Method and system for optimizing weak parts of double-spindle numerical control lathe

Abstract

The invention relates to the technical field of double-spindle numerical control lathes, and discloses a weak component optimization method and system for a double-spindle numerical control lathe, and the method comprises the steps: determining a to-be-optimized weak component of the double-spindle numerical control lathe; carrying out topological optimization and rule design to obtain a primary optimization weak component; performing sensitivity analysis on the size parameter of the primary optimization weak part, and screening out a to-be-optimized size parameter; constructing an experimental design to obtain a data set of multiple groups of to-be-optimized size parameter-objective functions; constructing a radial basis function neural network to obtain an approximate model reflecting the relationship between the size parameter to be optimized and the target function; optimizing the approximate model by adopting a non-inferior sorting genetic algorithm to obtain a Pareto solution set; and calculating the quality index parameters of each solution set in the Pareto solution set, selecting the solution set corresponding to the maximum quality index parameters as the optimal solution set, and taking the to-be-optimized size parameter corresponding to the optimal solution set as the optimized size. The weak component identification accuracy is high, and the optimization efficiency and effect are good.

Description

Technical Field

[0001] The invention relates to the technical field of dual-spindle CNC lathes, and in particular to a method and system for optimizing weak parts of dual-spindle CNC lathes. Background Art

[0002] In recent years, with the continuous development of society, the production and application scale of dual-spindle lathes has gradually expanded, and their processing quality has gradually improved, and the requirements for the stability and safety of lathe processing have become higher and higher. Compared with single-spindle lathes, dual-spindle lathes have higher requirements for production precision control. However, the overall work efficiency of dual-spindle lathes in practical applications is not high, and the lathe stability is insufficient, which seriously restricts the development of the machinery manufacturing industry. In the existing technology, there are deficiencies in the search and optimization of weak parts in the whole machine. At present, the search for weak parts only uses theoretical analysis or preliminary finite element analysis. The former not only has a large workload, but also has a large error with the actual situation, which is easy to cause misjudgment. The latter is easy to cause misjudgment of parts at stress concentration points, and the identification effect is not obvious; at the same time, the existing technology has a large workload for the optimization of weak parts, and the deviation of the results of size optimization is large, which lacks practical reference significance.

[0003] Therefore, there is an urgent need for a method and system for optimizing weak components of a dual-spindle CNC lathe to solve the above problems. Summary of the invention

[0004] Based on the above, the purpose of the present invention is to provide a method and system for optimizing weak parts of a dual-spindle CNC lathe, which has high accuracy in identifying weak parts and better optimization efficiency and effect.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for optimizing weak parts of a dual-spindle CNC lathe, comprising:

[0007] Establishing a finite element model of a dual-spindle CNC lathe, performing modal simulation analysis and calculating a modal mass distribution matrix, and determining weak components of the dual-spindle CNC lathe to be optimized;

[0008] Determine the objective function of the weak component to be optimized, perform topology optimization on the weak component to be optimized based on the SIMP variable density method, and perform rule design on the weak component to be optimized after topology optimization according to the manufacturing process to obtain an optimized weak component;

[0009] Using finite element software to perform sensitivity analysis on the dimensional parameters of the primary optimized weak components, and screening out the dimensional parameters to be optimized whose influence on the objective function reaches a preset degree;

[0010] According to the preset design range of the size parameter to be optimized, a central composite design method is used in the finite element software to construct an experimental design to obtain multiple sets of data sets of size parameters to be optimized-objective functions;

[0011] Constructing a radial basis function neural network, and using the data set to train the radial basis function neural network to obtain an approximate model reflecting the relationship between the size parameter to be optimized and the objective function;

[0012] A non-inferior sorting genetic algorithm is used to optimize the approximate model to obtain a Pareto solution set;

[0013] The quality index parameters of each solution set in the Pareto solution set are calculated, and the solution set corresponding to the maximum quality index parameter is selected as the optimal solution set, and the size parameter to be optimized corresponding to the optimal solution set is the optimized size.

[0014] As a preferred solution for the optimization method of weak parts of a dual-spindle CNC lathe, the modal mass distribution matrix is:

[0015]

[0016] In the formula, m i - modal mass of the i-th mode of the twin-spindle CNC lathe, [M] - mass matrix of the twin-spindle CNC lathe, {φ ki}-vibration shape components of each component corresponding to the i-th order modal vector of the dual-spindle CNC lathe, {φ ki}=[φ 1i ,φ 2i ,…,φ ni ], where n is the total number of components of the dual-spindle CNC lathe, k is the component number of the dual-spindle CNC lathe, k = 1, 2, 3,,,, n;

[0017] Assume that the mass of the dual-spindle CNC lathe is evenly distributed, that is, M1 = M2 = ... = M n =M a ,but:

[0018]

[0019] According to the finite element modal simulation, the maximum normalized vibration coefficient φ of each component of the dual-spindle CNC lathe described in the finite element modal vibration shape is obtained ki , φ of each mode 2 ki The largest corresponding component is the weak component to be optimized.

[0020] As a preferred solution of a method for optimizing weak parts of a dual-spindle CNC lathe, topological optimization of the weak parts to be optimized based on the SIMP variable density method includes:

[0021] Determine the initial structural shape, constraint conditions and objective function according to the weak component to be optimized;

[0022] According to the preset optimization target of the objective function, topological optimization is performed on the weak component to be optimized by gradually reducing the volume ratio by 20%-50%, and a material retention area and a material removal area are determined;

[0023] The material removal area is regularly designed in combination with the manufacturing process to obtain the primary optimized weak component.

[0024] As a preferred solution for the weak component optimization method of a dual-spindle CNC lathe, the central composite design method is used in the finite element software to construct an experimental design, including:

[0025] Establishing a finite element model of the primary optimized weak component;

[0026] Select central composite design test points: select a central point; 2 m-ζ cubic points, where m is the number of dimensional parameters to be optimized, ξ is the factorial coefficient, which is determined according to the dimensional parameters to be optimized; 2m axial points;

[0027] Determine the value range of the size parameter to be optimized, and obtain multiple groups of test sample points, where the test sample points are the size parameter to be optimized within the value range;

[0028] The response value corresponding to the once-optimized weak component finite element model under each group of the test sample points is calculated, and the response value is the objective function value corresponding to the once-optimized weak component finite element model under the size parameter to be optimized, thereby obtaining multiple sets of data sets of size parameters to be optimized-objective function.

