CN112989521B - Control method based on micro-bending forming size precision multi-objective optimization - Google Patents
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Abstract
The invention discloses a control method based on micro-bending forming size precision multi-objective optimization, belonging to the field of micro-forming size precision prediction and control, and comprising the following steps of: s1, measuring the micro-bending part based on the experimental design of the I optimization criterion to obtain the data of the rebound quantity and the bending force; s2, establishing a response surface model of the rebound quantity and a response surface model of the bending force based on a response surface method; s3, according to the response surface model of the springback quantity and the response surface model of the bending force, establishing a multi-target optimization model of the micro-bending forming size precision by fusing the springback quantity and the bending force by adopting an expectation function; s4, solving the multi-objective optimization model to obtain an experimental parameter combination of the optimal size precision of the microbending forming, and realizing the control based on the multi-objective optimization of the size precision of the microbending forming; the invention solves the problems of poor flexibility of an experimental design method, low accuracy of a prediction model, relatively complex multi-objective optimization method and the like in the existing technical scheme aiming at micro-bending forming.
Description
Technical Field
The invention belongs to the field of prediction and control of micro-forming size precision, and particularly relates to a control method based on micro-bending forming size precision multi-objective optimization.
Background
With the increasingly wide application of micro-bending parts in the fields of intelligent manufacturing, electronic communication, aerospace technology, life health, artificial intelligence, national defense and military and the like, the requirements on the dimensional accuracy and the forming quality of the micro-bending parts are more strict. At present, the research on the prediction and control of the dimensional accuracy of micro-bending forming is not complete, and the research has become a bottleneck problem which restricts the quality improvement of micro parts and the innovative development of micro-bending forming technology. Therefore, the multi-objective optimization control method for researching the dimensional accuracy of the complex micro-bending forming has very important significance for realizing high-accuracy prediction and accurate control of the dimensional accuracy and preparing the micro-bending parts with high accuracy and high quality.
In the micro-bending forming, the final size of the part is inconsistent with the design requirement due to the existence of the springback, and the final size may exceed a given tolerance range, so that the final size becomes a key factor influencing the dimensional accuracy and the forming quality of the micro-bending forming. The springback is not only influenced by a plurality of factors such as a processing method, a forming die, process parameters and the like, but also particularly influences the mechanical property of the material by the occurrence of a size effect after the characteristic size of the part is reduced to a micro size, thereby influencing the size precision of micro bending forming. Most of the current researches neglect the influence of the size effect on the forming precision of the microbend or only qualitatively analyze, and lack quantitative researches on the influence of the size effect.
At present, a prediction model for the dimensional accuracy of micro-bending forming is mostly constructed by a neural network, a support vector machine or a response surface method based on an orthogonal experimental design method, and has the defects of poor experimental design flexibility, more experimental times, time and labor consumption and the like. In the aspect of a multi-objective optimization control method, the existing research mostly adopts an NSGA-II method, the calculation complexity is higher, and the multi-objective optimization control research aspect of the micro bending forming size precision is not involved. In addition, at present, the micro-bending forming is mostly studied on relatively simple micro-bending parts with a single curvature, such as U-shaped parts and V-shaped parts, and the research on the dimensional accuracy of the multi-curvature and relatively complex micro-bending parts is less.
Generally speaking, the existing research ignores the quantitative influence condition of a key factor of a size effect on the micro-bending forming size precision, and has the problems of poor flexibility of an experimental design method, low precision of a prediction model, relatively complex multi-objective optimization control method and the like, and the research of the multi-objective optimization control method aiming at the complex micro-bending forming size precision is slightly insufficient.
