Extraction and characterization method for hysteresis characteristic of ferromagnetic material

Abstract

The invention discloses an extraction and characterization method for hysteresis characteristics of a ferromagnetic material. The extraction and characterization method comprises the following steps: extracting a Jiles-Atherton model parameter # imgabs0 #, calculating a correction coefficient # imgabs1 # of the Jiles-Atherton model parameter, and extracting the Jiles-Atherton model parameter under excitation frequencies f1 and f2 and excitation magnetic field intensity amplitude Hac03; extracting an eddy current loss factor k1 and an abnormal loss factor k2 (0, Hac03); extracting abnormal loss factors k2 (0, Hac04), k2 (0, Hac05)... k2 (0, Hac0n) corresponding to the dynamic hysteresis loops 104, 105... 10n; fitting a function y1 that the abnormal loss factor changes along with the excitation magnetic field intensity amplitude; fitting a function y2 that represents a mapping relationship between the abnormal loss factor and the excitation magnetic field intensity amplitude and between the abnormal loss factor and the direct current magnetic bias; and obtaining an expression of an abnormal loss factor k2 according to the function y1 and the function y2. The method can accurately predict the mapping relation between the magnetic induction intensity and the magnetic field intensity in the material.

Description

Technical Field

[0001] The invention relates to ferromagnetic materials, and in particular to a method for extracting and characterizing the hysteresis characteristics of ferromagnetic materials. Background Art

[0002] The hysteresis nonlinear characteristics of some ferromagnetic materials (such as rare earth giant magnetostrictive materials represented by Terfenol-D) are strongly affected by external factors such as bias magnetic field and excitation amplitude. Therefore, it is necessary to further expand the mathematical model used to describe the hysteresis characteristics of ferromagnetic materials in order to more accurately predict the loss of ferromagnetic materials under the influence of various external factors.

[0003] The Jiles-Atherton model explains the magnetization process of ferromagnetic materials as the bending and translation of magnetic domain walls. Its physical meaning is clear, and there are few parameters involved in the calculation. It can more accurately reflect the mapping relationship between the excitation magnetic field and the internal magnetization intensity of ferromagnetic materials. However, the parameters of the Jiles-Atherton model will change with changes in various external factors.

[0004] So far, the effects of DC bias and excitation levels on the hysteresis characteristics of materials have rarely been considered, and existing technologies are not sufficient to accurately predict the mapping relationship between the magnetic induction intensity and the magnetic field intensity inside the material. Summary of the invention

[0005] The technical problem to be solved by the present invention is to overcome the deficiencies of the above-mentioned background technology and provide a method for extracting and characterizing the hysteresis characteristics of ferromagnetic materials, which can more accurately predict the mapping relationship between the magnetic induction intensity and the magnetic field intensity inside the material.

[0006] The technical solution adopted by the present invention to solve the technical problem is a method for extracting and characterizing the hysteresis characteristics of a ferromagnetic material, comprising the following steps:

[0007] Step 1: Measure the excitation magnetic field strength amplitude H without applying DC bias ac01 Quasi-static hysteresis loop under 01 , extract the quasi-static hysteresis loop l 01 The Jiles-Atherton model parameters

[0008] Step 2: Measure the excitation magnetic field strength amplitude H without applying DC bias ac02 Quasi-static hysteresis loop under 02 , extract the quasi-static hysteresis loop l 02 The Jiles-Atherton model parameters

[0009] Step 3: Using Jiles-Atherton model parameters Calculate the correction coefficients of the Jiles-Atherton model parameters Thus, the modified Jiles-Atherton model parameters are obtained;

[0010] Step 4: Measure the excitation frequency f1 and the excitation magnetic field strength amplitude H without applying DC bias. ac03 Dynamic hysteresis loop under 031 , based on the modified Jiles-Atherton model parameters, the dynamic hysteresis loop l is extracted 031 Jiles-Atherton model parameters;

