Multi-condition response speed reducer box variable density topological optimization method

Abstract

The invention relates to the technical field of mechanical engineering, in particular to a multi-condition response speed reducer box variable density topological optimization method which comprises the following steps: S1, constructing a three-dimensional speed reducer box finite element model; s2, obtaining a plurality of stress distribution nephograms of the speed reducer box body; s3, carrying out topological optimization on the plurality of stress distribution nephograms; s4, the wall thickness of the speed reducer box body is adjusted, and the three-dimensional speed reducer box body finite element model is updated; and S5, verifying the updated finite element model of the three-dimensional speed reducer box body, determining that the speed reducer box body variable density topological optimization is successful when the verification is passed, and otherwise, repeating the step S3 and the step S4. According to the method, stress distribution under different installation modes and working conditions is considered, it is ensured that the design scheme can keep good performance in various environments, and meanwhile the design can better adapt to complex working conditions through the comprehensive stress distribution cloud atlas.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical engineering, and in particular to a variable density topology optimization method for a reducer housing with multi-conditional response. Background Art

[0002] The reducer is a common mechanical device, widely used in industries such as industry and transportation. Among them, the reducer housing is one of the important components of the reducer. It plays the role of support, sealing and shock absorption, and is the basis for ensuring the stability and safety of the entire operating system. When the reducer is working, the torque is transmitted between the shafts inside the reducer, and a large force is exerted on the housing. Therefore, the housing itself needs to have sufficient rigidity and strength, which leads to the fact that the structural design of the reducer housing often blindly increases the thickness of the housing wall to achieve the purpose of strengthening the structural strength and rigidity. This not only causes unnecessary waste of materials, but also increases the manufacturing cost of the housing. At the same time, the overall weight of the reducer is ignored, which increases transportation costs and industrial energy consumption. In addition, with the rapid development of my country's industry, the development of reducers towards lightweight has gradually become a trend. Therefore, it is a considerable challenge in research and development design to ensure or further improve the quality of the reducer while ensuring that the housing meets the strength, rigidity and noise standards.

[0003] In recent years, topology optimization finite element simulation has gradually been introduced into the design of lightweight engineering structures, becoming an important means to reduce production costs and energy consumption. Among them, variable density topology optimization is a density-based topology optimization method, which optimizes the topological structure by defining any point in the design area as a material or void with different densities. The advantages of the variable density topology optimization method are its good resolution and flexibility. By adjusting the initial material density distribution, the final topological structure can be adjusted, thereby reasonably allocating the material usage while ensuring the stiffness and strength of the structure. In addition, this method can also consider the influence of different constraints and material properties on the optimization results, in order to obtain a design solution that better meets actual needs.

[0004] At present, the research on variable density topology optimization often only performs variable density topology optimization on a certain stress mode of the product. However, in order to adapt to a wide range of working environments and effectively reduce costs, the reducer industry often has a "one box for multiple uses" situation, that is, the same box can be installed in different ways for different occasions, such as flange installation or foot installation, and it is also possible that a box has different foot installation methods. Therefore, traditional variable density topology optimization requires separate force analysis and optimization for each installation method, which undoubtedly increases the complexity and workload of the design. Secondly, the existing variable density topology optimization method cannot comprehensively consider all stress conditions of the product at the same time, which may lead to inaccurate optimization results and affect the performance and service life of the product. Summary of the invention

[0005] The purpose of the present invention is to provide a variable density topology optimization method for a reducer housing with multi-condition response, so as to solve the problem that the existing variable density topology optimization method proposed in the above background technology cannot comprehensively consider all stress conditions of the product at the same time, resulting in inaccurate optimization results and affecting the performance and service life of the product.

[0006] The technical solution of the present invention is: a multi-condition response speed reducer housing variable density topology optimization method, the speed reducer housing variable density topology optimization method specifically comprises the following steps:

[0007] S1: According to the specific working conditions of the reducer, a three-dimensional finite element model of the reducer housing is constructed;

[0008] S2: obtaining a plurality of stress distribution cloud diagrams of the reducer housing through the three-dimensional reducer housing finite element model;

[0009] S3: setting design variables, objective functions and constraints, and topologically optimizing the plurality of stress distribution cloud maps by a variable density method;

[0010] S4: According to the results obtained after topology optimization, the wall thickness of the reducer housing is adjusted, and the three-dimensional reducer housing finite element model is updated;

[0011] S5: Verify the updated three-dimensional finite element model of the reducer housing. If the verification is passed, the variable density topology optimization of the reducer housing is successful. Otherwise, repeat steps S3 and S4 until the variable density topology optimization of the reducer housing is successful.

