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

Abstract

The invention discloses a magnetostriction loop simulation method based on a microscopic statistical J-A model, and aims to solve the problems that an existing magnetostriction simulation method is complex in operation, has many to-be-solved parameters and neglects the hysteresis effect and the loss influence. The method comprises the steps that firstly, a magnetic moment angle distribution probability function is proposed based on the microscopic magnetic moment statistical principle; secondly, a magnetization intensity expression obtained through discrete summation of the probability distribution function is introduced into a traditional inverse J-A model, and the influence of a magnetic field on the magnetic performance is simulated; secondly, correcting a non-hysteresis magnetization function and introducing a magnetostriction model based on magnetic moment deformation; then, dynamically expanding the magnetostriction model, and incorporating eddy current loss and residual loss; and finally, constructing a micro statistical magnetostriction model considering the hysteresis effect in combination with the irreversible magnetization component. The built model is high in physical significance, can be applied to finite element numerical calculation and accurate iron core vibration estimation, is suitable for optimization of iron core design of electrical equipment such as motors and transformers, and has important practical value.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetostrictive loop calculation, and particularly to a magnetostrictive loop simulation method based on a microscopic statistical J-A model. Background Art

[0002] Soft magnetic materials are widely used in electrical equipment such as motors and transformers due to their low losses and high magnetic permeability. When these devices are operating, the iron core material in the magnetization process will generate a magnetostrictive effect, resulting in equipment vibration and noise pollution. The magnetostrictive effect is a physical phenomenon in which the size or shape of a soft magnetic material changes under the action of a magnetic field, and this change further causes mechanical vibration, which is one of the main reasons for the vibration and noise of electrical equipment.

[0003] At present, for the magnetostrictive simulation method of soft magnetic materials, a phenomenological model is mostly adopted. Although the phenomenological model has strong mathematical significance, in practical applications, it is difficult to determine its distribution function, and the operation process is complex, making it difficult to quickly reflect the magnetostrictive characteristics of soft magnetic materials. In addition, some scholars have proposed a magnetostrictive model based on the magnetic domain theory. This model considers the microscopic magnetization mechanism of soft magnetic materials, but there are many parameters to be determined in the model, and it largely depends on the accuracy of experimental data, which to a certain extent limits its application scope.

[0004] More critically, some existing magnetostrictive simulation methods often ignore the hysteresis effect of magnetostriction relative to magnetic flux density and magnetic field strength during the simulation process, that is, the magnetic hysteresis effect. The magnetic hysteresis effect is a non-linear and hysteretic relationship between the magnetization state and the magnetic field strength of a magnetic material under the action of a magnetic field, which is one of the important characteristics of magnetic materials. Ignoring the magnetic hysteresis effect will lead to a large deviation between the simulation results and the actual situation, thus unable to accurately predict the vibration of the iron core.

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

[0006] In summary, there are many deficiencies in the prior art when simulating the magnetostrictive characteristics of soft magnetic materials. Therefore, it is necessary to propose a more accurate and efficient magnetostrictive loop simulation method for soft magnetic materials based on the microscopic statistical J-A hysteresis model and dynamically expand it to better meet the needs of optimizing the design of the iron core of electrical equipment. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a method for simulating magnetostrictive hysteresis loops based on the microscopic statistical J-A model, so as to solve the technical problems existing in the field of magnetostrictive hysteresis loop calculation, such as inaccurate simulation methods, unclear physical meanings, and complex operations. Especially in simulating the magnetostrictive characteristics of soft magnetic materials under the action of a magnetic field, the prior art mostly adopts phenomenological models or magnetostrictive models based on magnetic domain theory. However, these models have limitations such as difficulty in determining the distribution function, complex operations, many parameters to be solved, and ignoring the influence of hysteresis effects and losses.

[0008] To solve the above technical problems, the technical solution adopted by the present invention is: a method for simulating magnetostrictive hysteresis loops based on the microscopic statistical J-A model, including the following steps: Step1: Based on the principle of microscopic magnetic moment statistics, an improved Boltzmann function is proposed to represent the magnetic moment angular distribution probability, and the magnetization intensity expression is obtained by discrete summation of the probability distribution function. Step2: The magnetization intensity expression obtained in Step1 is introduced into the traditional inverse J-A model to simulate the influence of the magnetic field on magnetic properties. Step3: The traditional non-hysteretic magnetization function expression is corrected and calculated, and introduced into the magnetostrictive model based on magnetic rectangular deformation. Step4: The magnetostrictive model is dynamically extended to incorporate the influence of eddy current loss and residual loss on magnetic properties, and the effective magnetic field strength expression is corrected. Step5: A microscopic statistical magnetostrictive model considering hysteresis effects is constructed by combining irreversible magnetization components.