[0029] As a preferred solution of a dual-spindle CNC lathe weak component optimization method, the radial basis neural network includes an input layer, a hidden layer and an output layer. The input of the input layer is x, X = [x1, x2, ..., x m ] T , where x m is the mth size parameter to be optimized, the action function of the neurons in the hidden layer is a Gaussian function, and the hidden layer neuron node is c, c = [c1, c2, ..., c d ], where d is the number of neuron nodes in the hidden layer, the action function of the neurons in the output layer is a linear function, and the output of the output layer is Y, Y = [y1, y2, ..., y e ], where y e is the e-th objective function, the weight vector ω between the hidden layer and the output layer is [ω 11 ,ω12 ,…,ω de ], so:

[0030]

[0031] Where: x m - input vector; c i - the center value of the i-th Gaussian function; δ- loss function, where b i - the width of the i-th Gaussian function; ω de -The weights of the single hidden layer in the output layer.

[0032] As a preferred solution of the weak component optimization method of a dual-spindle CNC lathe, it also includes evaluating the accuracy of the approximate model:

[0033] Calculate the coefficient of determination R 2 , root mean square error RMSE, mean absolute error MAE, mean relative error MRE:

[0034]

[0035] In the formula, q-total number of data sets; y i -The objective function value in the dataset; - The predicted objective function value of the approximate model;

[0036] If R 2 If the values ​​of , RMSE, MAE, and MRE are within the preset range, it is judged that the approximate model has achieved the preset accuracy.

[0037] As a preferred solution for a dual-spindle CNC lathe weak component optimization method, the non-inferior sorting genetic algorithm is used to optimize the approximate model, including:

[0038] Randomly initialize the population P0 and sort P0 to get the parent population P t , give the parent population P t Each individual in is assigned a serial number;

[0039] Using the binary tournament method in the population P t Extract individuals, perform crossover and mutation operations at the same time, and obtain the offspring population Q t ;

[0040] The population P t and Q t Combining to generate a new population R t =P t +Q t ;

[0041] Using R tTo perform non-domination, by estimating the crowding degree between individuals, N individuals are extracted according to the elite strategy to form a new generation of parent population P t+1 ;

[0042] Repeat steps 2 to 4 until the iteration reaches the termination condition.

[0043] As a preferred solution for the weak component optimization method of a dual-spindle CNC lathe, the quality index parameters of each solution set in the Pareto solution set are calculated as follows:

[0044] The number of solution sets that need to be ranked is recorded as s, and the original data matrix Y is obtained:

[0045]

[0046] where y ij - the raw value of the jth indicator of the ith object;

[0047] Normalize Y to get G:

[0048]

[0049] in,

[0050] For ij Perform weighted processing to obtain the weighted normative matrix Z:

[0051]

[0052] Among them, z ij =y i ' j ×ε(i=1,2···,n;j=1,2···,m), ε-weighting coefficient of the j-th indicator;

[0053] Sort the indicators to be evaluated, and use Z as the optimal and worst solutions respectively. + , Z - If we express it, we can get the optimal and worst values:

[0054]

[0055] Calculate the distance between the best and worst values ​​and different evaluation objects:

[0056]

[0057] Calculate the quality parameter indicators of each evaluation object:

[0058]

[0059] C iThe value of C is between [0, 1]. i The larger the value of , the better the corresponding evaluation object.

[0060] As a preferred solution of a dual-spindle CNC lathe weak component optimization method, after obtaining the optimized dimensions, the optimization effect is also verified:

[0061] Re-establishing a finite element model according to the optimized dimensions, and performing finite element analysis to obtain an objective function corresponding to the optimized dimensions;

[0062] The optimization rate is calculated based on the objective function corresponding to the optimized size and the objective function corresponding to the size before optimization.

[0063] A dual-spindle CNC lathe weak component optimization system, comprising:

[0064] Weak component analysis module, used to determine the weak components of dual-spindle CNC lathes;

[0065] A topology optimization module, used for performing topology optimization on the weak component;

[0066] The size optimization module is used to optimize the size of the weak component after topology optimization.

[0067] The beneficial effects of the present invention are:

[0068] The invention provides a method for optimizing weak parts of a dual-spindle CNC lathe. The method determines the weak parts to be optimized of the dual-spindle CNC lathe through modal simulation analysis and calculation of modal mass distribution matrix, and the weak parts identification accuracy is high. The appearance and shape of the weak parts to be optimized can be optimized first through topology optimization, and the structure of the once-optimized weak parts can be determined. The sensitivity analysis facilitates the subsequent targeted optimization of the dimensions to be optimized that affect the objective function, reduces the optimization workload, and improves the optimization efficiency. The central composite design method is then used to construct an experimental design, and multiple groups of data sets for training radial basis function neural networks can be obtained, which is convenient, fast, and efficient. The training also obtains an approximate model, which can reflect the mapping relationship between the dimension parameters to be optimized and the objective function, and the optimal solution set of the objective function can be found in the mapping space between the optimized dimension parameters and the objective function through a non-inferior sorting genetic algorithm. At the same time, by introducing a good or bad index parameter as a decision result of the optimal solution set of the objective function, the optimal solution set is finally obtained, thereby obtaining the optimized dimension, realizing the final optimization of the weak parts of the dual-spindle CNC lathe, and the obtained optimization result is relatively objective and has practical reference significance.

[0069] The present invention also provides a dual-spindle CNC lathe weak component optimization system, which includes a weak component analysis module, a topology optimization module and a size optimization module. By optimizing the weak components of the dual-spindle CNC lathe, the stability of the entire machine, the parts production stability and the processing efficiency can be effectively improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the contents of the embodiments of the present invention and these drawings without paying any creative work.

