CN113158432A - Stress and strain-containing JA hysteresis model parameter identification method - Google Patents
Stress and strain-containing JA hysteresis model parameter identification method Download PDFInfo
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Abstract
The invention belongs to the technical field of electromagnetism, and particularly relates to a stress and strain-containing JA hysteresis model parameter identification method. The JA hysteresis model parameter identification method comprises the following steps: introducing plastic strain to the silicon steel sheet; obtaining a hysteresis loop of the silicon steel sheet; calculating the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss according to the hysteresis loop of the silicon steel sheet; and determining the values of a, k, alpha and C in the model parameters according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss of the magnetic parameters. The stress and strain containing JA hysteresis model parameter identification method can identify the stress and strain containing JA hysteresis model parameter, and the identification method improves the accuracy and speed of JA hysteresis model parameter identification.
Description
Technical Field
The invention belongs to the technical field of electromagnetism, and particularly relates to a stress and strain-containing JA hysteresis model parameter identification method.
Background
With the wide application of non-oriented silicon steel in components such as motors and the like, the phenomenon that the magnetic performance of silicon steel sheet is degraded by the manufacturing process of silicon steel sheets is receiving more and more attention. The manufacturing processes specifically comprise blanking, welding, mechanical connection, winding, press mounting and the like, and the manufacturing processes can introduce complicated residual stress and plastic strain with different directions, different types and non-uniform distribution in the material, so that the magnetization resistance of the silicon steel material is increased sharply, and the loss of the silicon steel material is increased remarkably.
In the prior art, the JA hysteresis model parameters are generally identified by a genetic algorithm, a neural network, a particle swarm optimization and the like, but the stress and strain-containing hysteresis models are not involved in the conventional JA hysteresis model parameter identification methods, so that the stress and strain-containing JA hysteresis model parameters are difficult to identify.
Disclosure of Invention
The object of the present invention is to solve at least the problem of difficulty in identifying the parameters of the JA hysteresis model containing stress and strain. The purpose is realized by the following technical scheme:
the invention provides a stress and strain-containing JA hysteresis model parameter identification method, which comprises the following steps:
introducing plastic strain to the silicon steel sheet;
obtaining a hysteresis loop of the silicon steel sheet;
calculating the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss according to the hysteresis loop of the silicon steel sheet;
determining values of a, k, alpha and C in model parameters according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss of the magnetic parameters;
wherein a is a non-hysteresis magnetization behavior parameter, k is a magnetic domain wall concentration coefficient, alpha is a main field component, and C is a reversible magnetization coefficient.
According to the stress and strain-containing JA hysteresis model parameter identification method provided by the embodiment of the invention, plastic strain is firstly introduced into a silicon steel sheet to generate stress and strain in the silicon steel sheet, then the silicon steel sheet containing stress and strain is subjected to a magnetic test to obtain magnetic parameters of magnetic field intensity and magnetic induction intensity of the silicon steel sheet, then peak magnetic induction intensity, coercive force, ratio of remanence to coercive force and experimental values of hysteresis loss of the silicon steel sheet are calculated according to the magnetic field intensity and the magnetic induction intensity of the silicon steel sheet, and finally the values of a, k, alpha and C in the model parameters are determined according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental values of hysteresis loss. The stress and strain containing JA hysteresis model parameter identification method can identify the stress and strain containing JA hysteresis model parameter, and the identification method improves the accuracy and speed of JA hysteresis model parameter identification.
In some embodiments of the present invention, the determining the accurate values of a, k, α, and C in the model parameters according to the peak magnetic induction of the magnetic parameters, the coercivity, the ratio of remanence to coercivity, and the experimental value of hysteresis loss specifically includes the following steps:
determining rough estimated values of a, k, alpha and C in the model parameters respectively according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss of the magnetic parameters;
setting the limit values of a, k, alpha and C in the model parameters according to the rough estimated values of a, k, alpha and C in the model parameters;
and determining the accurate values of a, k, alpha and C in the model parameters according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss of the magnetic parameters.