[0012] Furthermore, the three-dimensional reducer housing finite element model is constructed as follows:

[0013] S1.1: According to the specific working conditions of the reducer, a three-dimensional reducer housing model is constructed using three-dimensional drawing software;

[0014] S1.2: Import the three-dimensional reducer housing model into the finite element analysis software, construct a three-dimensional reducer housing finite element model, and mesh the three-dimensional reducer housing finite element model, assign material properties, and apply boundary conditions.

[0015] Furthermore, a plurality of stress distribution cloud diagrams of the reducer housing are obtained, as follows:

[0016] S2.1: Create a GUI plug-in, and obtain user input parameters through the GUI plug-in;

[0017] S2.2: Analyze each installation mode of the three-dimensional reducer housing finite element model according to the user input parameters, and obtain corresponding stress distribution cloud map data from each analysis process;

[0018] S2.3: Obtain a stress distribution cloud map corresponding to each installation method according to the stress distribution cloud map data;

[0019] S2.4: Integrate the stress distribution cloud map corresponding to each installation method to obtain a comprehensive stress distribution cloud map.

[0020] Furthermore, the stress distribution cloud diagrams corresponding to each installation method are integrated as follows:

[0021] S2.4.1: Assign weights to the stress distribution contours for each installation method based on the importance or frequency of each installation method.

[0022] S2.4.2: Extract stress distribution data from each analysis task;

[0023] S2.4.3: Align all the stress distribution data, and perform weighted average calculation on the aligned stress distribution data to obtain a comprehensive stress distribution cloud map;

[0024] S2.4.4: Output the comprehensive stress distribution cloud map as an image or data file.

[0025] Furthermore, a plurality of the stress distribution cloud maps are topologically optimized as follows:

[0026] S3.1: The integrated stress distribution of the design area is used as the design variable, the variable density topology optimization of the reducer housing is used as the minimum mass of the housing as the objective function, and the maximum stress of the reducer housing structure is less than the allowable stress value as the constraint condition;

[0027] S3.2: Establish a topology optimization model based on the design area;

[0028] S3.3: topologically optimize the stress distribution cloud map through the topology optimization model.

[0029] Furthermore, the topology optimization model is established as follows:

[0030] S3.2.1: Divide the design area into units and use an equivalent density in each unit as a design variable;

[0031] S3.2.2: Establish an optimization model, specifically:

[0032] Findρ=(ρ1,ρ2...,ρ N )T

[0033] Among them: Findρ is to find the design variable, ρ1 is the equivalent density of the first unit, ρ2 is the equivalent density of the second unit, ρ N is the equivalent density of the Nth unit;

[0034] S3.2.3: According to the optimization model, the quality of the objective function model is minimized, specifically:

[0035]

[0036] Where: minM(ρ) is the minimization of the objective function model quality, N is the total number of units that can be divided into design areas, E e (ρ e ) is the elastic modulus of the e-th unit, ρ e is the equivalent density of the e-th unit, is the transpose of the displacement vector of the e-th unit, k0 is the stiffness matrix, u e is the displacement vector of the e-th unit.

[0037] Furthermore, the three-dimensional reducer housing finite element model is updated as follows:

[0038] S4.1: According to the results obtained after the topology optimization, determine the area where the wall thickness of the three-dimensional reducer housing needs to be adjusted;

[0039] S4.2: adjusting the wall thickness of the reducer housing according to the area to be adjusted in terms of wall thickness;

[0040] S4.3: Repeat steps S1 to S3 according to the adjusted and updated reducer housing to update the three-dimensional reducer housing finite element model.

[0041] Furthermore, the updated three-dimensional reducer housing finite element model is verified as follows:

[0042] S5.1: Analyze the updated three-dimensional reducer housing finite element model using finite element analysis software;

[0043] S5.2: Based on the analysis results, determine whether the updated three-dimensional reducer housing finite element model meets the initially set objective function and constraint conditions. When the initially set objective function and constraint conditions are met, the variable density topology optimization of the reducer housing is successful. Otherwise, repeat steps S3 and S4 until the updated three-dimensional reducer housing finite element model meets the initially set objective function and constraint conditions.

