Method for achieving hypoid mechanical arm light weight through motion stability model

Abstract

The invention discloses a method for achieving hypoid mechanical arm light weight through a motion stability model, and relates to the field of optimization design of mechanical arm products. Although the lightweight technology research of the mechanical arm has been well developed, the detail knocking at the initial stage of design mainly depends on the engineering experience of designers and finite element analysis software at present, and a unified design standard and evaluation system are lacked. Therefore, the motion stability of the mechanical arm is difficult to accurately predict and control in the optimization design process, so that the actual effect of lightweight design is influenced. According to the method, single evaluation indexes are integrated into double evaluation indexes on the basis of a compromise planning method, different attention degrees on optimization key points can be changed by adjusting weights, and the importance of motion stability and rigidity is fully considered in the lightweight design process; and a reliable technical route and a result evaluation method are provided for realizing light weight of the hypoid mechanical arm.

Description

Technical Field

[0001] The present invention relates to the field of robotics technology, combined with the field of structural design, and aims to optimize the design of the robotic arm to achieve lightweight while maintaining or improving its motion stability and work efficiency. The problem of excessive weight in some traditional industrial robotic arms limits their application in certain specific occasions, such as working in a small space, working continuously for a long time, etc. In addition, excessive weight also leads to problems such as high energy consumption, slow movement speed, and high maintenance cost of the robotic arm, which seriously restricts the further development of robotic arm technology. Lightweight design can not only reduce the weight of the robotic arm, but also improve its movement speed and flexibility, reduce energy consumption and maintenance costs. The research of the present invention is of great significance to achieve precise control of the motion stability of the quasi-hyperbolic robotic arm, reduce the mass of the robotic arm, and improve its work efficiency and accuracy. Background Art

[0002] As an indispensable and important equipment in modern industrial automation, the design and application of robotic arms are constantly evolving to meet the needs and technical challenges of different industries. As a key equipment in modern industrial automation, medical surgery, aerospace and other fields, the improvement of the performance of robotic arms has always been a hot topic of research. Among them, lightweight design is an important means to improve the performance of robotic arms, aiming to reduce the weight of the robotic arms to improve their movement speed, flexibility and adaptability, while reducing energy consumption and maintenance costs.

[0003] In recent years, domestic and foreign scholars and enterprises have been conducting increasingly in-depth research on lightweight technology for robotic arms, aiming to improve the flexibility and adaptability of robotic arms and reduce energy consumption and costs. Domestic research on lightweight technology for robotic arms has made good progress. Domestic research teams and enterprises have invested heavily in technological innovation, such as using high-strength lightweight materials and optimizing structural design to achieve lightweight robotic arms. At the same time, they are also constantly exploring new lightweight methods and technologies, such as using more advanced manufacturing processes and simulation technologies to optimize the design of robotic arms. Lightweight design is also highly dependent on lightweight materials, such as aluminum alloys and carbon fiber composites. However, these materials often have limitations in strength and stiffness, and it is difficult to meet the performance requirements of robotic arms under complex working conditions such as high loads and high speeds. The processing and manufacturing costs of some composite materials are also relatively high, which limits their widespread application. Therefore, the research and development of high-performance lightweight materials and the promotion and application of low-price materials need to be further strengthened.

[0004] Secondly, domestic robotic arms often pay insufficient attention to the importance of motion stability during the lightweight design process, which leads to deviation and jitter in the motion of the initially lightweight robotic arms, affecting their accuracy and work efficiency. Compared with domestic robotic arms, foreign robotic arms pay more attention to maintaining or improving motion stability during the lightweight process. By integrating advanced sensors and control systems, real-time monitoring and adjustment of the motion state of the robotic arms are achieved, but factors such as cost-effectiveness and sustainability still need to be considered to ensure their feasibility and competitiveness in practical applications.

[0005] In addition, the standardization and normalization of robot arm lightweight technology is low, and there is a lack of unified design standards and evaluation systems. Motion stability is one of the important indicators for evaluating the performance of a robot arm. However, the current evaluation methods for the motion stability of a robot arm are mostly based on empirical formulas or experimental data, which lack accuracy and reliability. This makes it difficult to accurately predict and control the motion stability of the robot arm during the lightweight design process, thus affecting the actual effect of the lightweight design.

