A multi-objective optimization method for process parameters of rocket tank bottom liquid drawing

Abstract

The present invention discloses a multi-objective optimization method for process parameters of rocket tank bottom liquid-filled deep drawing. Through theoretical deduction combined with simulation experiments, key process parameters are determined and the value range is clarified; quality indicators are obtained by combining engineering experience and references; required process parameter sample points are obtained by the optimal Latin hypercube sampling method, simulation experiments are designed, and an approximate model between process parameters and quality indicators is established by the Kriging interpolation method; the multi-objective optimization model is solved by the NSGA-III algorithm to obtain process parameters that meet the requirements, and the accuracy of the optimization results is verified by experiments. The present invention has a wide range of applications and various types of solution sets, which can meet the needs of process parameter optimization for different quality requirements under the plate liquid-filled deep drawing process.

Description

Technical Field

[0001] The invention belongs to the technical field of industrial production and manufacturing, and relates to a multi-objective process parameter optimization method based on the liquid filling deep drawing forming of the bottom of a rocket tank. Specifically, it is to select appropriate process parameters while ensuring that the forming quality of the bottom of the tank is as high as possible. It is applicable to the process parameter optimization of the liquid filling deep drawing forming process. Background Art

[0002] With the advent of the post-industrial era dominated by the service industry, the development of the service industry has opened another door for the manufacturing industry. Services have gradually penetrated into various fields of the production process. More and more services are used as intermediate input factors in the manufacturing industry. The manufacturing industry has gradually developed towards service-oriented development. The mutual penetration and mutual influence between the service industry and the manufacturing industry have become increasingly obvious, and an industrial form of mutual integration of the service industry and the manufacturing industry has gradually been formed - service-oriented manufacturing, also known as product service system.

[0003] As a key component of the launch vehicle tank, the tank bottom is a semi-ellipsoidal thin-walled shell structure that bears composite loads such as internal pressure and vibration. Due to the large size of the tank bottom, the previous forming method was to decompose the tank bottom into melon petals, form them separately, and then weld them together into an integral tank bottom. The performance of the separately formed melon petals is uneven, and forcing them to be assembled as a whole will produce welding residual stress and poor reliability. In order to overcome the defects of traditional forming methods, a number of studies represented by sheet liquid deep drawing technology have been formed in recent years and applied to the production of the new generation of rocket tank bottoms.

[0004] Sheet metal liquid filling deep drawing technology is an advanced sheet metal flexible forming method, which has many advantages over traditional process methods. It can not only improve the surface quality and limit drawing ratio of formed parts, but also reduce the production time and cost of molds. Due to the large size, thin wall and thickness-to-diameter ratio of large thin-walled components <3‰, wrinkles, cracks and other defects are very likely to occur when the sheet metal liquid filling deep drawing technology is used for overall forming. Therefore, it is very important to select appropriate process parameters when applying this technology.

[0005] The process parameters of liquid deep drawing often need to refer to the manual and use trial and error to obtain them. In order to reduce the cost of trial and error and shorten the production cycle, many researchers simulate the liquid deep drawing process through simulation, and combine theoretical models to study the relationship between process parameters and the quality of molded parts. However, the relationship between the quality of molded parts and process parameters is too complicated to be derived only through simulation or theoretical models. Combining simulation and proxy models, the relationship between design variables and response quantities can be obtained through a small number of simulation experiments. The bionic meta-heuristic algorithm is very effective in multi-objective optimization. Summary of the invention

[0006] In order to solve the quality problem of the above tank bottom liquid-filled deep drawing parts, the present invention provides a multi-objective optimization method for process parameters of tank bottom liquid-filled deep drawing. The method uses the Kriging model to model the liquid-filled deep drawing process of the tank bottom and identify the mapping relationship between quality indicators and process parameters. The multi-objective optimization is performed by the NSGA-III algorithm to obtain the optimal process parameters of the forming process. The method is compared with the particle swarm optimization (PSO) algorithm and the accuracy of the optimization results is experimentally verified.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] A multi-objective optimization method for process parameters of rocket tank bottom liquid drawing forming, the operation steps are as follows:

[0009] A. Determine the key process parameters and clarify the value range through theoretical deduction combined with simulation experiments;

[0010] B. Combine engineering experience and references to obtain quality indicators;

[0011] C. Determine the mathematical model of the optimization problem based on the actual process;

[0012] D. Obtain the required process parameter sample points through the optimal Latin hypercube sampling method and design simulation experiments;

[0013] E. Use Kriging interpolation method to establish an approximate model between process parameters and quality indicators;

[0014] F. Use the NSGA-III algorithm to solve the multi-objective optimization model, obtain the process parameters that meet the requirements, and experimentally verify the accuracy of the optimization results.

[0015] In step A, the range of key process parameters is determined. According to relevant literature and engineering experience, the pre-expansion pressure p0, the blank holding force F, the liquid chamber pressure p cr , radius of corner of blank holder r h These process parameters are taken as research objects. Among them, the value range of the process parameters is derived by the following formula.

[0016] (A1) Liquid chamber pressure

[0017] For the liquid filling drawing process, according to the force balance condition when the blank leaves the die radius, the force required for the liquid to lift the blank at the die radius is equal to the vertical drawing force of the blank at the die, as shown in formula (1).

[0018]

[0019] Solve σ by inverse equation Z ,have:

[0020]

[0021] In the formula, p cr ——Liquid chamber pressure (MPa);

[0022] σ Z ——Vertical tensile stress (MPa);

[0023] R p ——Punch radius (mm);

[0024] R d ——die radius (mm);

[0025] r d ——Radius of die corner (mm);

[0026] t——plate thickness (mm).

[0027] The differential equilibrium equation of the flange area during the liquid-filled deep drawing of the hemispherical part is:

[0028]

[0029] In the formula, σ r ——Radial stress (MPa);

[0030] σ θ ——Hoop stress (MPa);

[0031] r——radius of any point of the blank (mm);

[0032] f——friction stress (N).

[0033] For the fixed gap liquid drawing process, the friction between the blank and the blank holder can be ignored. Then the differential equilibrium equation of the flange area becomes:

[0034]

[0035] The selected materials meet the Mises yield criterion and are:

[0036] σ r -σ θ =σ s (5)

[0037] In the formula, σ s ——Material flow pressure (MPa).

[0038] For hardened materials, σ sIt needs to be calculated based on the strain hardening formula. As an estimate, the average value of the material's yield strength and tensile strength can be used.

[0039] Integrate equation (4), according to the boundary condition r = R, σ r =0, we get

[0040]

[0041] Where, R is the instantaneous blank radius (mm).

[0042] Considering that additional tensile stress will be generated when the blank passes through the die radius bending and reverse bending

[0043]

[0044] In the formula, σ ω ——Tensile stress caused by bending (MPa).

[0045] Combining the above formulas, we can get the following equilibrium equation:

[0046]

[0047] By reversing the equation, we can get p cr ,have:

[0048]

[0049] The above formula is the expression of the critical value of the liquid chamber pressure when the blank is separated from the die radius during the drawing process, the initial seal fails, and overflow occurs. If the influence of work hardening on flow stress during the deformation process is considered, usually when the flange area is deformed to 85% of the original size, the critical value of the liquid chamber pressure required at this time is also the largest, which can be expressed as:

[0050]

[0051] In the formula, R b ——Original blank radius.

[0052] (A2) Blank holding force

[0053] During the liquid filling deep drawing process, when the liquid overflows, the liquid pressure p in the concave mold cavity cr Basically the same as the liquid pressure near the die radius, the blank holder force is ideally balanced with the force of the liquid in the flange area, but the blank holder force is complex and changeable during the forming process, so it can be estimated based on the main parameters of the equipment. Its expression is as follows:

[0054]

[0055] Where, F——blanking force (N);

[0056] S f ——The pressing surface area of ​​the sheet (mm 2 ).