[0044] Furthermore, the analysis results of the updated three-dimensional reducer housing finite element model include but are not limited to stress distribution and deformation.

[0045] Furthermore, the judgment conditions for whether the variable density topology of the reducer housing is successfully optimized also include:

[0046] Whether the maximum stress of the updated three-dimensional reducer housing finite element model is less than the allowable stress value.

[0047] The present invention improves the variable density topology optimization method of the reducer housing that provides multi-conditional response, and has the following improvements and advantages compared with the prior art:

[0048] Firstly, the present invention ensures that the design can maintain good performance in a variety of environments by considering the stress distribution under different installation methods and working conditions. At the same time, by integrating the stress distribution cloud maps under different working conditions to form a comprehensive stress distribution cloud map, the design can better adapt to complex working conditions.

[0049] Second, the present invention optimizes the housing with the minimum mass as the goal, thereby helping to reduce the weight of the reducer housing, reduce material costs and transportation costs, and at the same time, through accurate analysis of stress distribution, can reduce the material of unnecessary parts, thereby further reducing the overall weight;

[0050] Thirdly, the present invention sets the maximum stress of the structure to be less than the allowable stress value as a constraint condition, thereby ensuring that the optimized design meets the safety standards. Meanwhile, by adjusting the position and shape of the reinforcing ribs, the local stress distribution of the structure is improved, thereby enhancing the overall stability of the structure.

[0051] Fourthly, the present invention uses a parametric design method to make the design process more flexible and can quickly adjust the design scheme. At the same time, it realizes automated finite element analysis by creating a GUI plug-in and writing a script program, which greatly improves the speed of design and analysis.

[0052] Fifthly, the present invention discovers potential problems in advance through simulation analysis, reduces the number of times physical prototypes are made, reduces costs, and simultaneously reduces waste by precisely controlling the distribution of materials, thereby reducing raw material costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The present invention will be further explained below in conjunction with the accompanying drawings and embodiments:

[0054] Figure 1 It is a schematic flow chart of the variable density topology optimization method of the reducer housing of the present invention;

[0055] Figure 2 It is a schematic diagram of the installation foot position of the reducer housing of the present invention;

[0056] Figure 3 It is a stress distribution cloud diagram of the reducer housing before the installation foot 1 of the reducer housing of the present invention is optimized;

[0057] Figure 4 It is a stress distribution cloud diagram of the reducer housing after the installation foot 1 of the reducer housing of the present invention is optimized;

[0058] Figure 5 It is a stress distribution cloud diagram of the reducer housing before the installation foot 2 of the reducer housing is optimized;

[0059] Figure 6 It is a stress distribution cloud diagram of the reducer housing after the installation foot 2 of the reducer housing is optimized. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] It should be noted that, in the description of the present invention, the terms "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside" and "outside" etc. indicating directions or positional relationships are based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore should not be understood as a limitation on the present invention.

[0062] Furthermore, it should be understood that for the sake of ease of description, the sizes of the various components shown in the drawings are not drawn according to actual proportions. For example, the thickness or width of certain layers may be exaggerated relative to other layers.

[0063] It should be noted that like reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined or described in one drawing, it will not require further detailed discussion and description in the description of the subsequent drawings.

[0064] refer to Figure 1-Figure 6 This embodiment provides a multi-condition response reducer housing variable density topology optimization method, and the reducer housing variable density topology optimization method specifically includes the following steps:

[0065] Step S1: According to the specific working conditions of the reducer, a three-dimensional reducer housing model is constructed using three-dimensional drawing software, and the constructed three-dimensional reducer housing model is stored and saved so as to be subsequently imported into the finite element analysis software to construct a three-dimensional reducer housing finite element model. The details are as follows:

[0066] Step S1.1: According to the specific working conditions of the reducer, a three-dimensional reducer housing model is constructed by three-dimensional drawing software. It is worth noting that the three-dimensional reducer housing model constructed in this embodiment is stored in STP format when it is stored, so as to facilitate subsequent import into finite element analysis software for operation.