[0006] In view of the existing shortcomings and limitations of the existing lightweight technology, the present invention proposes a method for lightweighting a quasi-hyperbolic robot arm using a motion stability model (MSM). The importance of motion stability is fully considered in the lightweight design process to achieve a dual improvement in the lightweight and motion stability of the robot arm. Summary of the invention

[0007] The present invention proposes a method for lightweighting a quasi-hyperbolic manipulator using a motion stability model, aiming to achieve accurate prediction and control of the motion stability of the manipulator by introducing the model, thereby realizing efficient and lightweight design of the manipulator.

[0008] 1. Select the basic goal of optimization. In order to meet the efficient and fast design rhythm and cycle, the optimization of the robot arm is often not achieved for a single goal, but is achieved simultaneously after setting multiple goals. For industrial robot arms, current manufacturing companies use the method of increasing efficiency and reducing costs to control costs and increase product profits, so lightweighting is the primary optimization direction. The mathematical model of the single-objective optimization problem is expressed as finding a decision variable vector under the following conditions so that the objective function reaches the extreme value. Specifically for the attribute of weight, the most important objective function is written through the general expression of the optimization problem:

[0009] MinG(x)=g(x)

[0010] Where G(x) represents the objective function of weight; g(x) represents the minimum weight value of the studied component measured by 3D software; x represents the series of dimensions of the studied component that are modified compared to the original model when the minimum weight index is met, x = [x1, x2, …, x n ], x i Represents a dimension that has been changed, and n is the number of dimensions that have been changed.

[0011] 2. Select the first evaluation index. The amplitude of the low-order frequency of the robot arm is usually large. When it is externally excited, it is more likely to produce significant vibration at the low-order frequency. Excessive vibration will affect the accuracy, stability and service life of the robot arm. The natural frequency of the robot arm is a reflection of its structural characteristics. The natural frequency of the low-order mode is usually low and easier to match the frequency of external excitation. When the frequency of the external excitation is close to or consistent with a certain low-order natural frequency of the robot arm, the robot arm will be excited to resonate. The vibration of the robot arm can be represented by the linear combination of the vibration modes of each order, but the low-order vibration mode usually has the greatest impact on the structural vibration. When studying the dynamic response of the robot arm, it is often necessary to pay more attention to its low-order natural frequency and vibration mode vector, which helps to simplify the analysis process. Analyzing the low-order frequency helps to evaluate the vibration of the robot arm when it is externally excited and take corresponding measures to reduce the vibration. Increasing the low-order frequency helps to avoid the robot arm from working at the resonant frequency, thereby protecting the structural safety of the robot arm. Specifically for the attribute of low-order frequency, the first evaluation index is written through the general expression of the optimization problem:

[0012] MaxF(y)=f(y)

[0013] Where F(y) represents the objective function of frequency; f(y) represents the maximum weight value of the first-order natural frequency of the studied component measured by 3D software; y represents the series of dimensions of the studied component that have been modified compared to the original model when the natural frequency is the maximum, y=[y1,y2,…,y n ],y i Represents a dimension that has been changed, and n is the number of dimensions that have been changed.

[0014] 3. Perform a single optimization on the frequency. Perform a single optimization on each evaluation index objective function to obtain its optimal solution when corresponding to a single objective. The purpose of this step is to determine the optimal state of each sub-objective under independent conditions. For frequency, in a multi-degree-of-freedom damping system, the natural frequency and damping characteristics of the system will affect the dynamic response of the system, and the analysis will be more complicated because it involves the system's mass matrix (M), damping matrix (C) and stiffness matrix (K). The natural frequency is usually obtained by solving the characteristic equation of the system. The characteristic equation is expressed by the following determinant:

[0015] |K-ω2 M-2ξωC|=0

[0016] Where ω is the angular frequency vector of the system, and ζ is the damping ratio vector, which represents the damping level of each degree of freedom. In the case of critical damping (ζ=1), the natural frequency of the system will become zero; in the case of overdamping (ζ>1), the system will not vibrate. The above determinant represents an eigenvalue problem, whose solution is the square of the natural angular frequency of the system, and each eigenvalue corresponds to a natural mode (or vibration mode) of the system.

[0017] Solve to get the expression of natural frequency: For a certain mode i, its natural frequency f nature for:

[0018] f nature =(1 / 2π)*sqrt(k sys / m)

[0019] Among them, k sys It represents the stiffness of the system in Newton / meter, which reflects the system's ability to resist deformation. m represents the mass of the system in kilograms. To achieve the increase of natural frequency, it is necessary to increase its stiffness and reduce its mass, which is consistent with the above analysis. sqrt is the square root function.