[0011] Step 5: Measure the excitation frequency f2 and the excitation magnetic field strength amplitude H without applying DC bias. ac03 Dynamic hysteresis loop under 032 , based on the modified Jiles-Atherton model parameters, the dynamic hysteresis loop l is extracted 032 Jiles-Atherton model parameters;

[0012] Step 6: According to the dynamic hysteresis loop l 031 Jiles-Atherton model parameters and dynamic hysteresis loop 032 The Jiles-Atherton model parameters are used to extract the eddy current loss factor k1 and the abnormal loss factor k2 (0, H ac03 );

[0013] Step 7: Without applying DC bias, measure the excitation frequency f3 and the excitation magnetic field strength amplitude H ac04 , H ac05 …H ac0n Dynamic hysteresis loop under 04 , l 05 …l 0n , respectively extract the dynamic hysteresis loop l 04 , l 05 …l 0n The Jiles-Atherton model parameters are based on the eddy current loss factor k1 and the dynamic hysteresis loop l 04 , l 05 …l 0n The Jiles-Atherton model parameters are used to extract the corresponding abnormal loss factors k2(0,H ac04 )、k2(0,H ac05 )…k2(0,H ac0n );

[0014] Step 8: According to the excitation magnetic field strength amplitude H ac04, H ac05 …H ac0n and abnormal loss factor k2(0,H ac04 )、k2(0,H ac05 )…k2(0,H ac0n ) Fitting the function y1 of abnormal loss factor changing with the amplitude of excitation magnetic field intensity:

[0015] Step 9: Measure different DC bias magnetic H at excitation frequency f4 dci Under different excitation magnetic field strength amplitude H acj Based on the multiple groups of dynamic hysteresis loops under the above conditions, the Jiles-Atherton model parameters of each group of dynamic hysteresis loops are extracted respectively. Based on the eddy current loss factor k1 and the Jiles-Atherton model parameters of each group of dynamic hysteresis loops, the corresponding abnormal loss factor k2 (H dci ,H acj );

[0016] Step 10: According to multiple sets of DC bias magnetic H dci , multiple groups of excitation magnetic field strength amplitude H acj And multiple groups of abnormal loss factors k2(H dci ,H acj ) fits the function y2 that characterizes the mapping relationship between the abnormal loss factor and the excitation magnetic field intensity amplitude and DC bias magnetism:

[0017] Step 11: Obtain the expression of abnormal loss factor k2 based on function y1 and function y2.

[0018] Furthermore, in step 1, the quasi-static hysteresis loop l 01 The Jiles-Atherton model parameters It is expressed as:

[0019]

[0020] Among them, M s01 a 01 α 01 c 01 k 01 They are the quasi-static hysteresis loops l 01 The saturation magnetization intensity coefficient, shape coefficient, domain wall interaction coefficient, reversibility coefficient and pinning coefficient under the Jiles-Atherton model.

[0021] Further, in step 2, the quasi-static hysteresis loop l 02 The Jiles-Atherton model parameters It is expressed as:

[0022]

[0023] Among them, M s02 a 02 α 02 c 02 k 02 They are the quasi-static hysteresis loops l 02 The saturation magnetization intensity coefficient, shape coefficient, domain wall interaction coefficient, reversibility coefficient and pinning coefficient under the Jiles-Atherton model.

[0024] Further, in step 3,

[0025]

[0026] Among them, β M β a β α β c β k They are respectively the correction coefficient of saturation magnetization coefficient, the correction coefficient of shape coefficient, the correction coefficient of domain wall interaction coefficient, the correction coefficient of reversibility coefficient and the correction coefficient of pinning coefficient.

[0027] Further, in step 8, the function y1 of the fitted abnormal loss factor changing with the amplitude of the excitation magnetic field intensity is expressed as:

[0028] k2(0,H ac )=p1·H ac +p2

[0029] Among them, k2(0,H ac ) is the excitation magnetic field strength amplitude H without DC bias ac Abnormal loss factor at time, H ac is the amplitude of the excitation magnetic field strength, p1 and p2 are intermediate coefficients.