[0067] Specifically, according to the working conditions of the reducer, including but not limited to the input power, input speed, motor weight, motor length and other parameters of the reducer, and according to the software functions of the 3D drawing software, the 3D drawing software to be used is determined, such as Cero, CATIA, etc. In this embodiment, the 3D drawing software used is set to Cero.

[0068] That is to say, the 3D reducer housing model is constructed by using the 3D drawing software Cero. It is worth noting that the constructed 3D reducer housing model should include all necessary components, such as installation feet, reinforcement ribs, etc., and consider the sealing and mechanical strength of the housing. At the same time, the model needs to be refined to ensure that the model meets the requirements of actual working conditions, such as adjusting the wall thickness of the reducer housing according to actual working conditions.

[0069] Step S1.2: Import the three-dimensional reducer housing model constructed in step S1.1 into the finite element analysis software in STP format, construct a three-dimensional reducer housing finite element model, and mesh the three-dimensional reducer housing finite element model, assign material properties, and apply boundary conditions.

[0070] Specifically, in this embodiment, the three-dimensional reducer housing model in STP format is opened by finite element analysis software (such as ABAQUS).

[0071] Furthermore, when meshing the model, a suitable mesh type should be selected, such as a second-order tetrahedral mesh. It is worth noting that the balance between computational accuracy and efficiency should be considered when meshing, and local refinement can be performed in stress concentration areas.

[0072] Furthermore, when assigning material properties and applying boundary conditions to the model, the corresponding material properties can be set in the three-dimensional reducer housing finite element model according to the physical properties of the reducer housing material (such as Young's modulus, Poisson's ratio, etc.). Similarly, according to the actual working conditions of the reducer, the boundary conditions of the model, such as fixed ends, loads, etc., are set to ensure that the boundary conditions accurately reflect the actual working conditions of the reducer housing. Specifically, refer to Table 1 below, which is a reference table for specific parameters.

[0073] Table 1

[0074] Material Young's modulus (MPa) Poisson's ratio <![CDATA[Density (Ton / mm 3 )]]> HT250 103000 0.26 7.2E-09 Input power (kW) Input speed (rpm) Motor weight (kg) Motor length (mm) 30 1470 376 960

[0075] Step S2: Obtain multiple stress distribution cloud maps of the reducer housing through the three-dimensional finite element model of the reducer housing obtained in step S1.2. In other words, a script program that can be executed in the finite element analysis software is written in a programming language. The program can submit calculations at the same time and obtain multiple stress distribution cloud maps of the same housing, and then integrate the multiple stress distribution cloud maps into a stress distribution cloud map under multiple installation methods. The details are as follows:

[0076] Step S2.1: Write a GUI plug-in program in Python, so that the created GUI plug-in can allow the user to input necessary parameters and start the analysis. In other words, the user input parameters can be obtained through the created GUI plug-in. It is worth noting that in this embodiment, the parameters input by the user are collected through the GUI plug-in, including but not limited to the grid size, the installation method list, the load value, the boundary condition type, and other possible analysis parameters.

[0077] Step S2.2: According to the user input parameters, each installation mode of the three-dimensional reducer housing finite element model is analyzed, and the corresponding stress distribution cloud map data is obtained from each analysis process. In other words, the three-dimensional reducer housing finite element model is loaded from the stored STP file, and the loaded three-dimensional reducer housing finite element model is imported into the finite element analysis software ABAQUS.

[0078] Specifically, after the three-dimensional reducer housing finite element model is imported into the finite element analysis software ABAQUS, the meshing, material property assignment and boundary conditions mentioned in step S1.2 will be performed. It is worth noting that in the process of meshing, material property assignment and boundary condition application mentioned in step S1.2, each installation method will be analyzed. In other words, an independent analysis task is submitted for each installation method, and the job is submitted using the Python interface in the finite element analysis software ABAQUS, and the analysis is waited for completion. Furthermore, while waiting for analysis, the corresponding stress distribution cloud map data is extracted from each analysis task.

[0079] Step S2.3: Obtain the stress distribution cloud map corresponding to each installation method according to the stress distribution cloud map data obtained in step S2.2. In other words, each installation method will generate a stress distribution cloud map.

