CN111444578A - An Automatic Calibration Method of Variable Modulus Model Parameters Based on Bending Technology - Google Patents

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

An Automatic Calibration Method of Variable Modulus Model Parameters Based on Bending Technology

technical field

The invention relates to the field of metal processing, in particular to an automatic calibration method for variable modulus model parameters based on a bending process.

Background technique

With the proposal of German Industry 4.0, the arrival of the era of intelligence has become a global consensus. Mastering the information of the controlled object is the premise of intelligent control on the production line, and the information of the controlled object is a high degree of abstraction of the controlled object data. In the bending forming process of high-strength materials, the elastic modulus will change with the plastic deformation. If the change of the elastic modulus of the sheet during processing can be automatically determined, then the product caused by the elastic modulus change can be reduced or even eliminated. The possibility of poor consistency after springback. The general elastic modulus measurement is carried out by offline calibration. On the basis of obtaining the uniaxial tensile experimental data of the material, the corresponding change value of the elastic modulus is extracted and calculated manually for many times. The process is cumbersome and the accuracy is low. Extraction results are not stable. Secondly, intelligent processing requires embedded programs, and manual intervention is not conducive to the realization of intelligent processing.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide an automatic calibration method for the parameters of the variable modulus model based on the bending process, to determine the elastic modulus of the curve change through a stable and accurate identification process, so as to avoid the product return caused by the change of the elastic modulus. The problem of poor consistency after bombing.

For solving the above-mentioned technical problems, the technical scheme adopted in the present invention is:

An automatic calibration method for variable modulus model parameters based on a bending process, comprising the following steps:

Step 1: Least-squares smoothing filtering is performed on the experimental data;

Step 2: standardize the experimental data after filtering;

Step 3: Extract the vector rotation angle data of the standard normalized value by the window vector method;

Step 4: Least squares smoothing filtering is performed on the vector corner data to obtain the corner filter value;

Step 5: Extract the peak feature point of the corner filter value;

Step 6: Filter adjacent peak feature points;

Step 7: perform data segmentation based on peak feature points;

Step 8: Identify the elastic modulus based on each piece of data.

A further improvement of the technical solution of the present invention is: in step 1, after processing to obtain multiple sets of experimental data, the filter window is selected as n _F =2m _F +1, and k-1 degree polynomial is used to fit the experimental data points in the window

为实验载荷拟合值；代入窗口内n_F组数据，得到n_F个 方程，构成k-1次线性方程组；为保证线性方程组有解，一般有n_F≥k；如下，Among them, j=im _F ,im _F +1,...,i+m _F , where i is the index of the experimental data, i=m _F +1,m _F +2,...,s,s is the total number of groups of experimental data,

is the fitting value of the experimental load; it is substituted into n _F groups of data in the window, and n _F equations are obtained to form a k-1 linear equation system; in order to ensure that the linear equation system has a solution, generally n _F ≥ k; as follows,

为残差；上式用矩阵表示为in,

is the residual; the above formula is represented by a matrix as

Y _F = X _F A _F +E _F (3)

为Find the least squares solution for A _F

for

为X^F的转置矩阵；故J的滤波值为in,

is the transposed matrix of X ^F ; so the filter value of J is

将其作为新载荷值

窗口步进值为1，求解下 一个窗口，直到所有点的滤波值全部求解完成。The filtered value of the i-th point is

use this as the new load value

The window step value is 1, and the next window is solved until all filter values of all points are solved.

The further improvement of the technical solution of the present invention is: in step 2,

为F_i滤波后的值，

为

滤波后最大值，

为

滤波后最小值，h_max为h_i滤波后最大值，h_min为h_i滤波后最小值，

为h_i滤 波后的归一化值，F_i ^norm为

滤波后的归一化值。Among them, the ith group of filtered data is

is the _filtered value of Fi,

for

The filtered maximum value,

for

The minimum value after filtering, h _max is the maximum value after _hi filtering, h _min is the minimum value after _hi filtering,

is the normalized value after _{hi filtering, and F i norm} ^is

The filtered normalized value.

