A compliant constant force mechanism topology optimization design method

Abstract

The application discloses a compliant constant force mechanism topology optimization design method, and belongs to the technical field of structure topology optimization; the design method comprises the following steps: establishing a design domain and performing finite element discretization, setting boundary conditions and initial material density distribution; introducing control parameters; constructing a nonlinear topology optimization model with the minimum weighted relative output error as the target, and adaptively selecting according to the output force of each control point according to the reference constant force value; calculating the output force by using a hyperelastic material model and an adaptive material interpolation function; calculating the sensitivity by using a strain energy difference method; adaptively updating the material interpolation parameter according to the comparison result of the maximum strain and the strain threshold value; sequentially updating the unit density after performing density filtering and projection filtering on the sensitivity; and outputting the optimal topology configuration after convergence is judged.

Description

Technical Field

[0001] This invention relates to the field of structural topology optimization technology, specifically to a topology optimization design method for compliant constant force mechanisms. Background Technology

[0002] Compliant constant-force mechanisms are those that output an approximately constant force within a given input displacement range through elastic deformation of their structure. Unlike traditional rigid mechanisms, compliant constant-force mechanisms can achieve constant force output without force sensors or active control systems, thus possessing significant application value in fields such as micro-nano manipulation, precision assembly, overload protection, and biomedical devices. Currently, the design of such mechanisms mainly relies on methods such as stiffness combination, curved beam, and topology optimization. Among these, topology optimization methods have become a cutting-edge direction in the design of constant-force mechanisms due to their advantages of automatically finding the optimal material distribution within the design domain and their high degree of design freedom.

[0003] However, existing topology-optimized methods for designing compliant constant-force mechanisms generally suffer from a core problem: the reference constant force value in the objective function lacks an adaptive selection mechanism. In nested loop methods, the reference force is only updated as the average output force after the outer loop converges. The first outer loop requires more than 120 inner loops to complete, resulting in slow convergence and low computational efficiency. While the bifurcation constraint method improves optimization stability, the reference force still needs to be manually preset. If the preset value deviates significantly from the actual optimal value, the optimization process may fail directly. The root cause of these problems is that existing methods do not solve the selection of the reference force as a quantifiable optimization subproblem in each iteration. They either rely on manual experience to specify a fixed value or approximate it through low-frequency coarse updates, lacking a mathematical criterion that can automatically and stably determine the optimal reference force in each iteration based on the current output force distribution at each control point.

[0004] While existing methods have achieved some success in terms of constant force output performance, the blindness and lag in the selection of reference forces limit optimization efficiency and increase the reliance on human experience in the design process. Therefore, how to automatically determine the optimal reference force in each iteration to guide the optimization process to stable convergence without relying on manual presets or inefficient nested loops has become an urgent technical problem to be solved in this field. Summary of the Invention

[0005] To address the problems mentioned in the background section, this invention provides a topology optimization design method for compliant constant-force mechanisms. The technical solution adopted by this invention is as follows:

[0006] A topology optimization design method for compliant constant force mechanisms includes the following steps:

[0007] S10: Establish the design domain information of the compliant constant force mechanism, perform finite element discretization on the design domain information, set boundary condition information, and provide initial material density distribution information;

[0008] S20: Introduce a set of control parameter information, which includes at least target volume fraction information, desired constant force range information, number of control points and their corresponding input displacement values, weight factor information for each control point, initial value information for adaptive material interpolation parameters, and strain threshold information.

[0009] S30: Construct nonlinear topology optimization model information for a compliant constant force mechanism with the objective function of minimizing the weighted relative output error. The reference constant force value information in the objective function information is adaptively selected in each iteration based on the current output force distribution of each control point.

[0010] S40: Based on the nonlinear finite element method, Neo-Hookean hyperelastic material model information and adaptive material interpolation function information are used to model the elements of the design domain information, and the output force information corresponding to the input displacement value information of each control point is calculated.

[0011] S50: The sensitivity values ​​of the objective function information to the density design variables of each unit are calculated using the strain energy difference method;

[0012] S60: Extract the maximum von Mises strain information of all units within the design domain information of the current iteration step, compare it with the strain threshold information, and adaptively update the adaptive material interpolation parameter information according to the preset piecewise function;

[0013] S70: The sensitivity value information is sequentially subjected to density filtering and Heaviside projection filtering, and the density design variable information of each unit is updated based on the filtered sensitivity information;

[0014] S80: Determine whether the optimization process meets the convergence condition information. If not, return to step S40 for the next iteration. If yes, output the final unit density distribution information as the optimal topology information of the compliant constant force mechanism.

[0015] By adopting the above technical solution, design domain information is established and discretized using finite element methods. Boundary conditions are set, and initial material density distribution information is provided to offer a geometric model and initial state for subsequent iterative optimization. Next, a set of control parameters is introduced, including target volume fraction information, desired constant force range information, number of control points and their corresponding input displacement values, weighting factors for each control point, initial values ​​of adaptive material interpolation parameters, and strain threshold information. These parameters are used throughout the optimization process, serving as constraints and adjustment bases to guide the evolution of material distribution. Then, a nonlinear topology optimization model is constructed with the objective function of minimizing the weighted relative output error. The reference constant force value is adaptively selected in each iteration based on the current output force distribution of each control point, allowing the reference benchmark of the objective function to automatically adjust as the structural performance gradually improves, without the need for manual pre-setting or nested loops. Based on this, Neo-Hookean hyperelastic material model information and adaptive material interpolation function information are used to model the design domain elements, calculating the output force information corresponding to the input displacement values ​​of each control point. By adjusting the material... The interpolation parameters adaptively change according to the strain state in each iteration, ensuring the numerical stability of the large deformation nonlinear finite element analysis without increasing the number of elements. The strain energy difference method is used to calculate the sensitivity value of the objective function to the density design variables of each element, eliminating the need for analytical derivation of complex objective function gradients and reducing the difficulty of sensitivity analysis. The maximum von Mises strain information of all elements in the design domain of the current iteration step is extracted and compared with the strain threshold information. The material interpolation parameter information is adaptively updated according to the preset piecewise function, so that the stiffness of low-density elements is enhanced when the deformation is too large and restored to a near-real physical model when the deformation is controllable, balancing numerical convergence and analysis accuracy. The sensitivity value information is sequentially filtered by density and Heaviside projection. The density design variable information of each element is updated based on the filtered sensitivity information to suppress the checkerboard phenomenon and reduce gray elements, making the final topology clear and easy to manufacture. The optimization process is judged to determine whether the convergence condition information is met. If not, the finite element analysis is returned to the next iteration. If yes, the final element density distribution information is output as the optimal topology information. By integrating the aforementioned adaptive reference force selection mechanism and adaptive material interpolation mechanism, the entire optimization process can automatically determine the optimal reference force and ensure numerical convergence without manual intervention, thereby efficiently outputting a clear topological configuration with the target constant force characteristics.

[0016] In a preferred embodiment, this application can be further configured such that step S10 specifically includes:

[0017] S101: Establish the design domain information, wherein the design domain information is a rectangular area;

[0018] S102: Discretize the design domain information using the finite element method, dividing it into multiple quadrilateral plane stress elements;

[0019] S103: Apply fixed constraint information to the bottom boundary of the design domain information, and apply symmetrical constraint information to the nodes at the displacement input end;

[0020] S104: The initial relative density information of each unit within the design domain information is uniformly set to the preset target volume fraction information.

