A method for topology optimization of jack hinged protruding structure

Abstract

The application relates to the field of structural optimization design, and discloses a kind of topological optimization method of jack hinged protruding structure, comprising establishing design domain finite element model, dividing designable and non-designable area and forming initial density field;The sensitivity of target flexibility is calculated and filtered;Based on the stress constraint sensitivity calculated by P-norm approximate maximum stress, it is dynamically weighted with the filtered sensitivity to form a revised sensitivity;According to the revised sensitivity, the unit density value is updated, and the draft angle constraint and the minimum wall thickness constraint are synchronously applied in the update iteration;Finally, numerical projection is applied to the density field to promote density binarization, and after meeting the convergence condition, post-processing such as removing isolated cells and adding fillets is performed, and the topological model is output.The application deeply integrates stress constraints and multiple casting process constraints, improves structural stiffness, avoids stress concentration, ensures the direct castability of the optimization result, and improves design efficiency.

Description

Technical Field

[0001] This invention relates to the field of structural optimization design, and in particular to a topology optimization method for a jack hinged protrusion structure. Background Technology

[0002] As a commonly used lifting device, the safety and reliability of jacks are directly related to the personal safety of operators and the stable operation of the equipment. In the overall structure of a jack, the articulated protrusion is a key force-transmitting component connecting the lifting arm and the main body, bearing complex alternating and impact loads. During actual service, this part is highly susceptible to plastic deformation or even fracture due to stress concentration, making it one of the main sources of risk for overall machine failure.

[0003] With the development of computer-aided engineering, additive manufacturing, and precision casting technologies, topology optimization has become a core tool in lightweight structural design. Traditional topology optimization methods typically aim to minimize compliance (i.e., maximize stiffness) and, combined with volume constraints, can automatically search for the optimal material distribution path within a given design domain. However, when translating these theoretical research results into practically manufacturable industrial products, existing technologies still face the following significant shortcomings: Traditional topology optimization often focuses on overall stiffness, lacking strict control over local stress levels. For components with sharp geometric transitions (such as the edge of the pin hole), like the hinged protrusion of a jack, simply minimizing stiffness often leads to local von Mises stresses far exceeding the material's allowable values. Existing stress constraint methods frequently suffer from high sensitivity noise and inaccurate P-norm approximations, resulting in optimization outcomes that sacrifice structural fatigue life and safety while achieving weight reduction.

[0004] The existing design process is usually "optimize first, then verify." That is, casting process simulation is only performed after topology optimization is completed. Once a serious shrinkage defect is found in a critical stress area (the root of the protrusion), the designer often needs to manually modify the geometric model based on experience. This not only destroys the original mechanical transmission path of the topology optimization, but may also lead to a deterioration of the stress level, forcing the designer to carry out a time-consuming and laborious full-parameter optimization iteration again.

[0005] Therefore, we propose a topology optimization method for the jack hinged protrusion structure to solve the above problems. Summary of the Invention

[0006] This invention provides a topology optimization method for a jack hinged protrusion structure, which solves the problem that the results of traditional topology optimization are difficult to apply in engineering due to neglecting stress constraints and casting process limitations.

[0007] The first aspect of the present invention provides a topology optimization method for a jack hinged protrusion structure. The topology optimization method for the jack hinged protrusion structure includes: establishing a finite element model of a design domain, wherein the design domain is divided into an undesignable region and a designable region, and assigning initial density values ​​to the designable elements in the designable region to form an initial density field. Finite element analysis is performed based on the initial density field or the updated density field during the iteration process to obtain the strain energy and stress value of each designable unit. The target compliance is calculated based on the strain energy. The initial sensitivity of the target compliance to the density value of the designable unit is solved, and the initial sensitivity is filtered to obtain the filtered sensitivity. The stress constraint sensitivity of the stress constraint to the density value of the designable unit is calculated based on the stress value, and the stress constraint sensitivity is combined with the filtered sensitivity to form a corrected sensitivity. The density value of the designable unit is updated using an optimization algorithm based on the modified sensitivity, and casting process constraints are applied during the update process to obtain the updated density field. The casting process constraints include at least draft angle constraints and minimum wall thickness constraints. Numerical projection is applied to the updated density field to make the density values ​​converge to binary. It is then determined whether the convergence condition is met. If the convergence condition is not met, the process returns to the step of performing finite element analysis based on the initial density field or the updated density field during the iteration process. If the convergence condition is met, the updated density field that meets the convergence condition is taken as the initial topological shape, and the initial topological shape is post-processed to output the topological model.

[0008] Optionally, in a first implementation of the first aspect of the present invention, the casting connection structure is a hinged protrusion structure of a jack; The undesignable area includes the units containing the pin holes and fixing holes used for assembly, and the unit density value of the undesignable area is fixed at 1.

[0009] Optionally, in a second implementation of the first aspect of the present invention, the step of performing finite element analysis based on the initial density field or the updated density field during the iteration process to obtain the strain energy and stress value of each designable element includes: The elastic modulus of each of the designable elements is calculated using a solid isotropic material penalty model; By applying loads and boundary constraints, the equilibrium equations are solved to obtain the nodal displacements; The strain energy of each designable unit is calculated based on the nodal displacement, and the von Mises stress is extracted as the stress value.