[0071] Figure 1 The process of the weak component optimization method of the dual-spindle CNC lathe provided by the embodiment of the present invention is Figure 1 ;

[0072] Figure 2 It is a structural schematic diagram of a dual-spindle CNC lathe provided by an embodiment of the present invention;

[0073] Figure 3 is a modal mass distribution diagram of the first six modes of a dual-spindle CNC lathe provided in an example of an embodiment of the present invention;

[0074] Figure 4 is a function image corresponding to different penalty factors provided by an embodiment of the present invention;

[0075] Figure 5 is a schematic structural diagram of an optimized front tool holder provided by an embodiment of the present invention;

[0076] Figure 6 is a diagram of a tool holder topology optimization process provided by an embodiment of the present invention;

[0077] Figure 7 is a schematic structural diagram of an optimized tool holder provided in an embodiment of the present invention;

[0078] Figure 8 is a cross-sectional view of an optimized tool holder provided in an embodiment of the present invention;

[0079] Fig. 9 is a schematic diagram of sensitivity analysis results provided by an embodiment of the present invention;

[0080] Fig.10 is a schematic diagram of central composite design test points provided by an embodiment of the present invention;

[0081] Fig.11 is a schematic diagram of the structure of a radial basis neural network provided by an embodiment of the present invention;

[0082] Fig.12 is a schematic diagram of a fitting space of an approximate model provided by an embodiment of the present invention;

[0083] Fig.13 is a flow chart of the NSGA-II algorithm provided by an embodiment of the present invention;

[0084] Fig.14 The process of the weak component optimization method of the dual-spindle CNC lathe provided by the embodiment of the present invention is Figure 2 .

[0085] In the figure:

[0086] 10. Double spindle CNC lathe; 1', optimized front tool holder; 1. Optimized rear tool holder. DETAILED DESCRIPTION

[0087] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention. It should also be noted that, for ease of description, only parts related to the present invention, rather than all structures, are shown in the accompanying drawings.

[0088] like Figures 1 to 14 As shown, this embodiment provides a method for optimizing weak parts of a dual-spindle CNC lathe, and the method for optimizing weak parts of a dual-spindle CNC lathe includes the following steps:

[0089] S100: Establish a finite element model of a dual-spindle CNC lathe, perform modal simulation analysis and calculate the modal mass distribution matrix, and determine the weak parts of the dual-spindle CNC lathe to be optimized;

[0090] In the weak link identification process of the dual-spindle CNC lathe, the weak links of the main components of the dual-spindle CNC lathe are mainly identified, and the finite element modal analysis of the dual-spindle CNC lathe under different processing conditions is performed to determine the weak components to be optimized of the dual-spindle CNC lathe, where different processing conditions include different processing steps of the two spindles or different assembly processing tools. Step S100 specifically includes:

[0091] S101: Establish a geometric model of a dual-spindle CNC lathe; illustratively, the three-dimensional model of the dual-spindle CNC lathe is as follows: Figure 2As shown in the figure, the three-dimensional model structure is complex. When establishing the geometric model of the dual-spindle CNC lathe, the dual-spindle CNC lathe is greatly simplified to reduce the difficulty of subsequent meshing and reduce the occupation of computer resources, thereby reducing the simulation operation time and improving efficiency under the premise of ensuring the accuracy of the finite element analysis results. That is, under the premise of ensuring that its structural mechanical properties are not affected, too many small parts and geometric features are deleted before simulation, for example: delete small parts that do not affect the overall frame structure of the dual-spindle CNC lathe, such as bolts, nuts, pins, rivets, cables, thin plates, etc.; fill in smaller holes; modify smaller fillets and chamfers to right angles; cut or fill smaller step surfaces, and straighten small taper slopes and small curvature surfaces.

[0092] S102: Import the geometric model into the finite element analysis software ANSYS to perform pre-processing for finite element analysis: including defining the material properties of the components, defining the stiffness and damping of the contact surface, and dividing the finite element mesh; applying constraints and cutting forces; adding constraints such as gravity acceleration, fixed support, and no sliding friction to the entire machine, and adding cutting forces to the main and secondary axes (i.e., dual spindles) and the tool holder.

[0093] S103: Perform modal simulation analysis and calculate the modal mass distribution matrix, and identify the weak links of the dual-spindle CNC lathe according to the vibration mode and modal mass distribution curve of the dual-spindle CNC lathe modal simulation. Under specific working conditions, some links or components of the dual-spindle CNC lathe may vibrate strongly. The parameters of the vibration energy of each component of the dual-spindle CNC lathe can be represented by the modal mass distribution matrix. When the modal mass distribution of a certain order of the dual-spindle CNC lathe mode is uneven and some mutations occur, the component with concentrated modal mass distribution is the weak link of the dual-spindle CNC lathe, that is, the component with the largest modal mass at this time is the corresponding weak link of the dual-spindle CNC lathe under this order of mode.

[0094] For example, under the working condition that the main spindle is used for rough turning and the sub-spindle is used for fine turning, the modal frequency and vibration shape of the dual-spindle CNC lathe are studied by finite element analysis. The modal analysis of the whole machine is performed, and its modal frequency is shown in the following table. As shown in Table 1, the modal frequency and vibration shape of the dual-spindle CNC lathe:

[0095] Table 1 Modal frequency and vibration type of dual-spindle CNC lathe

[0096]

[0097]

[0098] Under the above working conditions, the bottom-order vibration mode diagram is simulated, and the modal mass distribution of the dual-spindle CNC lathe can be preliminarily judged from the color diagram of the modal vibration mode, that is, the weak links of the dual-spindle CNC lathe can be preliminarily seen according to the bottom-order vibration mode diagram. For example, after modal simulation analysis, it is known that the weak links of the dual-spindle CNC lathe are concentrated in the tool holder, so the tool holder is the weak component to be optimized.

