A method for simulating magnetostrictive strain of soft magnetic materials under stress

Abstract

The invention discloses a method for simulating magnetostrictive strain of a soft magnetic material under stress. The method comprises the following steps: firstly assuming that the material is composed of a large number of magnetic domains, and performing six-fold refined triangulation on an icosahedron to determine the initial magnetization intensity directions of various magnetic domains; then constructing a mathematical model of the magnetization intensity and strain of the magnetic domains; deducing an expression for the Gibbs free energy of the magnetic domains when second-order stress is introduced to obtain an expression for the hysteresis-free volume fraction of the magnetic domains; and then constructing a mathematical model of the hysteresis-free magnetization intensity of the entire soft magnetic material based on the homogenization theory; finally, deriving a new magnetostrictive model of the soft magnetic material based on the principle of conservation of mesoscopic energy, and solving the model to simulate magnetostrictive curves of the soft magnetic material under different magnetic fields and stresses. The method can quickly and accurately simulate the magnetostrictive effect of the soft magnetic material under stress, thereby laying a theoretical and technical foundation for accurate simulation of the magnetomechanical properties of electrical equipment containing the soft magnetic material and for global structural optimization design thereof.

Description

Technical Field

[0001] The invention belongs to the field of magnetostrictive property analysis of soft magnetic materials, and particularly relates to a magnetostrictive strain simulation method of soft magnetic materials under stress. Background Art

[0002] Soft magnetic materials are widely used in the manufacture of cores for electrical equipment such as transformers and motors. However, it is worth noting that the magnetostrictive properties of soft magnetic materials will have a significant impact on other properties of the materials themselves and the electrical equipment they belong to (electromagnetic noise, energy loss, service life, etc.). In actual operation, due to the limitations of the manufacturing process and factors such as the external stress and magnetic field to which the electrical equipment is subjected during service, soft magnetic materials will inevitably produce magnetostrictive strain, which in turn affects the operating state of the electrical equipment. Therefore, the invention of an accurate, fast, and practical method for simulating the magnetostrictive properties of soft magnetic materials under stress plays an important supporting role in the accurate evaluation of the performance of electrical equipment and its global optimization.

[0003] However, existing simulation methods for magnetostrictive properties that simultaneously consider stress and magnetic field are mainly based on a macroscopic perspective and require a large amount of experimental data to fit the parameters. This makes it difficult to be applied in engineering and cannot reveal the mechanism of magnetostrictive strain of soft magnetic materials under stress. For example:

[0004] 1) Patent 1: "A Method for Modeling the Magnetostriction of Electrical Steel Sheets," Application Number: 2021111331510. This patent establishes an Everett function database by measuring a large amount of experimental data. It then interpolates and fits parameters based on the input magnetic flux density and stress comparison database to obtain the magnetostriction curve of the electrical steel sheet. However, this method is empirical and requires a large amount of experimental data to fit the parameters, making it less practical. Furthermore, the Everett function is a purely mathematical formula and cannot be used to analyze the magnetostrictive strain mechanism of soft magnetic materials under stress.

[0005] 2) Patent 2: "A Method for Analyzing Transformer Core Vibration Noise," Application Number: 2014107091020. This patent establishes an equivalent weak magnetic coupling model based on a large amount of collected data and empirical formulas to analyze the magnetostrictive strain patterns of transformer cores. However, this method is still empirical and requires extensive experimental data. Furthermore, the established weak magnetic coupling model has limited applicability and cannot analyze the magnetostrictive strain mechanisms of soft magnetic materials under stress.

[0006] 3) Literature 1: Luo Xu, Zhu Haiyan, Ding Yaping, Modified magnetization model of ferromagnetic materials based on magnetostrictive coupling effect [J]. Acta Physica Sinica, 2019, 68(18): 295-306. This literature combines the nonlinear magnetostrictive strain relationship in the Zheng Xiao-Jing-Liu Xing-En (ZL) hysteresis model with the hysteresis theory of the Jiles-Atherton (JA) hysteresis model, considers the influence of stress on the model parameters, and establishes a modified model for the influence of elastic-plastic stress on the magnetostrictive curve of soft magnetic materials. However, this modified model still belongs to a macroscopic hysteresis model, and introduces multiple additional parameters, which requires a large amount of experimental data and more calculation time, and it cannot fundamentally analyze the magnetostrictive strain mechanism of soft magnetic materials under stress.