[0009] In the preferred solution, the specific steps of Step1 are to characterize the macroscopic magnetic properties and magnetostrictive properties through the magnetic moment angular probability distribution function and the deformation related to the saturation magnetic moment direction. The local free energy of the magnetic moment includes the Zeeman energy and the magnetocrystalline anisotropy energy , and the improved function is used to define the magnetic moment angular probability distribution function considering the magnetic field , and the specific expression is as follows: (1) (2) (3) (4) In the formula, and correspond to the external magnetic field and the saturation magnetization intensity respectively; , , are the magnetic field strengths respectivelyH In 、 、 direction cosine of the direction; is the vacuum permeability; 、 、 are the magnetization intensity in 、 、 direction cosine of the direction; and is the magnetocrystalline anisotropy constant; represents the normalization 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 magnetic field direction.

[0010] In a preferred embodiment, the magnetization intensity of the Step1 is obtained by three-dimensional integration according to the probability distribution function defined to obtain the magnetization intensity under the action of the magnetic field , and its analytical expression is: (5) In the formula, is the angle between the magnetization direction of the magnetic moment and the magnetostriction measurement direction; is the magnetization direction of the magnetic moment in plane projection and direction angle.

[0011] In a preferred embodiment, the specific steps of the Step2 are to replace the anhysteretic magnetization intensity expression in the inverse J-A hysteresis model with the magnetization expression calculated based on the magnetic moment angular distribution probability function, and the effective magnetic field strength is corrected according to the influence of the magnetic field on the magnetic properties. The expression is as follows: (6) In the formula, represents the anhysteretic magnetization intensity; represents the effective magnetic field strength.

[0012] In a preferred embodiment, the specific steps of the Step3 are that the magnetostrictive strain is calculated according to the deformation related to the direction of the saturation magnetic moment, and the modified anhysteretic magnetization function is used to iteratively solve the magnetic field strength H and the single-valued magnetization intensity to obtain the fitting relationship of , where represents the magnetic domain wall interaction coefficient; denotes the coupling coefficient; furthermore, the expression for the magnetostrictive strain of the soft magnetic material is obtained as follows: (7) In the formula, denotes the magnetostrictive strain of the soft magnetic material; denotes the saturation magnetostriction; denotes the length of the atomic structure after deformation; denotes the length of the initial atomic structure; denotes the applied magnetic field.

[0013] In the preferred solution, in the said Step4, the effective magnetic field strength is corrected by adding a back field related to the eddy current loss and the residual loss. The eddy current loss field and the residual loss field are calculated according to the loss separation theory as follows: (8) In the formula, is the effective magnetic field strength considering dynamics; is the eddy current loss field strength; is the residual loss field strength; is the direction coefficient related to the direction; is the thickness of the soft magnetic material; is a dimensionless coefficient; is the cross-sectional area of the material laminate; is a statistical parameter characterizing the local magnetic field distribution of the magnet; is the conductivity of the soft magnetic material, is the magnetic flux density.

[0014] In the preferred solution, the specific steps of Step5 are to consider the influence of the irreversible magnetization component on the hysteresis effect between the magnetostriction and the magnetic flux density, and to construct the expression of the magnetostriction loop simulation method by introducing the undetermined coefficient and the shape coefficient varying with the material type as follows: (9) In the formula, is the magnetization intensity considering dynamics; 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 non-physical explanations; is the coupling coefficient.

