Flexible tooling design method based on topology optimization
By adopting a topology optimization-based flexible tooling design method, the problem that traditional tooling cannot simulate the real boundary of the test piece is solved, and the accurate simulation of the test piece boundary and the accuracy of the test results are improved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- DALIAN UNIV OF TECH
- Filing Date
- 2022-07-18
- Publication Date
- 2026-06-23
AI Technical Summary
Traditional tooling designs cannot accurately simulate the real boundary conditions of the test specimen, affecting the accuracy of the test.
A topology-optimized flexible tooling design method is adopted. The displacement and support reaction of the displacement constraint point of the test specimen are extracted by finite element analysis, local stiffness constraints are established, and the topology optimization design of the flexible tooling is carried out to obtain the optimized configuration and simulate the real boundary of the test specimen.
Accurately simulate the true boundaries of the test specimen, improve the accuracy and authenticity of the test, and ensure the test specimen is evaluated under real service conditions.
Smart Images
Figure CN115329623B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of flexible tooling design, specifically relating to a flexible tooling design method based on topology optimization. Background Technology
[0002] In mechanical testing, fixtures are typically used to fix the test specimen, simulating boundary conditions. Traditional fixture design methods generally rely on engineering experience, aiming to maximize fixture stiffness while considering the connection between the fixture and the test specimen, ensuring minimal deformation during testing. However, some test specimens exhibit deformation at the connection points within the overall model (including the test specimen and other connected components), meaning the specimen boundaries are not perfectly rigid. In such cases, using traditionally designed rigid fixtures to fix the specimen will fail to simulate the true boundary conditions, significantly impacting the accuracy of the test. Summary of the Invention
[0003] The purpose of this invention is to address the aforementioned shortcomings in the prior art by providing a flexible tooling design method based on topology optimization, thereby solving the problem that traditional techniques cannot simulate the real boundary conditions of test specimens, thus affecting the accuracy of the test.
[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0005] A flexible tooling design method based on topology optimization includes the following steps:
[0006] S1. Finite element analysis is performed on the test specimen in the overall model state to extract the displacement of the displacement constraint point and the support reaction force of the test specimen.
[0007] S2. Use the local stiffness constraint method to constrain the local displacement of the model;
[0008] S3. Based on the constraints of local displacement of the test piece, establish a topology optimization problem;
[0009] S4. Divide the design domain of the flexible tooling and construct the equivalent configuration of the flexible tooling;
[0010] S5. Based on the topology optimization problem, optimize the equivalent configuration of the flexible tooling to obtain the optimized configuration of the flexible tooling.
[0011] S6. Compare the simulation data of the test piece in the tooling clamping state with the simulation data of the test piece in the overall model. If the difference between the two is greater than the threshold, return to step S5; otherwise, end.
[0012] Furthermore, the displacement of the test specimen's displacement constraint point in step S1 includes X-direction displacement and Z-direction displacement; the support reaction force includes X-direction support reaction force, Y-direction support reaction force and Z-direction support reaction force.
[0013] Furthermore, in step S2, the local displacements of the model are constrained, and the local stiffness constraint function is:
[0014]
[0015] Among them, u zx u represents the calculated displacement at the local stiffness constraint at position z in the model. z This represents the given value of the displacement constraint at position z, where Z represents the number of constraint displacement points;
[0016] The sensitivity of the local stiffness constraint function to the element design variable ρ is calculated as follows:
[0017]
[0018] Furthermore, step S3 specifically includes:
[0019] A topology optimization problem is established with the objective of minimizing strain energy and the constraints of the design domain volume fraction being less than a given value and the displacements at the connection points and the extracted displacements being less than a given value.
[0020] find: ρ = {ρ1, ρ2, ..., ρ N} T
[0021] min:F T U = U T KU
[0022] st:F=KU
[0023]
[0024]
[0025] 0 < ρ min ≤ρ e ≤1,e=1,2,...,N
[0026] Where K represents the overall stiffness matrix of the structure, U represents the displacement vector, F represents the external load vector, T represents the vector transpose, and u zx u represents the calculated displacement at position z. z This represents the displacement constraint value at position z, where Z represents the number of constraint displacement points, and v e V represents the volume of a single unit cell. * ρ represents the volumetric material usage, and ρ represents the topological unit design variable. e ρ represents the density of a certain element, N represents the design domain being discretized into N elements, and ρ min Indicates the lower limit of density, u nThis indicates the displacement to be solved at the nth position, and 'a' represents the displacement constraint value.