[0099] In order to further determine the weakest link of the dual-spindle CNC lathe, it is also necessary to identify and analyze the weak links of the main moving parts of the dual-spindle CNC lathe according to the modal mass distribution matrix method:

[0100] The dynamic equation of free vibration of the dual-spindle CNC lathe is as follows:

[0101]

[0102] Where: n-dimensional column vector {x} represents the acceleration vector, velocity vector and displacement vector in the dual-spindle CNC lathe respectively; n-order matrices [M], [C], [K] represent the mass matrix, damping matrix and stiffness matrix in the dual-spindle CNC lathe respectively;

[0103] The characteristic equation corresponding to equation (1) can be expressed as:

[0104]

[0105] Where: i - characteristic root; {φ i}-mode shape vector corresponding to the characteristic root;

[0106] The eigenvector is normalized to obtain the corresponding modal mass. The modal mass of the i-th mode of the system can be expressed as:

[0107]

[0108] In the formula, m i - modal mass of the i-th mode of the twin-spindle CNC lathe, [M] - mass matrix of the twin-spindle CNC lathe, {φ ki}-vibration shape components of each component corresponding to the i-th order modal vector of the dual-spindle CNC lathe, {φ ki}=[φ 1i ,φ 2i ,…,φ ni ], where n is the total number of components of the dual-spindle CNC lathe, k is the component number of the dual-spindle CNC lathe, k = 1, 2, 3,,,, n;

[0109] Assume that the mass of the dual-spindle CNC lathe is evenly distributed, that is, M1=M2=…=M n =Ma ,but:

[0110]

[0111] From formula (4), we can know that the i-th order modal mass m of the dual-spindle CNC lathe is i The corresponding modal vibration vectors are used to determine the vibration component {φ ki}Sum of square modal mass M a The product of . The modal mass distribution of this order represents the energy distribution of the corresponding degrees of freedom or corresponding components of the dual-spindle CNC lathe under this order mode. When the modal mass distribution is uneven and some mutations occur, the more concentrated the degrees of freedom or components of the dual-spindle CNC lathe modal mass distribution are, the more likely they are to be the weak links of the dual-spindle CNC lathe under this order mode. Therefore, equation (4) can be written as follows:

[0112]

[0113] Where: ο-overlap multiplication operator;

[0114] The modal vibration shape of a dual-spindle CNC lathe is an inherent property of the dual-spindle CNC lathe structure. The modal mass distribution matrix represents the distribution of the energy of the dual-spindle CNC lathe in each degree of freedom. In the actual machine tool modal analysis, the value of each element in the mass matrix [M] of the machine tool is difficult to obtain, but the mass of each component is evenly distributed. From formula (5), we know that the relative size of the modal mass distribution vector can be obtained by the square of the vibration shape component of each component corresponding to the element of the vector. To express it, the modal mass distribution matrix of the dual-spindle CNC lathe is indirectly obtained, based on which the weak links of the dual-spindle CNC lathe, that is, the weak parts to be optimized, can be determined.

[0115] In this embodiment, the maximum normalized vibration mode coefficient φ of each component of the dual-spindle CNC lathe in the finite element modal vibration mode is obtained according to the finite element modal simulation. ki , from formula (5), we can see that the The component with the largest corresponding value is the weak component to be optimized. For example, as shown in Table 2, the maximum normalized vibration mode coefficient φ of each component of the first six modes of the dual-spindle CNC lathe is ki The square of:

[0116] Table 2 The components of the first six modes of the dual-spindle CNC lathe

[0117]

[0118] Refer to Figure 3 , it can be seen that the tool holder of the dual-spindle CNC lathe is the weak link in the first six modes of the dual-spindle CNC lathe, that is, the tool holder is the weak component to be optimized.

[0119] This embodiment uses a method that combines finite element and modal mass distribution matrix to identify the weak links of the dual-spindle CNC lathe, so that the identification result is more accurate, which solves the technical problem that stress concentration point components are prone to misjudgment when only the finite element image analysis method is used in the prior art, and solves the technical problems that the mass matrix is ​​difficult to obtain and the flexibility of the experimental measurement point location arrangement is poor when only the theoretical modal mass distribution matrix method is used in the prior art.

[0120] S200: determining the objective function of the weak component to be optimized, performing topology optimization on the weak component to be optimized based on the SIMP variable density method, and performing rule design on the weak component to be optimized after topology optimization according to the manufacturing process to obtain an optimized weak component;

[0121] Among them, the objective function is determined according to the weak parts to be optimized. In the multi-objective optimization of the dual-spindle CNC machine tool, frequency avoidance and stiffness improvement are the main goals, and the mass is as small as possible without affecting the first two goals. Frequency avoidance refers to the frequency that causes the resonance of the parts, that is, increasing the first-order frequency of the parts, and stiffness refers to the ability of the parts to resist deformation, that is, reducing the deformation of the parts. Exemplarily, the tool holder is the weak part to be optimized, and the first-order natural frequency f, maximum static deformation δ and mass m of the tool holder are used as the optimization objective function. When the tool holder is topologically optimized, the optimization purpose is to increase the first-order natural frequency, reduce the maximum static deformation and reduce the mass of the tool holder, that is, the optimized tool holder can have the highest possible first-order natural frequency, the lowest possible maximum static deformation and mass.

[0122] The topology optimization of the weak parts to be optimized based on the SIMP variable density method specifically includes:

[0123] S201: determining an initial structural shape, constraint conditions and objective function according to the weak component to be optimized;

[0124] S202: According to the preset optimization target of the objective function, topology optimization is performed on the weak component to be optimized to gradually reduce the volume ratio by 20%-50%, and a material retention area and a material removal area are determined;

[0125] For example, the topology optimization of the tool holder structure is carried out, with the maximum value of the first-order natural frequency (F(x)) and the minimum value of the static deformation (G(x)) under mass constraint as the objective function, and the mathematical model is established as shown in the following formula:

[0126]

[0127] Where: R n - Initial structural design area; x i-unit relative density vector, which is a design variable and represents the density value of each unit after discretization; u-the total number of grid units after discretization; w i -The weight of the i-th order objective function; is the maximum and minimum value of the single objective optimization of the i-th order objective function; f i(x) - objective function of the i-th order; v(x) - objective function of the volume, where v i - optimized unit volume; v min 、v max -Maximum and minimum values ​​of volume single-objective optimization; V * -Total volume constraint of the structure; To avoid the occurrence of singular stiffness matrix, x min As a small quantity, we can let x min =0.001, x i For [x min ,1] between consecutive values.

[0128] In order to make as many unit density values ​​as possible in the optimization results near [0, 1], the SIMP interpolation model is introduced to plan and convert the discrete density values ​​between 0 and 1 into continuous density values ​​between 0 and 1. At the same time, with the reference of the interpolation function, the units with intermediate density are penalized, which can avoid the appearance of intermediate density values, making the optimization process smoother and enabling the low-density units to be filtered out more quickly in subsequent material filtering.

[0129] The penalty form of the SIMP interpolation model for the intermediate density function is as follows:

[0130]

[0131] Where:

[0132] E i - elastic modulus of the ith element;

[0133] ρ i - relative density of the ith unit;

[0134] E0 - elastic modulus when the unit relative density is 1;

[0135] E min -Elastic modulus when the unit relative density is 0; assigned value u is the number of units in the structure.

