0113] (5).

[0114] Step 2: The microstatistical construction model is combined with the traditional inverse J-A hysteresis model, so that the improved hysteresis model can not only produce hysteresis effect but also have physical meaning; the non-hysteresis magnetization intensity expression in the inverse J-A hysteresis model is replaced by the magnetization expression calculated based on the magnetic moment angle distribution probability function, and the magnetic field intensity is corrected to the effective magnetic field intensity, so the expression of the microstatistical J-A hysteresis model is as follows:

[0115] (20)

[0116] In the formula, is the magnetization intensity; is the reversible magnetization intensity; is the irreversible magnetization intensity; is the effective magnetic flux density; is the effective magnetic field intensity; is the pinning parameter; is the domain wall bending parameter; coefficient introduced to prevent non-physical interpretation; coefficient of coupling.

[0117] Step 3: Magnetostriction strain is calculated according to the deformation related to the direction of the saturated magnetic moment. In order to reflect the mutual dependence of the magnetostriction and magnetization of the soft magnetic material in the magnetization process, the expression of the magnetostriction strain of the soft magnetic material is obtained as follows:

[0118] (21)

[0119] In the formula, is the corrected non-magnetic hysteresis magnetization.

[0120] Step 4: In order to consider the influence of the dynamic characteristics on the static inverse J-A model, based on the loss separation theory proposed by Bertotti, the effective magnetic field strength is corrected, and two counterfields related to eddy current and residual loss are added. Therefore, the expression of the effective magnetic field is corrected as follows:

[0121] (8).

[0122] Step 5: Since the magnetostriction and the magnetic flux density also have a hysteresis effect when the soft magnetic material is subjected to the magnetic field, after considering the influence of the irreversible magnetization component, the expression of the magnetostriction hysteresis loop simulation method based on the micro-statistical J-A model proposed by the application is as follows:

[0123] (9).

[0124] In order to verify the effectiveness of the application, amorphous alloy is selected as the experimental material, and the hysteresis characteristics and magnetostriction hysteresis loop of the amorphous alloy are simulated based on the above-mentioned dynamic expansion method. The material parameters of the amorphous alloy are shown in Table 1:

[0125]

[0126] By comparing the simulation results with the experimental results, the comparison graphs of the simulation results are shown in Figure 3 、 Figure 4 It is found that the method proposed by the application can accurately simulate the hysteresis characteristics and magnetostriction hysteresis loop of the amorphous alloy under the action of the magnetic field, and the effectiveness and practicability of the application are verified.

[0127] In the preferred scheme, the specific steps of Step 1 are to characterize the macroscopic magnetic characteristics and magnetostriction characteristics by the magnetic moment angle probability distribution function and the deformation related to the direction of the saturated magnetic moment. The local free energy of the magnetic moment includes the Zeeman energy and the magnetic crystal anisotropy energy , and an improved The function definition considers the magnetic moment angle probability distribution function of the magnetic field ; The above settings can more accurately describe the behavior of the magnet under different magnetic field conditions; then, in Step 2, the mathematical model of magnetostriction effect is established using these characteristic parameters, providing a theoretical basis for subsequent simulation analysis and optimization design.

[0128] In a preferred embodiment, the magnetization intensity of Step 1 is in a probability distribution function After definition, the magnetization intensity under the action of the magnetic field is obtained by three-dimensional integration ; The above settings ensure that the model can accurately simulate the influence of the magnetic field on the magnetization behavior of the material, and Step 2 will introduce a stress-dependent coefficient to further explore the variation of the magnetization intensity under different stresses.

[0129] In a preferred embodiment, the specific steps of Step 2 are to replace the non-hysteresis magnetization intensity expression in the inverse J-A hysteresis model with a magnetization expression calculated based on the magnetic moment angle distribution probability function, and the effective magnetic field intensity is modified according to the influence of the magnetic field on the magnetic properties; The above settings can significantly improve the prediction accuracy of the model for the magnetization behavior of the material, especially under complex magnetic field change conditions; subsequently, the model parameters are optimized by an iterative algorithm to ensure the accuracy of the hysteresis loop, providing reliable theoretical support for the design and performance analysis of magnetic materials.