对于窗口中心点第i个点的窗口内前m_R+1组标准化后的力行程数据

其中，j＝i-m_R,i-m_R+1,...,i；利用最小二乘法拟合一条直线，直线方程 为A further improvement of the technical solution of the present invention is: in step 3, the selection window width is n _R =2m _R +1 or

For the first m _R +1 group of normalized force stroke data within the window of the i-th point at the center of the window

Among them, j=im _R ,im _R +1,...,i; use the least squares method to fit a straight line, the straight line equation is

F=C ₁ h+D ₁ (9)

Among them, F is the load, h is the stroke, C ₁ is the slope of the fitted straight line, and D ₁ is the intercept of the fitted straight line;

其中， j＝i，...,i+m_R-1,i+m_R；利用最小二乘法拟合一条直线，直线方程为Force stroke data after group normalization within the window of the i-th point m _R +1

Among them, j=i,...,i+m _R -1,i+m _R ; use the least squares method to fit a straight line, the straight line equation is

F=C ₂ h+D ₂ (10)

Among them, C ₂ is the slope of the fitted straight line, and D ₂ is the intercept of the fitted straight line;

代入直线方程(9)，求得一个拟合载荷值

获得 点

将第i+m_R个点的行程

代入直线方程(10)，求得一个拟合载荷 值

获得点

结合窗口中心点

求得向量The itinerary of the im _Rth point

Substitute into equation (9) of the line to obtain a fitted load value

gain points

The itinerary of the i+mth point _R

Substitute into equation (10) of the line to obtain a fitted load value

gain points

Combine window center point

get vector

The calculation formula of the rotation angle α _o of the two vectors is:

对应的转角值；设置窗 口步进值为1，求解下一个窗口，直到所有的转角值全部求解完成。Take the calculated corner value α _o as the stroke of the center point of the window at this time

The corresponding corner value; set the window step value to 1, and solve the next window until all the corner values are solved.

The further improvement of the technical solution of the present invention is: in step 4, the width of the filtering window of the vector rotation angle data is n _α =2m _α +1, and the k-1 degree polynomial is used to fit the data points in the window:

为转角拟合值；代入窗口内n_α组数据，得到n_α个方程，构成k-1次 线性方程组，为保证线性方程组有解，一般有n_α≥k；如下，Wherein, here, i is the index of the vector angle data, i=m _α +1, m _α +2,..., t, t is the total number of groups of the vector angle data;

is the fitting value of the rotation angle; it is substituted into the n _α group of data in the window, and n _α equations are obtained to form a k-1 linear equation system. In order to ensure that the linear equation system has a solution, generally n _α ≥ k; as follows,

为残差；上式用矩阵表示为in,

is the residual; the above formula is represented by a matrix as

Y _α =X _α A _α +E _α (15)

为Find the least squares solution for A _α

for

为X_α的转置矩阵；故J的滤波值为in,

is the transposed matrix of X _α ; so the filter value of J is

窗口步进值为1，求解下一个窗口，直到所有 点的转角滤波值全部求解完成。The corner filter value of the i-th point is

The window step value is 1, and the next window is solved until all the corner filter values of all points are solved.

利用下列条件提取特征点A further improvement of the technical solution of the present invention is: in step 5, set the filtered vector rotation angle at a certain stroke h _i as

Extract feature points using the following conditions

满足上式条件时，将此处的行程及其角度值保存；最终获得的峰值点为β_ij，其中，i＝1,2,...,q、j＝1,2， q为获得峰值点的组数；当j＝1时，这个二维数组存储转角峰值点的角度值，当 j＝2时，存储其中转角峰值点对应的索引值。Among them, i=2,3,...,l; that is, there are l groups of filtered travel angle data; when

When the conditions of the above formula are satisfied, save the stroke and its angle value here; the final peak point obtained is β _ij , where i=1,2,...,q, j=1,2, q is the peak value obtained The number of groups of points; when j=1, this two-dimensional array stores the angle value of the corner peak point, and when j=2, stores the index value corresponding to the corner peak point.

