CN113642121A - Aluminum alloy brake caliper casting process parameter optimization method based on response surface design and multi-objective evolutionary algorithm - Google Patents
Aluminum alloy brake caliper casting process parameter optimization method based on response surface design and multi-objective evolutionary algorithm Download PDFInfo
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Abstract
A method for optimizing casting process parameters of an aluminum alloy brake caliper based on response surface design and a multi-objective evolutionary algorithm is characterized by comprising the following steps of: determining a test variable and an optimization target to construct a response surface test; obtaining a response value through a casting numerical simulation test, and establishing a plurality of response surface models reflecting input and output relations; and (4) carrying out optimization solution on the response surface model through a multi-objective evolutionary algorithm to obtain optimal process parameters. The invention solves the three or more mutually exclusive multi-target optimization problems in the evaluation indexes of the forming quality of the aluminum alloy brake caliper by applying the response surface design and the multi-target evolutionary algorithm, can obtain the uniformly distributed non-dominated solution set approaching the optimal front edge, effectively eliminates the casting defects, improves the mechanical property of the product, saves the development cost and shortens the development period.
Description
Technical Field
The invention belongs to the technical field of high-strength metal forming, and particularly relates to a method for optimizing casting process parameters of an aluminum alloy brake caliper based on response surface design and a multi-objective evolutionary algorithm.
Background
The brake caliper is a key component of a vehicle braking system and is subjected to pressure applied to two sides of a brake cylinder during working and huge vibration impact force generated in emergency braking, so that the requirements on the rigidity, the strength and the forming quality of the brake caliper are high in the automobile running process. The brake caliper is complex in structure and uneven in wall thickness distribution, the defect rate of the brake caliper is high in actual production, the defects are mainly generated at the wall thickness position, such as the middle position of two oil cylinder holes, the thickness of the position is large, molten metal flows slowly, a molten metal feeding channel is prone to being not smooth, therefore, casting defects are generated, and the driving safety of an automobile is seriously affected.
Currently, in actual production, the brake caliper mainly depends on experience of technicians to improve process parameters, and trial production and adjustment are continuously carried out. Therefore, defects cannot be effectively eliminated, and the production efficiency of enterprises can be reduced. Therefore, the invention provides the aluminum alloy brake caliper casting process parameter optimization method based on the response surface design and the multi-objective evolutionary algorithm, compared with the traditional parameter optimization method, the method has the advantages that the convergence effect is excellent when the multi-objective optimization is carried out aiming at the input and solving of the nonlinear casting process parameters, wherein three or more quality evaluation indexes are mutually exclusive, the optimization speed is high, and the result is accurate. The comprehensive quality of the castings can be improved, the research and development period is greatly shortened, the method of continuously trial and error by an empirical method in the past is replaced, and the economic benefit is improved.
Disclosure of Invention
The invention aims to provide an aluminum alloy brake caliper casting process parameter optimization method based on response surface design and multi-objective evolutionary algorithm aiming at the problems that the defects of castings cannot be effectively eliminated by means of empirical adjustment parameters in the casting production of the brake caliper at present, the mechanical property of products is low, and the production period is long.
The technical scheme of the invention is as follows:
a method for optimizing casting process parameters of an aluminum alloy brake caliper based on response surface design and a multi-objective evolutionary algorithm comprises the following steps:
the method comprises the following steps: determining a test variable and an optimization target to construct a response surface test;
the test variables are casting process parameters of the aluminum alloy brake caliper, including casting temperature, mold preheating temperature, mold thickness, heat exchange coefficient, casting speed and the like, and the optimization target is the comprehensive forming quality of the aluminum alloy brake caliper, including defect volume, mechanical property, solidification time, thermal stress and the like, wherein the mechanical property is reflected by the size of the distance between the secondary crystal support arms, and the smaller the value is, the better the mechanical property is. After the value ranges of the test variables are reasonably determined, a central combined test scheme is adopted to design a plurality of groups of tests.
Step two: obtaining response values through a casting numerical simulation test, and establishing a plurality of response surface models reflecting input and output relations;
and (3) introducing a three-dimensional model of a brake caliper gating system into finite element software, setting material properties, carrying out grid division, carrying out numerical simulation by taking the test variables in the step one as input, constructing a response surface model by taking the obtained comprehensive forming quality index value as output, carrying out fitting model inspection on the data, and outputting a regression model equation.