[0136] When the unit relative density ρ i = 1, the optimized unit behaves as a solid unit. i = 0, the optimized unit appears as an empty hole. By changing the penalty factor, the density area can be reduced. The penalty model corresponding to different penalty factors is plotted as follows: Figure 4 As shown in the figure, as the penalty factor p increases, the elastic modulus of the intermediate density moves closer to the two ends. When p increases further, more intermediate density units move closer to the value of 0, and the optimization model is difficult to converge at this time. Therefore, in order to better punish the intermediate density and avoid the occurrence of singular values, the penalty factor is selected to be 3. At this time, the intermediate density of most of the model is small, and the result of topological optimization is also clearer. Of course, in other embodiments, the penalty factor can also be selected to be 4 or 5, etc., which is specifically set according to actual needs.

[0137] By gradually increasing the amount of structural volume reduction, the material utilization of the dual-spindle CNC lathe can be maximized, while ensuring that objective functions such as overall stiffness and natural frequency can be maximized or minimized under different constraints. For example, in this implementation, the deformation can be minimized and the natural frequency can be maximized under the constraint of mass.

[0138] S203: Regularly design the material removal area in combination with the manufacturing process to obtain an optimized weak component.

[0139] For example, reference Figure 5 and Figure 6 After the topology optimization of the tool holder, the middle part of the tool holder is a non-important part that has little effect on the objective function and can be used as the main optimization range. Combined with the manufacturing process, such as the casting process, the main optimization range determined above is redesigned so that the redesigned tool holder can be manufactured by casting, for example Figure 7 As shown, in the topology optimization of the tool holder, more material is reduced in the middle part. After considering the processing technology, a cavity structure is adopted for the middle part.

[0140] By using topology optimization to optimize the shape and form of the weak component, the optimized weak component obtained after optimization has good physical and mechanical properties and uses less material than the weak component to be optimized.

[0141] S300: using finite element software to perform sensitivity analysis on the dimensional parameters of the primary optimized weak components, and screening out the dimensional parameters to be optimized whose influence on the objective function reaches a preset degree;

[0142] The structure of the tool holder after topology optimization includes several design dimensions including wall thickness, bottom pouring port, and internal cavity size, but some dimensions have no effect on the objective function. Finite element software is used to perform sensitivity analysis on the dimensional parameters of the weak components optimized at one time, which can distinguish between important and non-important dimensional parameters that have a greater or lesser impact on the objective function, so as to facilitate further optimization of important dimensional parameters, reduce subsequent workload, and improve optimization efficiency.

[0143] Specifically, the sensitivity analysis of the design dimensions is performed in the finite element analysis software ANSYS:

[0144] S301: Establish a geometric model of optimized weak components and perform finite element analysis pre-processing: including defining component material properties, applying constraints, etc.

[0145] S302: setting sensitivity parameters, the input parameters include the position and size of the bottom pouring port, the internal wall thickness, the internal cavity size, the position and thickness of the reinforcing ribs, and the output parameters include the objective function y, such as the first-order natural frequency y1 of the tool holder, the maximum static deformation y2 and the mass y3, y = {y1, y2, y3};

[0146] S303: Perform structural simulation analysis and calculation to obtain the correlation between each input parameter and each output parameter, and determine important dimensional parameters according to the correlation between each input parameter and each output parameter;

[0147] For example, Fig. 9 As shown in Figure 2, the wall thickness, bottom pouring port, internal casting hole and other dimensions of the tool holder have no significant effect on the first-order natural frequency, maximum static deformation and mass of the tool holder. The size of the internal cavity (such as Figure 8 The four dimensional parameters x1, x2, x3, x4 of the internal cavity are taken as important dimensional parameters, that is, the dimensional parameters x to be optimized, x={x1, x2, x3, x4}.

[0148] The dimensional parameters to be optimized are obtained through sensitivity analysis, which facilitates the subsequent direct optimization of the dimensional parameters to be optimized, so that the weak links after subsequent optimization have better physical and mechanical properties, saving optimization workload and improving optimization efficiency.

[0149] S400: constructing an experimental design using a central composite design method in a finite element software according to a preset design range of the size parameter to be optimized, and obtaining a plurality of data sets of the size parameter to be optimized-objective function;

[0150] Among them, the preset design range of the dimensional parameters to be optimized is set according to the design requirements and the actual casting requirements. For example, as shown in Table 3, the preset design range of the dimensional parameters to be optimized, that is, the optimization range of the dimensional parameters to be optimized is as follows:

[0151] Table 3 Optimization range of the size to be optimized

[0152]

[0153] After determining the design range of the dimensional parameters to be optimized, construct the CCD experimental design data in ANSYS:

[0154] S401: Establishing a finite element model of a primary optimized weak component;

[0155] S402: Select central composite design test point: Select a central point; 2 m-ζ cubic points, where m is the number of dimensional parameters to be optimized, ξ is the factorial coefficient, which is determined according to the dimensional parameters to be optimized; 2m axial points;

[0156] The central composite design test point consists of three parts, cubic point, axial point and center point:

[0157] Center point: Fig. 9 The center point O in the figure is the design center, and there is one center point;

[0158] Cubic point: Fig. 9 When there are m design variables, that is, m size parameters to be optimized, there are 2 m- ζ cubic points;

[0159] Axial point: Fig. 9 When there are m design variables, there are 2m axial points. Usually, the axial point is in the extended area, outside the range of the design variables. The distance from the axial point to point O is α, and the value of α is usually 1 to

[0160] S403: Determine a value range of the size parameter to be optimized, and obtain multiple groups of test sample points, where the test sample points are the size parameters to be optimized within the value range;

[0161] S404: Calculate and obtain the response value corresponding to the finite element model of the once-optimized weak component under each group of test sample points, where the response value is the objective function value corresponding to the finite element model of the once-optimized weak component under the size parameter to be optimized, thereby obtaining multiple sets of data sets of the size parameter to be optimized-objective function.