In some embodiments of the present invention, the determining the coarse evaluation values of a, k, α, and C in the model parameters according to the peak magnetic induction, the coercivity, the ratio of remanence to coercivity, and the experimental value of hysteresis loss specifically includes the following steps:
presetting initial values of a, k, alpha and C in model parameters;
adjusting the initial value of one model parameter, and controlling the initial values of the other three model parameters to be unchanged;
calculating the peak magnetic induction intensity, the coercive force, the ratio of residual magnetism to the coercive force and the rough calculation value of the hysteresis loss of the magnetic parameters according to the initial value of the adjusted model parameter;
calculating an error value between a rough calculated value of the magnetic parameter corresponding to the one model parameter and the experimental value;
and determining the rough estimation value of the model parameter according to the rough calculation value and the experimental value of the magnetic parameter within the range of a preset error value.
In some embodiments of the present invention, the calculating a rough value of peak magnetic induction of the magnetic parameter according to the model parameter a, or calculating a rough value of coercivity of the magnetic parameter according to the model parameter k, or calculating a rough value of a ratio of magnetic remanence to coercivity according to the model parameter α, or calculating a rough value of hysteresis loss of the magnetic parameter according to the model parameter C is calculated by the following formula:
B＝μ0(M+H) (2)
Mir＝1-CM (4)
wherein M is the magnetization intensity of the silicon steel sheet, and M is a middle variable; h is the intensity of the external magnetic field; b is magnetic induction intensity; μ 0 is the vacuum permeability, μ 0 is a constant; man is the magnetic intensity without hysteresis; mir is the irreversible magnetization; a is a non-magnetic hysteresis magnetization behavior model parameter; k is the domain wall concentration coefficient; α is the main field component; c is reversible susceptibility; 6 is a coefficient, and when the magnetic field intensity is increased, the value is 1; when the magnetic field intensity is reduced, the value is-1, and Ms is the saturation magnetization of the material.
In some embodiments of the invention, the error value of the experimental value of the magnetic parameter and the rough value of the magnetic parameter is calculated according to the following formula:
in some embodiments of the present invention, the predetermined error value ranges from 3% to 5%.
In some embodiments of the present invention, the determining the accurate values of a, k, α, and C in the model parameters according to the peak magnetic induction of the magnetic parameters, the coercivity, the ratio of remanence to coercivity, and the experimental value of hysteresis loss specifically includes the following steps:
setting the accurate estimation values of a, k, alpha and C in the model parameters in the limit value of each model parameter;
respectively calculating the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the precise value of hysteresis loss of the magnetic parameters according to the precise values of a, k, alpha and C in the model parameters;
respectively calculating error values of the experimental value and the accurate value of each magnetic parameter;
and determining the accurate values of a, k, alpha and C in the model parameters according to the minimum sum of the error values of the experimental values and the accurate values of the magnetic parameters.
In some embodiments of the present invention, after determining the accurate values of a, k, α, and C in the model parameter according to the minimum sum of the error values of the experimental value and the refined value of each magnetic parameter, the method further includes the following steps:
fitting a relation between a, k, alpha and C and stress strain in the model parameters according to the accurate values of a, k, alpha and C in the model parameters:
a＝70.4(0.026σr2-2.7σ+967.5e2)(101.2ε+2.5) (6)
k＝(-4.2σ2-841.2-47510)ε2+(10.3σ2+63.0σ+4157)ε-0.9σ+49.58 (7)
α＝(-2.8ε+0.4)×10-9σ3+(6.5ε-1.2)×10-9σ2+(3.0ε-0.5)×10-6σ-0.0001ε+1.8×10-5 (8)
C＝(-0.038σ2+1.1σ+163.7)ε2+(0.003σ2-0.1σ-14.1)ε+0.008σ+0.34 (9)
wherein σ is stress; ε is the plastic strain.
In some embodiments of the present invention, the introducing the plastic strain to the silicon steel sheet specifically includes the following steps:
plastic strain with different gradients is respectively introduced into a plurality of silicon steel sheets.
In some embodiments of the invention, the different gradients of plastic strain rolling are the same.