[0007] 4) Reference 2: Wu Jiaqi, Simulation of Magnetostrictive Properties of Electrical Steel Sheets Considering Stress Effects and Its Application [D]. Shenyang University of Technology, 2021. Magnetostrictive models based on the hyperbolic tangent function and the Helmholtz free energy were derived, respectively, successfully simulating the effects of tensile and compressive stresses on the magnetostrictive strain of magnetic materials. However, this method is based on empirical formulas and requires a large amount of experimental data to fit its parameters, making it difficult to apply in practice. Furthermore, this method only takes a macroscopic perspective and does not analyze the nature of the magnetostrictive strain of soft magnetic materials under stress.

[0008] 5) Reference 3: Chen Hao, Li Lin, Wang Yaqi, Simulation of Dynamic Magnetostrictive Characteristics of Electrical Steel Sheets Based on Energetic and Improved Jiles-Atherton-Sablik Models [J]. Proceedings of the CSEE, 2022: 1-11. This paper uses the dynamic magnetic field solved by the dynamic Energetic hysteresis model as a known quantity for the improved Jiles-Atherton-Sablik hysteresis model, and constructs a dynamic magnetostrictive inverse model with dynamic magnetic induction intensity as input. However, this method is still a macroscopic magnetostrictive model. Although it takes into account the influence of factors such as dynamic loss, it fails to reveal the magnetostrictive mechanism of soft magnetic materials, and requires a large amount of experimental data fitting parameters to improve accuracy.

[0009] To this end, it is necessary to start from the multi-scale magnetostrictive mechanism and energy conservation law of soft magnetic materials, combine with JA hysteresis theory, and propose a method to simulate the magnetostrictive strain of soft magnetic materials under stress. Summary of the Invention

[0010] The present invention aims to address the shortcomings of the above-mentioned existing methods for simulating magnetostrictive strain of soft magnetic materials and provide a new method for simulating magnetostrictive strain of soft magnetic materials under stress, so as to solve the shortcomings mentioned in the background technology.

[0011] In order to achieve the above object, the present invention provides the following technical solutions:

[0012] A method for simulating magnetostrictive strain of a soft magnetic material under stress comprises the following steps:

[0013] Step 1: Assume that the soft magnetic material is composed of a large number of magnetic domains with random distribution directions and a saturation magnetization intensity of M. s , the icosahedron is triangulated six times to obtain a sphere containing 10242 coordinate points, each of which is used to simulate the initial magnetization direction of a magnetic domain α in the soft magnetic material;

[0014] Step 2: Use mesoscopic magnetization theory and Hooke's law to construct the magnetization intensity M within a single magnetic domain α α , magnetostrictive stress ε α Mathematical model of

[0015] Step 3: According to Gibbs free energy W α The definition of anisotropy is divided into static magnetoenergy and magnetoelastic properties The sum of the three terms; and the second-order stress tensor is introduced into the magnetoelastic energy to derive a new Gibbs free energy expression;

[0016] Step 4: According to the Boltzmann distribution calculation principle, calculate the hysteresis-free volume fraction f of each magnetic domain α in turn an ; Then, based on the homogenization theory, the hysteresis-free magnetization intensity M of the soft magnetic material is established an Regarding the magnetization intensity M of the magnetic domain α , magnetostrictive strain ε α and the hysteresis-free volume fraction f corresponding to the magnetic domain an Mathematical models of equal parameters;

[0017] Step 5: Through the principle of conservation of mesoscopic energy and the volume fraction of magnetic domains f α The theory of magnetization change, combined with the hysteresis-free magnetization M obtained in the above steps an , establish a magnetic domain volume fraction f based on mesoscopic scale theory ασ The differential equation is then solved using the fourth-order Runge-Kutta method. Finally, based on the homogenization theory, the overall strain of the soft magnetic material under different stresses is obtained, and its magnetostriction curve is simulated.