[0030] Further, in step 9, i=1, 2, 3, 4…m; j=1, 2, 3, 4…m, and m is a non-zero natural number.

[0031] Further, in step 10, the fitted function y2 representing the mapping relationship between the abnormal loss factor and the excitation magnetic field intensity amplitude and the DC bias magnetization is expressed as:

[0032]

[0033] Among them, k 2,nor (H dc ,H ac ) is the DC bias magnetic H dc , the excitation magnetic field strength amplitude is H ac The normalized abnormal loss factor, H dc is the DC bias magnetization, Hac is the amplitude of the excitation magnetic field strength, and t1, t2, and t3 are intermediate coefficients.

[0034] Further, in step 11, the expression of abnormal loss factor k2 is obtained as:

[0035] k2=k2(0,H ac )×k 2,nor (H dc ,H ac ).

[0036] Compared with the prior art, the advantages of the present invention are as follows:

[0037] The present invention can identify M based on only a few material hysteresis loops. s ,a,α,c,k,β a ,β α ,β c ,β k , k1, p1, p2, t1, t2, t3 multiple parameters, the corresponding parameter identification process is simple and easy and requires fewer material hysteresis loops. In the entire DC bias-excitation level space, the extracted parameters can more accurately predict the mapping relationship between the magnetic induction intensity and the magnetic field intensity inside the material, and can provide theoretical support for the loss prediction of ferromagnetic materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart of a method according to an embodiment of the present invention.

[0039] Figure 2 It is the hysteresis loop under different excitation levels predicted based on the modified Jiles-Atherton model parameters in the embodiment of the present invention.

[0040] Figure 3 It is the variation trend of the normalized abnormal loss factor with the DC bias and excitation level in the embodiment of the present invention.

[0041] Figure 4 It is the mapping relationship between the modified Jiles-Atherton model parameters and the DC bias and excitation level. Among them, Figure (a) is the mapping relationship between the saturation magnetization coefficient and the DC bias and excitation level; Figure (b) is the mapping relationship between the shape coefficient and the DC bias and excitation level; Figure (c) is the mapping relationship between the domain wall interaction coefficient and the DC bias and excitation level; Figure (d) is the mapping relationship between the reversibility coefficient and the DC bias and excitation level; Figure (e) is the mapping relationship between the pinning coefficient and the DC bias and excitation level; Figure (f) is the mapping relationship between the eddy current loss factor and the DC bias and excitation level; Figure (g) is the mapping relationship between the abnormal loss factor and the DC bias and excitation level.

[0042] Figure 5 The hysteresis loops of the embodiments of the present invention under different DC bias and different frequency excitation signals. Figure (a) is the hysteresis loop under the DC bias of 0 and the excitation frequency of 400Hz; Figure (b) is the hysteresis loop under the DC bias of 20177A / m and the excitation frequency of 700Hz. DETAILED DESCRIPTION

[0043] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] In order to expand the application scope of the Jiles-Atherton model, the present invention provides a method for extracting and characterizing the hysteresis characteristics of ferromagnetic materials taking into account the coupling effect of DC bias and excitation level. Figure 1 , the method comprises the following steps:

[0045] Step 1: Measure the excitation magnetic field strength amplitude H without applying DC bias ac01 Quasi-static hysteresis loop under 01 , using particle swarm optimization to extract the quasi-static hysteresis loop l 01 The Jiles-Atherton model parameters

[0046]

[0047] Among them, M s01 a 01 α 01 c 01 k 01 They are the quasi-static hysteresis loops l 01 The saturation magnetization intensity coefficient, shape coefficient, domain wall interaction coefficient, reversibility coefficient and pinning coefficient under the Jiles-Atherton model.

[0048] Step 2: Measure the excitation magnetic field strength amplitude H without applying DC bias ac02 Quasi-static hysteresis loop under 02 , using particle swarm optimization to extract the quasi-static hysteresis loop l 02 The Jiles-Atherton model parameters

[0049]

[0050] Among them, M s02 a 02 α 02 c 02 k 02They are the quasi-static hysteresis loops l 02 The saturation magnetization intensity coefficient, shape coefficient, domain wall interaction coefficient, reversibility coefficient and pinning coefficient under the Jiles-Atherton model.