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Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like parts are designated by like reference numerals throughout the drawings. In the drawings:
fig. 1 is a schematic flow chart of a stress and strain-containing JA hysteresis model parameter identification method according to an embodiment of the present invention.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
It is to be understood that the terminology used herein is for the purpose of describing particular example embodiments only, and is not intended to be limiting. As used herein, the singular forms "a", "an" and "the" may be intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms "comprises," "comprising," "including," and "having" are inclusive and therefore specify the presence of stated features, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and/or groups thereof.
Although the terms first, second, third, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms may be only used to distinguish one element, component, region, layer or section from a second region, layer or section. Terms such as "first," "second," and other numerical terms when used herein do not imply a sequence or order unless clearly indicated by the context. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the example embodiments.
For convenience of description, spatially relative terms, such as "inner", "outer", "lower", "below", "upper", "above", and the like, may be used herein to describe one element or feature's relationship to another element or feature as illustrated in the figures. Such spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as "below" or "beneath" other elements or features would then be oriented "above" or "over" the other elements or features. Thus, the example term "below … …" can include both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
As shown in fig. 1, the invention provides a stress and strain-containing JA hysteresis model parameter identification method, which comprises the following steps:
s10: introducing plastic strain to the silicon steel sheet;
s20: obtaining a hysteresis loop of a silicon steel sheet;
s30: calculating the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss according to the hysteresis loop of the silicon steel sheet;
s40: determining values of a, k, alpha and C in model parameters according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss of the magnetic parameters;
wherein a is a non-hysteresis magnetization behavior parameter, k is a magnetic domain wall concentration coefficient, alpha is a main field component, and C is a reversible magnetization coefficient.
According to the stress and strain-containing JA hysteresis model parameter identification method provided by the embodiment of the invention, plastic strain is firstly introduced into a silicon steel sheet to generate stress and strain in the silicon steel sheet, then the silicon steel sheet containing stress and strain is subjected to a magnetic test to obtain magnetic parameters of magnetic field intensity and magnetic induction intensity of the silicon steel sheet, then peak magnetic induction intensity, coercive force, ratio of remanence to coercive force and experimental values of hysteresis loss of the silicon steel sheet are calculated according to the magnetic field intensity and the magnetic induction intensity of the silicon steel sheet, and finally the values of a, k, alpha and C in the model parameters are determined according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental values of hysteresis loss. The stress and strain containing JA hysteresis model parameter identification method can identify the stress and strain containing JA hysteresis model parameter, and the identification method improves the accuracy and speed of JA hysteresis model parameter identification.
The step S10 is specifically implemented by the following means:
selecting a silicon steel sheet with a certain thickness (such as 0.27mm), processing the silicon steel sheet into a plurality of silicon steel sheet samples with the same size (such as 200mm x 30mm), and stretching the silicon steel sheet samples by using an extensometer on a universal material testing machine so as to introduce plastic strain into the silicon steel sheet samples.
In this embodiment, there is no specific limitation on the thickness of the silicon steel sheet, the sample size of the silicon steel sheet, and the plastic deformation introduced into the silicon steel sheet test, and those skilled in the art can set the thickness of the silicon steel sheet, the sample size, and the magnitude of the introduced plastic strain as needed. In addition, in the present embodiment, the silicon steel sheet sample is processed in a processing manner that has little influence on the performance of the silicon steel sheet, so as to reduce the influence of the processing manner on the magnetic performance of the silicon steel sheet.
In the present embodiment, a silicon steel sheet sample having a thickness of 0.27mm, a length of 200mm and a width of 30mm is taken as an example. Plastic strains of 0, 0.01, 0.02, 0.04 and 0.06 are respectively introduced into different silicon steel sheet samples. And plastic deformation with more than or equal to 3 gradients is introduced into the silicon steel sheet sample to provide more data for fitting the formula of stress strain and model parameters, so that the accuracy of the fitting formula is improved. In addition, the loading direction of plastic deformation is kept in the same rolling direction, so that the difference of the magnetic properties of the silicon steel sheets caused by different rolling directions is avoided.