[0130] In a preferred embodiment, the specific steps of Step 3 are to calculate the magnetostriction strain according to the deformation related to the direction of the saturation magnetic moment, and to iteratively solve the magnetic field intensity and the single-valued magnetization intensity using the modified non-hysteresis magnetization function to obtain the fitting relationship, and then obtain the expression of the magnetostriction strain of the soft magnetic material; The above settings can accurately describe the strain behavior of the soft magnetic material under the action of the magnetic field, providing a solid theoretical basis for subsequent stress and strain analysis and optimization design, ensuring the accuracy and reliability of the performance prediction of the magnetostrictive device.

[0131] In a preferred embodiment, in Step 4, the effective magnetic field intensity is modified, and the counter field related to eddy current loss and residual loss is added, and the eddy current loss field and residual loss field are calculated according to the loss separation theory; The above settings can more accurately simulate the magnetic field distribution under actual working conditions, thereby improving the accuracy and efficiency of the magnetic field calculation, providing strong support for subsequent equipment optimization and fault diagnosis, and ensuring that the optimization adjustment of the magnetic field is more in line with actual needs.

[0132] In a preferred embodiment, the specific steps of Step 5 are to consider the influence of the irreversible magnetization component on the hysteresis effect between magnetostriction and magnetic flux density, and to introduce undetermined coefficients And shape factor varying with material type To construct the expression of magnetostriction hysteresis loop simulation method; the above setting can significantly improve the simulation accuracy, then the expression is verified by experimental data, and the undetermined coefficient is iteratively optimized until the simulation result is highly consistent with the experimental data, thereby completing the accurate simulation of magnetostriction hysteresis loop.

[0133] In summary, the present application proposes an innovative magnetostriction hysteresis loop simulation method based on microstatistical J-A model, which effectively solves the technical problems of inaccurate simulation method, unclear physical meaning and complex operation in the field of magnetostriction hysteresis loop calculation; compared with the prior art, the present application overcomes the limitations of the phenomenological model and the magnetostriction model based on magnetic domain theory, such as difficulty in determining the distribution function, complex operation, more parameters to be solved, and ignoring the influence of magnetic hysteresis effect and loss; by introducing the principle of micro-magnetic moment statistics and combining with the traditional J-A magnetic hysteresis model, the present application first proposes a new Boltzmann function to represent the magnetic moment angle distribution probability, which not only enhances the physical meaning of the model, but also significantly improves the accuracy of the simulation of the influence of the magnetic field on the magnetic properties; at the same time, the present application dynamically extends the magnetostriction model, and takes into account the influence of eddy current loss and residual loss on magnetic properties, so as to more comprehensively reflect the behavior of soft magnetic materials under dynamic magnetic field; in addition, through the modification of effective magnetic field, the eddy current loss field and the residual loss field are considered, which further improves the accuracy of the model in simulating complex magnetic hysteresis phenomenon. Combined with the irreversible magnetization component, the present application constructs a microstatistical magnetostriction model considering magnetic hysteresis effect, which helps to better understand the magnetic hysteresis behavior of soft magnetic materials under the action of magnetic field; the comparison chart of experimental data and simulation results fully demonstrates the accuracy and reliability of the method in simulating the magnetic hysteresis characteristics and magnetostriction hysteresis loop of soft magnetic materials. Therefore, the method of the present application has strong physical meaning, can consider the influence of magnetic hysteresis effect and loss on magnetic properties, is suitable for finite element numerical calculation, and is widely used in the design optimization of electrical equipment core, and provides strong support for the research and application in related fields.