[0027] Furthermore, step S4 specifically includes:
[0028] Based on the configuration of the components connected to the test piece, the initial configuration of the test fixture is determined. The connection points of the fixture boundary are retained, and the rest is used as the design domain. After the design domain is divided, the mesh is generated, and the support reaction force is extracted and applied to the corresponding constraint points. Fixed support boundary conditions are set, and local stiffness constraint conditions are set according to the extracted support reaction force.
[0029] Furthermore, step S5 specifically includes:
[0030] Define convergence conditions, initialize the pseudo-density of the cells, and provide initial iteration points;
[0031] PDE is used to filter the checkerboard grid values, and non-linear filtering is used to reduce the structure and optimize the final grayscale.
[0032] The finite element method is used to solve for various structural response quantities and to solve for the response of the objective constraint function.
[0033] Update the pseudo-density, iterate for the next round of calculation, perform sensitivity calculation, and solve for the derivative of the objective constraint function with respect to the physical density.
[0034] To solve for the filtering sensitivity, the derivative of the previous round with respect to the physical density is transformed into the derivative with respect to the pseudo-density using the chain rule.
[0035] Perform optimization and solve for the next round of pseudo-density using the moving asymptotic method optimizer;
[0036] Perform a convergence check to determine whether the iteration index meets the convergence condition. If the condition is met, the optimization ends; otherwise, repeat the loop to optimize again.
[0037] The flexible tooling design method based on topology optimization provided by this invention has the following beneficial effects:
[0038] This invention uses the test specimen in the overall model state as the research object for finite element analysis. The support reactions and displacements at the external connections of the test specimen are extracted from the finite element analysis results. These support reactions and displacements are used as the load and boundary displacement constraints of the tooling, respectively, to establish a tooling optimization problem. Then, a flexible tooling topology optimization design is carried out, mainly including: design domain partitioning, mesh generation, optimization and obtaining the optimized configuration, modeling the optimized configuration, and performing finite element analysis on the test specimen to obtain the performance parameters of the test specimen in the tooling clamping state. These parameters are compared with those of the test specimen in the overall model state. If the parameters are similar, it indicates that the boundary stiffness is equivalent and ideal, and the iteration stops.
[0039] Compared with tooling obtained by traditional design methods, the flexible tooling of this invention can accurately simulate the real boundary of the test piece and accurately assess the state of the test piece under real service conditions. Attached Figure Description
[0040] Figure 1 This is a flowchart of the present invention.
[0041] Figure 2 This is a schematic diagram of displacement constraints.
[0042] Figure 3 To design the domain partitioning effect.
[0043] Figure 4 This is a flowchart for topology optimization.
[0044] Figure 5 Optimize the topology configuration for the tooling.
[0045] Figure 6 To optimize the configuration model.
[0046] Figure 7 This is an assembly diagram of the tooling and test piece. Detailed Implementation
[0047] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.
[0048] Example 1, Reference Figure 1 This embodiment presents a topology-optimized flexible tooling design method. This method applies topology optimization technology to flexible tooling design, resulting in a simple design process. By controlling the local stiffness of the tooling, it accurately simulates the real boundary conditions of the test piece, improving the realism of the experiment. Specifically, it includes the following steps:
[0049] Step S1, local displacement extraction, specifically includes:
[0050] Finite element analysis was performed on the test specimen in the overall model state to extract the displacement of the displacement constraint point and the support reaction force of the test specimen.
[0051] Using the finite element analysis software Abaqus, the experimental specimen was analyzed in its overall model state. The displacements and support reactions at the external connections (displacement constraint points) were extracted. The displacement constraint points are shown below. Figure 2 As shown, the displacement and support reaction data are shown in Table 1:
[0052] Table 1 Extraction of displacement and support reaction values
[0053]
[0054] Step S2: Use the local stiffness constraint method to constrain the local displacements of the model:
[0055]
[0056] Among them, u zx u represents the calculated displacement at the local stiffness constraint at position z in the model. z This represents the given value of the displacement constraint at position z, where Z represents the number of constraint displacement points;
[0057] The sensitivity of the local stiffness constraint function to the element design variable ρ is calculated as follows:
[0058]
[0059] Step S3: Based on the constraints of local displacement of the test piece, establish a topology optimization problem, which is as follows:
[0060] A topology optimization problem is established with the objective of minimizing strain energy and the constraints of the design domain volume fraction being less than a given value and the displacements at the connection points and the extracted displacements being less than a given value.