The specific implementation mode of S20 is as follows: and when the frequency is 50Hz, the peak induction intensity Bm is 1T, and the silicon steel sheet sample is maintained at a certain stress, obtaining a hysteresis loop of the silicon steel sheet sample. The embodiment of the present invention is only illustrated by taking the frequency as 50Hz and the peak induced intensity Bm as 1T, and the magnitude of the selected frequency and the magnitude of the peak induced intensity Bm are not particularly limited, and those skilled in the art may select other frequencies or peak induced intensities Bm according to the requirement.
Specifically, the two ends of a strip-shaped silicon steel sheet sample are clamped and stretched or compressed, the silicon steel sheet sample cannot generate plastic deformation, so that a certain stress is formed in the silicon steel sheet, and then the silicon steel sheet is subjected to magnetic performance test under a certain frequency and peak induction strength. Specifically, stresses of-30 MPa, -10MPa, 0MPa, 10MPa, 30MPa can be introduced. The stress is not limited by the embodiment, and those skilled in the art can set the stress according to actual requirements.
It should be noted that, in the silicon steel sheet test, different gradient plastic strains are introduced first, and then different gradient stresses are introduced, so as to realize the orthogonality of the plastic strains and the stresses.
The specific implementation mode of S30 is as follows: and calculating magnetic performance parameters such as peak magnetic field intensity Hm, coercive force Hc, remanence Br, hysteresis loss Ph and the like of the silicon steel sheet sample according to the hysteresis loop (shown in Table 1). And calculating the ratio of the remanence to the coercive force according to the coercive force Hc and the remanence Br.
TABLE 1 magnetic Property parameters of silicon Steel sheets under different stresses and plastic strains
Further, step S40 is executed, namely, the values of a, k, α, and C in the model parameters are determined according to the peak magnetic induction of the magnetic parameters, the coercivity, the ratio of remanence to coercivity, and the experimental values of hysteresis loss. S40 specifically includes the steps of:
s41: determining rough estimated values of a, k, alpha and C in the model parameters respectively according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss of the magnetic parameters;
and roughly estimating the values of a, k, alpha and C in the model parameters through the peak value magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss of the magnetic parameters, so that the rough estimated values of a, k, alpha and C in the model parameters are close to the accurate values.
S41 specifically includes the following steps:
s411: presetting initial values of a, k, alpha and C in model parameters;
s412: adjusting the initial value of one model parameter, and controlling the initial values of the other three model parameters to be unchanged;
s413: calculating the peak magnetic induction intensity, the coercive force, the ratio of residual magnetism to the coercive force and the rough calculation value of the hysteresis loss of the magnetic parameters according to the initial value of the adjusted model parameter;
s414: calculating an error value between a rough calculated value of the magnetic parameter corresponding to the one model parameter and the experimental value;
s415: and determining the rough estimation value of the model parameter according to the rough calculation value and the experimental value of the magnetic parameter within the range of a preset error value.
Specifically, initial values of a, k, α, and C in the model parameters are set as a0、k0、α0、C0。
A is to0Adjusted to a plurality of a1Control k of0、α0、C0The value of (a) is unchanged;
according to k0、α0、C0And a plurality of1Respectively calculating a plurality of peak magnetic induction intensity estimated values;
respectively calculating difference values of a plurality of peak magnetic induction intensity estimated values and peak magnetic induction intensity experimental values;
determining a rough estimated value a of the model parameter a according to the difference value of the predicted peak value of the magnetic induction intensity and the experimental peak value of the magnetic induction intensity within a preset difference value range1；
Will k0Adjusted to a plurality of k1Control of a1、α0、C0The value of (a) is unchanged;
according to a1、α0、C0And a plurality of k1Respectively calculating a plurality of coercivity estimated values;
respectively calculating the difference value between a plurality of coercivity estimated values and a coercivity experimental value;
determining a rough estimated value k of the model parameter k according to the condition that the difference value between the coercivity estimated value and the coercivity experimental value is within a preset difference value range1；
Will be alpha0Adjusted to a plurality of alpha1Control of a1、k1、C0The value of (a) is unchanged;