[0021] By adopting the above technical solution, the design domain information is established. The design domain information is a rectangular region, which facilitates finite element mesh generation and can cover the main deformation region of the constant force mechanism. Then, the design domain information is discretized using the finite element method, dividing it into multiple quadrilateral plane stress elements. Each element serves as the basic decision unit for material distribution, and the uniformity of element size ensures the consistency of sensitivity calculation. Fixed constraint information is applied to the bottom boundary of the design domain information, and symmetric constraint information is applied to the nodes at the displacement input end. By utilizing the symmetry of the mechanism, the design domain is reduced to a half-domain for optimization, thereby significantly reducing the number of degrees of freedom in the finite element analysis and improving computational efficiency. The initial relative density information of each element within the design domain information is uniformly set to a preset target volume fraction information, so that the optimization starts from a uniform material distribution, avoiding the introduction of additional bias effects due to uneven initial density distribution, and providing a neutral and symmetrical starting state for subsequent iterations.

[0022] In a preferred embodiment, this application may be further configured such that the control parameter information in step S20 also includes SIMP penalty factor information, sensitivity analysis displacement increment coefficient information, convergence threshold information, number of continuous monitoring rounds information, density filtering radius information, and Heaviside projection threshold information.

[0023] By adopting the above technical solution, the control parameter information also includes SIMP penalty factor information, sensitivity analysis displacement increment coefficient information, convergence threshold information, continuous monitoring round number information, density filtering radius information, and Heaviside projection threshold information. SIMP penalty factor information is used to control the polarization of intermediate density elements towards 0 or 1 in the material interpolation function to obtain a clear topological configuration; the sensitivity analysis displacement increment coefficient information is used to determine the magnitude of the superimposed small displacement increments in the strain energy difference method, and its value directly affects the accuracy of sensitivity calculation; the convergence threshold information serves as a quantitative standard for determining whether optimization has ended, and its preset value determines the optimality of the final topological configuration in the sense of the objective function; the continuous monitoring round number information specifies the number of most recent iteration rounds used to calculate the relative change of the objective function, avoiding misjudgment of convergence due to accidental fluctuations in a single round; the density filtering radius information is used to spatially smooth the sensitivity values ​​and eliminate mesh dependence; the Heaviside projection threshold information is used to binarize the continuous density field, suppress gray-scale elements, and achieve a clear black-and-white topological configuration. The above parameters together constitute a complete control system for optimization iteration, ensuring the controllability, convergence, and output quality of the optimization process.

[0024] In a preferred example, this application can be further configured as follows: the topology optimization model constructed in step S30, with weighted relative output error Minimize as the objective function to obtain the current volume fraction of the design domain. Not exceeding the target volume fraction The constraint condition is expressed as follows:

[0025]

[0026]

[0027]

[0028]

[0029] in, Input displacement; Corresponding output force; The reference constant force value is selected for adaptive adaptation; For the first The weighting factors of each control point satisfy the following conditions: ; Number of control points; Represents the residual stress vector of the structure. Represents the force balance of the structure; and These represent the current volume fraction of the structure and its constraint value, respectively. and Let these represent the density value and its minimum value of the i-th cell, respectively. The value is set to 0.001.

[0030] By adopting the above technical solution, the objective function is to minimize the weighted relative output error, that is, to use the weighted sum of squares of the relative deviations between the output force of each control point and the reference constant force value as the optimization objective. When the objective function value approaches zero, the output force of each control point approaches the same reference constant force value, thus achieving constant force output characteristics. The constraints include structural force equilibrium constraints, requiring that the displacement field obtained by the finite element solution satisfy the discrete form of the equilibrium equation, ensuring that each iteration in the optimization process is based on a physically feasible deformation state; volume fraction constraints, requiring that the volume fraction of the current design domain does not exceed the preset target volume fraction, maximizing constant force performance under the premise of satisfying material usage limitations; and density boundary constraints, limiting the range of density values ​​for each element, with a minimum value set to 0.001 to avoid stiffness matrix singularities caused by zero-density elements in the finite element analysis. The above constraints together ensure that the optimization results achieve optimal constant force performance under the premise of physical feasibility, material constraints, and numerical stability, so that the final topology meets both functional requirements and engineering feasibility.

[0031] In a preferred embodiment, this application can be further configured such that the reference constant force value in step S30 is... The adaptive selection method is as follows: the output force of all control points in the current iteration step is... Rearrange in ascending order It is important to note that here... Not input displacement Corresponding output force Instead, it represents the first element in the output force. Small output force, therefore This is the smallest value in the above sequence. The value depends on the superscript. The value increases with the increase of the sum; based on the above premise, find the index that satisfies the following two cumulative and cross inequalities. :

[0032]

[0033]

[0034] Then take This serves as a reference constant force value for this round of iterations; it has been proven by mathematical induction that this selection method makes... The goal is to achieve the global minimum, which means minimizing the relative deviation between the output forces of each control point.

[0035] By adopting the above technical solution, the output forces of all control points in the current iteration step are rearranged into an output force sequence in ascending order. Then, the index satisfying two cumulative sum cross inequalities is found, and the output force value corresponding to that index is taken as the reference constant force value for this iteration. The first cumulative sum condition requires that the sum of the output forces of the first k terms in the sequence is greater than the sum of the output forces of the remaining terms, ensuring that the selected reference force is in the middle to later part of the entire sequence. The second cross inequality requires that the sum of the output forces of the first k-1 terms in the sequence is less than the sum of the output forces of the remaining terms, ensuring that the selected index is the minimum upper bound position satisfying the condition. It is proven by mathematical induction that this selection method makes the weighted sum of squares of the relative deviations between the output forces of each control point and the reference constant force value reach the global minimum. Thus, without relying on manual experience or nested loops, the optimal reference force that minimizes the relative deviation of each control point is automatically determined in each iteration, directly and fundamentally eliminating the need for manually preset reference forces or nested loops.

[0036] In a preferred embodiment, this application can be further configured such that the adaptive material interpolation function in step S40 is:

[0037]

[0038] in, For the first Young's modulus after interpolation of each unit; Young's modulus of solid materials; For the first The physical density of each unit; This is the SIMP penalty factor; These are adaptive material interpolation parameters, with a value range of [value range missing]. ,in , ;when At this point, the interpolation function degenerates into the classic SIMP model. ;when At this time, the elastic modulus of low-density and intermediate-density elements is increased, thereby enhancing their ability to resist excessive deformation and ensuring the smooth convergence of nonlinear finite element analysis.

[0039] By adopting the above technical solution, the Young's modulus after element interpolation is jointly determined by the Young's modulus of the solid material, the physical density of the element, the SIMP penalty factor, and the adaptive material interpolation parameter. When the adaptive material interpolation parameter is equal to zero, the interpolation function degenerates into a classical SIMP model, and the elastic modulus of low-density elements decreases rapidly with decreasing density. When the adaptive material interpolation parameter is greater than zero, the elastic modulus of low-density and intermediate-density elements is raised overall based on the SIMP penalty, giving them sufficient resistance to excessive deformation in large deformation analysis, thereby ensuring the smooth convergence of nonlinear finite element analysis. The lower limit of the parameter's value range is close to zero to ensure that it can degenerate into a classical SIMP model to achieve high analysis accuracy, while the upper limit is 0.8 to avoid severe material distortion caused by excessive raising. This design can balance the numerical stability and analysis accuracy of nonlinear topology optimization by adjusting a single scalar parameter without increasing the number of elements or changing the material constitutive equation.