[0015] A magnetostrictive hysteresis loop simulation method based on the microscopic statistical J-A model provided by the present invention has the following beneficial effects: 1. The present invention solves the problems of inaccurate simulation methods, unclear physical meaning, and complex operations in the field of magnetostrictive hysteresis loop calculation, overcomes the limitations of the existing phenomenological models or magnetostrictive models based on magnetic domain theory, and there are problems such as difficult determination of distribution functions, complex operations, more parameters to be solved, and ignoring the influence of hysteresis effects and losses in these models. By proposing a new method, the present invention effectively improves the accuracy and physical meaning of the simulation; 2. The present invention proposes a new probability distribution function of the magnetic moment angle, which can more accurately describe the distribution and change of the magnetic moment under the action of the magnetic field. This innovation makes the understanding of the magnetic moment angle distribution deeper and provides a solid foundation for the subsequent calculation of magnetization intensity and magnetostriction; 3. The present invention combines the microscopic statistical structure model with the traditional inverse J-A hysteresis model to form an improved hysteresis model with both hysteresis effects and physical meanings. By introducing microscopic statistical principles, the model enhances the physical meaning while maintaining mathematical simplicity and improves the accuracy of the simulation; 4. The present invention dynamically expands the magnetostrictive model to incorporate the influence of eddy current loss and residual loss on magnetic properties. This expansion enables the model to more accurately simulate the dynamic characteristics in the actual magnetization process and improves the practicality and accuracy of the model; 5. The present invention constructs a microscopic statistical magnetostrictive model considering hysteresis effects in combination with the irreversible magnetization component. This model can more accurately simulate the hysteresis relationship between magnetostriction and magnetic flux density and provides a powerful tool for the prediction and optimal design of magnetostrictive effects in core materials of electrical equipment; 6. The model established by the present invention has strong physical meanings, can more deeply reveal the magnetostrictive characteristics of soft magnetic materials under the action of the magnetic field, has hysteresis effects, can more accurately simulate the hysteresis phenomenon in the actual magnetization process, and improves the accuracy and practicality of the simulation; 7. The method of the present invention can be applied to the simulation of magnetostrictive characteristics of soft magnetic materials, provides strong support for the research in related fields, is particularly suitable for the prediction and optimal design of magnetostrictive effects in core materials of electrical equipment, and helps to improve the performance and reliability of electrical equipment; 8. The present invention proposes a magnetostrictive hysteresis loop simulation method based on the microscopic statistical J-A model. By introducing a probability distribution function, combining the microscopic statistical structure model with the traditional inverse J-A hysteresis model, dynamically expanding, and considering the irreversible magnetization component, etc., the accuracy and practicality of the simulation are improved; 9. The method of the present invention has broad application prospects in aspects such as the design and optimization of the iron core material of electrical equipment, the prediction of magnetostrictive effects, and the research on the magnetostrictive characteristics of soft magnetic materials. With the continuous development of related technologies, the method of the present invention is expected to provide more powerful support for the research and application in related fields. Description of the Drawings

[0016] The present invention will be further described below in conjunction with the drawings and embodiments: Figure 1 is the simulation flow chart of the method proposed by the present invention; Figure 2 is the explanatory diagram of the atomic structure of the isotropic unit of the present invention; Figure 3 is the comparison diagram between the simulated value and the experimental value of the hysteresis model under the magnetic flux density of 1.2T at the excitation frequency of 50Hz of the present invention; Figure 4 is the comparison diagram between the simulated value and the experimental value of the magnetostriction model under the magnetic flux density of 1.2T at the excitation frequency of 50Hz of the present invention. Detailed Embodiment

[0017] The technical solutions in the present invention will be further described below in conjunction with the drawings and embodiments: Embodiment 1 The following is the detailed embodiment of a magnetostriction loop simulation method based on the microscopic statistical J-A model described in the present invention. Through detailed steps and parameter settings, professionals in the same technical field can successfully reproduce the technical solution of the present invention based on this description.

[0018] As Figure 1 shown, a magnetostriction loop simulation method based on the microscopic statistical J-A model includes the following steps: Step 1: Based on the principle of microscopic magnetic moment statistics, a new Boltzmann function is proposed to represent the probability distribution of the magnetic moment angle, and the magnetization intensity expression is obtained by discrete summation of the probability distribution function; Step 2: The traditional inverse J-A model is introduced into the magnetization intensity expression obtained by discrete summation of the probability distribution function to simulate the influence of the magnetic field on magnetic properties; Step 3: The traditional non-hysteretic magnetization function expression is corrected and calculated, and introduced into the magnetostriction model based on magnetic rectangular deformation; Step 4: The magnetostriction model is dynamically extended to incorporate the influence of eddy current loss and residual loss on magnetic properties, and the effective magnetic field strength expression is corrected; Step 5: A microscopic statistical magnetostriction model considering the hysteresis effect is constructed by combining the irreversible magnetization component.