according to a1、k1、C0And a plurality of1Respectively calculating a plurality of estimated values of the ratio of the remanence to the coercive force;
respectively calculating the difference values of the predicted values of the ratios of the remanence to the coercive force and the experimental values of the ratios of the remanence to the coercive force;
determining the rough estimation value alpha of the model parameter alpha according to the difference value of the predicted value of the ratio of the remanence to the coercive force and the experimental value of the ratio of the remanence to the coercive force within the preset difference value range1；
C is to be0Adjusted to a plurality of C1Control of a1、k1、α1The value of (a) is unchanged;
according to a1、k1、α1And a plurality of C1Respectively calculating a plurality of hysteresis loss estimated values;
calculating the difference values of the hysteresis loss estimated values and the hysteresis loss respectively;
determining a rough estimated value C of the model parameter C according to the difference value of the hysteresis loss estimated value and the hysteresis loss experimental value within a preset difference value range1Finally, the rough estimated values a of a, k, alpha and C in the model parameters are obtained1、k1、α1、C1。
Calculating peak magnetic induction intensity, coercive force, ratio of remanence to coercive force and hysteresis loss according to initial values or rough estimated values of a, k, alpha and C in the model parameters, and calculating by the following formula:
B＝μ0(M+H) (2)
Mir＝1-CM (4)
wherein M is the magnetization intensity of the silicon steel sheet, and M is a middle variable; h is the intensity of the external magnetic field; b is magnetic induction intensity; μ 0 is the vacuum permeability, μ 0 is a constant; man is the magnetic intensity without hysteresis; mir is the irreversible magnetization; a is a non-magnetic hysteresis magnetization behavior model parameter; k is the domain wall concentration coefficient; α is the main field component; c is reversible susceptibility; delta is a coefficient, and when the magnetic field intensity is increased, the value is 1; when the magnetic field intensity is reduced, the value is-1, and Ms is the saturation magnetization of the material.
Substituting a, k, alpha and C in the model parameters into formulas 1-4 to obtain a formula related to the magnetic induction intensity B and the magnetic field intensity H, namely a hysteresis curve, the peak magnetic induction intensity Bm, the coercive force Hc, the ratio of the remanence Br to the coercive force Hc and the hysteresis loss Ph can be calculated according to the hysteresis curve, the model parameter a is related to the peak magnetic induction Bm, the model parameter k is related to the coercive force Hc, the model parameter alpha is related to the ratio of the remanence Br to the coercive force Hc, and the model parameter C is related to the hysteresis loss Ph, therefore, when three model parameters are fixed and one of the model parameters is changed, the ratio of the peak magnetic induction intensity Bm, the coercive force Hc, the residual magnetism Br and the coercive force Hc and one of the magnetic parameter estimated values of the hysteresis loss Ph, which are obtained through formula calculation, are different from the experimental value, and the estimated value of the changed magnetic parameter is compared with the experimental value to obtain an error value.
Further, the error values of the experimental values of the magnetic parameters and the rough values of the magnetic parameters in the steps S414 and S415 are calculated in percentage form according to the following formula:
specifically, the preset error value range in step S415 is 3% to 5%. If the error value of a certain magnetic parameter is within the range of 3% to 5%, the model parameter corresponding to the magnetic parameter may be set as a coarse estimation value.
The error range in this embodiment is set to 3% to 5% according to the accuracy of the rough estimation, and the error range may also be set to other range values, and those skilled in the art may set other error range values according to the requirement of the accuracy of the rough estimation.
Determining rough estimates a of a, k, alpha, C in model parameters1、k1、α1、C1A range of model parameters may then be determined based on the coarse estimate.
S42: setting the limit values of a, k, alpha and C in the model parameters according to the rough estimated values of a, k, alpha and C in the model parameters;
coarse estimation a of each model parameter1、k1、α1、C1Further limiting the precise range of the model parameters. In this embodiment, the upper limit value is 1.2 times of the model parameter, and the lower limit value is 0.8 times of the model parameter, but this embodiment does not limit other upper limit values and lower limit values, and those skilled in the art can set other upper limit values or lower limit values as required by accuracy.
S43: and determining the accurate values of a, k, alpha and C in the model parameters according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss of the magnetic parameters.