[0057] (A3) Radius of corner of blank holder

[0058] The larger the fillet radius of the blank holder, the higher the pre-expansion height of the sheet metal, and the larger the pre-expansion area. Using a larger fillet radius of the blank holder helps to improve the stress state of the blank after pre-expansion and the wall thickness distribution after forming. According to engineering experience and literature, the range of the fillet radius of the blank holder is 10-100mm.

[0059] Step B combines engineering experience and references to obtain quality indicators. The process parameter optimization problem has two objective functions:

[0060] (B1) Maximum thickness reduction rate

[0061] The sheet thickness will be reduced during the forming process. If the thinning is too large, the sheet will break. Select the maximum thickness reduction rate θ max To characterize the severity of sheet metal cracking, the smaller the maximum thickness reduction rate, the better. In industry, it is generally required that the maximum thickness reduction rate is less than 20% to be a qualified part. The definition of the maximum thickness reduction rate is as follows:

[0062]

[0063] Where, t0——original thickness of sheet;

[0064] t min ——The minimum thickness of the sheet after forming.

[0065] (B2) Vertical displacement of flange area U2

[0066] When the sheet is wrinkled, the blank holder will be lifted up, so the degree of wrinkling is indicated by measuring the vertical displacement U2 of the flange area. In industry, it is generally required that the wrinkling height is less than 1.2 times the sheet thickness. To minimize the wrinkling degree of the molded part, U2 max The smaller the better.

[0067] The step C determines the mathematical model of the optimization problem according to the actual process. In the liquid drawing of the tank bottom, the above optimization objectives are taken into account to optimize the quality of the formed part. Construct a nonlinear optimization model:

[0068]

[0069] Where y1, y2 are objective functions, X is the design variable, X = [p0, p cr ,F,r h ]. L, X U are the upper and lower limits of the design variable.

[0070] In step D, based on the mathematical model in step C, the required process parameter sample points are obtained by the optimal Latin hypercube sampling method, a simulation experiment is designed, and an approximate model between the process parameters and the quality indicators is established by the Kriging interpolation method.

[0071] In step F, the multi-objective optimization model is solved using the NSGA-III algorithm to obtain process parameters that meet the requirements. The reliability of the results is verified by comparing the optimization results with the PSO algorithm and combining simulation experiments. The required process parameters can be selected according to different quality requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 It is an overall block diagram of the multi-objective optimization method for process parameters of the tank bottom liquid filling deep drawing forming of the present invention.

[0073] Figure 2 It is a schematic diagram of the liquid filling deep drawing process of the present invention. DETAILED DESCRIPTION

[0074] The present invention will be further described below with reference to preferred embodiments in conjunction with the accompanying drawings.

[0075] Embodiment 1:

[0076] See also Figure 1 and Figure 2 , a multi-objective optimization method for process parameters of rocket tank bottom liquid filling deep drawing, the operation steps and method include:

[0077] A. Determine the key process parameters and clarify the value range through theoretical deduction combined with simulation experiments;

[0078] B. Combine engineering experience and references to obtain quality indicators;

[0079] C. Determine the mathematical model of the optimization problem based on the actual process;

[0080] D. Obtain the required process parameter sample points through the optimal Latin hypercube sampling method and design simulation experiments;

[0081] E. Use Kriging interpolation method to establish an approximate model between process parameters and quality indicators;

[0082] F. Use the NSGA-III algorithm to solve the multi-objective optimization model, obtain the process parameters that meet the requirements, and experimentally verify the accuracy of the optimization results.

[0083] A multi-objective optimization method for process parameters of liquid filling deep drawing of tank bottom is proposed. The Kriging model is used to model the process of liquid filling deep drawing of tank bottom and identify the mapping relationship between quality index and process parameters. The multi-objective optimization is performed by NSGA-III algorithm to obtain the optimal process parameters of the forming process. The method is compared with the particle swarm optimization (PSO) algorithm and the accuracy of the optimization results is experimentally verified.

