CN108519569A - JA hysteresis model parameter identification methods containing stress - Google Patents
JA hysteresis model parameter identification methods containing stress Download PDFInfo
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Abstract
The present invention provides a kind of JA hysteresis model parameter identification methods containing stress, including step：S1：Magnetism testing device containing elastic stress is set；S2：Sample to be tested is installed；S3：Alternating current is led to primary coil；S4：Treat test sample loading stress；S5：Acquire the induced current and induced voltage in secondary coil；S6：It calculates and obtains experiment magnetic field intensity and experiment magnetic induction intensity, calculate and obtain experiment magnetic hystersis loss value；S7：Revised hysteresis model is solved；S8：The peak magnetic induction prediction of strength value, peak field prediction of strength value and the magnetic hystersis loss predicted value that acquire are matched with experiment magnetic field intensity, experiment magnetic induction intensity and experiment magnetic hystersis loss value；S9：Parameter when using matching error minimum is as optimal value.A kind of JA hysteresis model parameter identification methods containing stress of the present invention can obtain the parameter distribution with external magnetic field strength and intensity of residual stresses variation, to determine that magnetic hystersis loss provides help.
Description
Technical field
The present invention relates to JA hysteresis model parameters identification field more particularly to a kind of JA hysteresis model parameters knowledges containing stress
Other method.
Background technology
In recent years, non-oriented electrical steel is widely used on the elements such as motor stator, and magnetic property is by more and more
Concern.And influence of the processing and manufacturing process of motor stator for its iron loss (summation of magnetic hystersis loss and eddy-current loss) is very big.
Studies have shown that manufacturing process can cause the iron loss of electrical sheet material to increase above 100%, wherein magnetic hystersis loss accounts for about total losses
60%.And the residual stress that manufacturing process introduces is to influence one of the most important factor of magnetic hystersis loss.
Magnetic hystersis loss be due to ferromagnetic material during magnetized the irreversible motion of neticdomain wall and magnetic domain magnetic away from turn over
Quote.Residual stress can influence the orientation of material internal easy magnetizing axis.According to magnetostrictive relative theory, residual stress
In the presence of can also cause minor change of the material in length and volume, and then affect the power of demagnetizing field.For a kind of mangneto
Coefficient of dilatation be positive material for, if along outer magnetic field direction exist pressure residual stress (σ ＜ 0), promote easy magnetizing axis
Influence far from outer magnetic field direction occupies leading role so that magnetic history becomes difficult, and magnetic hystersis loss increases；If along outer
Magnetic direction, which exists, draws residual stress (σ ＞ 0), when residual stress numerical value is smaller, easy magnetizing axis is promoted to tend to outer magnetic field direction
Influence occupy leading role so that magnetic history becomes easy, and magnetic hystersis loss reduces, and continues to increase with residual stress is drawn
Greatly, demagnetizing field can be caused to enhance, can magnetic history is become difficult, magnetic hystersis loss increases.
The stress of influence for to(for) magnetic hystersis loss, many scholars have carried out relevant research, wherein 1986 by
It is proposed in the article " Theory of ferromagnetic hysteresis " that D.C.Jiles and D.L.Atherton are delivered
Hysteresis model based on physics can accurately predict the M-H and BH curve of magnetic history, and parameter is less, thus obtain
It is widely applied.Scholar Sablik is based on Jiles-Atherton hysteresis models (hereinafter referred to as JA hysteresis models), has studied
Influence of the stress for magnetic hystersis loss, it is proposed that add stress influence item in Equivalent Magnetic Field, and give ferromagnetic material stress
Influence the expression formula of item：
Wherein, M is the intensity of magnetization；σ is residual stress, and positive value represents tensile stress, and negative value represents compression；μ0It is Vacuum Magnetic
Conductance；MsFor saturation magnetization；λ1And λ3It is coefficient.