Disclosure of Invention
Aiming at the defects in the prior art, the control method based on the multi-objective optimization of the micro-bending forming size precision solves the problems of poor flexibility of an experimental design method, low precision of a prediction model, relatively complex multi-objective optimization control method and the like in the existing technical scheme aiming at the micro-bending forming.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that: a control method based on micro-bending forming size precision multi-objective optimization comprises the following steps:
s1, preparing a micro-bending part based on the experimental design of the I optimization criterion, and measuring the micro-bending part to obtain resilience data and bending force data;
s2, establishing a response surface model of the springback quantity and a response surface model of the bending force based on a response surface method of an I optimization criterion, the springback quantity data and the bending force data, respectively evaluating the precision and the reliability of the response surface model of the springback quantity and the response surface model of the bending force, and establishing the response surface model of the springback quantity and the response surface model of the bending force which meet the requirements of prediction precision and reliability;
s3, according to the response surface model of the springback quantity and the response surface model of the bending force which meet the requirements of prediction precision and reliability, establishing a multi-target optimization model of the micro-bending forming size precision of the combined springback quantity and the bending force by adopting an expectation function;
s4, solving the multi-objective optimization model to obtain an experimental parameter combination of the optimal size precision of the micro-bending forming, and then utilizing the obtained experimental parameter combination to realize the accurate control of the size precision of the micro-bending part in the preparation process.
Further, step S1 includes the following substeps:
s11, selecting process parameters and material parameters according to a prior experiment;
s12, taking the process parameters and the material parameters as input variables, taking the rebound amount and the bending force as output variables, and obtaining an experimental Design based on an I optimization criterion by adopting Design-Expert software according to the number of the input variables, the horizontal number and the number of the output variables;
s13, according to the experimental design based on the I optimization criterion, adopting micro-bending forming equipment to obtain the prepared micro-bending part;
and S14, measuring the rebound quantity of the micro-bending part by using a high-precision two-dimensional imager, and measuring the bending force required by the preparation of the micro-bending part by using a charge amplifier to obtain the data of the rebound quantity and the data of the bending force.
Further, the process parameters in step S11 include: punch displacement and punch frequency;
the material parameters include: material thickness and grain size.
Further, in step S2, the response surface model of the springback amount and the response surface model of the bending force that satisfy the prediction accuracy and reliability requirements are both:
wherein,yin order to be a response quantity,x i is as followsiThe number of the input variables is changed,x j is as followsjThe number of the input variables is changed,β 0 is a constant number of times, and is,β i is a linear coefficient, and the linear coefficient,β ii in the form of a second-order coefficient,β ij in order to be the coefficient of interaction,εin order to be an experimental error, the method is,kis the number of input variables.
Further, in step S2, the accuracy of the response surface model of the springback amount or the bending force is evaluated by using:
wherein,
as a goodness of fit for the amount of springback or bending force,lin order to obtain the number of experiments,y t is as followstThe actual measured values of the sub-tests,
is as followstThe predicted value of the secondary test is,
is as followstAverage of actual measurements from the sub-trials.
Further, in step S2, the reliability of the response surface model of the springback amount or the bending force is evaluated by using:
wherein,Std.Devas a standard deviation of the amount of springback or bending force,y t is as followstThe actual measured values of the sub-tests,
is as followstThe average of the actual measurements of the sub-trials,lthe number of experiments.
Further, step S3 includes the following substeps:
s31, converting each response quantity into a single expectation function ranging from 0 to 1d m ；
S32, solving individual expectation functions by the equations (4), (5) and (6) respectively according to different purposes of single response optimizationd m ；
Wherein,yin order to be a response quantity,Tas a target value of the response amount,Lin order to be the lower limit of the target,Uin the case of the target upper limit,ris the weight size;
s33, constructing constraint conditions of input variables:
x L ≤x i ≤x U （7）
wherein,x i is as followsiThe number of the input variables is changed,x L is as followsiThe lower limit of the value of each input variable,x U the value of the input variable is the upper limit;
s34, according to the response surface model of the rebound quantity and the response surface model of the bending force which meet the requirements of prediction precision and reliability, and a plurality of independent expectation functionsd m Are combined into a total expectation functionDEstablishing a multi-objective optimization model of the micro-bending forming dimensional accuracy by fusing the rebound quantity and the bending force, wherein the total expectation functionDComprises the following steps:
wherein,Min order to be able to respond to the amount of the response quantity,d m is as followsmAn expectation function.
