CN111444578A - Automatic calibration method of variable modulus model parameters based on bending process - Google Patents

Automatic calibration method of variable modulus model parameters based on bending process Download PDF

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CN111444578A
CN111444578A CN201911147786.9A CN201911147786A CN111444578A CN 111444578 A CN111444578 A CN 111444578A CN 201911147786 A CN201911147786 A CN 201911147786A CN 111444578 A CN111444578 A CN 111444578A
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CN111444578B (en
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段永川
田乐
乔海棣
官英平
杨柳
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Yanshan University
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Abstract

The invention discloses an automatic calibration method of variable modulus model parameters based on a bending process, which relates to the field of metal processing and comprises the following steps: performing least square smoothing filtering on the experimental data; carrying out standard normalization processing on the filtered experimental data; extracting vector corner data of a standard normalization value by a window vector method; performing least square smoothing filtering on the vector corner data to obtain a corner filtering value; extracting peak characteristic points of the corner filter values; filtering adjacent peak feature points; carrying out data segmentation based on the peak characteristic points; elastic modulus identification is performed based on each piece of data. The method takes the force-stroke curve of the bending process of repeated loading and unloading as an example, the practicability of the on-line determination of the elastic modulus is verified, in the actual production process, the method can be used for efficiently identifying the characteristic points of the curve, so that a large amount of time and resource cost are saved, and the production efficiency of the product is improved.

Description

Automatic calibration method of variable modulus model parameters based on bending process
Technical Field
The invention relates to the field of metal processing, in particular to an automatic calibration method of variable modulus model parameters based on a bending process.
Background
With the introduction of the german industry 4.0, the arrival of the intelligent era has become a global consensus. The information for grasping the controlled object is the premise of intelligent control on the production line, and the information of the controlled object is the high abstraction of the controlled object data. In the bending forming process of high-strength materials, the elastic modulus can change along with plastic deformation, and if the change of the elastic modulus of the plate in the processing process can be automatically determined, the possibility of poor consistency of products after rebounding caused by the change of the elastic modulus can be reduced or even eliminated. The general elastic modulus measurement is carried out in an off-line calibration mode, on the basis of acquiring unidirectional tensile experimental data of the material, the corresponding change value of the elastic modulus is extracted and calculated for many times manually, the process is complicated, the precision is low, and the extraction result is unstable. Secondly, the intelligent processing requires an embedded program, and manual intervention is not favorable for realizing intelligent processing.
Disclosure of Invention
The technical problem to be solved by the invention is to provide an automatic calibration method of variable modulus model parameters based on a bending process, which determines the elastic modulus of curve change through a stable and accurate identification process and avoids the problem of poor consistency of products after rebound caused by elastic modulus change.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
an automatic calibration method of variable modulus model parameters based on a bending process comprises the following steps:
step 1: performing least square smoothing filtering on the experimental data;
step 2: carrying out standard normalization processing on the filtered experimental data;
and step 3: extracting vector corner data of a standard normalization value by a window vector method;
and 4, step 4: performing least square smoothing filtering on the vector corner data to obtain a corner filtering value;
and 5: extracting peak characteristic points of the corner filter values;
step 6: filtering adjacent peak feature points;
and 7: carrying out data segmentation based on the peak characteristic points;
and 8: elastic modulus identification is performed based on each piece of data.
The technical scheme of the invention is further improved as follows: in step 1, after a plurality of groups of experimental data are obtained by processing, a filtering window is selected as nF＝2mF+1, fitting the experimental data points in the window using a polynomial of degree k-1
Figure BDA0002282690920000021
Wherein j is i-mF,i-mF+1,...,i+mFWhere i is an index of experimental data, and i is mF+1,mF+ 2.. s, s is the total number of sets of experimental data,
Figure BDA0002282690920000022
fitting values for experimental loads; substituting n into the windowFGroup data, get nFAn equation, forming a k-1 linear equation system; to ensure that the system of linear equations has a solution, there is typically nFK is more than or equal to k; as follows below, the following description will be given,
Figure BDA0002282690920000023
wherein the content of the first and second substances,
Figure BDA0002282690920000024
is a residual error; the above formula is expressed by matrix as
YF＝XFAF+EF(3)
Find AFLeast squares solution of
Figure BDA0002282690920000025
Is composed of
Figure BDA0002282690920000026
Wherein the content of the first and second substances,
Figure BDA0002282690920000027
is XFThe transposed matrix of (2); so that J has a filter value of
Figure BDA0002282690920000028
The filtered value of the ith point is
Figure BDA0002282690920000029
Using it as new load value
Figure BDA00022826909200000210
And (4) solving the next window until all the filtered values of all the points are completely solved, wherein the window stepping value is 1.