[0061] find: ρ = {ρ1, ρ2, ..., ρ N} T
[0062] min:F T U = U T KU
[0063] st:F=KU
[0064]
[0065]
[0066] 0 < ρ min ≤ρ e ≤1,e=1,2,...,N
[0067] Where K represents the overall stiffness matrix of the structure, U represents the displacement vector, F represents the external load vector, T represents the vector transpose, and u zx u represents the calculated displacement at position z. z This represents the displacement constraint value at position z, where Z represents the number of constraint displacement points, and v e V represents the volume of a single unit cell. * ρ represents the volumetric material usage, and ρ represents the topological unit design variable.e ρ represents the density of a certain element, N represents the design domain being discretized into N elements, and ρ min Indicates the lower limit of density, u n This indicates the displacement to be solved at the nth position, and 'a' represents the displacement constraint value.
[0068] Step S4: Divide the design domain of the flexible tooling and construct its equivalent configuration, specifically as follows:
[0069] The purpose of optimizing flexible tooling is to equivalently adjust the stiffness of the components connected to the test piece and simulate the actual boundary conditions of the test piece.
[0070] To find the optimal equivalent configuration, based on the configuration of the components connecting to the test piece and considering the actual test site conditions, the initial configuration of the test fixture was determined. The connection points at the fixture boundaries were retained, and the remaining portion was designated as the design domain. The design domain division effect is as follows: Figure 3 As shown.
[0071] After completing the design domain division, mesh generation is performed. There are no specific requirements for the mesh type. The extracted support reactions are applied to the corresponding constraint points in the figure, and fixed support boundary conditions are set. Local stiffness constraint conditions are set according to the extracted support reactions.
[0072] Step S5: Based on the topology optimization problem, optimize the equivalent configuration of the flexible tooling to obtain the optimized configuration of the flexible tooling, specifically as follows:
[0073] refer to Figure 4 Topology optimization is performed based on the optimization problem;
[0074] First, define the convergence condition to determine when the loop ends; then initialize the pseudo-density of the cells to provide initial iteration points for optimization.
[0075] PDE filtering is used to solve numerical problems such as checkerboard patterns, and non-linear filtering is used to reduce the final grayscale value of the structure.
[0076] Solve for various structural response quantities and the response of the objective constraint function;
[0077] Update the pseudo-density and iterate for the next round of calculation; and solve for the sensitivity by solving for the derivative of the objective constraint function with respect to the physical density.
[0078] To solve for the filtering sensitivity, since there is a transformation in the filtering method between the pseudo-density and the physical density, it is necessary to use the chain rule to transform the derivative of the previous round with respect to the physical density into the derivative with respect to the pseudo-density.
[0079] Perform optimization and solve for the next round of pseudo-density using the moving asymptotic method optimizer;
[0080] Finally, a convergence check is performed to determine whether the iteration index meets the convergence condition. If the condition is met, the optimization ends; otherwise, the process is repeated.
[0081] The final local stiffness optimization results are shown in Table 2. The maximum deviation between the optimized and target displacement values at the three displacement constraint points in the x and z directions is 8.65%, and the minimum deviation is 0.72%, indicating a good optimization effect. The optimized configuration is obtained as follows: Figure 5 As shown, 3D modeling software was used to reconstruct the optimized features, and the modeling effect is as follows. Figure 6 As shown, the tooling and test piece are assembled, and the assembly result is as follows. Figure 7 As shown.
[0082] Table 2 Results of Local Stiffness Optimization
[0083]
[0084] Step S6: Compare the simulation data of the test piece in the tooling clamping state with the simulation data of the test piece in the overall model. If the difference between the two is greater than the threshold, return to step S5; otherwise, end.