[0080] Step S2.4: Integrate the stress distribution cloud maps corresponding to each installation method generated in step S2.3 to obtain a comprehensive stress distribution cloud map. In other words, the stress distribution cloud maps under multiple installation methods are integrated into a comprehensive stress distribution cloud map, and in this embodiment, the integration method of the stress distribution cloud maps under multiple installation methods can be based on weighted average or other mathematical methods.

[0081] Specifically, the process of integrating stress distribution cloud maps under multiple installation methods is as follows:

[0082] Step S2.4.1: Determine the weight. That is, assign a corresponding weight to each stress distribution cloud diagram according to the importance or frequency of each installation method.

[0083] Step S2.4.2: Data extraction. That is, extract stress distribution data from each analysis task.

[0084] Step S2.4.3: Data alignment and integration calculation. That is, ensure that the data of all stress distribution cloud maps are aligned for subsequent integration. Further, perform weighted averaging or other mathematical operations on all stress distribution cloud maps according to the weights determined in step S2.4.1 to obtain a comprehensive stress distribution cloud map.

[0085] Step S2.4.4: Output the results. That is, output the comprehensive stress distribution cloud map as a visual image or data file.

[0086] Step S3: Set the design variables, objective function and constraints, and use the variable density method to perform topological optimization on the multiple stress distribution cloud maps output in step S2.4.4. The details are as follows:

[0087] Step S3.1: Taking the integrated stress distribution of the design area as the design variable, the variable density topology of the reducer housing is optimized to the minimum mass of the housing, and the maximum stress of the reducer housing structure is less than the allowable stress value.

[0088] Specifically, in the process of setting the design variables, the integrated stress distribution of the design area is used as the design variable. That is, the entire design area is divided into multiple small units, and each unit has a design variable representing its density. The density variable determines whether the unit exists in the final design.

[0089] In the process of setting the objective function, the objective function of the variable density topology optimization of the reducer housing is usually the minimum mass of the housing. This means that we need to find a design that makes the mass of the housing as small as possible while satisfying all constraints.

[0090] In the process of setting constraints, the maximum stress of the structure is less than the allowable stress value, that is, in any case, the designed stress cannot exceed the maximum stress that the material can withstand. At the same time, the weak stress areas are thickened or the design of the reinforcement ribs is changed, and the areas with abundant stress are thinned. In other words, the sealing of the reducer housing needs to be ensured during the iteration process.

[0091] Step S3.2: Establish a topology optimization model based on the design area. The details are as follows:

[0092] Step S3.2.1: Divide the design area and use an equivalent density in each divided unit as a design variable. That is, divide the design area into N units, and each unit has an equivalent density as a design variable.

[0093] Step S3.2.2: Establishing an optimization model, which includes the process of finding design variables. That is, the optimization model in this embodiment is specifically:

[0094] Findρ=(ρ1,ρ2...,ρ N ) T

[0095] Among them: Findρ is to find the design variable, ρ1 is the equivalent density of the first unit, ρ2 is the equivalent density of the second unit, ρ N is the equivalent density of the Nth unit.

[0096] Step S3.2.3: According to the optimization model in step S3.2.2, the quality of the objective function model is minimized, specifically:

[0097]

[0098] Where: minM(ρ) is the minimization of the objective function model quality, N is the total number of units that can be divided into design areas, E e (ρ e ) is the elastic modulus of the e-th unit, ρ e is the equivalent density of the e-th unit, is the transpose of the displacement vector of the e-th unit, k0 is the stiffness matrix, u e is the displacement vector of the e-th unit.

[0099] Step S3.3: Perform topological optimization on the stress distribution cloud map through the topological optimization model in step S3.2, that is, perform topological optimization calculation using finite element analysis software ABAQUS or other finite element analysis software, and iteratively adjust the design variables to achieve the optimal solution.

[0100] Step S4: According to the results obtained after topology optimization in step S3.3, adjust the wall thickness of the reducer housing and update the three-dimensional reducer housing finite element model. The details are as follows:

[0101] Step S4.1: Based on the results obtained after topology optimization in step S3.3, especially the integrated stress distribution cloud map, key areas where wall thickness needs to be adjusted are identified. In other words, through the stress distribution cloud map, it is determined which areas of the reducer housing need to increase wall thickness to enhance structural strength, and which areas of the reducer housing need to reduce wall thickness to reduce weight.