[0051] Step 3: Using Jiles-Atherton model parameters Calculate the correction coefficients of the Jiles-Atherton model parameters Thus, the modified Jiles-Atherton model parameters are obtained;

[0052]

[0053] Among them, β M β a β α β c β k They are respectively the correction coefficient of saturation magnetization coefficient, the correction coefficient of shape coefficient, the correction coefficient of domain wall interaction coefficient, the correction coefficient of reversibility coefficient and the correction coefficient of pinning coefficient.

[0054] In this embodiment, H ac01 =73220A / m, H ac02 =1967A / m, Jiles-Atherton model parameters extracted using particle swarm algorithm As shown in the following table:

[0055] Quasi-static Jiles-Atherton model parameters

[0056]

[0057] Calculated correction coefficients for Jiles-Atherton model parameters for:

[0058]

[0059] The saturation magnetization M of giant magnetostrictive materials s Affected by temperature and prestress, but not by excitation level. At constant temperature and prestress, M s Should remain unchanged, β M =0.

[0060] Based on the modified Jiles-Atherton model parameters, the hysteresis loops under different excitation levels (different excitation magnetic field intensity amplitudes) are predicted. The prediction results are as follows: Figure 2The dashed line is the calculation result of the Jiles-Atherton model, and the solid line is the corresponding quasi-static hysteresis loop. The RMSE of the model calculation results is less than 0.008, and the deviation is less than 3%.

[0061] Step 4: Measure the excitation frequency f1 and the excitation magnetic field strength amplitude H without applying DC bias. ac03 Dynamic hysteresis loop under 031 Based on the modified Jiles-Atherton model parameters, the dynamic hysteresis loop is extracted using the particle swarm algorithm. 031 Jiles-Atherton model parameters;

[0062] Step 5: Measure the excitation frequency f2 and the excitation magnetic field strength amplitude H without applying DC bias. ac03 Dynamic hysteresis loop under 032 Based on the modified Jiles-Atherton model parameters, the dynamic hysteresis loop is extracted using the particle swarm algorithm. 032 Jiles-Atherton model parameters;

[0063] Step 6: According to the dynamic hysteresis loop l 031 Jiles-Atherton model parameters and dynamic hysteresis loop 032 The Jiles-Atherton model parameters are used to extract the eddy current loss factor k1 and the abnormal loss factor k2 (0, H ac03 ); Jiles-Atherton model parameters and two dynamic parameters (k1 and k2 (0, H ac03 )) will not change with the change of excitation frequency.

[0064] In this embodiment, f1=200 Hz, f2=400 Hz; the excitation magnetic field intensity amplitude H ac03 =1780A / m, the extracted eddy current loss factor k1=7.708×10 -6 , abnormal loss factor k2(0,H ac03 )=1.437×10 -6 .

[0065] The eddy current loss depends on the resistivity of the giant magnetostrictive material and the rate of change of the magnetization intensity M with time, and is independent of the magnitude of the DC bias. The abnormal loss factor is a statistical representation of the local coercive field distribution of the material. Therefore, in this method, the eddy current loss factor remains unchanged, and the abnormal loss factor is affected by the coupling of the DC bias and the excitation level.

[0066] In order to determine the mapping relationship between the abnormal loss factor and the excitation magnetic field strength amplitude under the condition of no DC bias, it is necessary to measure the dynamic hysteresis loop under different excitation magnetic field strength amplitudes. Therefore, step 7 is used to measure the dynamic hysteresis loop under different excitation magnetic field strength amplitudes.