Step three: optimizing and solving the response surface model through a multi-objective evolutionary algorithm to obtain optimal process parameters;
the multi-objective evolutionary algorithm converts the multi-objective optimization problem into single-objective optimization through a polymerization function, is suitable for nonlinear casting process parameter input and solving the multi-objective optimization with mutually exclusive three or more process evaluation indexes, the obtained solution set has uniformity, and finally, the optimal process parameters are selected according to actual production conditions.
Further, the method for calculating the distance between the secondary wafer support arms in the first step comprises the following steps:
λ2=(M·tf)n
in the formula: m-grain coarsening coefficient; n-grain growth factor. t is tf-local clotting time.
Further, the brake caliper gating system three-dimensional model in the second step comprises a casting, a mold, a sprue, a cross runner and an ingate.
Furthermore, the comprehensive molding quality indexes of the second step comprise defect volume, mechanical property, solidification time, thermal stress and the like.
Further, the fitting model test in the second step includes a variation coefficient, a decision coefficient, a correction value thereof, and the like.
Further, the regression model equation in the second step is as follows:
in the formula: x-random variable vector, each variable is independent; b0、bi、bii-a undetermined coefficient.
Further, the multi-objective evolutionary algorithm in the third step solves the response surface model, and an obtained non-dominated solution set needs to select a decomposition strategy, specifically a chebyshev aggregate formula:
wherein λ ═ λ1,λ2...λm]TThe slope of the direction of the seek is shown,represents an ideal reference point and hasx is the decision vector, Ω is the value range, and m is the number of objective functions.
Further, the used multi-objective evolutionary algorithm needs to set the population size N, N weight vectors, the number K of weight vectors in the neighborhood of each weight vector, a scaling factor and a cross probability.
Further, the operation flow of the multi-target evolutionary algorithm is as follows: carrying out initial sampling on a target problem, and simultaneously establishing an empty set EP for storing a non-dominated solution found by searching; traversing N subproblems, randomly selecting two individuals from neighbor vectors of each subproblem as parents, and generating a next generation solution by virtue of a genetic operator; and screening the individuals obtained after recombination and the population after the last iteration according to a preset rule, updating the population, and continuously performing iterative computation. And judging whether the operation is terminated according to a set termination condition, if so, outputting a non-dominated solution set, and otherwise, continuing iteration until the operation is terminated.
Further, the genetic operators comprise a crossover operator and a mutation operator, the crossover adopts a crossover scheme of differential evolution, and the mutation adopts a polynomial mutation scheme.
And further, when the obtained result does not meet the condition or exceeds the limited value range, repeating the steps from one step to three until the process parameter combination meeting the requirements is generated.
The invention has the beneficial effects that:
the method provided by the invention can be used for solving the mutually exclusive multi-target optimization problems of defect volume, mechanical property, solidification time and the like in the evaluation index of the forming quality of the aluminum alloy brake caliper, has high optimization speed and accurate result, can obtain a uniformly distributed non-dominated solution set approaching the optimal front edge, accords with the actual production condition, can effectively eliminate the casting defect, improves the mechanical property of the product, saves the development cost and shortens the development period.
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FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a numerical model diagram of a simulated runner system of the present invention.
FIG. 3 is a basic flow diagram of the multi-objective evolutionary algorithm of the present invention.
FIG. 4 is a diagram of the algorithm solution set distribution of the present invention.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
As shown in fig. 1-4
A method for optimizing casting process parameters of an aluminum alloy brake caliper based on response surface design and a multi-objective evolutionary algorithm. The flow chart is shown in figure 1: the method comprises the following steps:
the method comprises the following steps: determining a test variable and an optimization target to construct a response surface test;
in the embodiment, an aluminum alloy brake caliper low-pressure casting process scheme is selected, and the test variables are aluminum alloy brake caliper casting process parameters including pouring temperature, mold preheating temperature, heat transfer coefficient, mold wall thickness, pouring speed and the like.