Parameter in Sablik-Jiles-Atherton hysteresis models shares Ms, C, a, α, k, λ1And λ3.Wherein, MsFor material
The saturation magnetization of material is the property of material itself；C is reversible magnetization coefficient, is definite value；λ1And λ3Also it is constant coefficient；And join
Number a, tri- parameters of k, α change with the size of external magnetic field strength and stress.A is anhysteretic susceptibility, determines magnetization
The magnetic induction intensity that later stage can reach also is influenced by the pinning effect of early period is magnetized；K be neticdomain wall coefficient of concentration, with rectify
Stupid power is directly proportional；α is main field component, characterizes the slope of hysteresis loop interlude.This three parameters are all σ and Hm(outer magnetic
Peak value) complicated function.There has been no the researchs of this respect at present.Moreover, ground on what magnetic hystersis loss influenced about stress in the past
In studying carefully, experiment compression is up to 50Mpa or so, the pressure residual stress peak value about 150- brought much smaller than manufacturing process
200Mpa.Relevant research is also lacked for the parameter distribution under larger pressure residual stress.A set of accurate rational parameter is known
Other method is most important for the application of Sablik-Jiles-Atherton hysteresis models.
In conclusion existing research lacks the hysteresis model parameter identification method containing stress.It is answered therefore it provides one kind contains
The hysteresis model parameter identification method of power is extremely urgent.
Invention content
Deficiency in for the above-mentioned prior art, the present invention provide a kind of JA hysteresis model parameters identification side containing stress
Method, the residual stress that quantitative analysis manufacturing process is introduced into in the influence process of magnetic hystersis loss, provide one kind can determine compared with
The method of big residual stress lower die shape parameter can obtain the parameter distribution with external magnetic field strength and intensity of residual stresses variation,
To determine that magnetic hystersis loss provides help.
To achieve the goals above, the present invention provides a kind of JA hysteresis model parameter identification methods containing stress, including step
Suddenly：
S1：The one magnetism testing device containing elastic stress is set；The magnetism testing device packet containing elastic stress
It includes：One first sample fixing end, one second sample fixing end, a Stress Control device, a upper magnet yoke, a lower yoke, an insulation
Wire frame and a stress display device；The first sample fixing end and the second sample fixing end are laid along first direction；And
The first sample fixing end can reciprocally be sequentially connected with the Stress Control device along the first direction；On described
Yoke and the lower yoke are opposed to be set between the first sample fixing end and the second sample fixing end up and down；Institute
It states stress display device and connects the Stress Control device；Two opposed faces of the insulation wire frame are wound with a primary coil respectively
With a secondary coil；
S2：One sample to be tested is installed on the magnetism testing device containing elastic stress；
S3：Alternating current is led to the primary coil；
S4：Compression or tensile stress are loaded to the sample to be tested by the Stress Control device；
S5：Acquire the induced current and induced voltage in the secondary coil；
S6：It calculates and obtains experiment magnetic field intensity and experiment magnetic induction intensity, and is strong with the reality according to the experiment magnetic field
It tests magnetic induction intensity and calculates acquisition experiment magnetic hystersis loss value；
S7：It is solved using a MATLAB softwares pair revised hysteresis model, continues to optimize parameter, acquire a peak value
Magnetic induction intensity predicted value, a peak field prediction of strength value and a magnetic hystersis loss predicted value；
S8：The peak magnetic induction prediction of strength value, the peak field prediction of strength value and the magnetic hystersis loss is pre-
Measured value is matched with the experiment magnetic field intensity, the experiment magnetic induction intensity and the experiment magnetic hystersis loss value；
S9：Parameter when using matching error minimum is as optimal value.
Preferably, in the S6 steps, according to an experiment magnetic field intensity formula (1) and an experiment magnetic induction intensity formula
(2) it calculates and obtains the experiment magnetic field intensity and the experiment magnetic induction intensity：
Wherein, H is experiment magnetic field intensity, and B is experiment magnetic induction intensity；N1It is the number of turns of the primary coil, L is described
The length of equivalent magnetic circuit, N in sample to be tested2It is the number of turns of secondary coil, S is the cross-sectional area of the sample to be tested, I1It is
The electric current of the primary coil, U2It is the induced voltage of the secondary coil.
Preferably, the revised hysteresis model is：
DM/dH=((1-C) (M_an-M_irr))/(δ k- α (M_an-M_irr))+C (dM_an)/dH；
Wherein：
M_an=M_S [coth ((H+ α M)/a)-a/ (H+ α M)]；
M=M_irr+C (M_an-M_irr)；
μ _ 0 B=(M+H)；
Wherein, M is the intensity of magnetization, and C is reversible magnetization coefficient, and M_an is the anhysteretic intensity of magnetization, and M_irr is irreversible magnetic
Change intensity, δ is magnetizing parameters, and as dH/dt >=0, δ=1, as dH/dt ＜ 0, δ=- 1, k is neticdomain wall coefficient of concentration, and a is
Anhysteretic susceptibility, α are main field component, and M_S is saturation magnetization, and μ _ 0 is space permeability.