[0067] Step 7: Without applying DC bias, measure the excitation frequency f3 and the excitation magnetic field strength amplitude H ac04 , H ac05 …H ac0n Dynamic hysteresis loop under 04 , l 05 …l 0n , using particle swarm optimization to extract dynamic hysteresis loops l 04 , l 05 …l 0n The Jiles-Atherton model parameters are based on the eddy current loss factor k1 and the dynamic hysteresis loop l 04 , l 05 …l 0n The Jiles-Atherton model parameters are used to extract the corresponding abnormal loss factors k2(0,H ac04 )、k2(0,H ac05 )…k2(0,H ac0n );

[0068] In this embodiment, f3=200 Hz is selected; the excitation magnetic field intensity amplitude H ac04 =3955A / m, Hac 05 =5984A / m. The abnormal loss factor k2(0,H ac04 )=3.4899×10 -6 ,k2(0,H ac05 )=4.8755×10 -6 .

[0069] Step 8: According to the excitation magnetic field strength amplitude H ac04 , H ac05 …H ac0n and abnormal loss factor k2(0,H ac04 )、k2(0,H ac05 )…k2(0,H ac0n ) Fitting the function y1 of abnormal loss factor changing with the amplitude of excitation magnetic field intensity:

[0070] k2(0,H ac )=p1·H ac +p2

[0071] Among them, k2(0,H ac ) is the excitation magnetic field strength amplitude H without DC biasac Abnormal loss factor at time, H ac is the amplitude of the excitation magnetic field strength, p1 and p2 are intermediate coefficients.

[0072] In this embodiment, the fitted p1=8.194×10 -10 , p2=6.654×10 -8 ; Goodness of fit R 2 >0.99.

[0073] Step 9: Measure different DC bias magnetic H at excitation frequency f4 dci (i=1,2,3,4…m) and different excitation magnetic field strength amplitude H acj The Jiles-Atherton model parameters of each group of dynamic hysteresis loops are extracted by particle swarm optimization. Based on the eddy current loss factor k1 and the Jiles-Atherton model parameters of each group of dynamic hysteresis loops, the corresponding abnormal loss factor k2 (H dci ,H acj ); m is a non-zero natural number;

[0074] In this embodiment, f4=200Hz; DC bias magnetic H dc1 =7348A / m, H dc2 =13467A / m, H dc3 =26348A / m; excitation magnetic field strength amplitude H ac1 =870A / m, H ac2 =1575A / m, H ac3 =2245A / m. The corresponding abnormal loss factor k2(H dci ,H acj ), as shown in the following table:

[0075] Abnormal loss factor k2

[0076]

[0077] The abnormal loss factor k2(0,H ac ) is the reference value for the abnormal loss factor k2(H dci ,H acj ) are normalized as shown in the following table:

[0078] Abnormal loss factor k2 after normalization

[0079]

[0080] Observe the normalized abnormal loss factor k2,nor With the change of DC bias and excitation level, it can be known that the abnormal loss factor k2 is related to the distribution of the local coercive field of the material. Under the same excitation magnetic field intensity amplitude, as the bias magnetic field increases, the local coercive field of the material gradually increases, so the abnormal loss factor gradually increases; in addition, when the excitation magnetic field gradually increases, the magnetic permeability of the material gradually decreases, so under the same DC bias, the change rate of k2 relative to the DC bias is Gradually decrease.

[0081] Step 10: According to multiple sets of DC bias magnetic H dci (i=1,2,3,4…m), multiple groups of excitation magnetic field strength amplitude H acj (j=1,2,3,4…m) and multiple groups of abnormal loss factors k2(H dci ,H acj ) fits the function y2 that characterizes the mapping relationship between the abnormal loss factor and the excitation magnetic field intensity amplitude and DC bias magnetism:

[0082]

[0083] Among them, k 2,nor (H dc ,H ac ) is the DC bias magnetic H dc , the excitation magnetic field strength amplitude is H ac The normalized abnormal loss factor, H dc is the DC bias magnetization, H ac is the amplitude of the excitation magnetic field strength, and t1, t2, and t3 are intermediate coefficients.

[0084] In this embodiment, t1 = 0.006798, t2 = 0.9128, t3 = -0.6371; goodness of fit R2 = 0.9835. 2,nor The trend of changes with DC bias and excitation level is as follows Figure 3 shown.