The optimization target is the comprehensive forming quality of the aluminum alloy brake caliper, including defect volume, mechanical property, solidification time, thermal stress and the like, the defect volume, the mechanical property and the solidification time are used as the optimization target, wherein the mechanical property is reflected by the size of the distance between the secondary crystal arms, and the smaller the value is, the better the mechanical property is. After the factor levels of the test variables are reasonably determined, a central combined test scheme is adopted to design a plurality of groups of tests, and the factor levels are shown in table 1.
TABLE 1 test factor level table
Step two: obtaining response values through a casting numerical simulation test, and establishing a plurality of response surface models reflecting input and output relations;
and (3) importing a brake caliper gating system three-dimensional model into finite element software, wherein the model comprises a casting, a mould, a sprue, a cross gate and an ingate. Setting material properties and carrying out grid division, wherein a numerical model for simulating casting is shown in figure 2, numerical simulation is carried out by taking the test variable in the step one as input, and the obtained comprehensive forming quality index value is used as output to construct a response surface model, which is shown in table 2. Fitting model test is carried out on the data, and then a regression model equation is output.
TABLE 2 response surface test arrangement and results
The fitting model test comprises a coefficient of variation, a decision coefficient and a correction value thereof, in this example, as shown in table 3, the coefficient of variation of all three evaluation indexes is very small, and the decision coefficient and the correction value are close to 1, so that the fitting effect is good.
TABLE 3 fitting model test chart
The resulting regression equation is as follows:
step three: the response surface model is optimized and solved through a multi-objective evolutionary algorithm to obtain optimal process parameters
The multi-objective evolutionary algorithm has good effect on three or more mutually exclusive multi-objective optimization problems, the selected decomposition strategy is Chebyshev aggregate type as shown in the following,
wherein λ ═ λ1,λ2...λm]TThe slope of the direction of the seek is shown,represents an ideal reference point and hasx is a decision vector, omega is a value range, m is the number of objective functions and is 3, and the established multi-objective functions are shown as follows
xil<xi<xiu
In the formula xiTo design variables, xilAnd xiuThe values for the lower and upper limits of the design variables are shown in Table 1.
Wherein the population size N is 50, the neighbor number K is 10, the iteration times are 100, and the algorithm operation flow is as follows: carrying out initial sampling on a target problem, and simultaneously establishing an empty set EP for storing a non-dominated solution found by searching; traversing N subproblems, randomly selecting two individuals from neighbor vectors of each subproblem as parents, and generating a next generation solution by virtue of a genetic operator; and screening the individuals obtained after recombination and the population after the last iteration according to a preset rule, updating the population, and continuously performing iterative computation. Judging whether the solution is terminated according to a set termination condition, if so, outputting a non-dominated solution set, otherwise, continuing iteration until the termination, wherein the algorithm flow chart is shown in figure 3, and the solution set is shown in figure 4.
Because the control accuracy of each process parameter is limited during actual production, but within a controllable interval, the value of the final optimal process parameter is rounded near the optimal solution set, the pouring temperature is 680 ℃, the mold temperature is 330 ℃, and the heat transfer coefficient is 1700W/(m)2K) The thickness of the die wall is 20 mm.
To verify the results obtained from the optimization, the optimized process parameters were cast into the calculation software for calculation and compared to the results that were not optimized, as shown in table 4.
TABLE 4 comparison of quality indexes before and after optimization
It can be seen that the void volume of the brake caliper casting is reduced by 19.3%, the mechanical property is improved, the production period is shortened, and the comprehensive forming quality of parts is greatly improved.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes and modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention.
The parts not involved in the present invention are the same as or can be implemented using the prior art.
Claims (10)
1. A method for optimizing casting process parameters of an aluminum alloy brake caliper based on response surface design and a multi-objective evolutionary algorithm is characterized by comprising the following steps of:
the method comprises the following steps: determining a test variable and an optimization target to construct a response surface test;
the test variables are casting process parameters of the aluminum alloy brake caliper, including pouring temperature, mold preheating temperature, mold thickness, heat exchange coefficient and pouring speed, and the optimization target is the comprehensive forming quality of the aluminum alloy brake caliper; after the value range of each test variable is reasonably determined, a plurality of groups of tests are designed by adopting a central combined test scheme;
step two: obtaining response values through a casting numerical simulation test, and establishing a plurality of response surface models reflecting input and output relations;
introducing a three-dimensional model of an aluminum alloy brake caliper gating system into finite element software, setting material properties and carrying out grid division, carrying out numerical simulation by taking the test variables in the step one as input, constructing a response surface model by taking the obtained comprehensive forming quality index value as output, and outputting a regression model equation after carrying out fitting model inspection on the data;
step three: optimizing and solving the response surface model through a multi-objective evolutionary algorithm to obtain optimal process parameters;
the multi-objective evolutionary algorithm converts the multi-objective optimization problem into single-objective optimization through a polymerization function, is suitable for nonlinear casting process parameter input and solving the multi-objective optimization with mutually exclusive three or more quality evaluation indexes, the obtained solution set has uniformity, and finally, the optimal process parameters are selected according to actual production conditions.