Preferably, the parameter includes anhysteretic susceptibility, neticdomain wall coefficient of concentration and main field component.
Preferably, further include step S10：The parameter is expressed as stress and magnetic induction intensity according to the optimal value
Function.
Preferably, the S10 further comprises step：
Determine a current anhysteretic susceptibility a when fixation magnetic induction intensity0, current neticdomain wall coefficient of concentration k0With work as
Preceding main field component α0；
Obtain the current anhysteretic susceptibility a0, the current neticdomain wall coefficient of concentration k0With the current main field
Component α0Normalized parameter：
Anhysteretic susceptibility a, the neticdomain wall coefficient of concentration k and the main field component α are expressed as stress and magnetic
The function of induction：
Each coefficient is tested according to practical magnetism testing and is determined in formula (3).
The present invention makes it have following advantageous effect as a result of above technical scheme：
1, the present invention provides the quick methods for determining hysteresis model parameter, can determine different residual stress, different peaks
It is worth the relevant information of the magnetic hystersis loss and B-H loop under magnetic induction intensity, guidance is provided for further control iron loss.Theoretical mould
Type and engineering is practical is combined, it is convenient using MATLAB program solutions, it is easy to operate.
2, the present invention considers influence of the magnetic induction intensity variation to magnetic hysteresis parameters, is more in line with different inside motor stator
The different actual condition of the magnetic induction intensity of position, can be determined more accurately magnetic hystersis loss.
3, the present invention considers drawing, compression influences the asymmetry of magnetic hystersis loss.
Description of the drawings
Fig. 1 is the flow chart of the JA hysteresis model parameter identification methods containing stress of the embodiment of the present invention；
Fig. 2 is the structural schematic diagram of the magnetism testing device containing elastic stress of the embodiment of the present invention；
Fig. 3 is the structural schematic diagram of the sample to be tested of the embodiment of the present invention；
Fig. 4 is certain grade electric steel magnetism testing BH curve of the embodiment of the present invention；
Fig. 5~Fig. 7 is each parameter distribution figure of hysteresis model under certain grade electric steel 1.5T of the embodiment of the present invention；
Fig. 8~Figure 10 is certain grade electric steel hysteresis model parameter of the embodiment of the present invention with Magnetic Induction Density Distribution figure.
Specific implementation mode
Below according to 1~Fig. 8 of attached drawing, presently preferred embodiments of the present invention is provided, and be described in detail, enabled more preferable geographical
Solve function, the feature of the present invention.
Please refer to Fig.1~Fig. 3, a kind of JA hysteresis model parameter identification methods containing stress of the embodiment of the present invention, including
Step：
S1：The one magnetism testing device 2 containing elastic stress is set；Magnetism testing device 2 containing elastic stress includes：
One first sample fixing end 21, one second sample fixing end 22, a Stress Control device 23, a upper magnet yoke 241, a lower yoke
242, an insulation wire frame 25 and a stress display device 26；First sample fixing end 21 and the second sample fixing end 22 are along first party
To laying；And first sample fixing end 21 can along first direction reciprocally with Stress Control device 23 be sequentially connected；Upper magnetic
Yoke 241 and about 242 lower yoke are opposed to be set between the first sample fixing end 21 and the second sample fixing end 22；Stress is aobvious
Showing device 26 connects Stress Control device 23；Two opposed faces of insulation wire frame 25 are wound with a primary coil and a secondary wire respectively
Circle；In the present embodiment, Stress Control device 23 uses air compressor.