[0019] In this embodiment, the specific implementation steps and principles of calculating the magnetization intensity based on the magnetic moment angular distribution probability function are as follows: Soft magnetic materials will be spontaneously magnetized in the free state, and the magnetic moments 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, resulting in local regions of magnetic moment order. The macroscopic magnetic properties and magnetostrictive properties are characterized by the magnetic moment angular probability distribution function and the deformation related to the direction of the saturation magnetic moment.

[0020] When the atomic magnetic moments inside the material are affected by the magnetic field, the local free energy of the magnetic moments is summarized as the Zeeman energy and the magnetocrystalline anisotropy energy , introducing the influence of the external magnetic field on the equilibrium state, and the expression is as follows: (1) In the formula, is the vacuum permeability, taking H / m; is the magnetocrystalline anisotropy energy, which results from the interaction between the electron spin and orbital motion inside the material, causing the magnetic moments to align along the easy magnetization direction when the magnetic field acts. The expression is as follows: (2) In the formula, and are the magnetocrystalline anisotropy constants. When the soft magnetic material has macroscopic isotropy, then ; At this time, the local free energy of the magnetic moment can be expressed as: (3) By using the improved Boltzmann function to define the magnetic moment angular probability distribution function considering the magnetic field, the probability function can be expressed as: (10) To simplify the calculation, we assume that the probabilities of the magnetic moment distribution in all directions are the same, and perform an averaging operation on the magnetic moment angular distribution to obtain the probability distribution function as: (4) In the formula, is the angle between the projection of the magnetic moment magnetization direction on the plane and the direction, as shown in Figure 4 .

[0022] To solve the normalization function of the magnetic field, perform a three-dimensional integration on the magnetic moment angular distribution probability function and assign it a value of 1: (11) By calculating It is expressed as: (12) At this time, the proportion of the energy contribution made by each magnetic moment magnetization to the magnetic moment magnetization within the unit can be expressed as: (13) After the new probability function is defined, the magnetization intensity under the action of the magnetic field is obtained by solving a three-dimensional integral , and its analytical expression is: (5); In the formula, is the angle between the projection of the magnetic moment magnetization direction on the YZ plane and the Z direction, as Figure 2 shown.

[0023] Further, the specific implementation steps and principles of combining step 2 with the traditional inverse J-A model to simulate the influence of the magnetic field on magnetic properties are as follows: Combine the microscopic statistical structure model with the traditional inverse J-A hysteresis model to simulate the influence of the magnetic field on magnetic properties; the traditional J-A model is a hysteresis model considering the physical movement of domain walls, applicable to isotropic materials, and the parameter solution is relatively simple; we replace the non-hysteretic magnetization intensity expression in the inverse J-A hysteresis model with the magnetization expression calculated based on the probability function of the magnetic moment angular distribution, and correct the magnetic field intensity to the effective magnetic field intensity , so that the improved hysteresis model can not only produce hysteresis effects but also have physical meanings. The expression of the proposed microscopic statistical J-A hysteresis model: (6).

[0024] Further, the specific implementation steps and principles of introducing the magnetostriction model and correcting the non-hysteretic magnetization function in step 3 are as follows: The magnetostrictive strain is calculated according to the deformation related to the direction of the saturation magnetic moment, and the length of the initial atomic structure can be expressed in discrete or integral form: (14) In the formula, represents the deformation amount; represents the probability distribution function.

[0025] After applying the magnetic field, the angular distribution probability will change, and the changed atomic length is expressed as: (15) Combining the above initial atomic length and the changed atomic length, in order to reflect the mutual dependence relationship between magnetostriction and magnetization in the magnetization process of soft magnetic materials, we use the modified anhysteretic magnetization function for the magnetic field strength H and the single-valued magnetization intensity to perform iterative solution, and obtain the fitting relationship of , where represents the magnetic domain wall interaction coefficient; represents the coupling coefficient; furthermore, the magnetostrictive strain of the soft magnetic material can be expressed as: (7).

[0026] Furthermore, the specific implementation steps and principles of the step 4 for dynamically expanding the magnetostriction model and considering the loss influence are as follows: The total hysteresis loss of the soft magnetic material is mainly composed of the static hysteresis loss , the eddy current loss and the residual loss : (16) Among them, the eddy current loss is related to the thickness and conductivity of the soft magnetic material, and the residual loss is related to various factors such as the microstructure, physical properties and external working conditions of the soft magnetic material; then the expressions of the static hysteresis loss, eddy current loss and residual loss are respectively: (17) (18) (19) In the formula, is a dimensionless coefficient with a value of 0.1356; is the magnetization period; is the magnetic flux density.