[0018] Preferably, in step one, it is assumed that the soft magnetic material is composed of a large number of magnetic domains between the macroscopic and microscopic scales, that is, the mesoscopic scale. In the absence of external magnetic fields, stress and other factors, the initial magnetization direction of the magnetic domains is randomly distributed, and the soft magnetic material as a whole is not magnetic to the outside. Therefore, by triangulating the icosahedron six times, a sphere with 10242 coordinate points is obtained to simulate the initial magnetization direction of the magnetic domains in the soft magnetic material.

[0019] Preferably, the magnetization intensity M of the magnetic domain in step 2 is α , magnetostrictive stress ε α It can be expressed as:

[0020] M α =M s α=M s [α1 α2 α3] t

[0021]

[0022] Where α = [α1 α2 α3] t is the magnetization intensity M of the magnetic domain α α The initial magnetization direction; λ 100 ,λ 111 It is a cubic crystal along <100> 、 <111> The magnetostrictive strain constant at saturation magnetization in the direction.

[0023] Preferably, in step 3, the Gibbs free energy W α , anisotropy energy W α an , magnetostatic energy W α mag and magnetoelastic energy W α The expressions for σ are as follows:

[0024]

[0025]

[0026]

[0027]

[0028] in, Expressed as the first-order component of magnetoelastic energy, It is expressed as the second-order component of magnetoelastic energy, K1 and K2 are the anisotropy constants of the soft magnetic material, μ0 is the vacuum permeability constant, H is the external magnetic field, σ α is the stress tensor, E α is the fourth-order magnetostriction tensor, R α It is the second-order tensor formed by the cosine of the magnetization direction, and N is the sixth-order magnetostriction tensor.

[0029] Preferably, in step 4, according to the Boltzmann distribution principle, the expression of the hysteresis-free volume fraction is obtained as follows:

[0030]

[0031] in, is the adjustable parameter of the material, which is determined by the initial magnetic permeability χ0 of the hysteresis-free magnetization and the saturation magnetization M s Sure.

[0032] Preferably, in step 4, the hysteresis-free magnetization intensity M of the soft magnetic material is an for:

[0033] M an = <M α >=∑ α f an M α

[0034] Preferably, the intermediate energy conservation equation in step five is:

[0035]

[0036] Where k is the pinning coefficient between magnetic domains, δ M is a coefficient introduced to prevent non-physical solutions, δ is the directional coefficient, M irr is the irreversible magnetization component, M is the magnetization intensity,

[0037] According to the theory that the change of magnetic domain volume fraction causes the change of magnetization intensity, it can be obtained that:

[0038] dM ani =M s df ani

[0039] dM Hi =M s df αHi

[0040] dM σi =M s df ασi

[0041] Among them, M ani is the hysteresis-free magnetization of the i-th magnetic domain; M Hi is the magnetization intensity of the i-th magnetic domain under constant stress and variable magnetic field; M σi is the magnetization intensity of the i-th magnetic domain under constant magnetic field and variable stress; f ani is the hysteresis-free volume fraction of the i-th magnetic domain;

[0042] When the stress is fixed and the magnetic field changes, the model of volume fraction changing with magnetic field is as follows:

[0043]

[0044] When the external magnetic field is fixed and the stress varies, the model of volume fraction changing with stress is as follows:

[0045]

[0046] Among them, f αHi is the volume fraction of the ith magnetic domain when the stress is fixed and the magnetic field changes, f ασi is the volume fraction of the i-th magnetic domain when the magnetic field is fixed and the stress changes, k, k l is the pinning coefficient between magnetic domains in the two cases, al, al σ are the mean field parameters of the internal coupling of magnetic domains in the two cases, c and c σ is the reversible magnetic susceptibility in two cases, α i represents the initial magnetization direction of the i-th magnetic domain, σ kl It represents the stress under constant magnetic field and varying stress;

[0047] Finally, the fourth-order Runge-Kutta method is used to solve the relevant differential equations to obtain the volume fraction f of the magnetic domain α αH 、f ασ ,

[0048]