S2：One sample 1 to be tested is installed on the magnetism testing device 2 containing elastic stress；
S3：Alternating current is led to primary coil；
S4：Test sample 1, which is treated, by Stress Control device 23 loads compression or tensile stress；
S5：Acquire the induced current and induced voltage in secondary coil；
S6：Calculate obtain experiment magnetic field intensity and experiment magnetic induction intensity, and according to experiment magnetic field by force and experiment magnetic induction
Strength co-mputation obtains experiment magnetic hystersis loss value；
In S6 steps, calculates and obtain in fact according to an experiment magnetic field intensity formula (1) and an experiment magnetic induction intensity formula (2)
Test magnetic field intensity and experiment magnetic induction intensity：
Wherein, H is experiment magnetic field intensity, and B is experiment magnetic induction intensity；N1It is the number of turns of primary coil, L is to be measured has a try
The length of equivalent magnetic circuit, N in sample 12It is the number of turns of secondary coil, S is the cross-sectional area of sample 1 to be tested, I1It is primary coil
Electric current, U2It is the induced voltage of secondary coil.
S7：It is solved using a MATLAB softwares pair revised hysteresis model, continues to optimize parameter, acquire a peak value
Magnetic induction intensity predicted value, a peak field prediction of strength value and a magnetic hystersis loss predicted value；
Wherein, revised hysteresis model is：
DM/dH=((1-C) (M_an-M_irr))/(δ k- α (M_an-M_irr))+C (dM_an)/dH；
Wherein：
M_an=M_S [coth ((H+ α M)/a)-a/ (H+ α M)]；
M=M_irr+C (M_an-M_irr)；
μ _ 0 B=(M+H)；
Wherein, M is the intensity of magnetization, and C is reversible magnetization coefficient, and M_an is the anhysteretic intensity of magnetization, and M_irr is irreversible magnetic
Change intensity, δ is parameter (δ=1, when dH/dt >=0；δ=- 1, as dH/dt ＜ 0), k is neticdomain wall coefficient of concentration, and a is anhysteretic
Susceptibility, α are main field component, and M_S is saturation magnetization, and μ _ 0 is space permeability.
S8：By peak magnetic induction prediction of strength value, peak field prediction of strength value and magnetic hystersis loss predicted value and experiment magnetic
Field intensity, experiment magnetic induction intensity and experiment magnetic hystersis loss value are matched；
S9：Parameter when using matching error minimum is as optimal value.
Wherein, parameter includes anhysteretic susceptibility, neticdomain wall coefficient of concentration and main field component.
Further include step S10 in the present embodiment：Parameter is expressed as to the letter of stress and magnetic induction intensity according to optimal value
Number.
S10 further comprises step：
Determine a current anhysteretic susceptibility a when fixation magnetic induction intensity0, current neticdomain wall coefficient of concentration k0With work as
Preceding main field component α0；
Obtain current anhysteretic susceptibility a0, current neticdomain wall coefficient of concentration k0With current main field component α0Normalizing
Change parameter：
Anhysteretic susceptibility a, neticdomain wall coefficient of concentration k and main field component α are expressed as stress and magnetic induction intensity
Function：
Formula (3) each coefficient is tested according to the magnetism testing of actual specific grade electric steel and is determined.
Such as：Using a length of a, width b, thickness is the sample to be tested 1 of t；First by sample 1 to be tested from the second sample
The insert port of fixing end 22 is inserted into insulation wire frame 25；In the present embodiment, the length of sample 1 to be tested is insulation 25 length of wire frame
Twice, facilitate 1 end of sample to be tested grips and applies pressure.Insulation 12 internal voids size of wire frame is (a/2+
Δ a) × (b+ Δs b) × (t+ Δ t), wherein Δ are small amount, and Δ a=Δ b=Δ t=1mm respectively represent length direction, width
Spend direction, thickness direction smaller length, primarily to inside ensuring the magnetic line of force as possible by sample 1 to be tested.Insulated wire
Two opposed faces of frame 25 are wound with a primary coil and a secondary coil respectively, exciting current are passed through in primary coil, according to electricity
Law of magnetic induction generates the magnetic line of force inside insulation wire frame 25, due to sample 1 to be tested and 242 groups of upper magnet yoke 241 and lower yoke
At circuit magnetic resistance it is minimum, so magnetic line of force almost all by sample 1 to be tested inside.Secondary coil is also wrapped in insulated wire