[0027] In order to further generalize the static inverse J-A model to the dynamic model, based on the loss separation theory proposed by Bertotti, we modified the effective field , and added two back fields related to the eddy current and residual loss, then the expression of the effective magnetic field is modified as: (8) In the formula, is the direction coefficient related to the direction of , equal to 1 or -1.

[0028] Further, the specific implementation steps and principles of constructing the microscopic statistical magnetostriction model considering the hysteresis effect in Step 5 are as follows: When soft magnetic materials are under the action of a magnetic field, there is also a hysteresis effect between magnetostriction and magnetic flux density. The generation of the hysteresis phenomenon of magnetostriction is because the existence of this component is the result of the pinning effect hindering the magnetization process corresponding to the applied magnetic field. Therefore, when constructing the magnetostriction loop simulation model, we need to consider the influence of the irreversible magnetization component. The expression of a magnetostriction loop simulation method based on the microscopic statistical J-A model proposed in the present invention is: (9).

[0029] Embodiment 2 In another preferred embodiment, on the basis of Embodiment 1, this embodiment combines the accompanying drawings to elaborate in detail the specific implementation methods and steps of a magnetostriction loop simulation method based on the microscopic statistical J-A model of the present invention.

[0030] As Figure 1 shown in the simulation flow chart of the method proposed in the present invention, to realize the simulation of the magnetostriction loop of soft magnetic materials, it specifically includes the following steps: Step 1: Based on the magnetic moment angular distribution probability function, obtain the magnetization intensity of the soft magnetic material under the action of the magnetic field , and its analytical expression is: (5).

[0031] Step 2: Combine the microscopic statistical structure model with the traditional inverse J-A hysteresis model, so that the improved hysteresis model can not only generate the hysteresis effect but also have physical meaning; replace the non-hysteretic magnetization intensity expression in the inverse J-A hysteresis model with the magnetization expression calculated based on the magnetic moment angular distribution probability function, and correct the magnetic field intensity to the effective magnetic field intensity. Therefore, the expression of the proposed microscopic statistical J-A hysteresis model is as follows: (20) In the formula, is the magnetization intensity; is the reversible magnetization intensity; is the non-magnetizable intensity; is the effective magnetic flux density; is the effective magnetic field intensity; is the pinning parameter; is the domain wall bending parameter; is the coefficient introduced to prevent non-physical explanations; is the coupling coefficient.

[0032] Step 3: The magnetostrictive strain is calculated according to the deformation related to the direction of the saturation magnetic moment. To reflect the mutual dependence between magnetostriction and magnetization during the magnetization process of soft magnetic materials, the expression for the magnetostrictive strain of soft magnetic materials is obtained as follows: (21) where is the corrected anhysteretic magnetization intensity.

[0033] Step 4: To consider the influence of 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 back fields related to eddy current and residual loss are added. Then the expression for the effective magnetic field is corrected to: (8).

[0034] Step 5: Since there is also a hysteresis effect between magnetostriction and magnetic flux density when soft magnetic materials are subjected to a magnetic field, considering the influence of the irreversible magnetization component, the expression of a magnetostriction loop simulation method based on the microscopic statistical J-A model proposed in the present invention is: (9).

[0035] To verify the effectiveness of the present invention, we select amorphous alloy as the experimental material and simulate the hysteresis characteristics and magnetostriction loop of the amorphous alloy based on the above-mentioned dynamic expansion method. The material parameters of the amorphous alloy are shown in Table 1:

[0036] By comparing the simulation results with the experimental results, as shown in the comparison diagrams of the simulation results in Figure 3 and Figure 4 , we find that the method proposed in the present invention can accurately simulate the hysteresis characteristics and magnetostriction loop of amorphous alloy under the action of a magnetic field, verifying the effectiveness and practicability of the present invention.

[0037] In the preferred solution, the specific steps of Step 1 are to characterize the macroscopic magnetic properties and magnetostrictive properties through the magnetic moment angular probability distribution function and the deformation related to the direction of the saturation magnetic moment. The local free energy of the magnetic moment includes the Zeeman energy and the magnetocrystalline anisotropy energy , and the improved function is used to define the magnetic moment angular probability distribution function considering the magnetic field; the above settings can more accurately describe the behavior of the magnet under different magnetic field conditions; then, in Step 2, these characteristic parameters will be used to establish a mathematical model of the magnetostrictive effect, providing a theoretical basis for subsequent simulation analysis and optimization design.