[0085] Step 11: Obtain the expression of abnormal loss factor k2 based on function y1 and function y2:

[0086] k2=k2(0,H ac )×k 2,nor (H dc ,H ac ).

[0087] According to the above method, the mapping relationship between the modified Jiles-Atherton model parameters and the DC bias magnetization and the excitation magnetic field intensity amplitude can be obtained, such as Figure 4 shown.

[0088] The extracted parameters are used to characterize the hysteresis loop under different DC bias and excitation signals of different frequencies. The prediction results are as follows: Figure 5 This method can accurately predict the hysteresis characteristics of rare earth giant magnetostrictive materials in a large range of excitation frequency-excitation level-DC bias working conditions, and the error of the model calculation results is less than 5%.

[0089] The present invention can identify M based on only a few material hysteresis loops. s ,a,α,c,k,β a ,β α ,β c ,β k , k1, p1, p2, t1, t2, t3 multiple parameters, the corresponding parameter identification process is simple and easy and requires fewer material hysteresis loops. In the entire DC bias-excitation level space, the extracted parameters can more accurately predict the mapping relationship between the magnetic induction intensity and the magnetic field intensity inside the material, and can provide theoretical support for the loss prediction of ferromagnetic materials.

[0090] Those skilled in the art may make various modifications and variations to the present invention. If these modifications and variations are within the scope of the claims of the present invention and their equivalents, then these modifications and variations are also within the protection scope of the present invention.

[0091] The contents not described in detail in the specification are prior art known to those skilled in the art.

Claims

1. A method for extracting and characterizing the hysteresis characteristics of a ferromagnetic material, characterized in that: The following steps are involved: Step 1: Measure the excitation magnetic field strength amplitude H without applying DC bias ac01 Quasi-static hysteresis loop under 01 , extract the quasi-static hysteresis loop l 01 The Jiles-Atherton model parameters Step 2: Measure the excitation magnetic field strength amplitude H without applying DC bias ac02 Quasi-static hysteresis loop under 02 , extract the quasi-static hysteresis loop l 02 The Jiles-Atherton model parameters Step 3: Using Jiles-Atherton model parameters Calculate the correction coefficients of the Jiles-Atherton model parameters Thus, the modified Jiles-Atherton model parameters are obtained; Step 4: Measure the excitation frequency f1 and the excitation magnetic field strength amplitude H without applying DC bias. ac03 Dynamic hysteresis loop under 031 , based on the modified Jiles-Atherton model parameters, the dynamic hysteresis loop l is extracted 031 Jiles-Atherton model parameters; Step 5: Measure the excitation frequency f2 and the excitation magnetic field strength amplitude H without applying DC bias. ac03 Dynamic hysteresis loop under 032 , based on the modified Jiles-Atherton model parameters, the dynamic hysteresis loop l is extracted 032 Jiles-Atherton model parameters; Step 6: According to the dynamic hysteresis loop l 031 Jiles-Atherton model parameters and dynamic hysteresis loop 032 The Jiles-Atherton model parameters are used to extract the eddy current loss factor k1 and the abnormal loss factor k2 (0, H ac03 ); Step 7: Without applying DC bias, measure the excitation frequency f3 and the excitation magnetic field strength amplitude H ac04 , H ac05 …H ac0n Dynamic hysteresis loop under 04 , l 05 …l 0n , respectively extract the dynamic hysteresis loop l 04 , l 05 …l 0n The Jiles-Atherton model parameters are based on the eddy current loss factor k1 and the dynamic hysteresis loop l 04 , l 05 …l 0n The Jiles-Atherton model parameters are used to extract the corresponding abnormal loss factors k2(0,H ac04 )、k2(0,H ac05 )…k2(0,H ac0n ); Step 8: According to the excitation magnetic field strength amplitude H ac04 , H ac05 …H ac0n and abnormal loss factor k2(0,H ac04 )、k2(0,H ac05 )…k2(0,H ac0n ) Fitting the function y1 of abnormal loss factor changing with the amplitude of excitation magnetic field intensity: Step 9: Measure different DC bias magnetic H at excitation frequency f4 dci Under different excitation magnetic field strength amplitude H acj Based on the multiple groups of dynamic hysteresis loops under the above conditions, the Jiles-Atherton model parameters of each group of dynamic hysteresis loops are extracted respectively. Based on the eddy current loss factor k1 and the Jiles-Atherton model parameters of each group of dynamic hysteresis loops, the corresponding abnormal loss factor k2 (H dci ,H acj ); Step 10: According to multiple sets of DC bias magnetic H dci , multiple groups of excitation magnetic field strength amplitude H acj And multiple groups of abnormal loss factors k2(H dci ,H acj ) fits the function y2 that characterizes the mapping relationship between the abnormal loss factor and the excitation magnetic field intensity amplitude and DC bias magnetism: Step 11: Obtain the expression of abnormal loss factor k2 based on function y1 and function y2.