[0049]

[0050] Where, f αH (i+1), f ασ (i+1) is the volume fraction of the next magnetic domain in both cases, f αH (i) f ασ (i) is the volume fraction of the current magnetic domain in both cases, k 1H 、k 2H 、k 3H 、k 4H is the intermediate calculation amount of the Runge-Kutta method in the first case; k 1σ 、k 2σ 、k 3σ 、k 4σ is the intermediate computational cost of the Runge-Kutta method in the second case;

[0051] Then, the magnetostrictive strain in the multi-scale case is obtained through the homogenization principle in step 4:

[0052] ε H =ε αH =∑ α f αH ε αH

[0053] ε σ =ε ασ =∑ α f ασ ε ασ

[0054] Among them, ε αH , ε H are the magnetostrictive strain of the magnetic domain and the strain of the entire material under constant stress field and variable magnetic field respectively; ε ασ , ε σ They are the magnetostrictive strain of the magnetic domain under constant magnetic field and variable stress field and the strain of the entire material.

[0055] Beneficial effects of the present invention:

[0056] The present invention proposes a novel method for simulating the magnetostrictive strain of soft magnetic materials under stress, which combines a simplified multi-scale theory based on magnetic domains with the principle of mesoscopic energy conservation, fundamentally reveals the magnetization mechanism of soft magnetic materials, and simultaneously introduces second-order stress to accurately simulate the changing trend of the magnetostrictive curve of the soft magnetic material when the stress and magnetic field change, while ensuring that the modeling workload, simulation time, and the difficulty of parameter extraction are greatly reduced while improving the accuracy. This is of great significance for optimizing the structure of power equipment and reducing electromagnetic noise. The method belongs to a physical model and does not require a large amount of experimental data to fit its parameters. Therefore, it is highly practical and can be applied in different engineering environments. The method can also reveal the magnetostrictive strain mechanism of soft magnetic materials under different stresses. The method proposed in the present invention has clear physical significance and can quickly and accurately simulate the magnetostrictive effect of soft magnetic materials under stress, laying a theoretical and technical foundation for the accurate simulation of the magnetomechanical properties of electrical equipment containing soft magnetic materials and its global structural optimization design. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A three-dimensional view of the triangulated icosahedron;

[0058] Figure 2 A flow chart of a new method for simulating magnetostrictive strain of a soft magnetic material under stress;

[0059] Figure 3 It is the trend diagram of the magnetization intensity without hysteresis changing with stress and magnetic field;

[0060] Figure 4 The curves of experimental and simulated magnetostrictive strain of soft magnetic materials under 50MPa tensile stress are shown. DETAILED DESCRIPTION

[0061] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0062] As attached Figure 2 A flow chart of a method for simulating the magnetostrictive strain of soft magnetic materials under stress. To establish a new magnetostrictive model and accurately simulate the magnetostrictive strain of soft magnetic materials under different stresses and magnetic fields, the method specifically includes the following steps:

[0063] Step 1: Assuming that the soft magnetic material is composed of a large number of magnetic domains with random distribution, the icosahedron is triangulated six times to obtain a sphere with 10242 coordinate points. Each coordinate point is used to simulate a magnetic domain α in the soft magnetic material. i The direction of the initial magnetization intensity;

[0064] like Figure 1 Shown is a three-dimensional view of the icosahedron after six triangulations.

[0065] Step 2: Use mesoscopic magnetization theory and Hooke's law to construct the magnetization intensity M within a single magnetic domain α α , magnetostrictive strain ε α mathematical model.

[0066] First, it is assumed from step 1 that the soft magnetic material consists of a large number of magnetic domains, and its initial magnetization direction is also given by Figure 1 As shown, we can start from a single magnetic domain to analyze its magnetization intensity M α and magnetostrictive strain ε α , its mathematical model is as follows:

[0067] M α =M s α=M s [α1α2α3] t

[0068]

[0069] where α = [α1α2α3] t is the magnetization intensity M of the magnetic domain α α The initial magnetization direction; λ 100 ,λ 111 It is a cubic crystal along <100> 、 <111> The magnetostrictive strain constant of the direction saturation magnetization; when the soft magnetic material is isotropic, it is considered that λ 100 =λ 111 =λ m ,λ m is the maximum magnetostrictive strain constant of the magnetic material.