The technical scheme of the invention is further improved as follows: in the step 2, the process is carried out,
Figure BDA0002282690920000031
Figure BDA0002282690920000032
wherein the ith group of filtered data is
Figure BDA0002282690920000033
Figure BDA0002282690920000034
Is FiThe value of the filtered value is then compared to a threshold value,
Figure BDA0002282690920000035
is composed of
Figure BDA0002282690920000036
The maximum value after the filtering is carried out,
Figure BDA0002282690920000038
is composed of
Figure BDA0002282690920000039
Minimum value after filtering, hmaxIs hiMaximum value after filtering, hminIs hiThe minimum value after the filtering is carried out,
Figure BDA00022826909200000310
is hiFiltered normalized value, Fi normIs composed of
Figure BDA00022826909200000311
A filtered normalized value.
The technical scheme of the invention is further improved as follows: in step 3, the window width is selected to be nR＝2mR+1 or
Figure BDA00022826909200000312
Front m in window for ith point of window center pointR+1 normalized force stroke data set
Figure BDA00022826909200000313
Wherein j is i-mR,i-mR+1,... i; fitting a straight line by least square method, the equation of the straight line is
F＝C1h+D1(9)
Wherein F is the load, h is the stroke, C1To fit the slope of the line, D1Is the intercept of the fitted straight line;
for the point i after the window mR+1 normalized force stroke data set
Figure RE-GDA00023672268900000314
Wherein j ═ i.. i + mR-1,i+mR(ii) a Fitting a straight line by least square method, the equation of the straight line is
F＝C2h+D2(10)
Wherein, C2To fit the slope of the line, D2To fit straightThe intercept of the line;
the (i) th to m thRTravel of point
Figure BDA00022826909200000315
Substituting into equation (9) to obtain a fitted load value
Figure BDA00022826909200000316
Acquisition Point
Figure BDA00022826909200000317
The (i + m) thRTravel of point
Figure BDA00022826909200000318
Substituting into equation (10) to obtain a fitted load value
Figure BDA00022826909200000319
Acquisition point
Figure BDA00022826909200000320
Combined with the center point of the window
Figure BDA00022826909200000321
Finding a vector
Figure BDA0002282690920000037
Two vector corner αoIs calculated by the formula
Figure BDA0002282690920000041
Will calculate the obtained rotation angle value αoAs the stroke of the center point of the window at the moment
Figure BDA0002282690920000046
A corresponding angle of rotation value; and setting the window stepping value as 1, and solving the next window until all the rotation angle values are completely solved.
Further improvement of the technical scheme of the inventionThe method is characterized in that: in step 4, the width of the filter window of the vector corner data is nα＝2mα+1, fitting the data points within the window using a polynomial of degree k-1:
Figure BDA0002282690920000042
where i is an index of the vector corner data, and i is mα+1,mα+ 2.. and t, t is the total number of vector rotation angle data;
Figure RE-GDA0002533365850000043
is the corner fitting value; substituting n into the windowαGroup data, get nαAn equation forming a k-1 linear equation system, where n is the general equation for ensuring the solution of the linear equation systemαK is more than or equal to k; as follows below, the following description will be given,
Figure BDA0002282690920000043
wherein the content of the first and second substances,
Figure BDA0002282690920000049
is a residual error; the above formula is expressed by matrix as
Yα＝XαAα+Eα(15)
Find AαLeast squares solution of
Figure BDA00022826909200000410
Is composed of
Figure BDA0002282690920000044
Wherein the content of the first and second substances,
Figure BDA00022826909200000411
is XαThe transposed matrix of (2); so that J has a filter value of
Figure BDA0002282690920000045
The filtered value of the rotation angle at the ith point is
Figure BDA00022826909200000412
And (4) solving the next window until all the corner filtering values of all the points are solved, wherein the window stepping value is 1.
The technical scheme of the invention is further improved as follows: in step 5, a certain stroke h is setiIs the filter backward measure of rotation angle of
Figure BDA0002282690920000053
Extracting feature points using the following conditions
Figure BDA0002282690920000051
Wherein, i is 2, 3.·, l; i.e. total l groups of filtered travel angle data; when in use
Figure BDA0002282690920000054
When the above formula condition is satisfied, the stroke and the angle value are stored, and the finally obtained peak point is βijWherein, i is 1,2, and q, j is 1,2, and q is the number of groups for obtaining peak points; when j is 1, the two-dimensional array stores the angle value of the corner peak point, and when j is 2, the index value corresponding to the corner peak point is stored.
The technical scheme of the invention is further improved in that in step 6, in the extracted peak point set, similar points are filtered by using a window and a threshold value of angle change, when the angle value change of adjacent peak points is less than 20%, the peak points are combined, if the angle value difference of the adjacent peak points exceeds 20%, whether the point sequence difference of the two points is less than m α is judged, if so, the peak points are combined, and the formula is as follows
Figure BDA0002282690920000052
β is firstly1,j(j ═ 1,2), i.e. the transitions of the first set of peak pointsStoring the angular value and its index to gamma1,j(j is 1,2), then judging whether the next group of corner values and the indexes thereof meet the storage condition, if so, storing the corner values and the indexes thereof to gammaijIf not, the storage is not carried out; the step value is 1, the second point is judged, the process is the same, and the judgment of all the points is completed; finally, c groups of peak points are obtained; the feature points after this filtering are the feature points to be obtained. The technical scheme of the invention is further improved as follows: in the step 7, c groups of peak points are shared in the process of loading and unloading the bending male die for multiple times according to the screening result of the peak points; according to the curvilinear morphological characteristics obtained during the machining, the angle of rotation is determined: in the process of loading and unloading the primary bending male die, a first peak point is a yield point of a material in the bending process, a second peak point is a male die unloading starting point, and a third peak point is a male die unloading ending point; according to the characteristics, the bending data is processed in a segmented mode, and each unloading data segment is stored again.