[0020] 4. Select the second evaluation index. The stiffness of the robot arm directly affects its load capacity. A robot arm with higher stiffness can better resist deformation under the action of external forces, so that it can stably grasp and carry heavier workpieces. It also has a significant impact on motion accuracy. A robot arm with high stiffness can maintain smaller deformation when disturbed by external forces, thereby ensuring higher motion accuracy and positioning accuracy, and is not easily disturbed by external factors, so that it can complete work tasks more accurately. In practical applications, the stiffness and flexibility of the robot arm need to achieve a certain balance. Specifically for the attribute of stiffness, the second evaluation index is written through the general expression of the optimization problem:

[0021] MaxGD(z)=gd(z)

[0022] Where GD(z) represents the objective function of stiffness; gd(z) represents the maximum stiffness value of the studied component measured by 3D software; z represents the series of dimensions of the studied component that are modified compared to the original model when the maximum stiffness index is met, z = [z1, z2, …, z n ],z i Represents a dimension that has been changed, and n is the number of dimensions that have been changed.

[0023] 5. Single optimization of stiffness. In order to achieve computational consistency with the first two optimization goals, the calculation is performed by minimizing the optimization problem, so the flexibility index is used instead of the stiffness index to participate in the calculation. The flexibility r and strength K are usually inversely proportional. That is, the greater the flexibility, the stronger the deformation ability of the material, and the corresponding strength may be lower; on the contrary, the smaller the flexibility, the weaker the deformation ability of the material, and the higher the strength.

[0024] r=1 / K

[0025] For the strength evaluation of the robot arm, to maximize the strength, it can be evaluated by minimizing the flexibility. It is necessary to balance flexibility and strength when designing the structure. Excessive flexibility may cause excessive deformation of the structure in actual use, affecting the safety and functionality of the structure; while excessive strength may make the structure too rigid and difficult to adapt to changes in the external environment.

[0026] The generalized expression for flexibility is:

[0027] r=μL r / i r

[0028] Where μ is the length factor related to the member constraint condition, L r is the length of the rod, i r is the cross-sectional inertia radius. When the structure of the robotic arm being analyzed is completely determined, these three parameters can be determined by direct measurement.

[0029] When special consideration is given to the geometric properties of the material, the bending flexibility of the member is expressed as:

[0030] r=1 / (E*I)*(L j 3 / 3)*(1 / (1-γ 2 )

[0031] Where E is the elastic modulus of the material, I is the moment of inertia of the area, and L j is the length of the rod, and γ is the Poisson's ratio. Therefore, for the single optimization of flexibility r, in order to reduce the flexibility but not change the working range of the whole machine, it is necessary to increase the inertia radius of the section.

[0032] 6. Find a compromise evaluation, that is, to construct a function of the motion stability model (MSM). After determining the two evaluation criteria of increasing the low-order natural frequency and increasing the structural stiffness, the corresponding two single-objective functions need to be constructed into a dual-objective function. The compromise programming method is used to realize the construction of the dual-objective function. The obtained dual-objective function is the motion stability evaluation model function, where F OFIt is a dual objective function. Here, both evaluation indicators are set to minimize the trend, so the minimum value is taken. When the maximum value is required, the expression is changed to maxF in the calculation process. OF For bi-objective optimization and multi-objective optimization, it is necessary to find a common set L of design variables x, y, and z so that F(y) and GD(z) meet the expectations at the same time.

[0033]

[0034] Among them, ω is the weight of flexibility, q is the penalty factor, and r k (L) is the average function of the flexibility value, and is the flexibility extreme value of the kth working condition; f(L) is the average frequency function, f max and f min are the maximum and minimum average frequency values ​​respectively. c is the total number of working conditions, k is the number of the working condition currently being calculated. If only dangerous working conditions are studied, then n c and k are both 1.

[0035] 7. Identify constraints. i (L) and h j (L) represent the inequality constraints and equality constraints on the common set L, respectively, m e and n e Represent the number of inequality constraints and equality constraints respectively.

[0036] stg i (L)≤0,i=1,2,3,…,m e

[0037] h j (L)=0,j=1,2,3,...,n e

[0038] The common set of decision variables L is a vector, that is, L∈R n , these parameters are the independent variables of the optimization problem, and the optimal solution is found by adjusting their values. In the specific calculation, the equations and inequalities in the constraints are expressions related to the processing dimensions of the optimized parts. Because the product needs to be actually processed and manufactured after optimization, the absolute size and relative position of the hole are limited by the processing tools and machine tools, so researchers need to determine the equipment requirements of the product processing manufacturer in advance, and then restrict the dimension chain. Secondly, based on the principle of interchangeability, in order to facilitate assembly and maintenance, the dimensions involved in assembly and connection need to be designed in accordance with the national standard to avoid the second series of values.