A further improvement of the technical solution of the present invention is: in step 6, in the peak point set that has been extracted, use the window and the threshold value of the angle change to filter the similar points; when the angle value change of adjacent peak points is less than 20%, merge the peak points. If the difference between the angle values of adjacent peak points exceeds 20%, judge whether the difference between the two point sequences is less than mα, if it is less than, then merge the peak points, the formula is as follows

First, store β _1,j (j=1,2), that is, the corner values of the first group of peak points and their indices into γ _1,j (j=1,2), and then judge the next group of corner values and their indices. Whether the index satisfies the storage condition, if so, it is saved to γ _ij , if not, it is not saved; the step value is 1, the second point is judged, and the process is the same until all points are judged; finally, the c group is obtained Peak point; the filtered feature point is the feature point to be obtained. A further improvement of the technical solution of the present invention is: in step 7, according to the screening results of the peak points, during the loading and unloading process of multiple bending punches, there are a total of c groups of peak points; Rotation angle determination: During a bending punch loading and unloading process, the first peak point is the yield point of the material during the bending process, the second peak point is the punch unloading start point, and the third peak point is the punch unloading termination point; According to the above features, the bending processing data is segmented, and each unloading data segment is re-saved.

A further improvement of the technical solution of the present invention is: in step 8, after the data of the elastic loading section and each unloading section are extracted, the elastic modulus of each section is respectively re-determined; the elastic modulus is described in an exponential form as the total amount of strain function, as follows

E _u =E ₀ -(E ₀ -E _a )[1-exp(-ξε)] (20)

Among them, E ₀ is the default elastic modulus of the material, E _u is the real-time elastic modulus of the material, E _a is the saturated elastic modulus, ξ is the material parameter, and ε is the strain of the plate;

Simplify the V-shaped bending into a plane strain model, take the length direction of the plate as the x direction, the plate thickness direction as the y direction, and the center of the plate as the coordinate origin; at the abscissa x, under the action of the bending moment M generated by the punch load , the relationship between springback curvature and bending moment is as follows

为弯矩M卸载后任意一点x处曲率半径；t为板材厚度，b为板材宽 度；回弹后曲率的变化量进一步表达为：in,

is the radius of curvature at any point x after the bending moment M is unloaded; t is the thickness of the plate, and b is the width of the plate; the change in curvature after springback is further expressed as:

in,

Calculate the stroke h of the punch according to the coordinates of the plate, and obtain multiple sets of hF data under the real-time elastic modulus E _u through this V-shaped bending plane strain analytical model. The relationship is as follows:

F _i =f( _hi ,E _u ) (24)

Among them, i=1, 2, 3, ..., ψ, ψ is the index maximum value of the load displacement data obtained by the analytical model;

The objective function is defined as 0.5 times the sum of the squares of the residuals of the two sets of bending force data, and the objective function takes the minimum value when the analytical data and the processing data are close enough; the objective function of the elastic stage is defined as follows:

为算法做第k次尝试时确定的E_u，Ω_ue为包含解析模型和加工数据 的索引集合；目标函数的自变量范围为

对目标函数进行二次 近似，在第k次迭代时，得到近似函数：in,

E _u determined when the algorithm does the kth attempt, Ω _ue is the index set containing the analytical model and processing data; the range of the independent variables of the objective function is

Perform a quadratic approximation to the objective function, and at the k-th iteration, the approximate function is obtained:

为二次近似后算法自动在以

为中心，以Δ_k为半径的插值集合， j＝1,2,...,θ，θ为插值个数；离散目标函数的优化问题转化成二次近似函数极值 问题：in,

After the quadratic approximation, the algorithm automatically

as the center, with Δ _k as the radius of the interpolation set, j = 1, 2, ..., θ, θ as the number of interpolations; the optimization problem of discrete objective function is transformed into a quadratic approximate function extreme value problem:

Among them, d is the vector step size of each iteration, and _Δk is the confidence region radius at the kth iteration;

After the elastic loading and unloading data of each segment are processed, the elastic modulus of the loaded segment or each unloading is obtained online.