[0038] In the preferred solution, the magnetization intensity in Step1 is obtained by three-dimensional integration according to the magnetization intensity under the magnetic field after the probability distribution function is defined; the above settings ensure that the model can accurately simulate the influence of the magnetic field on the magnetization behavior of the material. At the same time, Step2 will introduce a stress-dependent coefficient, and by adjusting this coefficient, the variation law of the magnetization intensity under different stresses will be further explored. ; The above settings ensure that the model can accurately simulate the influence of the magnetic field on the magnetization behavior of the material. At the same time, Step2 will introduce a stress-dependent coefficient, and by adjusting this coefficient, the variation law of the magnetization intensity under different stresses will be further explored.

[0039] In the preferred solution, the specific steps of Step2 are to replace the anhysteretic magnetization intensity expression in the inverse J-A hysteresis model with the magnetization expression calculated based on the probability function of the magnetic moment angular distribution, and the effective magnetic field intensity is corrected 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 through an iterative algorithm to ensure the accuracy of the hysteresis loop, providing a reliable theoretical support for the design and performance analysis of magnetic materials.

[0040] In the preferred solution, the specific steps of Step3 are that the magnetostrictive strain is calculated according to the deformation related to the direction of the saturation magnetic moment, and the magnetic field intensity and the single-valued magnetization intensity are iteratively solved through the modified anhysteretic magnetization function to obtain the fitting relationship, and then the expression of the magnetostrictive strain of the soft magnetic material is obtained; 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, and ensuring the accuracy and reliability of the performance prediction of magnetostrictive devices.

[0041] In the preferred solution, in Step4, the effective magnetic field intensity is corrected by adding a back field related to the eddy current loss and the residual loss. The eddy current loss field and the 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 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 requirements.

[0042] In the preferred solution, the specific steps of Step5 are to consider the influence of the irreversible magnetization component on the hysteresis effect between magnetostriction and magnetic flux density, and construct an expression for the magnetostrictive loop simulation method by introducing a coefficient to be determined and a shape coefficient that varies with the material type; the above settings can significantly improve the simulation accuracy. Then, the experimental data is used to verify this expression, and the coefficient to be determined is iteratively optimized until the simulation results are in good agreement with the experimental data, thus completing the accurate simulation of the magnetostrictive loop.

[0043] In summary, the present invention proposes an innovative method for simulating magnetostrictive hysteresis loops based on microscopic statistical J-A model, which effectively solves the technical problems such as inaccurate simulation method, unclear physical meaning and complex operation in the field of magnetostrictive hysteresis loop calculation; compared with the prior art, the present invention overcomes the limitations of the phenomenological model and the magnetostrictive model based on magnetic domain theory, such as difficult determination of distribution function, complex operation, more parameters to be solved, and neglect of hysteresis effect and loss influence; by introducing the principle of microscopic magnetic moment statistics and combining it with the traditional J-A hysteresis model, the present invention first proposes a new Boltzmann function to represent the probability of magnetic moment angular distribution, which not only enhances the physical meaning of the model, but also significantly improves the accuracy of simulating the influence of magnetic field on magnetic properties; at the same time, the present invention dynamically expands the magnetostrictive model by incorporating 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 fields; in addition, through the correction of the effective magnetic field, the eddy current loss field and the residual loss field are considered, further improving the accuracy of the model in simulating complex hysteresis phenomena. Combining with the irreversible magnetization component, the present invention constructs a microscopic statistical magnetostrictive model considering hysteresis effect, which helps to more deeply understand the 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 hysteresis characteristics and magnetostrictive hysteresis loops of soft magnetic materials. Therefore, the method of the present invention has strong physical meaning, can consider the influence of hysteresis effect and loss on magnetic properties, is applicable to finite element numerical calculation, and is widely used in the design optimization of iron cores of electrical equipment, providing strong support for the research and application in related fields.