[0040] In a preferred embodiment, this application can be further configured such that the specific operation of the strain energy difference method in step S50 is: for the input displacement corresponding to each control point... A tiny increment is superimposed on the original displacement. ( Two nonlinear finite element analyses were performed respectively, and the strain energy increment of each element in the two analyses was extracted. Then calculate the output force. For unit physical density The sensitivity is:

[0041]

[0042] The derivative of the strain energy increment with respect to density is:

[0043] .

[0044] By employing the above technical solution, a small increment is superimposed on the input displacement corresponding to each control point, and two nonlinear finite element analyses are performed. The strain energy increment of each element in the two analyses is extracted, and then the sensitivity value of the output force to the physical density of each element is approximately calculated by using the partial derivative of the strain energy increment with respect to density. The physical principle of this method is that the rate of change of output force with respect to density can be indirectly measured by the change of strain energy in the finite element analysis, and the derivative of the strain energy increment with respect to density can be analytically obtained by the material interpolation function. The advantage of this method is that it avoids directly deriving the analytical sensitivity expression of the complex objective function with respect to the density variable. The sensitivity calculation can be completed using the results of the finite element analysis, which significantly reduces the theoretical difficulty and implementation complexity of sensitivity analysis in nonlinear topology optimization, allowing engineers to implement this optimization method without being proficient in sensitivity derivation.

[0045] In a preferred embodiment, this application can be further configured such that the adaptive updating of material interpolation parameters in step S60 is... The piecewise function is:

[0046]

[0047] in, For the first Material interpolation parameter values ​​used in the round iteration; This will be the updated value used in the next iteration; For the first The maximum von Mises strain of all elements in the design domain during round iteration; The strain threshold is set to 0.6. The significance of this update strategy is that when the maximum strain within the design domain does not exceed the threshold, it indicates that the current structural deformation is within a controllable range, thus reducing... To improve the accuracy of finite element analysis; when the maximum strain exceeds the threshold, it indicates a risk of excessive element deformation, increasing the risk of over-deformation. This is to enhance the stiffness of low-density elements and ensure the normal completion of finite element analysis.

[0048] By adopting the above technical solution, after each iteration, the maximum von Mises strain of all elements in the current design domain is extracted and compared with a preset strain threshold. When the maximum strain does not exceed the threshold, it indicates that the current structural deformation is within a controllable range. The material interpolation parameters are reduced to improve the accuracy of the finite element analysis and make the interpolation model closer to the real physical model. When the maximum strain exceeds the threshold, it indicates that there is a risk of excessive deformation of the elements. The material interpolation parameters are increased to enhance the deformation resistance of low-density elements and ensure that the finite element analysis can converge normally without collapsing due to element distortion. This update strategy improves the material interpolation parameters from being fixed to being adaptively adjusted according to the structural strain state. While ensuring the accuracy of the analysis, it provides sufficient numerical stability for the optimization process, taking into account both convergence and accuracy requirements. It avoids the problem of unsmooth switching between linear and nonlinear models in the energy interpolation method and the element multiplication problem in the method of adding hyperelastic materials.

[0049] In a preferred embodiment, this application can be further configured such that: in step S70, the sensitivity value information is subjected to density filtering and Heaviside projection filtering in sequence, specifically including: the sensitivity value information is first filtered by low-pass linear distance, and then filtered by Heaviside projection to suppress the checkerboard phenomenon and reduce grayscale units, and then the physical density information of each unit is updated by moving asymptote method or optimization criterion method.

[0050] By employing the above technical solution, the sensitivity information is first filtered through a low-pass linear distance filter. Using a preset filtering radius as the distance weight, the sensitivity of adjacent elements is smoothly averaged, eliminating grid dependence and preventing checkerboard patterns in the optimization results. Then, Heaviside projection filtering is applied. Through a step-like projection transformation of the density values, gray-level elements with intermediate values ​​are forced to polarize towards either 0 or 1, reducing gray-level regions in the final topology and making the structural boundaries clearer and easier to manufacture. Subsequently, the physical density information of each element is updated using either the moving asymptote method or the optimization criterion method. The moving asymptote method iteratively solves convex approximation subproblems, making it suitable for problems with multiple constraints and large-scale design variables. The optimization criterion method directly updates the density based on optimality conditions, offering high computational efficiency. These filtering and updating operations ensure that the topology optimization results meet both numerical stability requirements and engineering manufacturability.

[0051] In a preferred embodiment, this application can be further configured such that the convergence condition in step S80 is: calculating the nearest continuous... The objective function described in the round iteration The relative change, when the relative change is less than the preset convergence threshold When the value is 0.001, the optimization process is considered to have converged.

[0052] By employing the above technical solution, the relative change of the objective function in the most recent consecutive iterations is calculated, and this relative change is compared with a preset convergence threshold: when the relative change is less than the convergence threshold, the optimization process is determined to have converged, indicating that subsequent iterations have negligible improvement on the objective function, and further optimization will not produce substantial improvement; when the relative change is still greater than or equal to the convergence threshold, convergence is determined to have failed, and the process must return to step S40 for the next iteration. The physical meaning of this convergence condition is that when the relative change of the objective function in consecutive iterations is sufficiently small, i.e., the relative deviation between the output force and the reference force at each control point has stabilized, the topology configuration has reached its optimal state. By setting a convergence threshold and a number of consecutive monitoring rounds, this judgment criterion effectively avoids misjudgment of convergence due to accidental fluctuations in a single iteration, ensuring that the output topology configuration truly converges to a stable optimal solution.

[0053] The beneficial effects of the topology optimization design method for a compliant constant force mechanism of the present invention are as follows:

[0054] 1. The reference constant force value in the objective function is adaptively selected in each iteration based on the current distribution of output forces at each control point. By finding the output force that satisfies the cumulative sum and cross inequality conditions as the reference benchmark, it theoretically ensures that the relative deviation of the output force at each control point relative to the reference force reaches the global minimum. The entire optimization process does not require manual preset of the reference constant force value or nested loop iteration, completely eliminating the problems of deviation in optimization direction or slow convergence caused by improper selection of reference force in traditional methods. This allows the optimization process to automatically follow the gradual improvement of structural performance and stably approach the optimal constant force characteristics, significantly improving the versatility and adaptability of the optimization method for different design conditions and different target constant force levels.

[0055] 2. An interpolation parameter that can be dynamically adjusted according to the structural deformation state is introduced into the adaptive material interpolation function. By extracting the maximum von Mises strain information of all elements in the design domain of the current iteration step and comparing it with the preset strain threshold, the value of this parameter is automatically adjusted in each iteration according to the piecewise function: when the maximum strain does not exceed the threshold, the parameter is appropriately reduced to improve the accuracy of the finite element analysis; when the maximum strain exceeds the threshold, the parameter is appropriately increased to enhance the stiffness of the low-density elements, thereby ensuring the smooth convergence of the nonlinear finite element analysis. This adaptive adjustment mechanism takes into account both numerical stability and analysis accuracy in large deformation nonlinear topology optimization without increasing the number of elements or changing the material constitutive equation, and effectively avoids the finite element analysis collapse problem caused by excessive distortion of low-density elements in traditional methods.