Owing to having adopted the above-mentioned technical scheme, the technical progress that the present invention obtains is:

The invention designs an automatic calibration algorithm of variable modulus model parameters on the basis of online acquisition of the bending process data, which can stably and accurately identify the characteristic points of the machining load displacement curve, complete the data segmentation at the same time, and On this basis, the automatic calibration of the elastic modulus is realized, which avoids the problem of poor consistency of the product after rebound caused by the change of the elastic modulus. It avoids the use of artificial intelligence to automatically calibrate the elastic modulus, reduces the computing cost, avoids the docking problem between artificial intelligence and processing ports, and improves the recognition speed. The invention realizes the least squares smoothing filtering and normalization processing of the experimental data on the basis of acquiring the experimental data of the force stroke. Using the window vector method, the vector corner data of the experimental data that changes with the stroke is extracted, the least squares smoothing filtering of the corner data, and the identification and filtering of its peak point feature points are realized, and then the segmentation of the experimental data and the elastic loading are realized. The elastic modulus of the segment and each unloaded segment is determined online. The invention takes the bending process force stroke curve of multiple loading and unloading as an example to verify the practicability of the online determination of the elastic modulus. In the actual production process, this method can be used to efficiently identify the characteristic points of the curve and save a lot of time and resource costs, and improve the production efficiency of products.

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments or technical drawings of the present invention. For researchers of ordinary skill in the art, other drawings can also be obtained from these drawings without creative work;

Fig. 1 is a graph of the experimental data curve of the force stroke of the V-shaped bending process;

Fig. 2 is a graph of vector rotation angle data extracted by a V-shaped bending process;

FIG. 3 is a segmented data diagram of the processing data extracted by the V-shaped bending process.

Detailed ways

As shown in Figure 1, Figure 2, Figure 3, it is an automatic calibration method of variable modulus model parameters based on bending process. The following is a further description of the present invention with reference to the accompanying drawings and the specific embodiment of the V-shaped bending process applied in the present invention. illustrate.

Figure 1 is a graph of the experimental data of the force stroke of the V-shaped bending process. The curve in the figure is the processing data curve. The x-axis in the horizontal direction is the stroke, and the unit is mm; the y-axis in the vertical direction is the load, and the unit is N. From the figure, it can be observed that the bending force changes with the stroke. In the process of continuous multiple loading and unloading, the yield point of the material will change with each loading and unloading, and the elastic modulus will also change due to the internal damage of the material and other factors. change.

Figure 2 is a graph of the vector corner data extracted by the V-shaped bending process, the abscissa is the index number of the data, the ordinate is the punch loading stroke on the left, and the radian value of the corner on the right, the unit is mm and rad. Among the two curves, one curve is the change curve of the stroke with the index value, and the graph is basically a straight line, which is the process of loading the punch to 2mm, 4mm, 6mm, 8mm, 10mm and unloading. The other curve is the change curve of the vector angle value extracted from the force stroke experimental data with the index, and the graph is a zigzag continuous curve.

3 is a segmented data diagram of the processing data extracted by the V-shaped bending process in the present invention, the x-axis in the horizontal direction is the stroke, and the unit is mm; the y-axis in the vertical direction is the load, and the unit is N. As can be seen from the figure, after processing the feature points, the data is divided into three parts: elastic segment, plastic segment, and elastic unloading segment. The elastic segment is represented by a hollow square point, the plastic segment is represented by a hollow circular point, and the elastic unloading segment is represented by a hollow triangle point.