[0162] After determining the value range of the dimensional parameters to be optimized, the test platform automatically generates multiple groups of test sample points within the value range, that is, each parameter in the dimensional parameters to be optimized takes a value at a preset step length as a test sample point, and each test sample point is used as an input variable for a finite element simulation analysis of a weak component optimization. The finite element analyzes and calculates the objective function under each test sample point in turn, that is, finally obtaining multiple groups of dimensional parameters to be optimized-objective function data sets. For example, as shown in Table 4 below:

[0163] Table 4 Dataset of size parameters to be optimized-objective function

[0164]

[0165] S500: constructing a radial basis neural network, and using the data set to train the radial basis neural network to obtain an approximate model reflecting the relationship between the size parameter to be optimized and the objective function;

[0166] After obtaining multiple sets of data sets of size parameters-objective functions to be optimized by constructing an experimental design, the data sets can be used as training data for subsequent training of radial basis function neural networks. Specifically, the following steps are included:

[0167] S501: Randomly select several groups in the data set as training sets and several other groups as test sets. For example, the data volume of the training set: the test set is 7:3 or 8:2, etc., which is not limited here;

[0168] S502: Fig.10 As shown, the constructed radial basis neural network includes an input layer, a hidden layer and an output layer. The input of the input layer is x, X = [x1, x2, ..., x m ] T , where x m is the mth size parameter to be optimized, the action function of the neurons in the hidden layer is a Gaussian function, and the hidden layer neuron node is c, c = [c1, c2, ..., c d ], where d is the number of neuron nodes in the hidden layer, the action function of the neurons in the output layer is a linear function, and the output of the output layer is Y, Y = [y1, y2, ..., y e ], where y e is the e-th objective function, the weight vector ω between the hidden layer and the output layer is [ω 11 ,ω 12 ,...,ω de ], so:

[0169]

[0170] Where: x m - input vector; c i - the center value of the i-th Gaussian function; δ- loss function, where b i - the width of the i-th Gaussian function; ω de -The weights of the single hidden layer in the output layer.

[0171] Radial basis function neural network (RBF) has strong nonlinear fitting ability, can map complex linear relationships, has the advantages of fast learning speed and the ability to overcome local minimum values.

[0172] S503: Input the training set into the radial basis neural network for training, and use the test set to test the trained radial basis neural network. During the training process, iterative calculations are continuously performed to finally obtain ω de ,The approximate model reflects the relationship between the size parameter to be optimized and the objective function;

[0173] In order to evaluate the fitting accuracy of the approximate model, it also includes:

[0174] S504: Calculate the coefficient of determination R 2 , root mean square error RMSE, mean absolute error MAE, mean relative error MRE:

[0175]

[0176]

[0177] In the formula, q-total number of data sets; y i -The objective function value in the dataset; - The predicted objective function value of the approximate model;

[0178] If R 2 If the values ​​of RMSE, MAE, and MRE are within the preset range, the approximate model is judged to have reached the preset accuracy. For example, R 2 If the R is above 0.95, the RMSE is below 0.1, the MAE is below 0.1, and the MRE is below 0.1, the fitting accuracy of the approximate model reaches the preset accuracy. 2 , RMSE, MAE, and MRE do not all need to reach the preset range. If three of them reach the preset range, it can be judged that the fitting accuracy of the approximate model reaches the preset accuracy.

[0179] After the approximate model is obtained through training, the approximate model reflects the approximate relationship between the parameters to be optimized and the objective function, that is, the fitting space between the parameters to be optimized and the objective function within the value range is obtained, such as Fig.11 In this embodiment, as shown. Fig.12 As shown, after obtaining the approximate model, the following steps are performed:

[0180] S600: Use the non-inferior sorting genetic algorithm (NSGA-II) to optimize the approximate model and obtain the Pareto solution set;

[0181] Step S600 specifically includes:

[0182] S601: Randomly initialize population P0 and sort P0 to obtain parent population P t , give the parent population P t Each individual in is assigned a serial number;

[0183] S602: Use the binary tournament method in the parent population P t Extract individuals, perform crossover and mutation operations at the same time, and obtain the offspring population Q t ;

[0184] S603: Set the population P t and Q t Combining to generate a new population R t =P t +Q t ;

[0185] S604: Using R t To perform non-domination, by estimating the crowding degree between individuals, N individuals are extracted according to the elite strategy to form a new generation of parent population P t+1 ;

[0186] S605: Loop steps S602 to S604 until the iteration reaches the termination condition.

[0187] A brief description of the above steps: After randomly generating the initial population P0, sort the individuals in the initial population P0 to obtain the parent population P t , then the parent population P t Genetically generated offspring population Q t , the offspring population Q t and the parent population P t The new population R generated by the merger t ; By performing non-dominated calculations on the new population R t The Pareto rank of each individual in the population is divided into Pareto levels according to the size of the Pareto rank, and the crowding degree between the individuals is estimated, and the individuals with the lowest rank are placed in the new generation of parent population P first. t+1 Until this generation is full of the given population, the new generation of parent population P is placed in the order of ranking from large to small according to the degree of crowding. t+1 In; by the new generation of parent population P t+1 Genetically generate a new generation of offspring population Q t+1 , and repeat until the termination condition is reached, such as the population generation number reaches the set generation number. In this way, a Pareto solution set with a better fitting space can be obtained.

[0188] In this embodiment, after obtaining the approximate model, Matlab is used for programming, the approximate model obtained above is called, and the objective function is optimized based on the approximate model. For example, the objective function is optimized to be the maximum first-order natural frequency, the minimum static deformation, and the minimum mass. The code of the main loop of the NSGA-II algorithm is as follows:

[0189]

[0190] That is, in the approximate model Fig.11 The optimal objective function solution set is found in the fitting space shown in the figure to obtain the solution space, that is, the Pareto solution set is obtained by using the genetic algorithm. The Pareto solution set includes multiple objective function solution sets, and the objective function values ​​in each objective function solution set are similar. In order to continue to find the optimal solution set in the Pareto solution set, the following steps are performed:

[0191] S700: Calculate the quality index parameters of each solution set in the Pareto solution set, select the solution set corresponding to the maximum quality index parameter as the optimal solution set, and the size parameter to be optimized corresponding to the optimal solution set as the optimized size.