In conclusion, the beneficial effects of the invention are as follows:
(1) the invention introduces a response surface modeling method based on I optimization criterion and an expectation function to carry out multi-objective optimization and control on the dimensional accuracy of the complex micro-bending forming, carries out experimental design based on I optimization design criterion, can realize the minimum of the integral prediction variance or the average prediction variance of a regression model while overcoming the problem that the modeling cannot be carried out due to different input parameter levels, and has the advantages of flexible and reliable experimental design and higher accuracy of the prediction model.
(2) The invention adopts a response surface method based on I optimization criterion to establish a prediction model of the rebound quantity and the bending force, accurately maps the complex nonlinear relation between the rebound quantity and the bending force and various input parameters, realizes more accurate prediction, particularly quantitatively analyzes the material thickness and the grain size effect, and makes up the defects in the prior art and research.
(3) The method adopts the expectation function to establish a multi-objective optimization model, finds the balance point of the multi-objective optimization of the dimensional accuracy of the complex micro-bending part, has the advantages of simplicity, good operability and the like compared with the common NSGA-II algorithm, and can better control the accuracy while predicting the accuracy.
(4) The prediction accuracy and reliability of the rebound quantity and bending force model established based on the I optimization-response surface method are verified by introducing goodness-of-fit analysis and standard difference analysis.
(5) The invention not only realizes the high-precision prediction of the dimensional precision of the complex micro-bending forming, but also realizes the precise control of the dimensional precision by utilizing the established I optimization-response surface and the multi-objective optimization model.
Drawings
FIG. 1 is a flow chart of a control method based on microbend forming dimensional accuracy multi-objective optimization;
fig. 2 is a flowchart of step S2;
fig. 3 is a flowchart of step S3;
FIG. 4 is a diagram of a multi-objective optimization result (desirability) based on a desirability function;
FIG. 5 is a diagram of the result of multi-objective optimization (rebound) based on the expectation function;
FIG. 6 is a diagram of the result of multi-objective optimization (bending force) based on the expectation function.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
Introduction of optimization criteria:
in the customized experimental design, an appropriate optimization design criterion can be selected according to different requirements. Common optimization design criteria are: a-optimization criteria, D-optimization criteria, G-optimization criteria and I-optimization criteria. The A-optimization criterion is mainly to reduce the variance-trajectory of the covariance matrix; the D-optimization criterion is used for achieving the purpose of reducing the covariance of parameter estimation in the regression equation by using a test point selection criterion based on a D-optimization method; these two optimization criteria are commonly used in the parameter estimation research of first-order models, aiming to find factors having important influence on the process through factor tests or screening tests. The G-optimization criterion is mainly used to achieve minimization of the maximum prediction variance; the purpose of the I-optimization criterion (also called IV-, Q-, V-optimization criterion) is to minimize the overall or average prediction variance of the regression model. The I-optimization criterion is selected to construct the model so as to achieve higher prediction accuracy.
The method provided by the invention is further described by taking W-shaped complex micro-bending forming as a research object and CuZn37 yellow copper foil as an experimental material:
as shown in fig. 1, a control method based on multi-objective optimization of micro-bending forming size precision comprises the following steps:
s1, preparing a micro-bending part based on the experimental design of the I optimization criterion, and measuring the micro-bending part to obtain resilience data and bending force data;
step S1 includes the following substeps:
s11, selecting process parameters and material parameters according to prior experiments, wherein the process parameters comprise: punch displacement and punch frequency, material parameters including: material thickness and grain size.