[0102] Step S4.2: Adjust the wall thickness in the reducer housing according to the area to be adjusted in the wall thickness determined in step S4.1. Specifically, open the three-dimensional reducer housing finite element model through Creo or other three-dimensional drawing software, and adjust the wall thickness through the parametric design function in the software, that is, for the area that needs to be thickened, increase the wall thickness. For the area that can be thinned, reduce the wall thickness. It is worth noting that in the process of adjusting the wall thickness, it is necessary to ensure a smooth transition between the areas where the wall thickness changes to avoid stress concentration caused by sudden changes. At the same time, it is also necessary to ensure that the adjusted wall thickness will not interfere with other components in the reducer housing.

[0103] Step S4.3: According to the speed reducer housing adjusted and updated in step S4.2, steps S1 to S3 are repeated to update the three-dimensional speed reducer housing finite element model. In other words, the geometry of the speed reducer housing is updated in the three-dimensional drawing software to ensure that the model can accurately reflect the adjustment of the wall thickness. At the same time, the updated three-dimensional model is exported to the STP format and imported into the finite element analysis software for further updating.

[0104] Step S5: Verify the updated three-dimensional reducer housing finite element model obtained in step S4.3. If the verification is passed, the variable density topology optimization of the reducer housing is successful. Otherwise, repeat steps S3 and S4. The details are as follows:

[0105] Step S5.1: Analyze the updated three-dimensional reducer housing finite element model using finite element analysis software ABAQUS, where the analysis results include but are not limited to key indicators such as stress distribution and deformation.

[0106] Step S5.2: Based on the analysis results in step S5.1, determine whether the updated three-dimensional reducer housing finite element model meets the initially set objective function and constraint conditions, and at the same time check whether the maximum stress of the updated three-dimensional reducer housing finite element model is less than the allowable stress value to ensure whether the design of the reinforcement ribs effectively improves the structural performance.

[0107] When the verification results show that the model meets all the above requirements, the variable density topology optimization of the reducer housing is successful. Otherwise, repeat steps S3 and S4, readjust the position and shape of the reinforcement ribs, and verify again until the updated three-dimensional reducer housing finite element model meets the initially set objective function and constraints.

[0108] refer to Figure 3-Figure 6 It can be seen that Figure 3 This is the stress distribution cloud diagram of the reducer housing before the installation foot 1 is optimized in this embodiment. Figure 4 This is a stress distribution cloud diagram of the reducer housing after the installation foot 1 is optimized in this embodiment. Figure 5 This is the stress distribution cloud diagram of the reducer housing before the installation foot 2 is optimized in this embodiment. Figure 6 This is a stress distribution cloud diagram of the reducer housing after the installation foot 2 is optimized in this embodiment. Figure 3 and Figure 4 It can be seen from the comparison between them that it can help evaluate the effect of the optimization scheme in the installation position of the foot 1. Figure 5 and Figure 6 It can be seen from the comparison between them that it can help evaluate the effect of the optimization solution in the installation position of the base 2.

[0109] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A variable density topology optimization method for a reducer housing with multi-conditional response, characterized in that: The variable density topology optimization method for the reducer housing specifically comprises the following steps: S1: According to the specific working conditions of the reducer, a three-dimensional finite element model of the reducer housing is constructed; S2: obtaining a plurality of stress distribution cloud diagrams of the reducer housing through the three-dimensional reducer housing finite element model; S3: setting design variables, objective functions and constraints, and topologically optimizing the plurality of stress distribution cloud maps by a variable density method; S4: According to the results obtained after topology optimization, the wall thickness of the reducer housing is adjusted, and the three-dimensional reducer housing finite element model is updated; S5: Verify the updated three-dimensional finite element model of the reducer housing. If the verification is passed, the variable density topology optimization of the reducer housing is successful. Otherwise, repeat steps S3 and S4 until the variable density topology optimization of the reducer housing is successful.

2. The variable density topology optimization method for reducer housing with multi-conditional response according to claim 1 is characterized in that: The three-dimensional reducer housing finite element model is constructed as follows: S1.1: According to the specific working conditions of the reducer, a three-dimensional reducer housing model is constructed using three-dimensional drawing software; S1.2: Import the three-dimensional reducer housing model into the finite element analysis software, construct a three-dimensional reducer housing finite element model, and mesh the three-dimensional reducer housing finite element model, assign material properties, and apply boundary conditions.