2. The method for extracting and characterizing the hysteresis characteristics of ferromagnetic materials according to claim 1, characterized in that: In step 1, the quasi-static hysteresis loop l 01 The Jiles-Atherton model parameters It is expressed as: Among them, M s01 a 01 α 01 c 01 k 01 They are the quasi-static hysteresis loops l 01 The saturation magnetization intensity coefficient, shape coefficient, domain wall interaction coefficient, reversibility coefficient and pinning coefficient under the Jiles-Atherton model.

3. The method for extracting and characterizing the hysteresis characteristics of ferromagnetic materials according to claim 1, characterized in that: In step 2, the quasi-static hysteresis loop l 02 The Jiles-Atherton model parameters It is expressed as: Among them, M s02 a 02 α 02 c 02 k 02 They are the quasi-static hysteresis loops l 02 The saturation magnetization intensity coefficient, shape coefficient, domain wall interaction coefficient, reversibility coefficient and pinning coefficient under the Jiles-Atherton model.

4. The method for extracting and characterizing the hysteresis characteristics of ferromagnetic materials according to claim 1, characterized in that: In step 3, Among them, β M β a β α β c β k They are respectively the correction coefficient of saturation magnetization coefficient, the correction coefficient of shape coefficient, the correction coefficient of domain wall interaction coefficient, the correction coefficient of reversibility coefficient and the correction coefficient of pinning coefficient.

5. The method for extracting and characterizing the hysteresis characteristics of ferromagnetic materials according to claim 1, characterized in that: In step 8, the function y1 of the fitted abnormal loss factor changing with the amplitude of the excitation magnetic field intensity is expressed as: k2(0,H ac )=p1·H ac +p2 Among them, k2(0,H ac ) is the excitation magnetic field strength amplitude H without DC bias ac Abnormal loss factor at time, H ac is the amplitude of the excitation magnetic field strength, p1 and p2 are intermediate coefficients.

6. The method for extracting and characterizing the hysteresis characteristics of ferromagnetic materials according to claim 1, characterized in that: In step 9, i=1, 2, 3, 4…m; j=1, 2, 3, 4…m, where m is a non-zero natural number.

7. The method for extracting and characterizing the hysteresis characteristics of ferromagnetic materials according to claim 5, characterized in that: In step 10, the fitted function y2 representing the mapping relationship between the abnormal loss factor and the excitation magnetic field intensity amplitude and the DC bias magnetization is expressed as: Among them, k 2,nor (H dc ,H ac ) is the DC bias magnetic H dc , the excitation magnetic field strength amplitude is H ac The normalized abnormal loss factor, H dc is the DC bias magnetization, H ac is the amplitude of the excitation magnetic field strength, and t1, t2, and t3 are intermediate coefficients.

8. The method for extracting and characterizing the hysteresis characteristics of ferromagnetic materials according to claim 7, characterized in that: In step 11, the expression of abnormal loss factor k2 is obtained as: k2=k2(0,H ac )×k 2,nor (H dc ,H ac )。

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