S12, taking the process parameters and the material parameters as input variables, taking the rebound amount and the bending force as output variables, and obtaining an experimental Design based on an I optimization criterion by adopting Design-Expert software according to the number of the input variables, the horizontal number and the number of the output variables;
in this embodiment, the specific process of step S12 is:
4 factors of material thickness, grain size, punch displacement and punch frequency are used as input variables, and the rebound quantity and the bending force of the complex micro-bending forming are used as two output variables. Wherein the material thickness has 4 levels, 25 μm, 50 μm, 75 μm and 100 μm respectively; the grain size has 4 levels, and the grain size is obtained by annealing heat treatment under the conditions of 450 ℃ plus 1 hour heat preservation time, 550 ℃ plus 1 hour heat preservation time, 650 ℃ plus 1 hour heat preservation time and 650 ℃ plus 3 hours heat preservation time respectively; the punch displacement has 3 levels, 9.588mm, 9.635mm and 9.688mm respectively; the punch frequency had 3 levels, 0.15Hz, 0.20Hz and 0.25Hz, respectively.
S13, according to the experimental design based on the I optimization criterion, adopting micro-bending forming equipment to obtain the prepared micro-bending part;
and S14, measuring the rebound quantity of the micro-bending part by using a high-precision two-dimensional imager, and measuring the bending force required by the preparation of the micro-bending part by using a charge amplifier to obtain the data of the rebound quantity and the data of the bending force.
In this example, 56 sets of sample data were obtained by measuring the amount of springback and the bending force using a high-precision two-dimensional imager and a charge amplifier, respectively, as shown in table 1.
As shown in fig. 2, S2, establishing a response surface model of the springback amount and a response surface model of the bending force based on the response surface method of the I-optimization criterion, the springback amount data and the bending force data, evaluating the accuracy and the reliability of the response surface model of the springback amount and the response surface model of the bending force, respectively, and establishing a response surface model of the springback amount and a response surface model of the bending force which meet the requirements of the prediction accuracy and the reliability;
in this embodiment, step S2 specifically includes: according to the experimental data of the table 1, a response surface model is established by adopting a secondary model, and response surface models of the rebound quantity and the bending force are respectively obtained;
in step S2, the response surface model of the springback amount and the response surface model of the bending force that satisfy the prediction accuracy and reliability requirements are both:
wherein,yin order to be a response quantity,x i is as followsiThe number of the input variables is changed,x j is as followsjThe number of the input variables is changed,β 0 is a constant number of times, and is,β i is a linear coefficient, and the linear coefficient,β ii in the form of a second-order coefficient,β ij in order to be the coefficient of interaction,εin order to be an experimental error, the method is,kis the number of input variables.
In step S2, the accuracy of the response surface model of the springback amount or the bending force is evaluated by using:
wherein,
as a goodness of fit for the amount of springback or bending force,lin order to obtain the number of experiments,y t is as followstThe actual measured values of the sub-tests,
is as followstThe predicted value of the secondary test is,
is as followstAverage of actual measurements from the sub-trials.
In step S2, the reliability of the response surface model of the springback amount or the bending force is evaluated by using:
wherein,Std.Devas a standard deviation of the amount of springback or bending force,y t is as followstThe actual measured values of the sub-tests,
is as followstThe average of the actual measurements of the sub-trials,lthe number of experiments.
In this embodiment, the prediction accuracy of the established response surface model is evaluated, and the result shows that the goodness of fit of the response surface model of the springback value is 0.9406, which shows that the model has good fitting effect and high prediction accuracy.
The result shows that the goodness of fit of the response surface model of the bending force is 0.9920, which shows that the model has very good fitting effect, can well predict the change of the bending force and can obtain ideal prediction precision.
And carrying out reliability evaluation on the established response surface model.
The result shows that the standard deviation of the response surface model of the rebound quantity is 1.710, and the reliability of the model is high.
The result shows that the standard deviation of a response surface model of the bending force is 12.820, and the nonlinear relation between the response quantity and the influencing factors can be well described by using the model.