[0070] Step 3: Determine the Gibbs free energy W α The definition of anisotropy W α an , magnetostatic energy W α mag and magnetoelastic energy W α σ The sum of the three terms is listed, and the relevant expressions are listed. From the mesoscopic level, second-order stress is introduced into the magnetoelastic energy, and a new Gibbs free energy expression is derived.

[0071] Since the expression of the sixth-order stress tensor is extremely complex, only the more ideal cases are considered and the multi-scale theory is simplified to ensure that the calculation can be performed at the fastest speed without losing accuracy.

[0072]

[0073]

[0074] Where K1 and K2 are the anisotropy constants of the soft magnetic material. When the material is isotropic, the value of this parameter is 0.

[0075]

[0076] Where H is the external magnetic field, H1, H2, and H3 are the magnetic fields projected onto the three axes of the coordinate system by the actual external magnetic field; μ0 is the vacuum permeability constant.

[0077] In reality, the stresses applied to materials are extremely complex. When the stress is low, a simplification can be made, namely considering only first-order stress parameters, because the stress magnitude is not sufficient to alter the trend of the material's magnetostrictive strain characteristics. However, when the stress is relatively high, the strain trend of the soft magnetic material changes due to factors such as the influence of magnetic domains. This change is sufficient to affect the operation of the relevant machine on a macro scale. Therefore, second-order stress factors must be considered to accurately predict the relevant changes.

[0078]

[0079]

[0080]

[0081] Where W α σ1 is the first-order component of magnetoelastic energy; the operator ':' is the tensor scalar product operation; σ α is the second-order stress tensor; λ 100 ,λ 111 Responsible for the first-order magnetoelastic effect, W α σ2 The second-order component of the magnetoelastic energy is obtained, and the coefficient λ' s ,λ' s ' is responsible for the second-order magnetoelastic effect component; tr(σ α ) represents the trace of the second-order stress tensor matrix

[0082]

[0083] Where, σα is the stress tensor, E α is the fourth-order magnetostriction tensor, R α It is the second-order tensor formed by the cosine of the magnetization direction, and N is the sixth-order magnetostriction tensor.

[0084] The magnetization orientation of the magnetic domain α is key to calculating the Gibbs free energy. When there is no external magnetic field or stress, the magnetization direction of the material is determined by its inherent anisotropy, which can be calculated using the minimum Gibbs free energy. However, the calculation of the minimum Gibbs free energy typically involves derivative calculations, which is extremely complex. To avoid this complexity, in step one, it is assumed that the soft magnetic material is composed of a large number of randomly distributed magnetic domains. The icosahedron is then refined multiple times and normalized. The resulting three-dimensional diagram shows the coordinates of each point representing the initial magnetization direction of a particular magnetic domain α in the crystal coordinate system.

[0085] Step 4: Express the hysteresis-free volume fraction f of the magnetic domain of the soft magnetic material by the Boltzmann distribution law an The expression is then used to obtain the hysteresis-free magnetization M of the soft magnetic material based on the homogenization principle. an .

[0086] In step 1, after determining the direction cosines of the magnetic domain, the hysteresis-free volume fraction f of the magnetic domain can be determined by the Boltzmann distribution. an :

[0087]

[0088]

[0089] Where A s is the adjustable material parameter; χ0 is the initial magnetic permeability of the hysteresis-free magnetization; μ0 is the vacuum permeability.

[0090] The hysteresis-free volume fraction obtained in this way greatly reduces its complexity compared to the original simplification, making the model calculation more efficient.

[0091] Then the overall hysteresis-free magnetization M of the soft magnetic material an , hysteresis-free magnetostrictive strain ε an The magnetization intensity M of a single magnetic domain α can be α , magnetostrictive strain ε α and its hysteresis-free volume fraction f an Multiply the vectors and then add up the calculated results of all magnetic domains to get:

[0092] M an =M α =∑ α f anM α =M α1 ·f an1 +M α2 ·f an2 +…+M α n ·f an n

[0093] ε an =ε a =∑ a f an ε a =ε a1 ·f an1 +ε a2 ·f an2 +…+ε a n ·f an n

[0094] Step 5: Based on the simplified multi-scale theory and combined with the principle of mesoscopic energy conservation, a new hysteresis modeling method is obtained.