[0084] Embodiment 2:

[0085] This embodiment is basically the same as the first embodiment, with the following special features:

[0086] In this embodiment, the key process parameter value range is determined in the operation step A. According to relevant literature and engineering experience, the pre-expansion pressure p0, the blank holding force F, the liquid chamber pressure p cr , radius of corner of blank holder r h These process parameters are taken as research objects, and the value range of the process parameters is derived through the following formula.

[0087] (A1) Liquid chamber pressure

[0088] For the liquid filling drawing process, according to the force balance condition when the blank leaves the die radius, the force required for the liquid to lift the blank at the die radius is equal to the vertical drawing force of the blank at the die, as shown in formula (1).

[0089]

[0090] Solve σ by inverse equation Z ,have:

[0091]

[0092] In the formula, p cr ——Liquid chamber pressure (MPa);

[0093] σ Z ——Vertical tensile stress (MPa);

[0094] R p ——Punch radius (mm);

[0095] R d ——die radius (mm);

[0096] r d ——Radius of die corner (mm);

[0097] t——plate thickness (mm).

[0098] The differential equilibrium equation of the flange area during deep drawing of a hemispherical part is:

[0099]

[0100] In the formula, σ r ——Radial stress (MPa);

[0101] σ θ ——Hoop stress (MPa);

[0102] r——radius of any point of the blank (mm);

[0103] f——friction stress (N).

[0104] For the fixed gap liquid drawing process, the friction between the blank and the blank holder is ignored, and the differential equilibrium equation of the flange area becomes:

[0105]

[0106] The selected materials meet the Mises yield criterion and are:

[0107] σ r -σ θ =σ s (5)

[0108] In the formula, σ s ——Material flow pressure (MPa);

[0109] For hardened materials, σ s It needs to be found according to the strain hardening formula. As an estimate, the average value of the yield strength and tensile strength of the material is used;

[0110] Integrate equation (4), according to the boundary condition r = R, σ r =0, we get

[0111]

[0112] Where, R is the instantaneous blank radius (mm);

[0113] Considering that additional tensile stress will be generated when the blank passes through the die radius bending and reverse bending:

[0114]

[0115] In the formula, σ ω ——Tensile stress caused by bending (MPa);

[0116] Combining the above formulas, we can get the following equilibrium equation:

[0117]

[0118] By reversing the equation, we can get p cr ,have:

[0119]

[0120] The above formula is the expression of the critical value of the liquid chamber pressure when the blank is separated from the die radius during the liquid filling and drawing process, the initial seal fails, and overflow occurs. If the influence of work hardening on flow stress during the deformation process is considered, usually when the flange area is deformed to 85% of the original size, the critical value of the liquid chamber pressure required at this time is also the largest, expressed as:

[0121]

[0122] In the formula, R b ——Original blank radius;

[0123] (A2) Blank holding force

[0124] During the liquid filling deep drawing process, when the liquid overflows, the liquid pressure p in the concave mold cavity cr Basically the same as the liquid pressure near the die radius, the blank holder force is ideally balanced with the force of the liquid in the flange area. However, the blank holder force is complex and changeable during the forming process, so it is estimated based on the main parameters of the equipment; its expression is as follows:

[0125]

[0126] Where, F——blanking force (N);

[0127] S f ——The pressing surface area of ​​the sheet (mm 2 );

[0128] (A3) Radius of corner of blank holder

[0129] The larger the fillet radius of the blank holder, the higher the pre-expansion height of the sheet metal, and the larger the pre-expansion area; the use of a larger fillet radius of the blank holder helps to improve the stress state of the blank after pre-expansion and the wall thickness distribution after forming. According to engineering experience and literature, the value range of the fillet radius of the blank holder is 10-100mm.

[0130] The operation step B combines engineering experience and references to obtain quality indicators. The process parameter optimization problem has two objective functions:

[0131] (B1) Maximum thickness reduction rate

[0132] The sheet thickness will be reduced during the forming process. If the thinning is too large, the sheet will break. Select the maximum thickness reduction rate θ maxTo characterize the severity of sheet metal cracking, the smaller the maximum thickness reduction rate, the better; in industry, it is generally required that the maximum thickness reduction rate is less than 20% to be qualified. The definition of the maximum thickness reduction rate is as follows:

[0133]

[0134] Where, t0——original thickness of sheet;

[0135] t min ——The minimum thickness of the sheet after forming.