[0056] 3. The sensitivity value of the objective function to the density design variables of each element is calculated using the strain energy difference method. The sensitivity information is indirectly obtained by superimposing small perturbations on the input displacement corresponding to each control point and performing two nonlinear finite element analyses. This eliminates the need for analytical derivation of the explicit gradient expression of the complex nonlinear objective function with respect to the density variables, significantly reducing the theoretical difficulty and implementation complexity of sensitivity analysis in nonlinear topology optimization. At the same time, by sequentially applying density filtering and Heaviside projection filtering to the sensitivity values, the checkerboard phenomenon is effectively suppressed and the number of gray-scale elements is reduced. The final output topology configuration has clear boundaries and distinct black and white areas, which facilitates subsequent processing, manufacturing, and practical engineering applications. Attached Figure Description

[0057] Figure 1 This is a flowchart of an embodiment of the topology optimization design of a compliant constant force mechanism according to this application;

[0058] Figure 2 This is a diagram showing the design domain, its boundary conditions, and the optimized design results in Embodiment 1 of this application;

[0059] Figure 3 This is a diagram showing the design domain, its boundary conditions, and the optimized design results in Embodiment 2 of this application. Detailed Implementation

[0060] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] As attached Figure 1 As shown, this application discloses a topology optimization design method for compliant constant force mechanisms, including the following steps:

[0062] S10: Establish the design domain information of the compliant constant force mechanism, perform finite element discretization on the design domain information, set boundary condition information, and provide initial material density distribution information;

[0063] In this embodiment, the design domain information is the geometric space region data used to define the material distribution range of the compliant constant force mechanism; finite element discretization is the process of dividing a continuous design domain into a finite number of units; boundary condition information is the displacement constraint and mechanical constraint data applied on the boundary of the design domain; and the initial material density distribution information is the initial relative density value distribution of the material in each unit before the optimization begins.

[0064] Specifically, the design domain information of the compliant constant force mechanism is established, the design domain is discretized by finite element method and divided into multiple elements, and the bottom fixed constraint and the symmetric constraint of the displacement input end of the design domain are set as boundary condition information. The initial material density distribution information of each element is given, and the initial relative density is unified to the target volume fraction value, so as to provide a geometric model and starting state for subsequent iterative optimization.

[0065] S20: Introduce a set of control parameter information, which includes at least target volume fraction information, desired constant force range information, number of control points and their corresponding input displacement values, weight factor information for each control point, initial value information for adaptive material interpolation parameters, and strain threshold information.

[0066] In this embodiment, the control parameter information is a set of preset parameters used to constrain and guide the optimization process; the target volume fraction information is the upper limit of the proportion of the solid material in the design domain in the final topology configuration; the desired constant force range information is the input displacement range of the mechanism's output constant force; the number of control points information is the number of discrete locations selected within the desired constant force range to monitor the output force characteristics; the input displacement value information is the loaded displacement value corresponding to each control point; the weighting factor information is the importance coefficient of each control point in the objective function; the initial value information of the adaptive material interpolation parameter is the initial adjustment coefficient of the material interpolation function; and the strain threshold information is the critical strain value used to determine whether the element is excessively deformed.

[0067] Specifically, control parameter information is introduced, including the target volume fraction, the desired constant force range, the number of control points and the corresponding input displacement value of each control point, the weight factor of each control point, the initial value of the adaptive material interpolation parameter, and the strain threshold. These parameters are used throughout the optimization process as constraints and adjustment basis to guide the evolution of material distribution.

[0068] S30: Construct nonlinear topology optimization model information for a compliant constant force mechanism with the objective function of minimizing the weighted relative output error. The reference constant force value information in the objective function information is adaptively selected in each iteration based on the current output force distribution of each control point.

[0069] In this embodiment, the weighted relative output error is the weighted sum of squares of the relative deviations between the output force of each control point and the reference constant force value; the objective function information is the quantitative index that needs to be minimized during the optimization process; the nonlinear topology optimization model information is the topology optimization mathematical model that considers geometric nonlinear effects; and the reference constant force value information is the constant force value used as a benchmark in the objective function, which is automatically determined in each iteration based on the current distribution of the output forces of all control points.

[0070] Specifically, a nonlinear topology optimization model is constructed with the objective function of minimizing the weighted relative deviation between the output force of each control point and the adaptively selected reference force. The reference constant force value is automatically selected in each iteration by sorting the output forces of each control point and according to the cumulative and cross inequality conditions. This allows the reference benchmark of the objective function to be automatically adjusted as the structural performance gradually improves, without the need for manual preset or nested loops.

[0071] S40: Based on the nonlinear finite element method, Neo-Hookean hyperelastic material model information and adaptive material interpolation function information are used to model the elements of the design domain information, and the output force information corresponding to the input displacement value information of each control point is calculated.

[0072] In this embodiment, the nonlinear finite element method is a numerical solution method for finite elements that considers geometric nonlinear effects; the Neo-Hookean hyperelastic material model information is hyperelastic constitutive model data describing the stress-strain relationship of the material under large deformation; and the adaptive material interpolation function information is an interpolation function that automatically adjusts the stiffness of low-density elements according to the maximum strain state of the element in each iteration.

[0073] Specifically, the constitutive behavior of the elements is described using the Neo-Hookean hyperelastic material model, and the elastic modulus of the low-density elements is adjusted according to the maximum strain state of the current design domain using an adaptive material interpolation function. The output force information corresponding to the input displacement of each control point is calculated based on the nonlinear finite element method, so as to achieve accurate solution of the structural response under large deformation conditions.

[0074] S50: The sensitivity values ​​of the objective function information to the density design variables of each unit are calculated using the strain energy difference method;

[0075] In this embodiment, the strain energy difference method is a numerical method for calculating sensitivity by superimposing small increments on the displacement input at each control point and extracting the strain energy change of the element in two finite element analyses; the sensitivity value information is the partial derivative data of the objective function with respect to the density design variables of each element, which is used to guide the iterative update direction of the density variables.

[0076] Specifically, after superimposing small increments on the input displacements corresponding to each control point, nonlinear finite element analysis is performed. The strain energy increment of each element in the two analyses is extracted. Based on the derivative of the strain energy increment with respect to density, the sensitivity value of the output force to the density of each element is calculated. Thus, the sensitivity data can be obtained without analytically deriving the complex objective function gradient.

[0077] S60: Extract the maximum von Mises strain information of all units within the design domain information of the current iteration step, compare it with the strain threshold information, and adaptively update the adaptive material interpolation parameter information according to the preset piecewise function;

[0078] In this embodiment, the maximum von Mises strain information is the maximum value of the von Mises equivalent stress of all elements in the design domain in the current iteration step; the piecewise function is a mathematical function that determines the material interpolation parameter update amount by dividing the interval based on the comparison result of the maximum strain and the strain threshold.

[0079] Specifically, the maximum von Mises strain information of all elements in the design domain of the current iteration step is extracted and compared with a preset strain threshold. When the maximum strain does not exceed the threshold, the material interpolation parameter is reduced to improve the analysis accuracy. When the maximum strain exceeds the threshold, the material interpolation parameter is increased to enhance the deformation resistance of the low-density elements, thereby ensuring the smooth convergence of the nonlinear finite element analysis.