[0095] According to the principle of mesoscopic energy conservation, the following energy conservation equation is obtained:

[0096]

[0097]

[0098] The former is the energy conservation equation under constant stress and variable magnetic field; the latter is the energy conservation equation under constant magnetic field and variable stress. l is the pinning coefficient between magnetic domains; δ is the direction coefficient, when dH / dt>0 or dσ / dt>0, δ=1, when dH / dt<0 or dσ / dt<0, δ=-1; M irr is the irreversible magnetization component; μ0 is the vacuum permeability constant; δ M It is a coefficient introduced to prevent non-physical solutions, and its expression is as follows:

[0099]

[0100] Magnetization M and irreversible magnetization M irr The relationship is as follows:

[0101] M=M rev +M irr

[0102] M rev =c(M an -M irr )

[0103] Where M rev is the reversible magnetization component; M an is the hysteresis-free magnetization of the soft magnetic material derived above; c is the reversible magnetic susceptibility.

[0104] Irreversible magnetization M irr The differential equation is:

[0105]

[0106] Combining the above formula and the mesoscopic energy conservation equation, the macroscopic model can be derived as follows:

[0107]

[0108]

[0109] Where, al and a are the internal coupling mean field parameter of the magnetic domain and the shape parameter of the hysteresis-free magnetization curve, respectively;

[0110] Since the change in magnetization is due to the change in volume fraction, we can obtain:

[0111] dM ani =M s df ani

[0112] dM Hi =M s df aHi

[0113] dM σi =M s df aσi

[0114] f ani 、f αHi 、f ασi represents the hysteresis-free volume fraction and volume fraction of the i-th magnetic domain, M Hi is the magnetization intensity under constant stress and variable magnetic field, M σi Magnetism is the magnetization intensity when the magnetic field is constant and the stress is variable, M αi is the magnetization intensity of the i-th magnetic domain.

[0115] By using the above mesoscopic energy conservation equation and combining it with the simplified multi-scale theory, we can obtain the volume fraction f of the constant stress-varying magnetic field on the i-th magnetic domain of the magnetic material. αHi The relevant differential equation expression is:

[0116]

[0117] Volume fraction of stress with constant magnetic field on the i-th magnetic domain f ασiThe relevant differential equation expression is:

[0118]

[0119] Among them, f αHi is the volume fraction of the ith magnetic domain when the stress is fixed and the magnetic field changes, f ασi is the volume fraction of the i-th magnetic domain when the magnetic field is fixed and the stress changes, k, k l is the pinning coefficient between magnetic domains in the two cases, al, al σ are the mean field parameters of the internal coupling of magnetic domains in the two cases, c and c σ is the reversible magnetic susceptibility in two cases, α i represents the initial magnetization direction of the i-th magnetic domain, σ kl It represents the stress under constant magnetic field and varying stress;

[0120] Since the saturation magnetization M of the same material s and saturation magnetostriction coefficient λ m is fixed. Therefore, after determining the mathematical model, the experimental data measured under saturation magnetic induction intensity and different stress conditions can be used to fit the data in combination with the Matlab toolbox to obtain the saturation magnetization intensity M. s and saturation magnetostriction coefficient λ m . Then, combined with the algorithm, the specific values ​​of the model parameters al, a, c, and k are extracted.

[0121] Step 6: Solve the above differential equations according to the fourth-order Runge-Kutta method, and use the homogenization theory to obtain the magnetostrictive strain of the entire soft magnetic material, and then obtain the magnetostrictive strain curve of the soft magnetic material.