As shown in fig. 3, S3, establishing a multi-objective optimization model of microbending forming size accuracy that fuses the springback amount and the bending force by using an expectation function according to the response surface model of the springback amount and the response surface model of the bending force that meet the requirements of prediction accuracy and reliability;
step S3 includes the following substeps:
s31, converting each response quantity into a single expectation function ranging from 0 to 1d m ；
S32, according to different purposes (telescope, etc.) of single response optimization, the individual expectation functions can be solved by the formulas (4), (5) and (6)d m ；
Wherein,yin order to be a response quantity,Tas a target value of the response amount,Lin order to be the lower limit of the target,Uin the case of the target upper limit,ris the weight size;
s33, constructing constraint conditions of input variables:
x L ≤x i ≤x U （7）
wherein,x i is as followsiThe number of the input variables is changed,x L is as followsiThe lower limit of the value of each input variable,x U the value of the input variable is the upper limit;
in the present embodiment, the ideal spring back amount is 0 ° in the case of the W-shaped complex micro-bending part, and therefore, the desired function of the objective characteristics is selected for the spring back amount, and the ideal spring back amount is 0 °.
In the case of a W-shaped complex micro-bending part, in order to accurately control the dimensional accuracy of the part, it is desirable that the bending force be as small as possible, and therefore a desired function for the bending force is selected, which is desired to have small characteristics.
The springback quantity can directly influence the forming precision of the W-shaped complex micro-bending part, and the bending force is an indirect influence factor in comparison, so that the method is mainly used for controlling the forming dimensional precision in the later period. Therefore, in the optimized experimental setup, the importance of the amount of springback is set to 5, and the importance of the bending force is set to 1.
The constraint ranges of the respective influencing factors and the response amounts are shown in table 2.
wherein,Min order to be able to respond to the amount of the response quantity,d m is as followsmAn expectation function.
In this embodiment, Design-Expert software is used to perform multi-objective optimization modeling, and according to the constraint conditions set above, a multi-objective optimization experimental Design is completed, and 10 optimization results with the highest expectation (Desirability) are obtained, as shown in table 3.
According to the optimization results in the table, the expectation degree of the optimization condition solved by the expectation function is very close to 1, which shows that the response surface model of the rebound quantity and the bending force established based on the I optimization criterion is highly reliable. It should be noted that, in order to complete the verification experiment in the present embodiment, the levels of 4 factors are all limited to the level studied in the present embodiment when performing the optimization analysis, which is also an important reason why the expectation degree cannot reach 1.
S4, solving the multi-objective optimization model to obtain an experimental parameter combination of the optimal size precision of the micro-bending forming, and then utilizing the obtained experimental parameter combination to realize the accurate control of the size precision of the micro-bending part in the preparation process.
FIGS. 4, 5 and 6 are schematic diagrams of the results of the multi-objective optimization based on the expectation function provided by the present invention.
The multi-objective optimization results showed that the expectation of the multi-objective optimization results based on the expectation function was 0.980 (as shown in fig. 4), the spring-back amount at this time was 0.180 ° (as shown in fig. 5), and the bending force was 955.268N (as shown in fig. 6). The optimal parameters under this condition are: the thickness of the material was 75 μm, the grain size was the actual size measured under the heat treatment conditions of 650 ℃ plus 1 hour holding time, the punch displacement was 9.582mm, and the punch frequency was 0.2 Hz. The optimized parameter combination selected by the embodiment of the invention can meet the expected requirements in the practical engineering application.