Above frame 25, for detecting the induced voltage generated.Sample 1 to be tested be put into insulation wire frame 25 after, by upper magnet yoke 241 put down with
1 surface of sample contact to be tested, 1 lower surface of sample to be tested is contacted with lower yoke 242.Upper magnet yoke 241 and lower yoke 242 are pair
Claim structure, purpose is also for ensuring that the external magnetic field that 1 inside of sample to be tested is formed is uniform magnetic field, and upper magnet yoke 241 is by leading
Column 27 can be moved back and forth vertically, and guide post 27 can be connected on a lifting gear (not shown)；Guide post 27 is for limiting
The direction that upper magnet yoke 241 processed glides.Upper magnet yoke 241 and lower yoke 242 with sample 1 to be tested in addition to that can form closed magnetic circuit
Outside, moreover it is possible to play the role of preventing unstability.First sample fixing end 21 and the second sample fixing end 22 are by the two of sample 1 to be tested
End is clamped by rotational fastener knob 28, and being then driven the first sample fixing end 21 by air compressor generates displacement,
To generate the stress along 1 length direction of sample to be tested, the size of stress can directly read in seif-citing rate display device 26 and obtain
, and magnetism testing can be carried out when keeping stress constant；In the present embodiment, air can be used in stress display device 26
The included stress display instrument of compressor.The induced voltage that the exciting current and secondary coil of test generate inputs computer software
End, is obtained by calculation magnetic field intensity and magnetic induction intensity, obtains B-H loop and magnetic hystersis loss, and the experiment B-H of the present embodiment is bent
Line is as shown in Figure 4.
It is theoretical to be then based on modified JA magnetic hysteresis, is solved using MATLAB softwares, continuous Optimal Parameters a, k, α,
Solution obtains magnetic field intensity H and magnetic induction density B, and the B-H loop predicted.Magnetic hysteresis damage is calculated with the area of B-H loop
The predicted value of consumption.The predicted value of peak magnetic induction intensity, peak field intensity, magnetic hystersis loss is matched with experiment value,
Parameter a, k, α when with error minimum are optimal value.
In the present embodiment, first, B is determinedmThe distribution of parameter when=1.5T, B-H relationships when according to experiment, obtains 1.5T
When magnetic field intensity H with residual stress σ variation, it is theoretical based on modified JA magnetic hysteresis, parameter current a is calculated0,k0,α0With answering
The distribution of power, as shown in Fig. 5~Fig. 7.The distribution of parameter under tension and compression stress is obtained by fitting, parameter is expressed as to point of stress
Section function：
a0=-0.75 σ+70.21 (σ ＜ 0)
a0=-0.40 σ+70.21 (σ >=0)
k0=-1.07 σ+50.03 (σ ＜ 0)
k0=-0.43 σ+50.03 (σ >=0)
α0=0.5 (σ≤- 15MPa)
α0=0.067 σ+1.5 (- 15MPa ＜ σ ＜ 0)
α0=1.5 (σ >=0)
As shown in Fig. 8~Figure 10, be under different stress, magnetic hysteresis parameters with magnetic induction intensity variation.Under same stress, magnetic
Stagnant parameter is in preferable linear relationship with magnetic induction intensity, by handling parameter normalizationCurve is oblique
Rate is expressed as the function of stress.In conjunction with front parameter current a0,k0,α0Distribution, can solve to obtain different stress, different magnetic
Parameter distribution under induction, to solve B-H relationships and magnetic hystersis loss.Parameter expression is：
A=a0(-0.0019σ2+0.0428σ+0.2231)(B-1.5)+1；
K=k0(-0.0002σ2+0.0122σ+0.5846)(B-1.5)+1；
α=α0(σ ＜ 0)；
The α of α=0.55640(B-1.5)+1 (σ≥0)；
Sample result shows that the present invention is combined revised JA magnetic hysteresis theory with mathematical software, can pass through determination
Parameter is expressed as stress and magnetic induction intensity by parameter distribution and normalized parameter with the changing rule of magnetic induction intensity when 1.5T
Function, preferably calculate BH curve and magnetic hystersis loss, for further control magnetic hystersis loss Assistance And Instruction is provided.
The present invention has been described in detail with reference to the accompanying drawings, those skilled in the art can be according to upper
It states and bright many variations example is made to the present invention.Thus, certain details in embodiment should not constitute limitation of the invention, this
Invention will be using the range that the appended claims define as protection scope of the present invention.