[0122]

[0123]

[0124] k1=df a [H(i),f a (i), δ, δ M ]

[0125]

[0126]

[0127] k4=df a [H(i)+h,f a (i)+hk3,δ,δ M ]

[0128] Where h is the step length; when the stress is constant and the magnetic field is variable, h = H(i+1)-H(i); when the magnetic field is constant and the stress is variable, h = σ(i+1)-σ(i); f αH (i+1), f ασ (i+1) is the volume fraction of the next magnetic domain in both cases, f αH (i) f ασ (i) is the volume fraction of the current magnetic domain in the two cases, and k1, k2, k3, and k4 are the intermediate calculation quantities of the Runge-Kutta method.

[0129] Finally, combined with the homogenization theory:

[0130] ε H =ε aH =∑ a f aH ε aH

[0131] ε σ =ε aσ =∑ a f aσ ε aσ

[0132] Among them, ε αH , ε H The magnetostrictive strain of the magnetic domain and the strain of the material as a whole under constant stress field and variable magnetic field; ε ασ , ε σ is the magnetostrictive strain of the magnetic domain under constant magnetic field and variable stress field and the strain of the entire material. The magnetostrictive strain of the soft magnetic material can be obtained by the above formula, and then the magnetostrictive strain curve of the material under constant stress, variable magnetic field and constant magnetic field, variable stress can be simulated. Figure 4 The curves of the experimental and simulated magnetostriction curves of magnetic materials under the maximum magnetic density of 1.7T and tensile stress of 50MPa are shown. The global average error can be reduced to about 4.5%, which proves the correctness of the method.

Claims

1. A method for simulating magnetostrictive strain of a soft magnetic material under stress, characterized by: The following steps are involved: Step 1: Assume that the soft magnetic material is composed of a large number of magnetic domains with random distribution directions and a saturation magnetization intensity of M. s , the icosahedron is triangulated six times to obtain a sphere containing 10242 coordinate points, each of which is used to simulate the initial magnetization direction of a magnetic domain α in the soft magnetic material; Step 2: Use mesoscopic magnetization theory and Hooke's law to construct the magnetization intensity M within a single magnetic domain α α , magnetostrictive strain ε α Mathematical model of Step 3: According to Gibbs free energy W α The definition of anisotropy is divided into static magnetoenergy and magnetoelastic properties The sum of three items; The second-order stress tensor is introduced into the magnetoelastic energy and a new Gibbs free energy expression is derived. Step 4: According to the Boltzmann distribution calculation principle, calculate the hysteresis-free volume fraction f of each magnetic domain α in turn an ; Then, based on the homogenization theory, the hysteresis-free magnetization intensity M of the soft magnetic material is established an , about the magnetization intensity M of the magnetic domain α , magnetostrictive strain ε α and the hysteresis-free volume fraction f corresponding to the magnetic domain an Mathematical model of parameters; Step 5: Through the principle of conservation of mesoscopic energy and the volume fraction of magnetic domains f α The theory of magnetization change, combined with the hysteresis-free magnetization M obtained in the above steps an , establish a magnetic domain volume fraction f based on mesoscopic scale theory ασ The differential equation is then solved using the fourth-order Runge-Kutta method. Finally, based on the homogenization theory, the overall strain of the soft magnetic material under different stresses is obtained, and its magnetostriction curve is simulated.

2. The method for simulating magnetostrictive strain of a soft magnetic material under stress according to claim 1, wherein: In step one, it is assumed that the soft magnetic material is composed of a large number of magnetic domains between the macroscopic and microscopic scales, that is, the mesoscopic scale. In the absence of external magnetic fields and stress factors, the initial magnetization directions of the magnetic domains are randomly distributed, and the soft magnetic material as a whole does not show magnetism to the outside. Therefore, by triangulating the icosahedron six times, a sphere with 10,242 coordinate points is obtained to simulate the initial magnetization direction of the magnetic domains in the soft magnetic material.

3. The method for simulating magnetostrictive strain of a soft magnetic material under stress according to claim 1, wherein: The magnetization intensity M of the magnetic domain in step 2 α , magnetostrictive strain ε α Expressed as: M α =M s α=M s [a1a2a3] t Where α = [α1 α2 α3] t is the magnetization intensity M of the magnetic domain α α The initial magnetization direction; λ 100 ,λ 111 It is a cubic crystal along <100> 、 <111> The magnetostrictive strain constant at saturation magnetization in the direction.