[0080] S70: The sensitivity value information is sequentially subjected to density filtering and Heaviside projection filtering, and the density design variable information of each unit is updated based on the filtered sensitivity information;

[0081] In this embodiment, density filtering is a spatial filtering operation that performs a weighted average of the sensitivity values ​​of adjacent cells with a preset radius; Heaviside projection filtering is an operation that polarizes the continuous density field to either 0 or 1 through a step projection transformation; and the cell density design variable information is the material relative density value of each cell.

[0082] Specifically, the sensitivity information is first filtered by low-pass linear distance to eliminate grid dependence, then filtered by Heaviside projection to suppress checkerboard phenomenon and reduce grayscale cells. Subsequently, the physical density information of each cell is updated using the moving asymptote method or optimization criterion method, so that the final topology is clear and easy to manufacture.

[0083] S80: Determine whether the optimization process meets the convergence condition information. If not, return to step S40 for the next iteration. If yes, output the final unit density distribution information as the optimal topology information of the compliant constant force mechanism.

[0084] In this embodiment, the convergence condition information is the termination criterion data used to determine whether the optimization process has reached the optimal state; the element density distribution information is the final material relative density numerical distribution of each element; and the optimal topology configuration information is the final material layout scheme that satisfies the objective function minimization and constraint requirements.

[0085] Specifically, the relative change of the objective function in the most recent consecutive iterations is calculated. When the relative change is less than the preset convergence threshold, the optimization is determined to have converged, and the final element density distribution information is output as the optimal topology information of the compliant constant force mechanism. When the relative change is still greater than or equal to the convergence threshold, the process returns to the next iteration. This process is repeated until the convergence condition is met, ensuring that the output topology has converged to a stable optimal solution.

[0086] In one embodiment, step S10 specifically includes:

[0087] S101: Establish the design domain information, wherein the design domain information is a rectangular area;

[0088] S102: Discretize the design domain information using the finite element method, dividing it into multiple quadrilateral plane stress elements;

[0089] S103: Apply fixed constraint information to the bottom boundary of the design domain information, and apply symmetrical constraint information to the nodes at the displacement input end;

[0090] S104: The initial relative density information of each unit within the design domain information is uniformly set to the preset target volume fraction information.

[0091] In this embodiment, the rectangular region is a rectangular geometric space with a defined side length; the quadrilateral plane stress element is a finite element type suitable for in-plane stress analysis of thin plates; the fixed constraint information is the boundary condition that constrains the displacement of nodes in all directions; the symmetric constraint information is the displacement coordination boundary condition applied using the structural symmetry; and the initial relative density information is the material filling ratio value of each element at the initial optimization moment.

[0092] Specifically, a rectangular region is established as the design domain information, and it is discretized into multiple quadrilateral plane stress elements using the finite element method. Fixed constraints are applied to the bottom boundary of the design domain, and symmetric constraints are applied to the nodes at the displacement input end to reduce the amount of computation by utilizing structural symmetry. The initial relative density of each element is uniformly set to the target volume fraction value to provide a neutral starting state for optimization.

[0093] In one embodiment, the control parameter information in step S20 further includes SIMP penalty factor information, displacement increment coefficient information of sensitivity analysis, convergence threshold information, number of continuous monitoring rounds information, density filtering radius information, and Heaviside projection threshold information.

[0094] In this embodiment, the SIMP penalty factor information is an exponential parameter used in the penalty model for solid isotropic materials to penalize intermediate density values, causing them to cluster towards 0 or 1; the displacement increment coefficient information for sensitivity analysis is an increment ratio coefficient used in the strain energy difference method when applying a small perturbation to the input displacement; the convergence threshold information is a critical value used to determine whether the relative change of the objective function has reached the convergence criterion; the number of continuous monitoring rounds information is the number of iteration rounds used to continuously statistically analyze the changes in the objective function when determining the convergence condition; the density filtering radius information is a radius value used in the density filtering operation to determine the influence range of neighboring cells; and the Heaviside projection threshold information is a threshold parameter used in the Heaviside projection function to map continuous density to binary density.

[0095] Specifically, the control parameter information also includes SIMP penalty factor information to control the penalty intensity of the material interpolation model on intermediate density elements, displacement increment coefficient information of sensitivity analysis to determine the amplitude of displacement disturbance in strain energy difference method, convergence threshold information to set the judgment criteria for optimization termination, continuous monitoring round information to avoid misjudgment of convergence due to accidental fluctuations, density filter radius information to control the effective range of density filtering, and Heaviside projection threshold information to adjust the sharpness of projection filtering. These supplementary parameters further improve the control system of the optimization process.

[0096] In one embodiment, the topology optimization model constructed in step S30 is used to weight the relative output error. Minimize as the objective function to obtain the current volume fraction of the design domain. Not exceeding the target volume fraction The constraint condition is expressed as follows:

[0097]

[0098]

[0099]

[0100]

[0101] in, Input displacement; Corresponding output force; The reference constant force value is selected for adaptive adaptation; For the first The weighting factors of each control point satisfy the following conditions: ; Number of control points; Represents the residual stress vector of the structure. Represents the force balance of the structure; and These represent the current volume fraction of the structure and its constraint value, respectively. and Let these represent the density value and its minimum value of the i-th cell, respectively. The value is set to 0.001.

[0102] In this embodiment, the weighted relative output error is the sum of the relative output errors after integrating the weights of each control point in the objective function; the volume fraction is the ratio of the volume of the solid material in the design domain to the total volume of the design domain; the residual stress vector is the residual force vector formed by the imbalance between internal and external forces at the nodes in the nonlinear finite element analysis; the force equilibrium is the state in which the internal and external forces of the structure reach equilibrium under a given load; the density value is the relative density value of the element material; the minimum density value is the lower limit of the allowable density value of the element.

[0103] Specifically, the topology optimization model uses the minimization of weighted relative output error as its objective function, which integrates the weighting factors of each control point and the relative output error. Simultaneously, it uses the constraint that the current volume fraction of the design domain does not exceed the target volume fraction to ensure that the optimization results meet the material usage limits. It uses structural force equilibrium as a constraint to ensure that the mechanical analysis in each iteration step satisfies the equilibrium equations. Finally, it uses the constraint that the density values ​​of each element are between the minimum density value and 1 to ensure the physical feasibility of the design variables. This optimization model pursues output force stability while also considering material economy and mechanical feasibility.

[0104] In one embodiment, the reference constant force value in step S30 The adaptive selection method is as follows: the output force of all control points in the current iteration step is... Rearrange in ascending order It is important to note that here... Not input displacement Corresponding output force Instead, it indicates the first of the output forces. Small output force, therefore This is the smallest value in the above sequence. The value depends on the superscript. The value increases with the increase of the sum; based on the above premise, find the index that satisfies the following two cumulative and cross inequalities. :

[0105]

[0106]

[0107] Then take This serves as a reference constant force value for this round of iterations; it has been proven by mathematical induction that this selection method makes... The goal is to achieve the global minimum, which means minimizing the relative deviation between the output forces of each control point.