A technical scheme of an automatic calibration method for variable modulus model parameters based on bending process is as follows:

1. Perform least squares smoothing filtering on the experimental data.

There are 12,000 sets of bending process force stroke data loaded and unloaded multiple times. The filter window is selected as n _F = 2m _F +1 = 41, m _F = 20, and a quadratic polynomial is used to fit the experimental data points in the window.

为实验载 荷拟合值。代入窗口内41组数据，可得到41个方程，构成二次超定线性方程 组。Among them, j=i-20,i-19,...,i+20, i is the index of the experimental data, i=21,22,...,12000,

Fitted values for the experimental loads. Substitute 41 sets of data in the window, and 41 equations can be obtained, forming a quadratic overdetermined linear equation system.

为残差。上式用矩阵表示为in,

is the residual. The above formula is represented by a matrix as

Y _F = X _F A _F +E _F (3)

为Find the least squares solution for A _F

for

为X^F的转置矩阵。故J的滤波值为in,

is the transpose matrix of ^XF . Therefore, the filter value of J is

将其作为新载荷值

窗口步进值为1，求解下 一个窗口，如上所述，依次类推，直到所有点的滤波值全部求解完成。The filtered value of the i-th point is

use this as the new load value

The window step value is 1, and the next window is solved, as described above, and so on, until all the filter values of all points are solved.

2. After filtering the experimental data, normalize the data.

值，通过将代入的实验数据与初设值比较，得到滤波后的 行程最大值h_max＝10mm、力最大值值

行程最小值h_min＝0mm、力最小值

Set the value of _hi after filtering,

By comparing the substituted experimental data with the initial value, the filtered maximum stroke value h _max =10mm and the maximum force value are obtained.

Minimum stroke h _min = 0mm, minimum force

为F_i滤波后的值，

为

滤波后最大值，

为

滤波后最小值，h_max为h_i滤波后最大值，h_min为h_i滤波后最小值，

为h_i滤 波后的归一化值，F_i ^norm为

滤波后的归一化值。Among them, the ith group of filtered data is

is the _filtered value of Fi,

for

The filtered maximum value,

for

The minimum value after filtering, h _max is the maximum value after _hi filtering, h _min is the minimum value after _hi filtering,

is the normalized value after _{hi filtering, and F i norm} ^is

The filtered normalized value.

3. Use the window vector method to extract the vector angle data of the experimental data.

If the adaptive window rule is used, the following conditions can be used to judge:

Assume that the threshold value of the horizontal axis of the window is Δh _c =0.35, and the threshold value of the vertical axis is ΔF _c =0.4, and the condition for judging the number of points in the window is

的索引，s为实验数据的总组数12000。以基点为 基准，j以步进值为1向后寻找，当基点后某点

的横坐标

或者纵坐 标

满足条件时，其索引i+j与基点索引i的差ω作为窗口点数

where i is the base point

The index, s is the total number of groups of experimental data 12000. Based on the base point, j is searched backward with a step value of 1, when a point after the base point

abscissa

or ordinate

When the conditions are met, the difference ω between its index i+j and the base point index i is used as the number of window points

其中， j＝i-25,i-24,...,i。利用最小二乘法拟合一条直线，直线方程为If a fixed number of window points is used, the window width is selected as n _R = 2m _R +1 = 51, m _R = 25, for the first 26 groups of normalized force stroke data in the window of the i-th point of the center point of the window

where, j=i-25,i-24,...,i. Using the least squares method to fit a straight line, the equation of the straight line is

F=C ₁ h+D ₁ (9)

Among them, F is the load, h is the stroke, C ₁ is the slope of the fitted straight line, and D ₁ is the intercept of the fitted straight line.