[0136] (B2) Vertical displacement of flange area U2

[0137] When the sheet is wrinkled, the blank holder will be lifted up, so the degree of wrinkling is indicated by measuring the vertical displacement U2 of the flange area. In industry, it is generally required that the wrinkling height is less than 1.2 times the sheet thickness. To minimize the wrinkling degree of the molded part, U2 max The smaller the better.

[0138] The operation step C determines the mathematical model of the optimization problem according to the actual process. In the liquid filling deep drawing forming of the tank bottom, the above optimization objectives are taken into account to optimize the quality of the formed part; the pre-expansion pressure p0, the liquid chamber pressure p cr , blank holder force F, blank holder radius r h These process parameters are used to construct a nonlinear optimization model:

[0139]

[0140] Where y1, y2 are objective functions, X is the design variable, X = [p0, p cr ,F,r h ]. L , X U are the upper and lower limits of the design variable.

[0141] The operation step D obtains the required process parameter sample points by the optimal Latin hypercube sampling method, designs the simulation experiment and the step E uses the Kriging interpolation method to establish an approximate model between the process parameters and the quality index. Kriging interpolation regards the response of the simulation model as a realization of a random process containing a regression term. This method is applied to actual work, and the response surface is represented in an explicit form according to the optimization variable.

[0142] Embodiment three:

[0143] In this embodiment, a multi-objective optimization method for process parameters of liquid-filled deep drawing of rocket tank bottom is mainly used to solve the problem that wrinkles and cracks are easy to occur when the bottom of a large tank is integrally formed by liquid-filled deep drawing technology. It has sample collection, approximate model establishment, and multi-objective optimization model solution modules. The approximate model establishment module includes the determination of key process parameters and their value ranges, the determination of quality indicators, the establishment of mathematical models for optimization problems, and the modeling of approximate relationships between process parameters and quality indicators, such as Figure 1 shown.

[0144] Liquid drawing is divided into two processes:

[0145] (1) The punch does not move, and the liquid chamber provides a certain pre-expansion force, so that the sheet is squeezed and deformed upward to form a reverse expansion zone.

[0146] (2) The punch begins to move downward, driving the sheet metal to deform downward. Under the dual action of the punch and the liquid chamber pressure, the tank bottom is formed. Figure 2 shown.

[0147] The present invention will be further described below by taking the liquid filling deep drawing forming of a rocket tank bottom as an example in conjunction with the accompanying drawings.

[0148] Reference Figure 1 , the implementation steps of the present invention are as follows:

[0149] (1) The tank bottom is made of 2219 aluminum alloy sheet, which meets the Mises yield criterion. The sheet radius is 2100 mm, the punch radius is 1669 mm, the blank holder radius is 1670 mm, the sheet thickness is 8 mm, and the die corner radius is 100 mm. The key process parameters and their value ranges are determined based on theoretical analysis and simulation.

[0150] Select the pre-expansion pressure p0, the blank holding force F, and the liquid chamber pressure p cr , radius of corner of blank holder r h These process parameters were taken as research objects.

[0151] X=[p0,p cr ,F,r h ]. L =[0,0,1000,10],X U =[2,6,2000,100] is the upper and lower limits of the design variables.

[0152] (2) Combining engineering experience and references, the maximum thickness reduction rate of the sheet and the wrinkling height of the flange area are selected as quality indicators y1 and y2, respectively.

[0153] (3) Determine the mathematical model of the optimization problem based on the above process parameters and quality indicators.