Claims

1. A magnetostrictive loop simulation method based on a microscopic statistical JA model, characterized in that: The following steps are involved: Step 1: Based on the statistical principle of microscopic magnetic moment, an improved Boltzmann function is proposed to represent the probability of magnetic moment angle distribution, and the expression of magnetization intensity is obtained by discrete summation of the probability distribution function; Step 2: Introduce the magnetization intensity expression obtained in Step 1 into the traditional inverse JA model to simulate the influence of magnetic field on magnetic properties; Step 3: Modify and calculate the traditional hysteresis-free magnetization function expression and introduce it into the magnetostriction model based on magnetic rectangular deformation; Step 4: Dynamically expand the magnetostrictive model, incorporate the effects of eddy current loss and residual loss on magnetic properties, and modify the expression of effective magnetic field intensity; Step 5: Construct a microscopic statistical magnetostriction model considering the hysteresis effect by combining the irreversible magnetization component.

2. The magnetostrictive loop simulation method based on the microscopic statistical JA model according to claim 1, characterized in that: The specific steps of Step 1 are to characterize the macroscopic magnetic properties and magnetostrictive properties through the probability distribution function of the magnetic moment angle and the deformation related to the saturation magnetic moment direction, and the local free energy of the magnetic moment Zeeman energy and magnetocrystalline anisotropy energy , and use the improved Function definition: Probability distribution function of magnetic moment angle considering magnetic field , the specific expression is as follows: （1）； （2）； （3）； （4）； In the formula, and They correspond to the external magnetic field and saturation magnetization intensity respectively; , , The magnetic field strength is H exist 、 、 Direction cosines of direction; is the vacuum permeability; , , The magnetization intensity exist 、 、 Direction cosines of direction; and is the magnetocrystalline anisotropy constant; represents 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.

3. The magnetostrictive loop simulation method based on the microscopic statistical JA model according to claim 2, characterized in that: The magnetization intensity of Step 1 is in the probability distribution function After the definition, the magnetization intensity under the magnetic field is obtained according to the three-dimensional integral , its analytical expression is: （5）； In the formula, is the angle between the magnetization direction of the magnetic moment and the magnetostriction measurement direction; The magnetization direction is Plane projection and The angle of direction.

4. The magnetostrictive loop simulation method based on the microscopic statistical JA model according to claim 1, characterized in that: The specific steps of Step 2 are to replace the hysteresis-free magnetization intensity expression in the inverse JA hysteresis model with the magnetization expression calculated based on the magnetic moment angle distribution probability function, and correct the magnetic field intensity to the effective magnetic field intensity according to the mean field theory, and the expression is as follows: （6）； In the formula, It represents the hysteresis-free magnetization; Represents the effective magnetic field.

5. The magnetostrictive loop simulation method based on the microscopic statistical JA model according to claim 1, characterized in that: The specific steps of Step 3 are: the magnetostrictive strain is calculated according to the deformation related to the saturation magnetic moment direction, and the modified hysteresis-free magnetization function is used. Magnetic field strength H and the single-valued magnetization Perform iterative solution and obtain The fitting relationship of represents the domain wall interaction coefficient; Represents the coupling coefficient, and then the expression of magnetostrictive strain of soft magnetic materials is obtained, as follows: （7）； In the formula, It represents the magnetostrictive strain of soft magnetic materials; represents saturation magnetostriction; Represents the length of the atomic structure after deformation; represents the length of the initial atomic structure; represents the external magnetic field.

6. The magnetostrictive loop simulation method based on the microscopic statistical JA model according to claim 1, characterized in that: In Step 4, the effective magnetic field strength Corrections are made to add the reverse fields related to eddy current loss and residual loss. The eddy current loss field and residual loss field are calculated according to the loss separation theory, as follows: （8）； In the formula, To consider the dynamic effective magnetic field strength; is the eddy current loss field intensity; is the residual loss field strength; is with Direction-dependent directional coefficient; is the thickness of soft magnetic material; is the dimensionless coefficient; is the cross-sectional area of ​​the material lamination; It is a statistical parameter that characterizes the local magnetic field distribution of a magnet; is the electrical conductivity of the soft magnetic material, is the magnetic flux density.

7. The magnetostrictive loop simulation method based on the microscopic statistical JA model according to claim 1, characterized in that: 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 introduce the unknown coefficient and shape factor that varies with material type The expression used to construct the simulation method of magnetostrictive loop is: （9）； In the formula, To consider the dynamic magnetization; is the non-magnetizable intensity; is the coefficient to be determined; is the shape factor that varies with material type; is the pinning parameter; is the domain wall bending parameter; coefficients introduced to prevent non-physical interpretations; is the coupling coefficient.

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