[0108] In this embodiment, output force sorting is an operation that rearranges the output force values ​​of each control point in ascending order; the cumulative sum inequality is a comparison condition for determining the selection position of the reference constant force value; the cross inequality is a comparison condition used in conjunction with the cumulative sum inequality to determine the selection position of the reference constant force value; the index is the position number of each value in the ordered sequence after output force sorting; the global minimum is the minimum value that the relative deviation reaches among all possible reference constant force selection methods; the relative deviation is the degree of deviation of the output force of each control point from the reference constant force value.

[0109] Specifically, the output forces of all control points in the current iteration step are rearranged in ascending order. Then, the index position that simultaneously satisfies both cumulative and cross inequalities is found, and the output force value corresponding to that position is used as the reference constant force value for this iteration. This selection method has been proven by mathematical induction to achieve a global minimum of the relative deviation of the output force of each control point relative to the reference constant force value. That is, the optimal benchmark value that minimizes the relative dispersion between the output forces is selected from all possible reference constant force values, thereby effectively guiding the optimization process towards a more uniform and stable output force.

[0110] In one embodiment, the adaptive material interpolation function in step S40 is:

[0111]

[0112] in, For the first Young's modulus after interpolation of each unit; Young's modulus of solid materials; For the first The physical density of each unit; This is the SIMP penalty factor; These are adaptive material interpolation parameters, with a value range of [value range missing]. ,in , ;when At this point, the interpolation function degenerates into the classic SIMP model. ;when At this time, the elastic modulus of low-density and intermediate-density elements is increased, thereby enhancing their ability to resist excessive deformation and ensuring the smooth convergence of nonlinear finite element analysis.

[0113] In this embodiment, the interpolated Young's modulus is the unit elastic modulus value calculated by the material interpolation function; the solid material Young's modulus is the Young's elastic modulus of the solid material in a non-porous state; the physical density is the unit physical density value obtained after filtering and projection processing; the low-density unit is the unit with a relatively low material density value; and the intermediate-density unit is the unit with a material relative density value between 0 and 1.

[0114] Specifically, the adaptive material interpolation function establishes the mathematical relationship between the interpolated Young's modulus of the element and the Young's modulus of the solid material, the element physical density, the SIMP penalty factor, and the adaptive material interpolation parameter. When the adaptive material interpolation parameter is zero, the interpolation function degenerates into a classical SIMP model; when the parameter is positive, the elastic modulus of low-density and intermediate-density elements is increased overall, thereby enhancing their ability to resist excessive deformation. The core function of this adaptive interpolation function is to ensure the smooth convergence of the nonlinear finite element analysis and avoid numerical analysis failure caused by excessive distortion of low-density elements under large deformation conditions.

[0115] In one embodiment, the specific operation of the strain energy difference method in step S50 is as follows: for the input displacement corresponding to each control point A tiny increment is superimposed on the original displacement. ( Two nonlinear finite element analyses were performed respectively, and the strain energy increment of each element in the two analyses was extracted. Then calculate the output force. For unit physical density The sensitivity is:

[0116]

[0117] The derivative of the strain energy increment with respect to density is:

[0118] .

[0119] In this embodiment, the strain energy increment is the change in strain energy of the element before and after the displacement disturbance; the derivative of the strain energy increment with respect to density is the sensitivity of the strain energy increment to changes in element density.

[0120] Specifically, for each control point, a small increment is superimposed on the original input displacement. Two nonlinear finite element analyses are then performed, and the strain energy increment of each element in the two analyses is extracted. The sensitivity of the output force to the element's physical density is then calculated. The core of this method lies in indirectly solving for the sensitivity information through numerical difference, avoiding the complexity of direct differentiation. This method is particularly suitable for sensitivity analysis of nonlinear problems. The derivative of the strain energy increment with respect to density is directly calculated based on the analytical expression of the adaptive material interpolation function.

[0121] In one embodiment, the adaptive update of material interpolation parameters in step S60 The piecewise function is:

[0122]

[0123] in, For the first Material interpolation parameter values ​​used in the round iteration; This will be the updated value used in the next iteration; For the first The maximum von Mises strain of all elements in the design domain during round iteration; The strain threshold is set to 0.6. The significance of this update strategy is that when the maximum strain within the design domain does not exceed the threshold, it indicates that the current structural deformation is within a controllable range, thus reducing... To improve the accuracy of finite element analysis; when the maximum strain exceeds the threshold, it indicates a risk of excessive element deformation, increasing the risk of over-deformation. This is to enhance the stiffness of low-density elements and ensure the normal completion of finite element analysis.

[0124] In this embodiment, the maximum von Mises strain is the maximum value of the von Mises strain among all elements in the design domain; the update value is the new value of the adaptive material interpolation parameter to be used in the next iteration; the controllable range is the safe strain range in which structural deformation will not cause numerical analysis failure.

[0125] Specifically, the piecewise function for adaptively updating material interpolation parameters adopts different update strategies based on the comparison between the maximum von Mises strain and the strain threshold in the design domain of the current iteration step. When the maximum strain does not exceed the threshold, it indicates that the current structural deformation is within a controllable range, and the material interpolation parameters are appropriately reduced to improve the accuracy of the finite element analysis. When the maximum strain exceeds the threshold, it indicates a risk of excessive element deformation, and the material interpolation parameters are appropriately increased to enhance the stiffness of low-density elements. This adaptive update strategy achieves a balance between analytical accuracy and computational stability by dynamically adjusting the material interpolation parameters, ensuring that the nonlinear finite element analysis can be completed normally in each iteration step while avoiding the adverse effects of overly conservative parameter settings on optimization accuracy.

[0126] In one embodiment, step S70 involves sequentially performing density filtering and Heaviside projection filtering on the sensitivity value information. Specifically, the sensitivity value information is first filtered by low-pass linear distance, then filtered by Heaviside projection to suppress the checkerboard effect and reduce grayscale units. Subsequently, the physical density information of each unit is updated using the moving asymptote method or optimization criterion method.

[0127] In this embodiment, Heaviside projection filtering is a density projection transformation method based on the Heaviside step function; the checkerboard phenomenon is a numerical pseudo-phenomenon in topology optimization where the material density is distributed in a checkerboard pattern; grayscale cells are fuzzy cells with density values ​​between 0 and 1, making it impossible to clearly determine the presence or absence of material; the moving asymptote method is a sequential optimization algorithm based on the idea of ​​convex approximation; and the optimization criterion method is a heuristic update algorithm based on the optimality criterion.

[0128] Specifically, the processing of sensitivity values ​​involves two sequential steps: density filtering and Heaviside projection filtering. First, the sensitivity values ​​are filtered using a low-pass linear distance filter, which performs a weighted average of the sensitivity values ​​within each cell's neighborhood, eliminating numerical noise and grid dependence. Then, Heaviside projection filtering maps the continuous density distribution to either 0 or 1, effectively suppressing checkerboard patterns and reducing the number of grayscale cells. Finally, the moving asymptote method or optimization criterion method is used to update the physical density information of each cell based on the filtered sensitivity information. This dual filtering strategy ensures the numerical stability and topological clarity of the optimization results.

[0129] In one embodiment, the convergence condition in step S80 is: calculating the nearest continuous... The objective function described in the round iteration The relative change, when the relative change is less than the preset convergence threshold When the value is 0.001, the optimization process is considered to have converged.

[0130] In this embodiment, the relative change of the objective function is the relative fluctuation of the objective function value in the most recent consecutive iterations; the preset convergence threshold is a pre-set critical value used to determine whether the optimization has converged.