其中， j＝i,i+1,...,i+25。利用最小二乘法拟合一条直线，直线方程为26 groups of normalized force stroke data after the center point of the window

Among them, j=i, i+1,...,i+25. Using the least squares method to fit a straight line, the equation of the straight line is

F=C ₂ h+D ₂ (10)

Among them, C ₂ is the slope of the fitted straight line, and D ₂ is the intercept of the fitted straight line.

代入直线方程(9)，求得一个拟合载荷值

获得 点

将第i+25个点的行程

代入直线方程(10)，求得一个拟合载荷 值

获得点

结合窗口中心点

求得向量Put the itinerary of the i-25th point

Substitute into equation (9) of the line to obtain a fitted load value

gain points

Put the itinerary of the i+25th point

Substitute into equation (10) of the line to obtain a fitted load value

gain points

Combine window center point

get vector

The calculation formula of the rotation angle α _o of the two vectors is:

The calculated rotation angle value α _o is used as the rotation angle value corresponding to the stroke h _i ^norm of the center point of the window at this time. The window step value is 1, and the next window is solved, as described above, and so on, until all corner values are solved.

4. Perform the least squares smoothing filtering on the vector corner data to obtain the corner filter value.

The width of the filtering window of the vector angle data is n _α =2m _α +1=41, m _α =20, and the data points in the window are fitted by a quadratic polynomial:

为转角拟 合值。代入窗口内41组数据，可得到41个方程，构成二次超定线性方程组。 如下，Among them, j=i-20,i-19,...,i+20, i is the index of the experimental data, i=21,22,...,12000,

is the fitted value of the corner. Substitute 41 sets of data in the window, and 41 equations can be obtained, forming a quadratic overdetermined linear equation system. as follows,

为残差。上式用矩阵表示为in,

is the residual. The above formula is represented by a matrix as

Y _α =X _α A _α +E _α (15)

为Find the least squares solution for A _α

for

为X_α的转置矩阵。故J的滤波值为in,

is the transpose matrix of X _α . Therefore, the filter value of J is

窗口步进值为1，求解下一个窗口，如上所 述，依次类推，直到所有点的转角滤波值全部求解完成。The filtered corner value of the i-th point is

The window step value is 1, and the next window is solved, as described above, and so on, until all the corner filter values of all points are solved.

5. Extract the peak feature points of the corner filter value.

利用下列条件提取特征点Use the condition with the largest adjacent value to filter all the filtered angle values, and set the filtered vector rotation angle at a certain stroke _hi as

Extract feature points using the following conditions

满足上式条件时，将此处的行程及其角度值保存。最终获得的峰值点为β_ij，其中，i＝1,2,...,q、 j＝1,2，q＝32为获得峰值点的组数。当j＝1时，这个二维数组存储转角峰值点的角 度值，当j＝2时，存储其中转角峰值点对应的索引值。Among them, i=2,3,...,l, there are l=12000 groups of filtered travel angle data. when

When the conditions of the above formula are satisfied, save the stroke and its angle value here. The finally obtained peak point is β _ij , where i=1, 2, . When j=1, this two-dimensional array stores the angle value of the corner peak point, and when j=2, stores the index value corresponding to the corner peak point.

6. The filtering process of adjacent peak feature points.

In the extracted peak point set, there are many points with adjacent angle values, and the similar points can be filtered by using the window and the threshold value of the angle change.

When the angle value change of adjacent peak points is less than 20%, the peak points are merged; if the difference between the angle values of adjacent peak points exceeds 20%, it is judged whether the difference between the two point sequences is less than m _α , if it is less than, then merge Peak point, the formula is as follows

First, store β _1,j (j=1,2), that is, the corner values of the first group of peak points and their indices into γ _1,j (j=1,2), and then judge the next group of corner values and their indices. Whether the index satisfies the save condition, if so, save to γ _ij , if not, do not save. The step value is 1, and the second point is judged, and the process is as above until all points are judged. Finally, c=19 sets of peak points can be obtained. The feature points after this filtering are the feature points to be obtained.