[0192] Step S700 specifically includes:

[0193] S701: The number of solution sets that need to be ranked is recorded as s, and the original data matrix Y is obtained:

[0194]

[0195] where y ij -The original value of the jth index of the i-th object, that is, the jth index in the i-th solution set;

[0196] S702: Normalize Y to obtain G:

[0197]

[0198] in,

[0199] S703: Yes ij Perform weighted processing to obtain the weighted normative matrix Z:

[0200]

[0201] Among them, z ij =y ij '×ε(i=1,2,...,s;j-1,2,...,m),ε-weighting coefficient of the jth index;

[0202] S704: Sort the indicators to be evaluated, and the best and worst solutions are represented by Z + , Z - If we express it, we can get the optimal and worst values:

[0203]

[0204] S705: Calculate the distances between the best and worst values ​​and different evaluation objects:

[0205]

[0206] S706: Calculate the quality parameter index of each evaluation object:

[0207]

[0208] C i The value of C is between [0, 1]. i The larger the value of , the better the corresponding evaluation object.

[0209] Through the above steps, we can get the quality parameter index C of each solution set. i , poor parameter index C i The evaluation object corresponding to the maximum, that is, the corresponding solution set is the optimal solution set, and the size parameter to be optimized corresponding to the optimal solution set can be obtained, and the size parameter to be optimized is the optimized size.

[0210] For example, as shown in Table 5, among the 100 solution sets, the quality parameter index corresponding to each group is calculated, among which the quality parameter index of the 67th group is the largest, that is, the 67th group is the optimal solution set:

[0211] Table 5 Pareto solution set quality index parameters

[0212]

[0213]

[0214] The optimization size corresponding to the 67th optimal solution set is:

[0215] Table 6 Optimized dimensions of tool holder

[0216]

[0217] After obtaining the Pareto solution set through the NSGA-Ⅱ algorithm, the quality index parameters are introduced as the decision-making results to obtain the optimal solution, and finally the optimized size is obtained to complete the optimization of the weak parts of the dual-spindle CNC lathe.

[0218] like Fig.13 As shown, S800: after obtaining the optimized size, the optimization effect is also verified:

[0219] S801: re-establishing a finite element model according to the optimized size, and performing finite element analysis to obtain an objective function corresponding to the optimized size;

[0220] In order to combine the actual processing technology, the optimized dimensions obtained above are rounded and re-modeled and calculated so that the calculated objective function is closer to the actual value.

[0221] S802: Calculate the optimization rate according to the objective function corresponding to the size after optimization and the objective function corresponding to the size before optimization.

[0222] By calculating the optimization rate, the effect of optimization can be intuitively known and the effectiveness of optimization can be verified. If the optimization is verified to be effective, the final optimized size is obtained, thereby obtaining the optimized structure of the weak component. If the optimization is verified to be invalid or the optimization effect is not good, then return to step S600, use the non-inferior sorting genetic algorithm to re-optimize the approximate model, and then continue to step S700 to find the optimal solution set of the Pareto solution set obtained by re-optimization.

[0223] For example, under the optimized dimensions of the above example, the comparison between the objective function calculated by remodeling the tool holder and the objective function before optimization is shown in Table 7 below:

[0224] Table 7 Comparison of objective functions before and after tool holder optimization

[0225]

[0226] It can be seen from the above table that after the tool holder is optimized, the first-order natural frequency increases from 381.33Hz to 508.98Hz, an increase of 36.33%, the maximum deformation decreases from 0.0028mm to 0.0017mm, a decrease of 39.28%, and the mass is reduced by 17.13% on the original basis. The optimization effect is significant.

[0227] In this embodiment, the weak parts to be optimized of the dual-spindle CNC lathe are determined by modal simulation analysis and calculation of the modal mass distribution matrix, and the weak parts identification accuracy is high; the appearance and shape of the weak parts to be optimized can be optimized first by topology optimization, and the structure of the weak parts to be optimized can be determined; sensitivity analysis facilitates the subsequent targeted optimization of the dimensions to be optimized that affect the objective function, reduces the optimization workload, and improves the optimization efficiency; and then the central composite design method is used to construct an experimental design to obtain multiple groups of data sets for training radial basis neural networks, which is convenient, fast and efficient; an approximate model is obtained through training, which can reflect the mapping relationship between the dimension parameters to be optimized and the objective function, and the optimal solution set of the objective function can be found in the mapping space between the optimized dimension parameters and the objective function through a non-inferior sorting genetic algorithm. At the same time, by introducing the good and bad index parameters as the decision result of the optimal solution set of the objective function, the optimal solution set is finally obtained, thereby obtaining the optimized dimension, and realizing the final optimization of the weak parts of the dual-spindle CNC lathe. The obtained optimization results are relatively objective and have practical reference significance.

[0228] This embodiment also provides a dual-spindle CNC lathe weak component optimization system, which includes a weak component analysis module, a topology optimization module and a size optimization module. The weak component analysis module is used to determine the weak components of the dual-spindle CNC lathe to implement the above step S100; the topology optimization module is used to perform topology optimization on the weak components to implement the above step S200; the size optimization module is used to perform size optimization on the weak components after topology optimization to implement the above steps S300 to S700. By optimizing the weak components of the dual-spindle CNC lathe, the stability of the whole machine, the stability of parts production and the processing efficiency can be effectively improved.

[0229] Note that the above are only preferred embodiments of the present invention and the technical principles used. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in more detail through the above embodiments, the present invention is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A method for optimizing weak parts of a dual-spindle CNC lathe, characterized in that: include: Establishing a finite element model of a dual-spindle CNC lathe, performing modal simulation analysis and calculating a modal mass distribution matrix, and determining weak components of the dual-spindle CNC lathe to be optimized; Determine the objective function of the weak component to be optimized, perform topology optimization on the weak component to be optimized based on the SIMP variable density method, and perform regular design on the weak component to be optimized after topology optimization according to the manufacturing process to obtain an optimized weak component; Using finite element software to perform sensitivity analysis on the dimensional parameters of the primary optimized weak components, and screening out the dimensional parameters to be optimized whose influence on the objective function reaches a preset degree; According to the preset design range of the size parameter to be optimized, a central composite design method is used in the finite element software to construct an experimental design to obtain multiple sets of data sets of size parameters to be optimized-objective functions; Constructing a radial basis function neural network, and using the data set to train the radial basis function neural network to obtain an approximate model reflecting the relationship between the size parameter to be optimized and the objective function; A non-inferior sorting genetic algorithm is used to optimize the approximate model to obtain a Pareto solution set; The quality index parameters of each solution set in the Pareto solution set are calculated, and the solution set corresponding to the maximum quality index parameter is selected as the optimal solution set, and the size parameter to be optimized corresponding to the optimal solution set is the optimized size.