Specifically, S43 specifically includes the following steps:
s431: setting the accurate estimation values of a, k, alpha and C in the model parameters in the limit value of each model parameter;
s432: respectively calculating the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the precise value of hysteresis loss of the magnetic parameters according to the precise values of a, k, alpha and C in the model parameters;
s433: respectively calculating error values of the experimental value and the accurate value of each magnetic parameter;
s434: and determining the accurate values of a, k, alpha and C in the model parameters according to the minimum sum of the error values of the experimental values and the accurate values of the magnetic parameters.
Specifically, the fine estimated values a of a, k, α, and C in the model parameters are set within the limits of the model parameters2、k2、α2、C2Respectively substituting the fine estimation values of a group of model parameters into formulas 1-4, calculating to obtain a group of fine estimation values of magnetic parameters, respectively comparing the fine estimation values of a group of magnetic parameters with experimental values of the magnetic parameters, calculating error values of the magnetic parameters, and adding the error values of a group of magnetic parameters to obtain error valuesAnd setting the accurate estimation values of other groups of model parameters, circulating the calculation process to obtain the sum of a plurality of groups of error values, and comparing the sum of the plurality of groups of error values, wherein the accurate estimation value of the group of model parameters with the minimum sum of the error values is the accurate value of a, k, alpha and C in the model parameters. Corresponding model parameter ranges are set according to model parameters under different stresses and plastic strains in table 1, and different accurate values are finally calculated under different stresses and plastic strains according to S42 and S43, as shown in table 2.
TABLE 2 JA hysteresis model parameters of silicon steel sheet under different stress and plastic strain
In some embodiments of the present invention, after the step of S43, the method further comprises the following steps:
s44, fitting a relation between a, k, alpha and C and stress strain in the model parameters according to the accurate values of a, k, alpha and C in the model parameters (shown in Table 2), wherein the relation is as follows:
a＝70.4(0.026σ2-2.7σ+967.5ε2)(101.2ε+2.5) (6)
k＝(-4.2σ2-841.2-47510)ε2+(10.3σ2+63.0σ+4157)ε-0.9σ+49.58 (7)
α＝(-2.8ε+0.4)×10-9σ3+(6.5ε-1.2)×10-9σ2+(3.0ε-0.5)×10-6σ-0.0001ε+1.8×10-5 (8)
C＝(-0.038σ2+1.1σ+163.7)ε2+(0.003σ2-0.1σ-14.1)ε+0.008σ+0.34 (9)
wherein σ is stress; ε is the plastic strain.
And a, k, alpha and C in JA model parameters can be quickly calculated through the formula.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are also included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (10)
1. A stress and strain-containing JA hysteresis model parameter identification method is characterized by comprising the following steps:
introducing plastic strain to the silicon steel sheet;
obtaining a hysteresis loop of the silicon steel sheet;
calculating the peak magnetic induction intensity, the coercive force, the ratio of the residual magnetism to the coercive force and the experimental value of the hysteresis loss of the magnetic parameters according to the hysteresis loop of the silicon steel sheet;
determining values of a, k, alpha and C in model parameters according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss of the magnetic parameters;
wherein a is a non-hysteresis magnetization behavior parameter, k is a magnetic domain wall concentration coefficient, alpha is a main field component, and C is a reversible magnetization coefficient.
2. The method for identifying the stress-and-strain-containing JA hysteresis model parameter as claimed in claim 1, wherein the values of a, k, α and C in the model parameter are determined according to the peak magnetic induction, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss of the magnetic parameter, and specifically comprises the following steps:
determining rough estimated values of a, k, alpha and C in model parameters respectively according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss of the magnetic parameters;
setting the limit values of a, k, alpha and C in the model parameters according to the rough estimated values of a, k, alpha and C in the model parameters;
and determining the accurate values of a, k, alpha and C in the model parameters according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force and the experimental value of hysteresis loss of the magnetic parameters.