The result is as follows:

7. Data segmentation based on peak feature points.

According to the screening results of peak points, during the loading and unloading process of multiple bending punches, there are a total of c groups of peak points. The first peak point is the yield point of the material in the bending process, the second peak point is the start point of punch unloading, and the third peak point is the end point of punch unloading; according to the above characteristics, the bending processing data is segmented. Save each unloaded data segment again.

After each peak feature point is obtained, the data is divided by the feature point, as shown in Figure 3. A total of 5 segments of elastic unloading segment data can be obtained.

8. Recognition of elastic modulus based on data of each segment.

After extracting the data of the elastic loading section and each unloading section, the elastic modulus of each section is re-determined respectively; the elastic modulus is described as a function of the total strain in an exponential form (YUM model), as shown in the following formula

E _u =E ₀ -(E ₀ -E _a )[1-exp(-ξε)] (20)

Among them, E ₀ is the default elastic modulus of the material, E _u is the real-time elastic modulus of the material, E _a is the saturated elastic modulus, ξ is the material parameter, and ε is the strain of the plate;

In order to calculate the relationship between punch load and punch displacement in the elastic process, the V-shaped bending is simplified into a plane strain model, with the length direction of the plate as the x direction, the plate thickness direction as the y direction, and the center of the plate as the coordinate origin; At the coordinate x, under the action of the bending moment M generated by the punch load, the relationship between the springback curvature and the bending moment is as follows

为弯矩M卸载后任意一点x处曲率半径；t为板材厚度，b为板材宽 度；回弹后曲率的变化量进一步表达为：in,

is the radius of curvature at any point x after the bending moment M is unloaded; t is the thickness of the plate, and b is the width of the plate; the change in curvature after springback is further expressed as:

in,

In this way, when the abscissa x is known, the bending moment M under the real-time elastic modulus E _u of the plate is calculated, and the bending moment M is generated by the punch load F _x ; The stroke h of the punch; Therefore, multiple sets of hF data under the real-time elastic modulus E _u are obtained through this V-shaped bending plane strain analytical model (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:

F _i =f( _hi ,E _u ) (24)

Among them, i=1, 2, 3, ..., ψ, ψ is the index maximum value of the 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 internal hardening and damage; in order to obtain the elastic modulus of the material online, on the basis of the above process, if there is an E _u value such that If the "gap" between the data of the analytical model and the unloading data of each processing section is small enough, then the E _u value is within a reasonable range, which is used as the elastic modulus of the current material;

The objective function is defined as 0.5 times the sum of the squares of the residuals of the two sets of bending force data, and the objective function takes the minimum value when the analytical data and the processing data are close enough; the objective function of the elastic stage is defined as follows:

为算法做第k次尝试时确定的E_u，Ω_ue为包含解析模型和加工数据 的索引集合；目标函数的自变量范围为

对目标函数进行二次 近似，在第k次迭代时，有近似函数：in,

E _u determined when the algorithm does the kth attempt, Ω _ue is the index set containing the analytical model and processing data; the range of the independent variables of the objective function is

Perform a quadratic approximation to the objective function, and at the k-th iteration, there is an approximate function:

为二次近似后算法自动在以

为中心，以Δ_k为半径的插值集合， j＝1,2,...,θ，θ为插值个数；因此，离散目标函数的优化问题转化成二次近似函 数极值问题：in,

After the quadratic approximation, the algorithm automatically

is the interpolation set with Δ _k as the radius, j = 1, 2, ..., θ, θ is the number of interpolations; therefore, the optimization problem of discrete objective function is transformed into a quadratic approximation function extreme value problem:

Among them, d is the vector step size of each iteration, and _Δk is the confidence region radius at the kth iteration;

After the above algorithm processes the elastic loading and unloading data of each segment, the elastic modulus of the loaded segment or each unloading is obtained online.