[0039] 8. Calculation of initial data. Test the ANSYS Workbench software and establish the original model of the robotic arm. The original model also needs to be simplified, and the parts that are not involved in lightweighting should be "deleted" or "hidden" to save computing resources. The model implements subsequent calculations in the Static Structural module of ANSYS Workbench. Define the material properties in "Engineering Data", divide different types of grids according to the computing resources that the computer can provide, and further determine the overall unit length and grid division method of the model. Set the boundary conditions for the solution, including fixed constraints and loads, etc. The boundary conditions required for the solution come from the joint torque value group of the robotic arm joint in dangerous posture movement. The value group is a matrix, and the length of the matrix is ​​the divided time step. The solution result of the original model is obtained by solving, and the deformation cloud map and equivalent stress cloud map are output.

[0040] 9. Lightweighting. ANSYS software is also used to achieve lightweighting of robotic arm components. Load a topology optimization module in the Workbench platform and associate it with the "Solution" cell of the static analysis (or modal analysis) module. Define the optimization area through "Geometry" and "Named Selection", and auxiliary selection can also be performed by excluding areas. According to design requirements, select the optimization target, such as mass minimization, volume minimization, or global stress (Global Von-Mises Stress) constraints. According to the needs of this study, the optimization target is selected as Mass. Add response constraints, set the retained mass percentage and maximum allowable stress, and start calculating the topology optimization results. Get the topology optimization results and view the retained area of ​​the model.

[0041] 10. Design verification and geometry processing. First, start the verification system. Start the design verification system from the result option of the topology optimization system and establish a data transfer link. Transfer the optimized STL format file and the original CAD model to the geometry module of the verification system, use SpaceClaim to perform geometry correction, and edit and convert the STL file into a solid geometry model. Solve and check whether the optimized geometry model can achieve the design goal. If not, readjust the optimization goal or response constraint until the optimization result meets the requirements. Satisfactory optimization results are expressed by the following inequality:

[0042] g after ≤p g *g before

[0043] f after ≥p f *fbefore

[0044] gd after ≥p gd *gd before

[0045] Among them, the after subscript represents the data after a certain optimization, and the before subscript represents the corresponding data before optimization. i represents the degree of expected optimization, which is defined by the researcher based on the actual situation of the product. The degree of expected optimization of weight, first-order natural frequency, and stiffness can be different, but p is required f With p dg is a number greater than 1, p g It is a number less than 1. Finally, the simulation results of the original model and the optimized model are compared. According to the simulation results and topology optimization results, the original model is adjusted several times to ensure smooth edges and facilitate processing and manufacturing.

[0046] 9. Multi-level evaluation of optimization results. For lightweight output results, use F OF When F OF When the maximum value is obtained, it means that the lightweighting result is unsatisfactory. OF When the minimum value is obtained, it means that the lightweight result can well meet the expected goal. In this process, due to the different research focuses of different scientific research teams, this adjustment can be achieved by changing the weight. If the setting needs to improve the structural stiffness of the robot arm more, the weight can be taken as a larger value to make the objective function focus more on flexibility and stiffness; if the setting needs to maintain the stability of the robot arm more, the weight can be taken as a smaller value to make the objective function focus more on frequency. The focus selection problem in the multi-objective optimization problem can be achieved by adjusting a parameter.

[0047] Therefore, in this method, lightweight is taken as the primary optimization goal, and natural frequency and stiffness are taken as secondary optimization goals and evaluation indicators. During optimization, multiple goals of weight reduction, low-order natural frequency increase, and stiffness increase can be achieved simultaneously. The optimization process is a process that requires repeated verification and feedback. The overall process of this method is as follows: Figure 1 shown. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 A flow chart for the overall calculation of the present invention;

[0049] Figure 2 It is a certain type of hyperbolic robot arm on the market used in the calculation examples of the present invention;

[0050] Figure 3It is a comparison cloud diagram of the main parameters of the robot arm before optimization in the example of the present invention;

[0051] Figure 4 It is the final optimization model of the hyperbolic manipulator in the example of the present invention;

[0052] Figure 5 It is a comparison cloud diagram of the main parameters of the robot arm after optimization in the example of the present invention. DETAILED DESCRIPTION

[0053] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that the relative arrangement of components and steps, numerical expressions and numerical values ​​set forth in these embodiments do not limit the scope of the present invention unless otherwise specifically stated.