2. The method for optimizing the casting process parameters of the aluminum alloy brake caliper based on the response surface design and the multi-objective evolutionary algorithm according to claim 1, wherein the comprehensive forming quality indexes of the aluminum alloy brake caliper in the first step comprise defect volume, mechanical properties, solidification time and thermal stress; the mechanical property is reflected by the size of the distance between the secondary crystal arms, and the smaller the value is, the better the mechanical property is.
3. The method for optimizing the casting process parameters of the aluminum alloy brake caliper based on the response surface design and the multi-objective evolutionary algorithm according to claim 2, wherein the calculation method of the distance between the secondary crystal arms is as follows:
λ2=(M·tf)n
in the formula: m-grain coarsening coefficient; n-grain growth factor. t is tf-local clotting time.
4. The method for optimizing the casting process parameters of the aluminum alloy brake caliper based on the response surface design and the multi-objective evolutionary algorithm according to claim 1, wherein the three-dimensional model of the aluminum alloy brake caliper gating system in the second step comprises three-dimensional models of a casting, a mold, a sprue, a cross runner and an ingate; and in the second step, the fitting model test comprises a variation coefficient, a decision coefficient and a correction value thereof.
5. The method for optimizing the casting process parameters of the aluminum alloy brake caliper based on the response surface design and the multi-objective evolutionary algorithm according to claim 1, wherein the regression model equation in the second step is as follows:
in the formula: x-random variable vector, each variable is independent; b0、bi、bii-a undetermined coefficient.
6. The method for optimizing the parameters of the aluminum alloy brake caliper casting process based on the response surface design and the multi-objective evolutionary algorithm according to claim 1, wherein the multi-objective evolutionary algorithm in the third step solves the response surface model to obtain a non-dominated solution set, and a decomposition strategy, specifically a Chebyshev polymeric method, needs to be selected:
7. The method for optimizing the casting process parameters of the aluminum alloy brake caliper based on the response surface design and the multi-objective evolutionary algorithm according to claim 5, wherein the evolutionary algorithm is used by setting a population size N and N weight vectors, the number K of the weight vectors in the neighborhood of each weight vector, a scaling factor and a cross probability.
8. The method for optimizing the parameters of the aluminum alloy brake caliper casting process based on the response surface design and the multi-objective evolutionary algorithm according to claim 5, wherein the operation process is as follows: carrying out initial sampling on a target problem, and simultaneously establishing an empty set EP for storing a non-dominated solution found by searching; traversing N subproblems, randomly selecting two individuals from neighbor vectors of each subproblem as parents, and generating a next generation solution by virtue of a genetic operator; and screening the individuals obtained after recombination and the population after the last iteration according to a preset rule, updating the population, and continuously performing iterative computation. And judging whether the operation is terminated according to a set termination condition, if so, outputting a non-dominated solution set, and otherwise, continuing iteration until the operation is terminated.
9. The method for optimizing aluminum alloy brake caliper casting process parameters based on response surface design and multi-objective evolutionary algorithm as claimed in claim 6, wherein the genetic operators comprise crossover operators and mutation operators, the crossover adopts a crossover scheme of differential evolution, and the mutation adopts a polynomial mutation scheme.
10. The method for optimizing parameters in an aluminum alloy brake caliper casting process based on response surface design and multi-objective evolutionary algorithm as claimed in any one of claims 1-2, 4-6, wherein when the obtained result does not meet the condition or exceeds the limited value range, the steps one to three are repeated until the process parameter combination meeting the requirements is generated.
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