Claims

1. A method for simulating magnetostrictive hysteresis loops based on a micro-statistical JA model, characterized in that, Includes the following steps: Step 1: Based on the statistical principle of microscopic magnetic moments, an improved Boltzmann function is proposed to represent the probability distribution of the magnetic moment angle. The magnetization expression is obtained by discretizing and summing the distribution function of this probability. Specifically, the macroscopic magnetic properties and magnetostrictive properties are characterized by the correlation deformation between the magnetic moment angle probability distribution function and the saturation magnetic moment direction, and the local free energy of the magnetic moment is also considered. Including Seman and magnetocrystalline anisotropy and using improved The function is defined as the probability distribution function of the magnetic moment angle considering the magnetic field. The specific expression is as follows: （1）； （2）； （3）； （4）； In the formula, and These correspond to the external magnetic field and the saturation magnetization, respectively. , , These are the magnetic field strengths. H exist 、 、 The direction cosine; The vacuum permeability; , , Magnetization Intensity exist 、 、 The direction cosine; and is the magnetocrystalline anisotropy constant; The normalized function representing the magnetic field; It is a parameter related to the initial magnetic susceptibility of the material; The angle between the atomic magnetic moment and the direction of the magnetic field; Step 2: Introduce the magnetization expression obtained in Step 1 into the traditional inverse JA model to simulate the effect of the magnetic field on the magnetic properties; Step 3: Modify and calculate the traditional hysteresis-free magnetization function expression, and introduce it into the magnetostrictive model based on magnetic rectangular deformation. Specifically, the magnetostrictive strain is calculated based on the deformation related to the saturation magnetic moment direction, using the modified hysteresis-free magnetization function. For magnetic field strength H and single-value magnetization By performing iterative solutions, we obtain The fitting relationship; where, Indicates the domain wall interaction coefficient; The coupling coefficient is used to derive the expression for the magnetostrictive strain of soft magnetic materials, as follows: （7）； In the formula, This represents the magnetostrictive strain of soft magnetic materials; Indicates saturation magnetostriction; Indicates the length of the atomic structure after deformation; Indicates the length of the initial atomic structure; Indicates an external magnetic field; Step 4: Dynamically extend the magnetostrictive model to incorporate the effects of eddy current loss and residual loss on magnetic properties, and revise the expression for effective magnetic field strength. Step 5: Construct a micro-statistical magnetostriction model that considers the hysteresis effect by combining the irreversible magnetization component.

2. The magnetostrictive hysteresis loop simulation method based on the micro-statistical JA model according to claim 1, characterized in that: The magnetization intensity in Step 1 is based on the probability distribution function. After definition, the magnetization intensity under the action of the magnetic field is obtained by three-dimensional integration. Its parsing expression is: （5）； In the formula, The angle between the magnetization direction of the magnetic moment and the magnetostriction measurement direction; For the direction of magnetization of magnetic moment in Plane projection and The angle between directions.

3. The magnetostrictive hysteresis loop simulation method based on the micro-statistical JA model according to claim 2, characterized in that: The specific steps of Step 2 are as follows: replace the hysteresis-free magnetization expression in the inverse JA hysteresis model with a magnetization expression calculated based on the magnetic moment angle distribution probability function, and correct the magnetic field strength to the effective magnetic field strength according to the mean field theory. The expression is as follows: （6）； In the formula, Indicates hysteresis-free magnetization; Indicates the effective magnetic field.

4. The magnetostrictive hysteresis loop simulation method based on the micro-statistical JA model according to claim 3, characterized in that: In Step 4, the effective magnetic field strength To correct this, a counter-field related to eddy current loss and residual loss is added. The eddy current loss field and residual loss field are calculated based on the loss separation theory, as follows: （8）； In the formula, To take into account the dynamic effective magnetic field strength; The intensity of the eddy current loss field; The remaining loss field strength; Is with Direction-dependent directional coefficients; The thickness of the soft magnetic material; The coefficient is dimensionless. This represents the cross-sectional area of ​​the material laminations; Statistical parameters characterizing the local magnetic field distribution of a magnet; The conductivity of soft magnetic materials, denoted as magnetic flux density.

5. The magnetostrictive hysteresis loop simulation method based on the micro-statistical JA model according to claim 4, characterized in that: The specific steps in Step 5 are as follows: Consider the influence of the irreversible magnetization component on the hysteresis effect between magnetostriction and magnetic flux density, and introduce undetermined coefficients. Shape factor varying with material type The expression for constructing the magnetostrictive hysteresis loop simulation method is as follows: （9）； In the formula, To take into account dynamic magnetization; The non-magnetizable intensity; These are coefficients to be determined; The shape factor varies with the material type; Pinning parameters; Domain wall bending parameters; Coefficients introduced to prevent non-physical interpretations; is the coupling coefficient.

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