[0154] (4) Combined with the simulation sample data, Kriging was used to fit the experimental values ​​and the predicted values, and an approximate model with high fitting accuracy was obtained. The coefficient of determination R2 of the model is (0.9370, 0.9419), indicating that the model can fully explain the relationship between the response variable and the design variable. The mean square error MSE of the model is (7.749%, 7.261%), both less than 10%, which further confirms the goodness of the fit, indicating that the deviation between most of the predicted data points and the experimental data points is very small.

[0155] (5) The NSGA-III algorithm is used to solve the multi-objective optimization model and obtain the process parameters that meet the requirements. The reliability of the results is verified by comparing them with the optimization results of the PSO algorithm and combining them with simulation experiments. The required process parameters can be selected according to different quality requirements.

[0156] The optimization results obtained by the two algorithms are shown below:

[0157] Table 1 Verification of process parameter optimization results

[0158]

[0159] It can be seen from the results that the relative errors of the optimization values ​​obtained by the two algorithms are within the allowable range, indicating that the optimization results are relatively accurate. And on the basis of ensuring that each target value is within a certain range, each target has its own emphasis, which can meet the different quality requirements of the tank bottom forming parts.

[0160] A multi-objective optimization method for process parameters of liquid-filled deep drawing of rocket tank bottom is provided. The key process parameters are determined and the value range is clarified through theoretical deduction combined with simulation experiments. The quality index is obtained by combining engineering experience and references. The required process parameter sample points are obtained through the optimal Latin hypercube sampling method, and simulation experiments are designed. The approximate model between process parameters and quality indexes is established by using the Kriging interpolation method. The multi-objective optimization model is solved by using the NSGA-III algorithm to obtain process parameters that meet the requirements, and the accuracy of the optimization results is verified by experiments. The above embodiment has a wide range of applications and various types of solution sets are obtained, which can meet the needs of process parameter optimization for different quality requirements under the plate liquid-filled deep drawing process.

[0161] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments. Various changes can be made according to the purpose of the invention of the present invention. Any changes, modifications, substitutions, combinations or simplifications made according to the spirit and principle of the technical solution of the present invention should be equivalent replacement methods. As long as they meet the purpose of the invention of the present invention and do not deviate from the technical principles and inventive concepts of the present invention, they belong to the protection scope of the present invention.