The technical scheme of the invention is further improved as follows: in step 8, after data of the elastic loading section and each unloading section are extracted, respectively re-determining the elastic modulus of each section; the modulus of elasticity is described exponentially as a function of the total strain as follows
Eu＝E0-(E0-Ea)[1-exp(-ξ)](20)
Wherein E is0As a material default modulus of elasticity, EuAs real-time modulus of elasticity of the material, EaThe saturated elastic modulus is shown, ξ is a material parameter, and the strain generated by the plate is shown;
simplifying the V-shaped bending into a plane strain model, taking the length direction of the plate as the x direction, the thickness direction of the plate as the y direction, and the center of the plate as the origin of coordinates; at the abscissa x, under the action of a bending moment M generated by the load of the male die, the relationship between the rebound curvature and the bending moment is as follows
Figure BDA0002282690920000061
Wherein the content of the first and second substances,
Figure BDA0002282690920000065
the curvature radius at any point x after the bending moment M is unloaded; t is the thickness of the plate, b is the width of the plate; the amount of change in curvature after rebound is further expressed as:
Figure BDA0002282690920000062
wherein the content of the first and second substances,
Figure BDA0002282690920000063
Figure BDA0002282690920000064
calculating the stroke h of the male die according to the coordinates of all parts of the plate, and obtaining a plurality of groups of real-time elastic modulus E through the V-shaped bent plane strain analysis modeluThe following h-F data are related as follows:
Fi＝f(hi,Eu) (24)
wherein, i ═ 1,2, 3., ψ, ψ are index maximum values of load displacement data obtained by the analytical model;
defining an objective function as 0.5 times of the sum of the squares of the residuals of the two groups of bending force data, and taking the minimum value of the objective function when the analytic data and the processed data are close enough; defining an elastic phase objective function as follows:
Figure BDA0002282690920000071
wherein the content of the first and second substances,
Figure BDA0002282690920000074
e determined on the kth trial for the algorithmu，ΩueAn index set containing analytical models and processing data; the argument range of the objective function is
Figure BDA0002282690920000075
For the objective functionAnd performing quadratic approximation to obtain an approximation function in the k iteration:
Figure BDA0002282690920000072
wherein the content of the first and second substances,
Figure BDA0002282690920000076
automatically for the algorithm after quadratic approximation
Figure BDA0002282690920000077
Centered at ΔkThe interpolation set of the radius is represented, j is 1, 2. The optimization problem of the discrete objective function is converted into a quadratic approximation function extreme value problem:
Figure BDA0002282690920000073
where d is the vector step size per iteration, ΔkIs the confidence domain radius at the kth iteration;
and after the elastic loading and each section of unloading data are processed, the elastic modulus of the loading section or each unloading section is obtained on line.
Due to the adoption of the technical scheme, the invention has the technical progress that:
according to the invention, on the basis of on-line acquisition of bending process processing data, an automatic calibration algorithm of variable modulus model parameters is designed, so that the characteristic points of a processing load displacement curve can be stably and accurately identified, data segmentation is simultaneously completed, the automatic calibration of the elastic modulus is realized on the basis, and the problem of poor consistency of products after resilience caused by elastic modulus change is avoided. The method avoids using artificial intelligence to automatically calibrate the elastic modulus, reduces the operation cost, avoids the butt joint problem of the artificial intelligence and the processing port, and improves the identification speed. On the basis of acquiring force stroke experimental data, the invention realizes the least square smooth filtering and standardized normalization processing of the experimental data. The method comprises the steps of extracting vector corner data of experimental data changing along with the process by using a window vector method, realizing least square smooth filtering of the corner data, identifying and filtering peak point characteristic points of the corner data, and then realizing segmentation of the experimental data and online determination of the elastic modulus of an elastic loading section and each unloading section. The method takes the force-travel curve of the bending process of repeated loading and unloading as an example, the practicability of the on-line determination of the elastic modulus is verified, and in the actual production process, the method can be used for efficiently identifying the characteristic points of the curve, so that a large amount of time and resource cost are saved, and the production efficiency of the product is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, it is obvious that the drawings in the following description are only some embodiments or technical drawings of the present invention, and for a researcher of ordinary skill in the art, other drawings can be obtained according to the drawings without creative efforts;
FIG. 1 is a graph of force stroke experimental data for a V-bend process;
FIG. 2 is a graph of vector corner data extracted by a V-bend process;
fig. 3 is a segmented data diagram of processing data extracted by the V-bending process.