[0085] Specifically, the simulation data of the test piece in the tooling clamping state is compared with the simulation data of the test piece in the overall model. If the simulation data of the previous and subsequent simulations differ significantly and do not meet the test requirements, the optimization parameters, including weight parameters and design domain volume fraction, are adjusted and optimized again until the simulation results of the test piece in the tooling clamping state and the overall model state are similar and meet the test requirements, and the iteration is terminated.
[0086] Example 2: This example uses the design of a test fixture for a tail nozzle regulating plate as an example to introduce the effect of the technical solution. The design is based on the method in Example 1. After comparison by finite element analysis, the overall deformation trend and stress distribution of the test piece are consistent in the fixture clamping state and the overall model state, and the stress value deviation at the test point is no more than 3%.
[0087] Although specific embodiments of the invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of this patent. Various modifications and variations that can be made by a person skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of this patent.
Claims
1. A flexible tooling design method based on topology optimization, characterized in that, Includes the following steps: S1. Finite element analysis is performed on the test specimen in the overall model state to extract the displacement of the displacement constraint point and the support reaction force of the test specimen. S2. Use the local stiffness constraint method to constrain the local displacement of the model; In step S2, the local displacement of the model is constrained, and the local stiffness constraint function is: in, This represents the calculated displacement at the local stiffness constraint at position z in the model. This represents the given value of the displacement constraint at position z, where Z represents the number of constraint displacement points; Perform local stiffness constraint function with respect to element design variables Sensitivity calculation: ； S3. Based on the constraints of local displacement of the test piece, establish a topology optimization problem; S4. Divide the design domain for the flexible tooling and construct its equivalent configuration, which specifically includes: Based on the configuration of the components connected to the test piece, the initial configuration of the test fixture is determined. The connection point of the fixture boundary is retained, and the rest is used as the design domain. After the design domain is divided, the mesh is generated, and the support reaction force is extracted and applied to the corresponding constraint points. Fixed support boundary conditions are set, and local stiffness constraint conditions are set according to the extracted support reaction force. S5. Based on the topology optimization problem, optimize the equivalent configuration of the flexible tooling to obtain the optimized configuration of the flexible tooling, which specifically includes: Define convergence conditions, initialize the pseudo-density of the cells, and provide initial iteration points; PDE is used to filter the checkerboard grid values, and non-linear filtering is used to reduce the structure and optimize the final grayscale. The finite element method is used to solve for various structural response quantities and to solve for the response of the objective constraint function. Update the pseudo-density, iterate for the next round of calculation, perform sensitivity calculation, and solve for the derivative of the objective constraint function with respect to the physical density. To solve for the filtering sensitivity, the derivative of the previous round with respect to the physical density is transformed into the derivative with respect to the pseudo-density using the chain rule. Perform optimization and solve for the next round of pseudo-density using the moving asymptotic method optimizer; A convergence check is performed to determine if the iteration index meets the convergence condition. If the condition is met, the optimization ends; otherwise, the loop continues for optimization. S6. Compare the simulation data of the test piece in the tooling clamping state with the simulation data of the test piece in the overall model. If the difference between the two is greater than the threshold, return to step S5; otherwise, end.
2. The flexible tooling design method based on topology optimization according to claim 1, characterized in that, The displacement of the test specimen's displacement constraint point in step S1 includes X-direction displacement and Z-direction displacement; the support reaction force includes X-direction support reaction force, Y-direction support reaction force and Z-direction support reaction force.
3. The flexible tooling design method based on topology optimization according to claim 1, characterized in that, Step S3 specifically includes: A topology optimization problem is established with the objective of minimizing strain energy and the constraints of the design domain volume fraction being less than a given value and the displacements at the connection points and the extracted displacements being less than a given value. in, Represents the total stiffness matrix of the structure. Represents the displacement vector. Let T denote the external load vector, and T denote the vector transpose. This represents the calculated displacement at position z. This represents the displacement constraint value at position z, where Z represents the number of constraint displacement points. Represents the unit volume. Indicates the volumetric amount of material used. Indicates the topological unit design variable. This represents the density of a certain element, where N indicates that the design domain is discretized into N elements. Indicates the lower limit of density. This indicates the displacement at the nth position. This represents the displacement constraint value.