[0131] Specifically, the convergence condition is as follows: calculate the relative change of the objective function over the most recent consecutive iterations; when this relative change is less than a preset convergence threshold, the optimization process is considered to have converged. This convergence judgment strategy avoids misjudging convergence due to accidental fluctuations in a single iteration by continuously monitoring the stability of the objective function over multiple iterations. The setting of the number of consecutive monitoring iterations ensures the reliability of the convergence judgment, while the setting of the convergence threshold controls the accuracy of the optimization results. When the convergence condition is met, it indicates that the objective function has stabilized, and further iterations contribute very little to performance improvement. At this point, the final topology is output as the optimization result.

[0132] A specific embodiment of the topology optimization design method for a compliant constant force mechanism proposed in this application is as follows:

[0133] Example 1:

[0134] As attached Figure 2 As shown, this embodiment provides a topology optimization design method for compliant constant force mechanisms, specifically applied to the design of large-stroke compliant constant force mechanisms, using high-toughness nylon PA11 material.

[0135] Step S1: Establish the design domain. The design domain is a rectangular region with dimensions of 180mm × 30mm and a thickness of 1mm. The design domain is discretized using the finite element method, dividing it into 180 × 30 quadrilateral plane stress elements (element side length 1mm). Fixed constraints are applied to the bottom boundary of the design domain. Considering the symmetry of the mechanism, to reduce the degrees of freedom in the finite element analysis and improve computational efficiency, only the right half of the design domain is optimized, and symmetric constraints are applied to the nodes at the displacement input end of this half-domain. The initial relative density of each element within the design domain is uniformly set to 0.4 (i.e., the target volume fraction). ).

[0136] Step S2: Introduce a set of control parameters. Number of control points. The value is set to 3, and the input displacements corresponding to the three control points are evenly distributed within the desired constant force range. Within mm, that is mm mm mm. The weighting factor is set with equal weights—because the output force corresponding to exactly one of the three control points is selected as the reference force. (its relative error term) The weighting factors for the remaining two items are all taken as follows: The solid material is high-toughness nylon PA11 with a Young's modulus of [missing value]. MPa, Poisson's ratio The tensile strength is 48 MPa, and the elongation at break is 45%. Initial values ​​for adaptive material interpolation parameters. Its lower limit upper limit Strain threshold SIMP penalty factor Displacement increment coefficient in sensitivity analysis Convergence threshold Continuous monitoring rounds Density filtration radius mm, with a Heaviside projection threshold of 0.5.

[0137] Step S3, construct the topology optimization model. (Using equation...) The objective function is the current volume fraction. These are constraints. Reference force. In each iteration, the output forces are sorted and the cumulative and cross inequality conditions are automatically selected: the three output forces obtained from the current finite element analysis are arranged in ascending order as follows: Seeking satisfaction and index ,Pick .

[0138] Step S4, Nonlinear Finite Element Analysis. The Neo-Hookean hyperelastic material model is used to describe the mechanical behavior of the elements, and its strain energy function is: ,in The initial shear modulus, This is the initial bulk modulus. The element elastic modulus is obtained using an adaptive interpolation function. Calculation. The input displacements of the three control points are solved using the Newton-Raphson iterative method. mm mm The nodal displacement field corresponding to mm is used to extract the sum of the reaction forces at the loading nodes as the output force. , , Before optimization (under the initial uniform density distribution state), the three output forces were as follows: N、 N、 N, the output force increases monotonically with the input displacement, and does not have the characteristic of constant force output.

[0139] Step S5, Sensitivity Analysis. For the displacement of each control point... A small increment is superimposed on the original displacement. ( ,Right now mm mm (mm), perform a new nonlinear finite element analysis, and extract the strain energy increment of each element. The formula for calculating sensitivity is:

[0140]

[0141] in .

[0142] Step S6, Adaptive Update. After each iteration, extract the maximum von Mises strain of all elements within the current design domain. .like ,but ,make Decrease to improve analytical accuracy; if ,but ,make Incremental increases are used to enhance the deformation resistance of low-density elements. Updated This is used in step S4 of the next iteration. In this embodiment, the entire process is optimized. The value generally maintains a downward trend – initial value Ultimately, it dropped to During this period, the strain exceeding the threshold condition was not triggered.

[0143] Step S7, design variable update. The sensitivity value is first filtered through a low-pass linear distance (filter radius). The physical density of each element is then adjusted using a Heaviside projection filter (projection threshold 0.5) to suppress the checkerboard effect and reduce grayscale units. Subsequently, the moving asymptote method (MMA) is used to update the physical density of each element. .

[0144] Step S8, Convergence Determination. Calculate the relative change in the objective function value over the last 5 rounds. If this change is less than... Convergence is determined at this point. In this embodiment, the convergence condition is met after 41 iterations, and the objective function value decreases to [value missing]. The output forces corresponding to the three control points at convergence are respectively N、 N、 N, the three are very close, indicating that the obtained mechanism has the characteristic of constant force output.

[0145] A complete force-displacement simulation analysis was performed on the optimized topology: A series of input displacements from 1 mm to 28 mm were applied to the displacement input end using finite element software, the corresponding output forces were recorded, and the output force-input displacement curves were plotted. A fifth-order polynomial was used to fit the data points to obtain the force-displacement function relationship, and the goodness of fit was determined. Within a given constant force range of 7–21 mm, the relative output error is calculated according to the criterion of minimizing the relative output error. That is, the force fluctuation does not exceed 2.68%. When the input displacement is between 0 and 7 mm, it is the preload stage (the output force increases with the increase of displacement), between 7 and 21 mm is the constant force output stage (the output force is almost unchanged), and above 21 mm is the overload stage (the output force resumes its growth trend). The three characteristic curves conform to the standard force-displacement characteristics of a constant force mechanism.

[0146] Example 2:

[0147] As attached Figure 3 As shown, this embodiment differs from Embodiment 1 only in the setting of the desired constant force range, to verify the design adaptability of the method of the present invention to different constant force range requirements. The optimization steps are consistent with those of Embodiment 1.

[0148] In step S1, the design domain size, mesh generation, boundary conditions, and initial material density distribution are the same as in Example 1. In step S2, the desired constant force range is changed to... mm, the input displacements corresponding to the three control points are respectively mm mm mm; other control parameters – material properties (PA11) , , , All of these are consistent with Example 1.

[0149] After 84 iterations, the optimization meets the convergence condition (the relative change in the objective function in the last 5 iterations is <0.001). The end value is Force-displacement simulation analysis was performed on the obtained constant force mechanism. The force-displacement function relationship was obtained by fifth-order polynomial fitting, and the goodness of fit was... Within a given constant force range of 10–30 mm, the relative output error .

[0150] The results of this embodiment and Embodiment 1 show that, under the same design domain size, this method can design compliant constant force mechanisms that meet different constant force stroke requirements by only changing the constant force range parameters—the constant force range proportion in Embodiment 1 is [missing information]. Example 2 is upgraded to The length of the constant force range increased from 14 mm to 20 mm. This demonstrates the good adaptability of the method of this invention to different design requirements for constant force ranges.