Detailed Description
Referring to fig. 1,2 and 3, a method for automatically calibrating a variable modulus model parameter based on a bending process is shown, and the present invention is further described below with reference to the accompanying drawings and a specific embodiment of a V-bending process applied in the present invention.
FIG. 1 is a force stroke experimental data curve diagram of a V-shaped bending process, wherein the curve is a processing data curve, and an x axis in a horizontal direction is a stroke with the unit of mm; the vertical y-axis is the load in N. It can be observed from the figure that the bending force varies with the stroke, and during the continuous multiple loading and unloading processes, the yield point of the material changes with each loading and unloading, and the elastic modulus also changes due to factors such as damage inside the material.
FIG. 2 is a data graph of vector corner data extracted by a V-shaped bending process, wherein the abscissa is the index number of the data, and the ordinate is the loading stroke of a male die positioned on the left side and the camber value of a corner positioned on the right side, and the units are mm and rad respectively. In the two curves, one curve is a curve of the stroke changing along with the index value, the graph is basically linear, and the curve is the process that the convex die is loaded to 2mm, 4mm, 6mm, 8mm and 10mm and unloaded. The other curve is a curve of the change of the vector angle value extracted from the force stroke experimental data along with the index, and the graph is a zigzag continuous curve.
FIG. 3 is a sectional data diagram of processing data extracted by the V-bend process of the present invention, wherein the x-axis in the horizontal direction is the stroke and the unit is mm; the vertical y-axis is the load in N. As can be seen in the figure, after processing the feature points, the data is divided into three parts: elastic section, plastic section, elasticity uninstallation section. The elastic section is represented by open square dots, the plastic section by open circular dots, and the elastic unloading section by open triangular dots.
The technical scheme of the automatic calibration method of the variable modulus model parameters based on the bending process is as follows:
1. and performing least square smoothing filtering on the experimental data.
The conventional 12000 groups of bending process force travel data loaded and unloaded for multiple times are selected with a filter window of nF＝2mF+1＝41、mFThe experimental data points within the window were fitted using a quadratic polynomial as 20
Figure BDA0002282690920000091
Where j is i-20, i-19,.., i +20, i is the index of the experimental data, i is 21, 22.., 12000,
Figure BDA0002282690920000092
fitting values for experimental loads. And substituting 41 groups of data in the window to obtain 41 equations to form a secondary overdetermined linear equation set.
Figure BDA0002282690920000101
Wherein the content of the first and second substances,
Figure BDA0002282690920000106
is the residual error. The above formula is expressed by matrix as
YF＝XFAF+EF(3)
Find AFLeast squares solution of
Figure BDA0002282690920000107
Is composed of
Figure BDA0002282690920000102
Wherein the content of the first and second substances,
Figure BDA0002282690920000108
is XFThe transposed matrix of (2). So that J has a filter value of
Figure BDA0002282690920000103
The filtered value of the ith point is
Figure BDA0002282690920000109
Using it as new load value
Figure BDA00022826909200001010
The window step value is 1 and the next window is solved, as described above, and so on until all the filtered values at all the points are completely solved.
2. After the experimental data are filtered, the data are normalized.
H after filteringiValue (c),
Figure BDA00022826909200001011
A value obtained by comparing the substituted experimental data with the initial value to obtain a filtered maximum value h of the strokemaxMaximum force of 10mmValue of
Figure BDA00022826909200001012
Minimum value of travel hmin0mm, force minimum
Figure BDA00022826909200001013
Figure BDA0002282690920000104
Figure BDA0002282690920000105
Wherein the ith group of filtered data is
Figure BDA00022826909200001014
Figure BDA00022826909200001015
Is FiThe value of the filtered value is then compared to a threshold value,
Figure BDA00022826909200001016
is composed of
Figure BDA00022826909200001017
The maximum value after the filtering is carried out,
Figure BDA00022826909200001018
is composed of
Figure BDA00022826909200001019
Minimum value after filtering, hmaxIs hiMaximum value after filtering, hminIs hiThe minimum value after the filtering is carried out,
Figure BDA00022826909200001020
is hiFiltered normalized value, Fi normIs composed of
Figure BDA00022826909200001021
Filtered normalizationAnd (4) converting the value.
3. And extracting vector corner data of the experimental data by using a window vector method.
If the adaptive window rule is adopted, the following conditions can be used for judgment:
setting the window abscissa threshold value of the window as delta hc0.35, threshold Δ F on ordinatecThe condition for judging the number of points in the window is 0.4
Figure BDA0002282690920000111
Wherein i is a base point
Figure BDA0002282690920000114
S is 12000 for the total number of experimental data. Based on the base point, j is searched backwards with the step value as 1, when a certain point is behind the base point
Figure BDA0002282690920000116
Abscissa of
Figure BDA0002282690920000115
Or longitudinal coordinates
Figure BDA0002282690920000117
When the condition is satisfied, the difference omega between the index i + j and the index i of the base point is used as the number of window points
Figure BDA0002282690920000118
If a fixed number of window points is used, the window width is selected to be nR＝2mR+1＝51、mR25, the first 26 sets of normalized force travel data in the window at point i of the center point of the window
Figure BDA0002282690920000119
Wherein j is i-25, i-24. Fitting a straight line by least square method, the equation of the straight line is
F＝C1h+D1(9)
WhereinF is the load, h is the stroke, C1To fit the slope of the line, D1Is the intercept of the fitted line.