2. The method for optimizing weak parts of a dual-spindle CNC lathe according to claim 1, characterized in that: Modal mass distribution matrix: In the formula, m i - modal mass of the i-th mode of the twin-spindle CNC lathe, [M] - mass matrix of the twin-spindle CNC lathe, {φ ki }-vibration shape components of each component corresponding to the i-th order modal vector of the dual-spindle CNC lathe, {φ ki }=[φ 1i ,φ 2i ,…,φ ni ], where n is the total number of components of the dual-spindle CNC lathe, k is the component number of the dual-spindle CNC lathe, k = 1, 2, 3,,,, n; Assume that the mass of the dual-spindle CNC lathe is evenly distributed, that is, M1 = M2 = ... = M n =M a ,but: According to the finite element modal simulation, the maximum normalized vibration coefficient φ of each component of the dual-spindle CNC lathe described in the finite element modal vibration shape is obtained ki , φ of each mode 2 ki The largest corresponding component is the weak component to be optimized.

3. The method for optimizing weak parts of a dual-spindle CNC lathe according to claim 1, characterized in that: The topology optimization of the weak component to be optimized based on the SIMP variable density method includes: Determine the initial structural shape, constraint conditions and objective function according to the weak component to be optimized; According to the preset optimization target of the objective function, topological optimization is performed on the weak component to be optimized by gradually reducing the volume ratio by 20%-50%, and a material retention area and a material removal area are determined; The material removal area is regularly designed in combination with the manufacturing process to obtain the primary optimized weak component.

4. The method for optimizing weak parts of a dual-spindle CNC lathe according to claim 1, characterized in that: The central composite design method is used in the finite element software to construct the experimental design including: Establishing a finite element model of the primary optimized weak component; Select central composite design test points: select a central point; 2 m-ζ cubic points, where m is the number of dimensional parameters to be optimized, ξ is the factorial coefficient, which is determined according to the dimensional parameters to be optimized; 2m axial points; Determine the value range of the size parameter to be optimized, and obtain multiple groups of test sample points, where the test sample points are the size parameter to be optimized within the value range; The response value corresponding to the once-optimized weak component finite element model under each group of the test sample points is calculated, and the response value is the objective function value corresponding to the once-optimized weak component finite element model under the size parameter to be optimized, thereby obtaining multiple sets of data sets of size parameters to be optimized-objective function.

5. The method for optimizing weak parts of a dual-spindle CNC lathe according to claim 1, characterized in that: The radial basis neural network comprises an input layer, a hidden layer and an output layer. The input of the input layer is x, X=[x1, x2, ..., x m ] T , where x m is the mth size parameter to be optimized, the action function of the neurons in the hidden layer is a Gaussian function, and the hidden layer neuron node is c, c = [c1, c2, ..., c d ], where d is the number of neuron nodes in the hidden layer, the action function of the neurons in the output layer is a linear function, and the output of the output layer is Y, Y = [y1, y2, ..., y e ], where y e is the e-th objective function, the weight vector ω between the hidden layer and the output layer is [ω 11 ,ω 12 ,…,ω de ], so: Where: x m - input vector; c i - the center value of the i-th Gaussian function; δ- loss function, where b i - the width of the i-th Gaussian function; ω de -The weights of the single hidden layer in the output layer.

6. The method for optimizing weak parts of a dual-spindle CNC lathe according to claim 1, characterized in that: It also includes the accuracy evaluation of the approximate model: Calculate the coefficient of determination R 2 , root mean square error RMSE, mean absolute error MAE, mean relative error MRE: Where, q-total number of data sets; y i -The objective function value in the dataset; - The predicted objective function value of the approximate model; If R 2 If the values ​​of , RMSE, MAE, and MRE are within the preset range, it is judged that the approximate model has achieved the preset accuracy.

7. The method for optimizing weak parts of a dual-spindle CNC lathe according to claim 1, characterized in that: The optimization of the approximate model using a non-inferior sorting genetic algorithm includes: Randomly initialize the population P0 and sort P0 to get the parent population P t , give the parent population P t Each individual in is given a serial number; Using the binary tournament method in the population P t Extract individuals, perform crossover and mutation operations at the same time, and obtain the offspring population Q t ; The population P t and Q t Combining to generate a new population R t =P t +Q t ; Using R t To perform non-domination, by estimating the crowding degree between individuals, N individuals are extracted according to the elite strategy to form a new generation of parent population P t+1 ; Repeat steps 2 to 4 until the iteration reaches the termination condition.

8. The method for optimizing weak parts of a dual-spindle CNC lathe according to claim 1, characterized in that: Calculating the quality index parameters of each solution set in the Pareto solution set includes: The number of solution sets that need to be ranked is recorded as s, and the original data matrix Y is obtained: where y ij - the raw value of the jth indicator of the ith object; Normalize Y to get G: in, For ij Perform weighted processing to obtain the weighted normative matrix Z: Among them, z ij =y ij '×ε(i=1,2,...,s;j-1,2,...,m),ε-weighting coefficient of the jth index; Sort the indicators to be evaluated, and use Z as the optimal and worst solutions respectively. + , Z - If we express it, we can get the optimal and worst values: Calculate the distance between the best and worst values ​​and different evaluation objects: Calculate the quality parameter indicators of each evaluation object: C i The value of C is between [0, 1]. i The larger the value of is, the better the corresponding evaluation object is.

9. The method for optimizing weak parts of a dual-spindle CNC lathe according to claim 1, characterized in that: After obtaining the optimized size, the optimization effect is also verified: Re-establishing a finite element model according to the optimized size, and performing finite element analysis to obtain an objective function corresponding to the optimized size; The optimization rate is calculated based on the objective function corresponding to the optimized size and the objective function corresponding to the size before optimization.

10. A dual-spindle CNC lathe weak component optimization system, characterized in that: include: Weak component analysis module, used to determine the weak components of dual-spindle CNC lathes; A topology optimization module, used for performing topology optimization on the weak component; The size optimization module is used to optimize the size of the weak component after topology optimization.

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