[0151] In summary, the compliant constant-force mechanism topology optimization design method provided by this invention, by constructing an adaptive reference force selection mechanism and an adaptive material interpolation mechanism, and integrating the two into the same iterative framework, can stably and efficiently converge to a compliant constant-force mechanism topology configuration with the target constant-force output characteristics without manual intervention. Examples 1 and 2 verify the effectiveness and versatility of this method from two dimensions: basic design and different constant-force ranges, respectively: the proportion of constant-force ranges can be increased from 46.7% to 66.7%, and the relative output error is always controlled within 4%. This method not only avoids dependence on manually preset reference forces or nested loops in principle, significantly improving optimization efficiency (approximately 113% higher than the method with added hyperelastic materials), but also... Closed-loop adaptive adjustment of parameters ensures numerical stability while keeping finite element analysis errors within an acceptable engineering range.

[0152] The present invention and its embodiments have been described above. This description is not restrictive. The accompanying drawings are only one embodiment of the present invention. The actual structure is not limited to this. In short, if a person skilled in the art is inspired by this description and designs a similar structure and embodiment without departing from the spirit of the present invention, such design should fall within the protection scope of the present invention.

Claims

1. A topology optimization design method for a compliant constant force mechanism, characterized in that: Includes the following steps: S10: Establish the design domain information of the compliant constant force mechanism, perform finite element discretization on the design domain information, set boundary condition information, and provide initial material density distribution information; S20: Introduce a set of control parameter information, which includes at least target volume fraction information, desired constant force range information, number of control points and their corresponding input displacement values, weight factor information for each control point, initial value information for adaptive material interpolation parameters, and strain threshold information. S30: Construct nonlinear topology optimization model information for a compliant constant force mechanism with the objective function of minimizing the weighted relative output error. The reference constant force value information in the objective function information is adaptively selected in each iteration based on the current output force distribution of each control point. S40: Based on the nonlinear finite element method, Neo-Hookean hyperelastic material model information and adaptive material interpolation function information are used to model the elements of the design domain information, and the output force information corresponding to the input displacement value information of each control point is calculated. S50: The sensitivity values ​​of the objective function information to the density design variables of each unit are calculated using the strain energy difference method; S60: Extract the maximum von Mises strain information of all units within the design domain information of the current iteration step, compare it with the strain threshold information, and adaptively update the adaptive material interpolation parameter information according to the preset piecewise function; S70: The sensitivity value information is sequentially subjected to density filtering and Heaviside projection filtering, and the density design variable information of each unit is updated based on the filtered sensitivity information; S80: Determine whether the optimization process meets the convergence condition information. If not, return to step S40 for the next iteration. If yes, output the final unit density distribution information as the optimal topology information of the compliant constant force mechanism.

2. The topology optimization design method for a compliant constant force mechanism according to claim 1, characterized in that: Step S10 specifically includes: S101: Establish the design domain information, wherein the design domain information is a rectangular area; S102: Discretize the design domain information using the finite element method, dividing it into multiple quadrilateral plane stress elements; S103: Apply fixed constraint information to the bottom boundary of the design domain information, and apply symmetrical constraint information to the nodes at the displacement input end; S104: The initial relative density information of each unit within the design domain information is uniformly set to the preset target volume fraction information.

3. The topology optimization design method for a compliant constant force mechanism according to claim 1, characterized in that: The control parameter information in step S20 also includes SIMP penalty factor information, displacement increment coefficient information of sensitivity analysis, convergence threshold information, number of continuous monitoring rounds information, density filtering radius information, and Heaviside projection threshold information.

4. The topology optimization design method for a compliant constant force mechanism according to claim 1, characterized in that: The topology optimization model constructed in step S30 is used to weight the relative output error. Minimize as the objective function to obtain the current volume fraction of the design domain. Not exceeding the target volume fraction The constraint condition is expressed as follows: ； ； ； ； in, Input displacement; Corresponding output force; The reference constant force value is selected for adaptive adaptation; For the first The weighting factors of each control point satisfy the following conditions: ; Number of control points; Represents the residual stress vector of the structure. Represents the force balance of the structure; and These represent the current volume fraction of the structure and its constraint value, respectively. and Let these represent the density value and its minimum value of the i-th cell, respectively. The value is set to 0.

001.

5. The topology optimization design method for a compliant constant force mechanism according to claim 4, characterized in that: The reference constant force value in step S30 The adaptive selection method is as follows: the output force of all control points in the current iteration step is... Rearrange in ascending order It is important to note that here... Not input displacement Corresponding output force Instead, it represents the first element in the output force. Small output force, therefore This is the smallest value in the above sequence. The value depends on the superscript. The value increases with the increase of the sum; based on the above premise, find the index that satisfies the following two cumulative and cross inequalities. : ； ； Then take This serves as a reference constant force value for this round of iterations; It has been proven by mathematical induction that this selection method makes The goal is to achieve the global minimum, which means minimizing the relative deviation between the output forces of each control point.

6. The topology optimization design method for a compliant constant force mechanism according to claim 1, characterized in that: The adaptive material interpolation function in step S40 is: ； in, For the first Young's modulus after interpolation of each unit; Young's modulus of solid materials; For the first The physical density of each unit; This is the SIMP penalty factor; These are adaptive material interpolation parameters, with a value range of [value range missing]. ,in , ;when At this point, the interpolation function degenerates into the classic SIMP model. ;when At this time, the elastic modulus of low-density and intermediate-density elements is increased, thereby enhancing their ability to resist excessive deformation and ensuring the smooth convergence of nonlinear finite element analysis.

7. The topology optimization design method for a compliant constant force mechanism according to claim 1, characterized in that: The specific operation of the strain energy difference method in step S50 is as follows: for the input displacement corresponding to each control point... A tiny increment is superimposed on the original displacement. ( Two nonlinear finite element analyses were performed respectively, and the strain energy increment of each element in the two analyses was extracted. Then calculate the output force. For unit physical density The sensitivity is: ； The derivative of the strain energy increment with respect to density is: 。 8. The topology optimization design method for a compliant constant force mechanism according to claim 1, characterized in that: The adaptive update of material interpolation parameters in step S60 The piecewise function is: ； in, For the first Material interpolation parameter values ​​used in the round iteration; This will be the updated value used in the next iteration; For the first The maximum von Mises strain of all elements in the design domain during round iteration; The strain threshold is set to 0.

6. The significance of this update strategy is that when the maximum strain within the design domain does not exceed the threshold, it indicates that the current structural deformation is within a controllable range, thus reducing... To improve the accuracy of finite element analysis; when the maximum strain exceeds the threshold, it indicates a risk of excessive element deformation, increasing the risk of over-deformation. This is to enhance the stiffness of low-density elements and ensure the normal completion of finite element analysis.

9. The topology optimization design method for a compliant constant force mechanism according to claim 1, characterized in that: In step S70, the sensitivity value information is subjected to density filtering and Heaviside projection filtering in sequence. Specifically, the sensitivity value information is first filtered by low-pass linear distance, and then filtered by Heaviside projection to suppress the checkerboard phenomenon and reduce grayscale units. Subsequently, the physical density information of each unit is updated by the moving asymptote method or the optimization criterion method.

10. The topology optimization design method for a compliant constant force mechanism according to claim 1, characterized in that: The convergence condition in step S80 is: calculating the nearest continuous... The objective function described in the round iteration The relative change, when the relative change is less than the preset convergence threshold When the value is 0.001, the optimization process is considered to have converged.

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