Claims

1. A multi-objective optimization method for process parameters of rocket tank bottom liquid drawing, characterized in that: The method comprises: A. Determine the key process parameters and clarify the value range through theoretical deduction combined with simulation experiments; B. Combine engineering experience and references to obtain quality indicators; C. Determine the mathematical model of the optimization problem based on the actual process; D. Obtain the required process parameter sample points through the optimal Latin hypercube sampling method and design the simulation experiment; E. Use Kriging interpolation method to establish an approximate model between process parameters and quality indicators; F. Use the NSGA-III algorithm to solve the multi-objective optimization model, obtain the process parameters that meet the requirements, and experimentally verify the accuracy of the optimization results; In step A, the range of key process parameters is determined; according to relevant literature and engineering experience, the pre-expansion pressure p0, the blank holding force F, the liquid chamber pressure p cr , radius of corner of blank holder r h These process parameters are taken as research objects, and the value range of process parameters is derived through the following formula; (A1) Liquid chamber pressure For the liquid filling deep drawing process, according to the force balance condition when the blank leaves the die radius, the force required for the liquid to lift the blank at the die radius is equal to the vertical drawing force of the blank at the die, as shown in formula (1); Solve σ by inverse equation Z ,have: In the formula, p cr ——Liquid chamber pressure (MPa); σ Z ——Vertical tensile stress (MPa); R p ——Punch radius (mm); R d ——die radius (mm); r d ——Radius of die corner (mm); t——plate thickness (mm); The differential equilibrium equation of the flange area during deep drawing of a hemispherical part is: In the formula, σ r ——Radial stress (MPa); σ θ ——Hoop stress (MPa); r——radius of any point of the blank (mm); f——friction stress (N); For the fixed gap liquid drawing process, the friction between the blank and the blank holder is ignored, and the differential equilibrium equation of the flange area becomes: The selected materials meet the Mises yield criterion and are: s r -s θ =s s (5) In the formula, σ s ——Material flow pressure (MPa); For hardened materials, σ s It needs to be found according to the strain hardening formula. As an estimate, the average value of the yield strength and tensile strength of the material is used; Integrate equation (4), according to the boundary condition r = R, σ r =0, we get Where, R is the instantaneous blank radius (mm); Considering that additional tensile stress will be generated when the blank passes through the die radius bending and reverse bending: In the formula, σ ω ——Tensile stress caused by bending (MPa); Combining the above formulas, we can get the following equilibrium equation: By reversing the equation, we can get p cr ,have: The above formula is the expression of the critical value of the liquid chamber pressure when the blank is separated from the die radius during the liquid filling and drawing process, the initial seal fails, and overflow occurs; if the influence of work hardening on the flow stress during the deformation process is considered, when the flange area is deformed to 85% of the original size, the critical value of the liquid chamber pressure required at this time is also the largest, expressed as: In the formula, R b ——Original blank radius; (A2) Blank holding force During the liquid filling deep drawing process, when the liquid overflows, the liquid pressure p in the concave mold cavity cr Basically the same as the liquid pressure near the die radius, the blank holder force is ideally balanced with the force of the liquid in the flange area. However, the blank holder force is complex and changeable during the forming process, so it is estimated based on the main parameters of the equipment; its expression is as follows: Where, F——blanking force (N); S f ——The pressing surface area of ​​the sheet (mm 2 ); (A3) Radius of corner of blank holder The larger the fillet radius of the blank holder, the greater the pre-expansion height of the sheet metal, and the larger the pre-expansion area; the use of a larger fillet radius of the blank holder helps to improve the stress state of the blank after pre-expansion and the wall thickness distribution after forming; according to engineering experience and literature, the value range of the fillet radius of the blank holder is 10-100mm; The step B combines engineering experience and references to obtain quality indicators; the process parameter optimization problem has two objective functions: (B1) Maximum thickness reduction rate The sheet thickness will be reduced during the forming process. If the thinning is too large, the sheet will break. Select the maximum thickness thinning rate θ max To characterize the severity of sheet metal cracking, the smaller the maximum thickness reduction rate, the better; in industry, it is generally required that the maximum thickness reduction rate is less than 20% for qualified parts; the definition of the maximum thickness reduction rate is as follows: Where, t0——original thickness of sheet; t min ——Minimum thickness of sheet metal after forming; (B2) Vertical displacement of flange area U2 When the sheet is wrinkled, the blank holder will be lifted up, so the degree of wrinkling is indicated by measuring the vertical displacement U2 of the flange area. In industry, it is generally required that the wrinkling height is less than 1.2 times the sheet thickness. To minimize the wrinkling degree of the molded part, U2 max The smaller the better; The step C determines the mathematical model of the optimization problem according to the actual process; in the liquid filling deep drawing forming of the tank bottom, the above optimization goals are taken into account to optimize the quality of the formed part; the pre-expansion pressure p0, the liquid chamber pressure p cr , blank holder force F, blank holder radius r h These process parameters are used to construct a nonlinear optimization model: Where y1, y2 are objective functions, X is the design variable, X = [p0, p cr ,F,r h ];X L , X U are the upper and lower limits of the design variables; The step D obtains the required process parameter sample points by the optimal Latin hypercube sampling method, designs the simulation experiment and the step E uses the Kriging interpolation method to establish an approximate model between the process parameters and the quality index; the Kriging interpolation regards the response of the simulation model as a realization of a random process including a regression term; the method is applied to actual work, and the response surface is expressed in an explicit form according to the optimization variable.

2. The multi-objective optimization method for process parameters of rocket tank bottom liquid filling deep drawing as claimed in claim 1 is characterized by: In step F, the multi-objective optimization model is solved by using the NSGA-III algorithm to obtain process parameters that meet the requirements; the reliability of the results is verified by comparing with the optimization results of the PSO algorithm and combining simulation experiments; and the required process parameters are selected according to different quality requirements.

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