[0054] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered as part of the specification.

[0055] A method for realizing lightweighting of a quasi-hyperbolic manipulator using a motion stability model, comprising:

[0056] (1) Determine the main optimization objectives and evaluation indicators based on the actual optimization needs of the product, write out the function in the mathematical format of a single-objective optimization problem, set the optimization direction to the minimum value, and take a negative value for the expression on the right side of the corresponding equation;

[0057] (2) Analyze the physical meaning and practical implications of the evaluation index to obtain the independent variables of the evaluation index and the extreme value of the single optimization;

[0058] (3) Determine the weights of the evaluation indicators and write the expression of the dual objective function through the compromise programming method;

[0059] (4) Check the product manual provided by the manufacturer and list the movement restrictions by field measurement;

[0060] (5) Input joint torque and constraint conditions, divide the grid, and calculate the deformation and equivalent elastic stress of the model;

[0061] (6) Setting the retention threshold and performing topology optimization to obtain a reference lightweight model, and using modeling software to redesign the model so that the edges are smooth and continuous for easy processing;

[0062] (7) Execute the finite element simulation calculation step again to obtain the deformation and equivalent elastic stress of the optimized model, and analyze whether the lightweight simulation calculation results meet expectations;

[0063] (8) According to the F in the MSM model OF The value of is used to evaluate the redesign results, and the weights are adjusted according to different optimization requirements.

[0064] Analyze again whether the theoretical calculation results of lightweighting meet expectations;

[0065] Through this method, the robot arm can be effectively lightweight while performing additional multi-objective optimization, and an intuitive evaluation index model can be used to judge the optimization results.

[0066] The following uses a robot arm currently available on the market as an example to illustrate the specific implementation of the present invention. The robot arm model is CT-HYP-10, and its motion is provided by six rotating joints. It is often used in welding scenes. Its 3D design model and physical machine are as follows: Figure 2 As shown in the figure. The motion constraints of the robot arm come from the range of motion of its joints. The range of motion of the first three joints is ±170°, -160°~90°, -90°~175°, and the range of motion of the last three joints is ±180°. For this product, the degree of expected optimization is defined as p g 、p f 、p gd They are 0.9, 1.1, and 1.1 respectively.

[0067] First, calculate the deformation and equivalent elastic stress cloud diagram of the key components of the robot arm when they are not optimized, such as Figure 3 As shown. The maximum deformation of the upper arm, lower arm and elbow is 0.225mm, 0.038mm and 0.0053mm respectively. The assembly center of the upper arm and lower arm at the flange is obviously deviated from the initial position. The deformation is amplified layer by layer through the rod-shaped components, which will further affect the influence of the subsequent joints on the robot arm posture, greatly reducing the trajectory accuracy of the robot arm end effector and the working stability of the welding equipment. The upper arm and lower arm with larger deformation have better optimization potential, and the lightweight solution is performed for each of them. Topology optimization is performed in Ansys and the model is redesigned according to the simulation results. The MSM model is used to evaluate the optimization results of the robot arm. Here, the focus on frequency and stiffness is set to be equally important, so the weight is taken as 0.5, and the F in the MSM model is calculated. OF Repeat the optimization and evaluation steps to obtain the optimal solution, and modify the model according to the feasibility of manufacturing. The final robot arm model is as follows Figure 4 Calculate the deformation and equivalent elastic stress cloud diagram of the key components in the robot after optimization, as shown in Figure 5As shown, at this time, the deformation of the upper arm and the lower arm of the robot are 0.17225mm and 0.050591mm respectively. The reduction in deformation proves the improvement of stiffness; the first-order natural frequencies of the upper arm and the lower arm change from 196.180HZ and 191.150HZ to 187.47HZ and 202.52HZ. Although the low-order frequency of the upper arm is slightly reduced, the benefit brought by its weight reduction is better than the frequency fluctuation. The mass of the upper arm is reduced by 0.914Kg and the mass of the lower arm is reduced by 0.157Kg. The results still have reliable reference value and key significance.