On the basis of obtaining the data segments in the above steps, the algorithm determines the elastic modulus of each segment as follows:

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 n_F＝2m_F+1, fitting the experimental data points in the window using a polynomial of degree k-1

Wherein j is i-m_F,i-m_F+1,...,i+m_FWhere i is an index of experimental data, and i is m_F+1,m_F+ 2.. s, s is the total number of sets of experimental data,

fitting values for experimental loads; substituting n into the window_FGroup data, get n_FAn equation, forming a k-1 linear equation system; to ensure that the system of linear equations has a solution, there is typically n_FK is more than or equal to k; as follows below, the following description will be given,

wherein,

is a residual error; the above formula is expressed by matrix as

Y_F＝X_FA_F+E_F(3)

Find A_FLeast squares solution of

Is composed of

Wherein,

is a transposed matrix of XF; so that J has a filter value of

The filtered value of the ith point is

Using it as new load value

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,

wherein the ith group of filtered data is

Is F_iThe value of the filtered value is then compared to a threshold value,

is composed of

The maximum value after the filtering is carried out,

is composed of

Minimum value after filtering, h_maxIs h_iMaximum value after filtering, h_minIs h_iThe minimum value after the filtering is carried out,

is h_iThe normalized value of the filtered value is then,

is composed of

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 n_R＝2m_R+1 or

Front m in window for ith point of window center point_R+1 normalized force stroke data set

Wherein j is i-m_R,i-m_R+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 m_R+1 normalized force stroke data set

Wherein j ═ i.. i + m_R-1,i+m_R(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 th_RTravel of point

Substituting into equation (9) to obtain a fitted load value

Acquisition point

The (i + m) th_RTravel of point

Substituting into equation (10) to obtain a fitted load value

Acquisition point

Combined with the center point of the window

Finding a vector

Two vector corner α_oIs calculated by the formula

Will calculate the obtained rotation angle value α_oAs the stroke of the center point of the window at the moment

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 n_α＝2m_α+1, fitting the data points within the window using a polynomial of degree k-1:

where i is an index of the vector corner data, and i is m_α+1,m_α+ 2.. and t, t is the total number of vector rotation angle data;

is the corner fitting value; substituting n into the window_αGroup data, get n_αAn equation to form a k-1 linear equation system, and to ensure that the linear equation system has a solution, the equation is generalHas n_αK is more than or equal to k; as follows below, the following description will be given,

wherein,

is a residual error; the above formula is expressed by matrix as

Y_α＝X_αA_α+E_α(15)

Find A_αLeast squares solution of

Is composed of

Wherein,

is X_αThe transposed matrix of (2); so that J has a filter value of

The filtered value of the rotation angle at the ith point is

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 set_iIs the filter backward measure of rotation angle of

Extracting feature points using the following conditions

Wherein, i is 2, 3.·, l; i.e. total l groups of filtered travel angle data; when in use

When the above formula condition is satisfied, the stroke and the angle value are stored, and the finally obtained peak point is β_ijWherein, 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 m_αIf the peak value is smaller than the threshold value, the peak value points are merged, and the formula is as follows

β is firstly_1,j(j ═ 1,2), i.e. the angle values of the first set of peak points and their indices are stored in γ_1,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 gamma_ijIf 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

E_u＝E₀-(E₀-E_a)[1-exp(-ξ)](20)

Wherein E is₀As a material default modulus of elasticity, E_uAs real-time modulus of elasticity of the material, E_aSaturated 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

Wherein,

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:

wherein,

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 bending_uThe following h-F data are related as follows:

F_i＝f(h_i,E_u) (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:

wherein,

e determined on the kth trial for the algorithm_u，Ω_ueAn index set containing analytical models and processing data; the argument range of the objective function is

Performing quadratic approximation on the target function, and obtaining an approximation function in the k iteration:

wherein,

automatically for the algorithm after quadratic approximation

Centered at Δ_kThe 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:

where d is the vector step size per iteration, Δ_kIs 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.

Images