Claims (6)
1. A control method based on micro-bending forming size precision multi-objective optimization is characterized by comprising the following steps:
s1, preparing a micro-bending part based on the experimental design of the I optimization criterion, and measuring the micro-bending part to obtain resilience data and bending force data;
s2, establishing a response surface model of the springback quantity and a response surface model of the bending force based on a response surface method of an I optimization criterion, the springback quantity data and the bending force data, respectively evaluating the precision and the reliability of the response surface model of the springback quantity and the response surface model of the bending force, and establishing the response surface model of the springback quantity and the response surface model of the bending force which meet the requirements of prediction precision and reliability;
s3, according to the response surface model of the springback quantity and the response surface model of the bending force which meet the requirements of prediction precision and reliability, establishing a multi-target optimization model of the micro-bending forming size precision of the combined springback quantity and the bending force by adopting an expectation function;
step S3 includes the following substeps:
s31, converting each response quantity into a single expectation function d ranging from 0 to 1m；
S32, solving the individual expectation functions d according to different purposes of single response optimization by the formulas (1), (2) and (3) respectivelym；
Wherein y is a response, T is a target value of the response, L is a target lower limit, U is a target upper limit, and r is the weight;
s33, constructing constraint conditions of input variables:
xL≤xi≤xU (4)
wherein x isiIs the ith input variable, xLIs the lower limit of the ith input variable, xUThe value of the input variable is the upper limit;
s34, according to the response surface model of the rebound quantity and the response surface model of the bending force which meet the requirements of prediction precision and reliability, and a plurality of individual expectation functions dmCombining the two into a total expectation function D, and establishing a micro bending forming size precision multi-objective optimization model fusing the springback quantity and the bending force, wherein the total expectation function D is as follows:
D＝(d1·d2·…·dm·…·dM) (5)
where M is the number of responses, dmIs the mth expectation function;
s4, solving the multi-objective optimization model to obtain an experimental parameter combination of the optimal size precision of the micro-bending forming, and then utilizing the obtained experimental parameter combination to realize the accurate control of the size precision of the micro-bending part in the preparation process.
2. The control method based on the multi-objective optimization of the micro-bending forming dimensional accuracy is characterized in that the step S1 comprises the following sub-steps:
s11, selecting process parameters and material parameters according to a prior experiment;
s12, taking the process parameters and the material parameters as input variables, taking the rebound amount and the bending force as output variables, and obtaining an experimental Design based on an I optimization criterion by adopting Design-Expert software according to the number of the input variables, the horizontal number and the number of the output variables;
s13, according to the experimental design based on the I optimization criterion, adopting micro-bending forming equipment to obtain the prepared micro-bending part;
and S14, measuring the rebound quantity of the micro-bending part by using a high-precision two-dimensional imager, and measuring the bending force required by the preparation of the micro-bending part by using a charge amplifier to obtain the data of the rebound quantity and the data of the bending force.
3. The control method based on multi-objective optimization of micro-bending forming dimensional accuracy according to claim 2, wherein the process parameters in the step S11 include: punch displacement and punch frequency;
the material parameters include: material thickness and grain size.
4. The microbend-forming dimensional accuracy multi-objective optimization-based control method according to claim 1, wherein the response surface model of the springback amount and the response surface model of the bending force that satisfy the prediction accuracy and reliability requirements in step S2 are both:
wherein y is the response, xiIs the ith input variable, xjIs the jth input variable, beta0Is a constant number, betaiIs a linear coefficient, betaiiIs a second order coefficient, betaijFor the interaction coefficients, ε is the experimental error and k is the number of input variables.
5. The control method based on the microbend forming dimensional accuracy multi-objective optimization according to claim 1, wherein the accuracy of the response surface model of the springback amount or the bending force is evaluated in step S2, and the models are:
wherein,
the goodness of fit for the amount of springback or bending force, l the number of experiments, ytIs the actual measurement value of the t-th test,
is the predicted value of the t-th trial,
the average of the actual measurements from the t-th trial.
6. The control method based on the microbend forming dimensional accuracy multi-objective optimization according to claim 1, wherein the reliability of the response surface model of the springback amount or the bending force is evaluated in step S2, and the models are:
dev is the standard deviation of the spring back or bending force, ytIs the actual measurement value of the t-th test,
the average value of the actual measured values of the t test is shown, and l is the number of tests.
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