Force travel data normalized to 26 sets behind window center point
Figure BDA00022826909200001110
Where j ═ i, i + 1. Fitting a straight line by least square method, the equation of the straight line is
F＝C2h+D2(10)
Wherein, C2To fit the slope of the line, D2Is the intercept of the fitted line.
The stroke of the i-25 th point
Figure BDA00022826909200001111
Substituting into equation (9) to obtain a fitted load value
Figure BDA00022826909200001112
Acquisition Point
Figure BDA00022826909200001113
Stroke of i +25 th point
Figure BDA00022826909200001114
Substituting into equation (10) to obtain a fitted load value
Figure BDA00022826909200001115
Acquisition point
Figure BDA00022826909200001116
Combined with the center point of the window
Figure BDA00022826909200001117
Finding a vector
Figure BDA0002282690920000112
Two vector corner αoIs calculated by the formula
Figure BDA0002282690920000113
Will calculate the obtained rotation angle value αoAs the stroke h of the center point of the window at this timei normCorresponding angle of rotation values. The window step value is 1, and the next window is solved, as described above, and so on until all the rotation angle values are solved completely.
4. And performing least square smoothing filtering on the vector corner data to obtain a corner filtering value.
The width of the filter window for vector corner data is nα＝2mα+1＝41、mαThe data points within the window are fitted using a quadratic polynomial as 20:
Figure BDA0002282690920000121
where j is i-20, i-19,.., i +20, i is the index of the experimental data, i is 21, 22.., 12000,
Figure BDA0002282690920000125
is a rotation angle fitting value. And substituting 41 groups of data in the window to obtain 41 equations to form a secondary overdetermined linear equation set. As follows below, the following description will be given,
Figure BDA0002282690920000122
wherein the content of the first and second substances,
Figure BDA0002282690920000126
is the residual error. The above formula is expressed by matrix as
Yα＝XαAα+Eα(15)
Find AαLeast squares solution of
Figure BDA0002282690920000127
Is composed of
Figure BDA0002282690920000123
Wherein the content of the first and second substances,
Figure BDA0002282690920000128
is XαThe transposed matrix of (2). So that J has a filter value of
Figure BDA0002282690920000124
The filtered angle of rotation value of the ith point is
Figure BDA0002282690920000129
And (4) solving the next window when the window stepping value is 1, and repeating the steps until all the corner filtering values of all the points are completely solved.
5. And extracting the peak characteristic points of the corner filter values.
Screening all the filtered angle values by using the condition of maximum proximity value, and setting a certain travel hiIs the filtered vector rotation angle of
Figure BDA00022826909200001210
Extracting feature points using the following conditions
Figure BDA0002282690920000131
Wherein, i is 2, 3.., l, and there are a total of 12000 sets of filtered stroke angle data. When in use
Figure BDA0002282690920000134
When the above formula condition is satisfied, the stroke and the angle value are stored, and the finally obtained peak point is βijWhere i is 1,2, q, j is 1,2, and q is 32, which is the number of groups from which peak points are obtained. When j is 1, the two-dimensional array stores the angle value of the corner peak point, and when j is 2, the index value corresponding to the corner peak point is stored.
6. And (5) filtering adjacent peak characteristic points.
In the extracted peak point set, there are many points adjacent to the angle value, and the similar points can be filtered by using a window and a threshold value of the angle change.
When the angle value change of the adjacent peak points is less than 20%, merging the peak points; if the difference between the angle values of the adjacent peak points exceeds 20%, judging whether the difference between the point sequences of the two points is less than mαIf the peak value is smaller than the threshold value, the peak value points are merged, and the formula is as follows
Figure BDA0002282690920000132
β is firstly1,j(j ═ 1,2), i.e. the angle values of the first set of peak points and their indices are stored in γ1,j(j is 1,2), then judging whether the next group of corner values and the indexes thereof meet the storage condition, if so, storing the corner values and the indexes thereof to gammaijIf not, the data is not stored. The step value is 1, and the second point is judged, and the process is as above until all the points are judged to be finished. Finally, the peak points of the set c-19 can be obtained. The feature points after this filtering are the feature points to be obtained.
The results are as follows:
Figure BDA0002282690920000133
Figure BDA0002282690920000141
7. data segmentation based on peak feature points.
According to the screening result of the peak points, c groups of peak points are shared in the process of loading and unloading the bending male die for multiple times; according to the morphological characteristics of the curve obtained in the machining process, the curve is determined through the rotation angle: in the loading and unloading process of the primary bending male die, a first peak point is a yield point of a material in the bending process, a second peak point is a male die unloading starting point, and a third peak point is a male die unloading ending point; according to the characteristics, the bending processing data is segmented, and each unloading data segment is saved again.