4. The method for simulating magnetostrictive strain of a soft magnetic material under stress according to claim 1, wherein: Gibbs free energy W in step 3 α , anisotropic energy static magnetoenergy and magnetoelastic properties The expression is as follows: in, Expressed as the first-order component of magnetoelastic energy, It is expressed as the second-order component of magnetoelastic energy, K1 and K2 are the anisotropy constants of the soft magnetic material, μ0 is the vacuum permeability constant, H is the external magnetic field, σ α is the stress tensor, E α is the fourth-order magnetostriction tensor, R α It is the second-order tensor formed by the cosine of the magnetization direction, and N is the sixth-order magnetostriction tensor.

5. The method for simulating magnetostrictive strain of a soft magnetic material under stress according to claim 1, wherein: In step 4, according to the Boltzmann distribution principle, the expression of the hysteresis-free volume fraction is obtained as follows: in, is the adjustable parameter of the material, which is determined by the initial magnetic permeability χ0 of the hysteresis-free magnetization and the saturation magnetization M s Sure.

6. The method for simulating magnetostrictive strain of a soft magnetic material under stress according to claim 1, wherein: The hysteresis-free magnetization intensity M of the soft magnetic material in step 4 an for: M an =<M α >=∑ α f an M α 。 7. The method for simulating magnetostrictive strain of a soft magnetic material under stress according to claim 1, wherein: Step 5: The energy conservation equation at the intermediate level is: Where k is the pinning coefficient between magnetic domains, δ M is a coefficient introduced to prevent non-physical solutions, δ is the directional coefficient, M irr is the irreversible magnetization component, M is the magnetization intensity, According to the theory that the change of magnetic domain volume fraction causes the change of magnetization intensity, it can be obtained that: dM ani =M s df ani dM Hi =M s df αHi dM σi =M s df ασi Among them, M ani is the hysteresis-free magnetization of the i-th magnetic domain; M Hi is the magnetization intensity of the i-th magnetic domain under constant stress and variable magnetic field; M σi is the magnetization intensity of the i-th magnetic domain under constant magnetic field and variable stress; f ani is the hysteresis-free volume fraction of the i-th magnetic domain; When the stress is fixed and the magnetic field changes, the model of volume fraction changing with magnetic field is as follows: When the external magnetic field is fixed and the stress varies, the model of volume fraction changing with stress is as follows: Among them, f αHi is the volume fraction of the ith magnetic domain when the stress is fixed and the magnetic field changes, f ασi is the volume fraction of the i-th magnetic domain when the magnetic field is fixed and the stress changes, k, k l is the pinning coefficient between magnetic domains in the two cases, al, al σ are the mean field parameters of the internal coupling of magnetic domains in the two cases, c and c σ is the reversible magnetic susceptibility in two cases, α i represents the initial magnetization direction of the i-th magnetic domain, σ kl It represents the stress under constant magnetic field and varying stress; Finally, the fourth-order Runge-Kutta method is used to solve the relevant differential equations to obtain the volume fraction f of the magnetic domain α αH 、f ασ , Where, f αH (i+1), f ασ (i+1) is the volume fraction of the next magnetic domain in both cases, f αH (i) f ασ (i) is the volume fraction of the current magnetic domain in both cases, k 1H 、k 2H 、k 3H 、k 4H is the intermediate calculation amount of the Runge-Kutta method in the first case; k 1σ 、k 2σ 、k 3σ 、k 4σ is the intermediate computational cost of the Runge-Kutta method in the second case; Then, the magnetostrictive strain in the multi-scale case is obtained through the homogenization principle in step 4: e H =<e αH >=∑ α f αH e αH e σ =<e ασ >=S α f ασ e ασ Among them, ε αH , ε H are the magnetostrictive strain of the magnetic domain and the strain of the entire material under constant stress field and variable magnetic field respectively; ε ασ , ε σ They are the magnetostrictive strain of the magnetic domain under constant magnetic field and variable stress field and the strain of the entire material.

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