Claims (6)
1. a kind of JA hysteresis model parameter identification methods containing stress, including step：
S1：The one magnetism testing device containing elastic stress is set；The magnetism testing device containing elastic stress includes：One
First sample fixing end, one second sample fixing end, a Stress Control device, a upper magnet yoke, a lower yoke, one insulation wire frame and
One stress display device；The first sample fixing end and the second sample fixing end are laid along first direction；And described
One sample fixing end can reciprocally be sequentially connected with the Stress Control device along the first direction；The upper magnet yoke and
The lower yoke is opposed to be set between the first sample fixing end and the second sample fixing end up and down；The stress
Display device connects the Stress Control device；Two opposed faces of the insulation wire frame are wound with a primary coil and primary respectively
Grade coil；
S2：One sample to be tested is installed on the magnetism testing device containing elastic stress；
S3：Alternating current is led to the primary coil；
S4：Compression or tensile stress are loaded to the sample to be tested by the Stress Control device；
S5：Acquire the induced current and induced voltage in the secondary coil；
S6：It calculates and obtains experiment magnetic field intensity and experiment magnetic induction intensity, and is strong with the experiment magnetic according to the experiment magnetic field
Induction, which calculates, obtains experiment magnetic hystersis loss value；
S7：It is solved using a MATLAB softwares pair revised hysteresis model, continues to optimize parameter, acquire a peak induction
Answer prediction of strength value, a peak field prediction of strength value and a magnetic hystersis loss predicted value；
S8：By the peak magnetic induction prediction of strength value, the peak field prediction of strength value and the magnetic hystersis loss predicted value
It is matched with the experiment magnetic field intensity, the experiment magnetic induction intensity and the experiment magnetic hystersis loss value；
S9：Parameter when using matching error minimum is as optimal value.
2. the JA hysteresis model parameter identification methods according to claim 1 containing stress, which is characterized in that the S6 steps
In, it calculates according to an experiment magnetic field intensity formula (1) and an experiment magnetic induction intensity formula (2) and obtains the experiment magnetic field intensity
With the experiment magnetic induction intensity：
Wherein, H is experiment magnetic field intensity, and B is experiment magnetic induction intensity；N1It is the number of turns of the primary coil, L is described to be measured
It has a try the length of equivalent magnetic circuit in sample, N2It is the number of turns of secondary coil, S is the cross-sectional area of the sample to be tested, I1It is described
The electric current of primary coil, U2It is the induced voltage of the secondary coil.
3. the JA hysteresis model parameter identification methods according to claim 2 containing stress, which is characterized in that after the amendment
Hysteresis model be：
DM/dH=((1-C) (M_an-M_irr))/(δ k- α (M_an-M_irr))+C (dM_an)/dH；
Wherein：
M_an=M_S [coth ((H+ α M)/a)-a/ (H+ α M)]；
M=M_irr+C (M_an-M_irr)；
μ _ 0 B=(M+H)；
Wherein, M is the intensity of magnetization, and C is reversible magnetization coefficient, and M_an is the anhysteretic intensity of magnetization, and M_irr is that irreversible magnetization is strong
Degree, δ is magnetizing parameters, and as dH/dt >=0, δ=1, as dH/dt ＜ 0, δ=- 1, k is neticdomain wall coefficient of concentration, and a is non-magnetic
Stagnant susceptibility, α are main field component, and M_S is saturation magnetization, and μ _ 0 is space permeability.
4. the JA hysteresis model parameter identification methods according to claim 3 containing stress, which is characterized in that the parameter packet
Include anhysteretic susceptibility, neticdomain wall coefficient of concentration and main field component.
5. the JA hysteresis model parameter identification methods according to claim 4 containing stress, which is characterized in that further include step
S10：The parameter is expressed as to the function of stress and magnetic induction intensity according to the optimal value.
6. the JA hysteresis model parameter identification methods according to claim 5 containing stress, which is characterized in that the S10 into
One step includes step：
Determine a current anhysteretic susceptibility a when fixation magnetic induction intensity0, current neticdomain wall coefficient of concentration k0With current master
Want field component α0；
Obtain the current anhysteretic susceptibility a0, the current neticdomain wall coefficient of concentration k0With the current main field component
α0Normalized parameter：
The parameter is expressed as to the function of stress and magnetic induction intensity：
Each coefficient is tested according to practical magnetism testing and is determined in formula (3).
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