After each peak feature point is obtained, data is divided into data using the feature points, as shown in fig. 3. A total of 5 segments of elastic unload segment data are available.
8. And identifying the elastic modulus based on each piece of data.
After data of the elastic loading section and the unloading sections are extracted, respectively re-determining the elastic modulus of each section; the modulus of elasticity is described exponentially as a function of the total strain (YUM model) as follows
Eu＝E0-(E0-Ea)[1-exp(-ξ)](20)
Wherein E is0As a material default modulus of elasticity, EuAs real-time modulus of elasticity of the material, EaThe saturated elastic modulus is shown, ξ is a material parameter, and the strain generated by the plate is shown;
in order to calculate the relation between the male die load and the male die displacement in the elastic process, simplifying the V-shaped bending into a plane strain model, taking the length direction of a plate as the x direction, the thickness direction of the plate as the y direction, and the center of the plate as a coordinate origin; at the abscissa x, under the action of a bending moment M generated by the load of the male die, the relationship between the rebound curvature and the bending moment is as follows
Figure BDA0002282690920000151
Wherein the content of the first and second substances,
Figure BDA0002282690920000155
the curvature radius at any point x after the bending moment M is unloaded; t is the thickness of the plate, b is the width of the plate; the amount of change in curvature after rebound is further expressed as:
Figure BDA0002282690920000152
wherein the content of the first and second substances,
Figure BDA0002282690920000153
Figure BDA0002282690920000154
thus, the sheet material is calculated at a known abscissa x at a real-time modulus of elasticity EuBending moment M by punch load FxThe result is obtained; at the moment, calculating the stroke h of the male die according to the coordinates of all parts of the plate; therefore, a plurality of groups of real-time elastic modulus E are obtained through the plane strain analytical model of the V-shaped bendinguh-F data (the number of data sets depends on the resolution of the length direction of the plate or the sampling interval); at this time, there is the following relationship:
Fi＝f(hi,Eu) (24)
wherein, i ═ 1,2, 3., ψ, ψ are index maximum values of load displacement data obtained by the analytical model;
during the elastic loading or each unloading process, the elastic modulus of the material changes due to hardening, damage and the like in the material; in order to obtain the modulus of elasticity of the material on-line, on the basis of the above process, if there is an EuThe value is such that the "gap" between the analytical model data and the off-load data for each stage of the process is sufficiently small, then EuThe value is in a reasonable range, and the value is taken as the elastic modulus of the current material;
defining an objective function as 0.5 times of the sum of the squares of the residuals of the two groups of bending force data, and taking the minimum value of the objective function when the analytic data and the processed data are close enough; defining an elastic phase objective function as follows:
Figure BDA0002282690920000161
wherein the content of the first and second substances,
Figure BDA0002282690920000165
e determined on the kth trial for the algorithmu，ΩueAn index set containing analytical models and processing data; the argument range of the objective function is
Figure BDA0002282690920000166
Performing quadratic approximation on the target function, wherein in the k iteration, an approximation function is provided:
Figure BDA0002282690920000162
wherein the content of the first and second substances,
Figure BDA0002282690920000167
automatically for the algorithm after quadratic approximation
Figure BDA0002282690920000168
Centered at ΔkThe interpolation set of the radius is represented, j is 1, 2. Thus, the optimization problem of the discrete objective function translates into a quadratic approximation function pole value problem:
Figure BDA0002282690920000163
where d is the vector step size per iteration, ΔkIs the confidence domain radius at the kth iteration;
after the elastic loading and unloading data of each section are processed by the algorithm, the elastic modulus of the loading section or each unloading section is obtained on line.
On the basis of obtaining the data segments of the above steps, the elastic modulus determination result of each segment by the algorithm is as follows:
Figure BDA0002282690920000164

Claims (9)

1. an automatic calibration method of variable modulus model parameters based on a bending process is characterized by comprising the following steps:
step 1: performing least square smoothing filtering on the experimental data;
step 2: carrying out standard normalization processing on the filtered experimental data;
and step 3: extracting vector corner data of a standard normalization value by a window vector method;
and 4, step 4: performing least square smoothing filtering on the vector corner data to obtain a corner filtering value;
and 5: extracting peak characteristic points of the corner filter values;
step 6: filtering adjacent peak feature points;
and 7: carrying out data segmentation based on the peak characteristic points;
and 8: elastic modulus identification is performed based on each piece of data.