3. The variable density topology optimization method for reducer housing with multi-conditional response according to claim 1 is characterized in that: Obtain multiple stress distribution cloud diagrams of the reducer housing, as follows: S2.1: Create a GUI plug-in, and obtain user input parameters through the GUI plug-in; S2.2: Analyze each installation mode of the three-dimensional reducer housing finite element model according to the user input parameters, and obtain corresponding stress distribution cloud map data from each analysis process; S2.3: Obtain a stress distribution cloud map corresponding to each installation method according to the stress distribution cloud map data; S2.4: Integrate the stress distribution cloud map corresponding to each installation method to obtain a comprehensive stress distribution cloud map.

4. The variable density topology optimization method for reducer housing with multi-conditional response according to claim 3 is characterized in that: The stress distribution cloud diagrams corresponding to each installation method are integrated as follows: S2.4.1: Assign weights to the stress distribution contours for each installation method based on the importance or frequency of each installation method. S2.4.2: Extract stress distribution data from each analysis task; S2.4.3: Align all the stress distribution data, and perform weighted average calculation on the aligned stress distribution data to obtain a comprehensive stress distribution cloud map; S2.4.4: Output the comprehensive stress distribution cloud map as an image or data file.

5. The variable density topology optimization method for reducer housing with multi-conditional response according to claim 1 is characterized in that: The multiple stress distribution cloud maps are topologically optimized as follows: S3.1: The integrated stress distribution of the design area is used as the design variable, the variable density topology optimization of the reducer housing is used as the minimum mass of the housing as the objective function, and the maximum stress of the reducer housing structure is less than the allowable stress value as the constraint condition; S3.2: Establish a topology optimization model based on the design area; S3.3: topologically optimize the stress distribution cloud map through the topology optimization model.

6. The variable density topology optimization method for reducer housing with multi-conditional response according to claim 5 is characterized in that: The topology optimization model is established as follows: S3.2.1: Divide the design area into units and use an equivalent density in each unit as a design variable; S3.2.2: Establish an optimization model, specifically: Findρ=(ρ1,ρ2......,ρ N ) T Among them: Findρ is to find the design variable, ρ1 is the equivalent density of the first unit, ρ2 is the equivalent density of the second unit, ρ N is the equivalent density of the Nth unit; S3.2.3: According to the optimization model, the quality of the objective function model is minimized, specifically: Where: min M(ρ) is the minimization of the objective function model quality, N is the total number of units that can be divided into design areas, E e (ρ e ) is the elastic modulus of the e-th unit, ρ e is the equivalent density of the e-th unit, is the transpose of the displacement vector of the e-th unit, k0 is the stiffness matrix, u e is the displacement vector of the e-th unit.

7. The variable density topology optimization method for reducer housing with multi-conditional response according to claim 1 is characterized in that: The three-dimensional reducer housing finite element model is updated as follows: S4.1: According to the results obtained after the topology optimization, determine the area where the wall thickness of the three-dimensional reducer housing needs to be adjusted; S4.2: adjusting the wall thickness of the reducer housing according to the area to be adjusted in terms of wall thickness; S4.3: Repeat steps S1 to S3 according to the adjusted and updated reducer housing to update the three-dimensional reducer housing finite element model.

8. The multi-condition response reducer housing variable density topology optimization method according to claim 1 is characterized in that: The updated three-dimensional reducer housing finite element model is verified as follows: S5.1: Analyze the updated three-dimensional reducer housing finite element model using finite element analysis software; S5.2: Based on the analysis results, determine whether the updated three-dimensional reducer housing finite element model meets the initially set objective function and constraint conditions. When the initially set objective function and constraint conditions are met, the variable density topology optimization of the reducer housing is successful. Otherwise, repeat steps S3 and S4 until the updated three-dimensional reducer housing finite element model meets the initially set objective function and constraint conditions.

9. The variable density topology optimization method for reducer housing with multi-conditional response according to claim 8 is characterized in that: The updated analysis results of the three-dimensional reducer housing finite element model include but are not limited to stress distribution and deformation.

10. The variable density topology optimization method for reducer housing with multi-conditional response according to claim 8, characterized in that: The judgment conditions for whether the variable density topology of the reducer housing is successfully optimized also include: Whether the maximum stress of the updated three-dimensional reducer housing finite element model is less than the allowable stress value.

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