3. The method for identifying the stress-and-strain-containing JA hysteresis model parameter of claim 2, wherein the rough estimation values of a, k, α, and C in the model parameter are respectively determined according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force, and the experimental value of hysteresis loss of the magnetic parameter, and specifically comprises the following steps:
presetting initial values of a, k, alpha and C in model parameters;
adjusting the initial value of one model parameter, and controlling the initial values of the other three model parameters to be unchanged;
calculating the peak magnetic induction intensity, the coercive force, the ratio of residual magnetism to the coercive force and the rough calculation value of the hysteresis loss of the magnetic parameters according to the initial value of the adjusted model parameter;
calculating an error value between a rough calculated value of the magnetic parameter corresponding to the one model parameter and the experimental value;
and determining the rough estimation value of the model parameter according to the rough calculation value and the experimental value of the magnetic parameter within the range of a preset error value.
4. The method for identifying the stress-and-strain-containing JA hysteresis model parameter of claim 3, wherein the calculation of the peak magnetic induction intensity, the coercive force, the ratio of the remanence to the coercive force and the rough value of the hysteresis loss of the magnetic parameter from the initial value of the adjusted model parameter is calculated according to the following formulas:
B＝μ0(M+H) (2)
Mir＝1-CM (4)
wherein M is the magnetization intensity of the silicon steel sheet, and M is a middle variable; h is the intensity of the external magnetic field; b is magnetic induction intensity; mu.s0Is a vacuum permeability, mu0Is a constant; manHas no hysteresis magnetization; mirIrreversible magnetization; a is a non-magnetic hysteresis magnetization behavior model parameter; k is the domain wall concentration coefficient; α is the main field component; c is reversible susceptibility; delta is a coefficient, and when the magnetic field intensity is increased, the value is 1; when the magnetic field intensity is reduced, the value is-1, and Ms is the saturation magnetization of the material.
5. The method of claim 3, wherein the calculating the error value between the rough value and the experimental value of the magnetic parameter corresponding to the one model parameter is calculated according to the following equation:
6. the method for identifying parameters of the JA hysteresis model with stress and strain according to claim 5, wherein the preset error value ranges from 3% to 5%.
7. The method for identifying the stress-and-strain-containing JA hysteresis model parameter as claimed in claim 2, wherein the accurate values of a, k, α, and C in the model parameter are determined jointly according to the peak magnetic induction intensity, the coercive force, the ratio of remanence to coercive force, and the experimental value of hysteresis loss of the magnetic parameter, and specifically comprises the following steps:
setting the accurate estimation values of a, k, alpha and C in the model parameters in the limit value of each model parameter;
respectively calculating the magnetic parameter peak value magnetic induction intensity, the coercive force, the ratio of remanence/coercive force and the precise value of hysteresis loss according to the precise values of a, k, alpha and C in the model parameters;
respectively calculating error values of the experimental value and the accurate value of each magnetic parameter;
and determining the accurate values of a, k, alpha and C in the model parameters according to the minimum sum of the error values of the experimental values and the accurate values of the magnetic parameters.
8. The method for identifying the parameters of the JA hysteresis model with stress and strain according to claim 7, wherein after the sum of the error values of the experimental value and the refined value of each magnetic parameter is the minimum, the accurate values of a, k, α and C in the model parameters are determined, the method further comprises the following steps:
fitting a relation between a, k, alpha and C and stress strain in the model parameters according to the accurate values of a, k, alpha and C in the model parameters:
a＝70.4(0.026σ2-2.7σ+967.5ε2)(101.2ε+2.5) (6)
k＝(--4.2σ2-841.2-47510)ε2+(10.3σ2+63.0σ+4157)ε-0.9σ+49.58 (7)
α＝(-2.8ε+0.4)×10-9σ3+(6.5ε-1.2)×10-9σ2+(3.0ε-0.5)×10-6σ-0.0001ε+1.8×10-5 (8)
C＝(--0.038σ2+1.1σ+163.7)ε2+(0.003σ2-0.1σ-14.1)ε+0.008σ+0.34 (9)
wherein σ is stress; ε is the plastic strain.
9. The stress and strain containing JA hysteresis model parameter identification method of claim 1, wherein the introducing of plastic strain to the silicon steel sheet specifically comprises the steps of:
plastic strain with different gradients is respectively introduced into a plurality of silicon steel sheets.
10. The stress-and-strain-containing JA hysteresis model parameter identification method of claim 9, wherein the plastic strain rolling directions of the different gradients are the same.
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