2. The automatic calibration method of the variable modulus model parameters based on the bending process as claimed in claim 1, is characterized in that: in step 1, after a plurality of groups of experimental data are obtained by processing, a filtering window is selected as nF＝2mF+1, fitting the experimental data points in the window using a polynomial of degree k-1
Figure FDA0002282690910000011
Wherein j is i-mF,i-mF+1,...,i+mFWhere i is an index of experimental data, and i is mF+1,mF+ 2.. s, s is the total number of sets of experimental data,
Figure FDA0002282690910000012
fitting values for experimental loads; substituting n into the windowFGroup data, get nFAn equation, forming a k-1 linear equation system; to ensure that the system of linear equations has a solution, there is typically nFK is more than or equal to k; as follows below, the following description will be given,
Figure FDA0002282690910000013
wherein the content of the first and second substances,
Figure FDA0002282690910000014
is a residual error; the above formula is expressed by matrix as
YF＝XFAF+EF(3)
Find AFLeast squares solution of
Figure FDA0002282690910000015
Is composed of
Figure FDA0002282690910000016
Wherein the content of the first and second substances,
Figure FDA0002282690910000021
is a transposed matrix of XF; so that J has a filter value of
Figure FDA0002282690910000022
The filtered value of the ith point is
Figure FDA0002282690910000023
Using it as new load value
Figure FDA0002282690910000024
And (4) solving the next window until all the filtered values of all the points are completely solved, wherein the window stepping value is 1.
3. The automatic calibration method for the variable modulus model parameters based on the bending process as claimed in claim 1, wherein: in the step 2, the process is carried out,
Figure FDA0002282690910000025
Figure FDA0002282690910000026
wherein the ith group of filtered data is
Figure FDA0002282690910000027
Figure FDA0002282690910000028
Is FiThe value of the filtered value is then compared to a threshold value,
Figure FDA0002282690910000029
is composed of
Figure FDA00022826909100000210
The maximum value after the filtering is carried out,
Figure FDA00022826909100000211
is composed of
Figure FDA00022826909100000212
Minimum value after filtering, hmaxIs hiMaximum value after filtering, hminIs hiThe minimum value after the filtering is carried out,
Figure FDA00022826909100000213
is hiThe normalized value of the filtered value is then,
Figure FDA00022826909100000214
is composed of
Figure FDA00022826909100000215
A filtered normalized value.
4. The automatic calibration method for the variable modulus model parameters based on the bending process as claimed in claim 1, wherein: in step 3, the window width is selected to be nR＝2mR+1 or
Figure RE-FDA00023672268800000217
Front m in window for ith point of window center pointR+1 normalized force stroke data set
Figure RE-FDA00023672268800000218
Wherein j is i-mR,i-mR+1,... i; fitting a straight line by least square method, the equation of the straight line is
F＝C1h+D1(9)
Wherein F is the load, h is the stroke, C1To fit the slope of the line, D1Is the intercept of the fitted straight line;
for the point i after the window mR+1 normalized force stroke data set
Figure RE-FDA00023672268800000219
Wherein j ═ i.. i + mR-1,i+mR(ii) a Fitting a straight line by least square method, the equation of the straight line is
F＝C2h+D2(10)
Wherein, C2To fit the slope of the line, D2Is the intercept of the fitted straight line;
the (i) th to m thRTravel of point
Figure RE-FDA0002367226880000031
Substituting into equation (9) to obtain a fitted load value
Figure RE-FDA0002367226880000032
Acquisition point
Figure RE-FDA0002367226880000033
The (i + m) thRTravel of point
Figure RE-FDA0002367226880000034
Substituting into equation (10) to obtain a fitted load value
Figure RE-FDA0002367226880000035
Acquisition point
Figure RE-FDA0002367226880000036
Combined with the center point of the window
Figure RE-FDA0002367226880000037
Finding a vector
Figure RE-FDA0002367226880000038
Two vector corner αoIs calculated by the formula
Figure RE-FDA0002367226880000039
Will calculate the obtained rotation angle value αoAs the stroke of the center point of the window at the moment
Figure RE-FDA00023672268800000310
A corresponding angle of rotation value; and setting the window stepping value as 1, and solving the next window until all the rotation angle values are completely solved.
5. The automatic calibration method for the variable modulus model parameters based on the bending process as claimed in claim 1, wherein: in step 4, the width of the filter window of the vector corner data is nα＝2mα+1, fitting the data points within the window using a polynomial of degree k-1:
Figure RE-FDA00025333658400000310
where i is an index of the vector corner data, and i is mα+1,mα+ 2.. and t, t is the total number of vector rotation angle data;
Figure RE-FDA00025333658400000311
is the corner fitting value; substituting n into the windowαGroup data, get nαAn equation to form a k-1 linear equation system, and to ensure that the linear equation system has a solution, the equation is generalHas nαK is more than or equal to k; as follows below, the following description will be given,
Figure RE-FDA00025333658400000312
wherein the content of the first and second substances,
Figure RE-FDA00025333658400000313
is a residual error; the above formula is expressed by matrix as
Yα＝XαAα+Eα(15)
Find AαLeast squares solution of
Figure RE-FDA0002533365840000041
Is composed of
Figure RE-FDA0002533365840000042
Wherein the content of the first and second substances,
Figure RE-FDA0002533365840000043
is XαThe transposed matrix of (2); so that J has a filter value of
Figure RE-FDA0002533365840000044
The filtered value of the rotation angle at the ith point is
Figure RE-FDA0002533365840000045
And (4) solving the next window until all the corner filtering values of all the points are completely solved when the window stepping value is 1.