Claims

1. A method for lightweighting a quasi-hyperbolic manipulator using a motion stability model, characterized in that include: 1). Determine the basic optimization goal based on the actual optimization needs of the product; For the weight attribute, the main objective function is written through the general expression of the optimization problem: MinG(x)=g(x) Where x represents the series of dimensions of the studied component that have been modified compared to the original model when the minimum weight index is met, x = [x1, x2, …, x n ], x i represents a certain dimension that has been modified, and n is the number of dimensions that have been modified; G(x) represents the objective function of weight; g(x) represents the minimum weight value of the studied component measured by 3D software; 2). Select the first evaluation indicator; The first evaluation indicator: MaxF(y)=f(y) Where y represents the series of dimensions of the component being studied that have been modified compared to the original model when the natural frequency is the largest, y = [y1, y2, …, y n ],y i represents a certain dimension that has been modified, and n is the number of dimensions that have been modified; F(y) represents the objective function of frequency; f(y) represents the maximum weight value of the first-order natural frequency of the studied component measured by 3D software; 3). Single optimization of frequency; The mass matrix (M), damping matrix (C), and stiffness matrix (K) of the system; the natural frequency is usually obtained by solving the characteristic equation of the system; the characteristic equation is expressed by the following determinant: |K-oh 2 M-2xC|=0 Where ω is the angular frequency vector of the system, ζ is the damping ratio vector, which represents the damping level of each degree of freedom; Solve to get the expression of natural frequency: For a certain mode i, its natural frequency f nature for: f nature =(1 / 2π)*sqrt(k sys / m) Among them, k sys It represents the stiffness of the system in Newton / meter, which reflects the ability of the system to resist deformation, and m represents the mass of the system in kilograms; sqrt is the square root function; 4). Select the second evaluation indicator; For the attribute of stiffness, write the second evaluation index: MaxGD(z)=gd(z) Where z represents the series of dimensions of the studied component that have been modified compared to the original model when the maximum stiffness index is met, z = [z1, z2, …, z n ],z i represents a certain dimension that has been modified, and n is the number of dimensions that have been modified; GD(z) represents the objective function of stiffness; gd(z) represents the maximum stiffness value of the studied component measured by 3D software; 5). Single optimization of stiffness; The flexibility r and strength K are usually inversely proportional; that is, the greater the flexibility, the stronger the deformation ability of the material, and the corresponding strength may be lower; conversely, the smaller the flexibility, the weaker the deformation ability of the material, and the higher the strength; r＝1 / K The generalized expression for flexibility is: r=μL r / i r Where μ is the length factor related to the member constraint condition, L r is the length of the rod, i r is the radius of inertia of the cross section. When the structure of the analyzed manipulator is completely determined, these three parameters are determined by direct measurement; 6) Find a compromise The compromise programming method is used to construct the dual objective function, and the obtained dual objective function is the motion stability evaluation model function, where F OF It is a dual objective function. Here, both evaluation indicators are set to minimize the trend, so the minimum value is taken; Where L is the common set of design variables x, y, and z, which can make F(y) and GD(z) meet the expectations at the same time, ω is the weight of flexibility, q is the penalty factor, and r k (L) is the average function of the flexibility value, and is the flexibility extreme value of the kth working condition; f(L) is the average frequency function, f max and f min is the maximum and minimum average frequency value; n c is the total number of working conditions, k is the number of the working condition currently being calculated; if only dangerous working conditions are studied, then n c and k are both 1; 7). Determine the constraints; i (L) and h j (L) represent the inequality constraints and equality constraints on the common set L, respectively, m e and n e Represent the number of inequality constraints and equality constraints respectively; s.t.g i (L)≤0,i=1,2,3,…,m e h j (L)=0,j=1,2,3,...,n e The common set of decision variables L is a vector, that is, L∈R n ; 8). Set the retention threshold and perform topology optimization to obtain a reference lightweight model. Use modeling software to redesign the model so that the edge is smooth and continuous for easy processing; perform finite element simulation calculation steps to obtain the deformation and equivalent elastic stress of the model after optimization, and analyze whether the lightweight simulation calculation results meet expectations; 9). According to the MSM model, OF The value of is used to evaluate the redesign results, the weights are adjusted according to different optimization requirements, and the lightweight theoretical calculation results are analyzed again to see whether they meet the expectations. The optimization is terminated when both the simulation calculation results and the theoretical calculation results meet the expectations. The satisfactory optimization results are expressed by the following inequality: g after ≤p g *g before f after ≥p f *f before gd after ≥p gd *gd before 。 2. The method according to claim 1, characterized in that: When the geometric properties of the material are also considered, the bending flexibility of the rod is expressed as: r=1 / (E*I)*(L j 3 / 3*(1 / (1-c 2 ) Where E is the elastic modulus of the material, I is the moment of inertia of the area, and L j is the member length and γ is the Poisson's ratio.

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