6. The automatic calibration method for the variable modulus model parameters based on the bending process as claimed in claim 1, wherein: in step 5, a certain stroke h is setiIs the filter backward measure of rotation angle of
Figure FDA0002282690910000041
Extracting feature points using the following conditions
Figure FDA0002282690910000042
Wherein, i is 2, 3.·, l; i.e. total l groups of filtered travel angle data; when in use
Figure FDA0002282690910000043
When the above formula condition is satisfied, the stroke and the angle value are stored, and the finally obtained peak point is βijWherein, i is 1,2, and q, j is 1,2, and q is the number of groups for obtaining peak points; when j is 1, the two-dimensional array stores the angle value of the corner peak point, and when j is 2, the index value corresponding to the corner peak point is stored.
7. The automatic calibration method for the variable modulus model parameters based on the bending process as claimed in claim 1, wherein: in step 6, filtering similar points by using a window and a threshold value of angle change in the extracted peak point set; when the angle value change of the adjacent peak points is less than 20%, merging the peak points; if the difference between the angle values of the adjacent peak points exceeds 20%, judging whether the difference between the point sequences of the two points is less than mαIf the peak value is smaller than the threshold value, the peak value points are merged, and the formula is as follows
Figure FDA0002282690910000044
β is firstly1,j(j ═ 1,2), i.e. the angle values of the first set of peak points and their indices are stored in γ1,j(j is 1,2), then judging whether the next group of corner values and the indexes thereof meet the storage condition, if so, storing the corner values and the indexes thereof to gammaijIf not, not storing; judging a second point with the stepping value of 1 in the same process until all the points are judged to be finished; finally, c groups of peak points are obtained; the feature points after this filtering are the feature points to be obtained.
8. The automatic calibration method for the variable modulus model parameters based on the bending process as claimed in claim 1, wherein: in the step 7, c groups of peak points are shared in the process of loading and unloading the bending male die for multiple times according to the screening result of the peak points; according to the morphological characteristics of the curve obtained in the machining process, the curve is determined through the rotation angle: in the process of loading and unloading the primary bending male die, a first peak point is a yield point of a material in the bending process, a second peak point is a male die unloading starting point, and a third peak point is a male die unloading ending point; according to the characteristics, the bending data is processed in a segmented mode, and each unloading data segment is stored again.
9. The automatic calibration method for the variable modulus model parameters based on the bending process as claimed in claim 1, wherein: in step 8, after data of the elastic loading section and each unloading section are extracted, respectively re-determining the elastic modulus of each section; the modulus of elasticity is described exponentially as a function of the total strain as follows
Eu＝E0-(E0-Ea)[1-exp(-ξ)](20)
Wherein E is0As a material default modulus of elasticity, EuAs real-time modulus of elasticity of the material, EaSaturated modulus of elasticity, ξ material parameters, strain occurring in the sheet;
simplifying the V-shaped bending into a plane strain model, taking the length direction of the plate as the x direction, the thickness direction of the plate as the y direction, and the center of the plate as the origin of coordinates; at the abscissa x, under the action of a bending moment M generated by the load of the male die, the relationship between the rebound curvature and the bending moment is as follows
Figure FDA0002282690910000051
Wherein the content of the first and second substances,
Figure FDA0002282690910000052
the curvature radius at any point x after the bending moment M is unloaded;t is the thickness of the plate, b is the width of the plate; the amount of change in curvature after rebound is further expressed as:
Figure FDA0002282690910000053
wherein the content of the first and second substances,
Figure FDA0002282690910000054
Figure FDA0002282690910000055
calculating the stroke h of the male die according to the coordinates of all parts of the plate, and obtaining a plurality of groups of real-time elastic modulus E through the plane strain analytical model of the V-shaped bendinguThe following h-F data are related as follows:
Fi＝f(hi,Eu) (24)
wherein, i ═ 1,2, 3., ψ, ψ are index maximum values of load displacement data obtained by the analytical model;
defining the objective function as 0.5 times of the sum of the squares of the residual errors of the two groups of bending force data, and taking the minimum value of the objective function when the analytic data and the processing data are close enough; defining an elastic phase objective function as follows:
Figure FDA0002282690910000061
wherein the content of the first and second substances,
Figure FDA0002282690910000062
e determined on the kth trial for the algorithmu，ΩueAn index set containing analytical models and processing data; the argument range of the objective function is
Figure FDA0002282690910000063
Performing quadratic approximation on the target function, and obtaining an approximation function in the k iteration:
Figure FDA0002282690910000064
wherein the content of the first and second substances,
Figure FDA0002282690910000065
automatically for the algorithm after quadratic approximation
Figure FDA0002282690910000066
Centered at ΔkThe interpolation set of the radius is represented, j is 1, 2. The optimization problem of the discrete objective function is converted into a quadratic approximation function extreme value problem:
Figure FDA0002282690910000067
where d is the vector step size per iteration, ΔkIs the confidence domain radius at the kth iteration;
and after the elastic loading and each section of unloading data are processed, the elastic modulus of the loading section or each unloading section is obtained on line.
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