[0010] Optionally, in a third implementation of the first aspect of the present invention, filtering the initial sensitivity includes: Calculate the spatial distance from the designable unit to the preset reference position; The filter radius of the designable unit is dynamically adjusted based on the spatial distance. The smaller the spatial distance, the smaller the filter radius. The filtered sensitivity is obtained by calculating the initial sensitivity based on the filter radius.

[0011] Optionally, in a fourth implementation of the first aspect of the present invention, the step of calculating the stress constraint sensitivity of the stress constraint to the density value of the designable unit based on the stress value includes: The stress values ​​of the designable unit are approximated as the global maximum stress using the P-norm function, and a stress constraint function is constructed. The stress constraint sensitivity is obtained by solving the sensitivity of the stress constraint function to the density value of the designable element using the adjoint method.

[0012] Optionally, in a fifth implementation of the first aspect of the present invention, combining the stress constraint sensitivity with the filtered sensitivity to form a modified sensitivity includes: The stress constraint sensitivity and the filtered sensitivity are weighted and summed using a preset weighting coefficient, wherein the preset weighting coefficient is dynamically adjusted based on the ratio of the maximum stress in the current design domain to the allowable stress of the material. When the ratio is greater than a first preset threshold, the preset weight coefficient of the stress constraint sensitivity is increased; when the ratio is less than a second preset threshold, the preset weight coefficient of the stress constraint sensitivity is decreased, and the first preset threshold is greater than the second preset threshold.

[0013] Optionally, in the sixth implementation of the first aspect of the present invention, the optimization algorithm is the optimal criterion method, and the update process combines the bisection method to solve for the volume fraction constraint; The draft angle constraint in the casting process constraint includes: calculating the density gradient value between adjacent designable units in the draft direction; if the density gradient value exceeds a preset gradient upper limit, reducing the density value of the designable unit with the higher density value until the density gradient value does not exceed the preset gradient upper limit. The minimum wall thickness constraint in the casting process constraint includes: gradually increasing the threshold parameter used for the numerical projection during the update process to suppress the generation of features smaller than the preset wall thickness size.

[0014] Optionally, in the seventh implementation of the first aspect of the present invention, the numerical projection is a Heaviside projection; The determination of whether the convergence condition is met includes: calculating the absolute average of the density changes of all the designable units between the currently obtained updated density field and the previously obtained updated density field; if the absolute average is less than a preset convergence threshold, it is determined that the convergence condition is met.

[0015] Optionally, in an eighth implementation of the first aspect of the present invention, after the output topology model, a step of verifying and correcting the topology model is further included: The topological model is imported into the simulation model to perform solidification process simulation and obtain the predicted results of shrinkage distribution. Based on the predicted shrinkage distribution, the shrinkage region and its shrinkage volume ratio are extracted. If the shrinkage volume ratio is higher than a preset threshold, the topology model is locally thickened to obtain a corrected topology model. The modified topology model is re-verified by finite element static analysis. If its mechanical performance deviation is within the allowable range, the modified topology model is output as the final result.

[0016] Optionally, in a ninth implementation of the first aspect of the present invention, the local thickening process specifically involves increasing the material thickness along the normal direction of the outer surface of the shrinkage region, wherein the amount of thickening is positively correlated with the product of the shrinkage volume fraction and the reference thickness.

[0017] Beneficial effects: It breaks the traditional disconnect between shape and process in topology optimization. By directly embedding draft angle constraints and minimum wall thickness constraints into the sensitivity update stage of optimization iteration, it eliminates the generation of negative draft angles and excessively thin wall thicknesses from the source. This makes the output topology configuration no longer a laboratory model that is theoretically light but cannot be cast in practice, but an engineering structure that is inherently castable, thus shortening the cycle from conceptual design to mold manufacturing. Based on the ratio of current stress to allowable stress, the system intelligently switches between prioritizing compliance reduction and stress reduction, maintaining strength in critical areas and pursuing lightweighting in safe areas, thereby maximizing material utilization. The filter radius is adaptively adjusted according to spatial location. High-frequency mechanical details are preserved at the root of complex stress, while the checkerboard effect is suppressed in the main body region, ensuring the mechanical fidelity and numerical stability of the optimization results. A feedback loop for casting process simulation was introduced. By identifying shrinkage risk areas and making targeted local thickening, the contradiction between topology optimization results and casting quality was resolved. This ensured that the final structure was not only safe in mechanical analysis, but also avoided early fatigue fracture caused by internal defects after actual casting, which significantly improved the product yield and service life. By combining the optimal criterion method with the bisection method of Lagrange multipliers, and with the binarization processing of Heaviside projection, the iterative oscillation or divergence problem caused by the introduction of multiple hard constraints is effectively alleviated. It can stably converge to a clear 0 / 1 density field, reduce manual intervention in post-processing, and enhance the reliability of automated design. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of an embodiment of the topology optimization method for the jack hinged protrusion structure in this invention. Detailed Implementation

[0019] This invention provides a topology optimization method for a jack hinged protrusion structure, addressing the problem that traditional topology optimization methods, due to neglecting stress constraints and casting process limitations, are difficult to apply in engineering. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0020] For ease of understanding, the specific process of the embodiments of the present invention is described below. Please refer to [link / reference]. Figure 1 One embodiment of the topology optimization method for the jack hinged protrusion structure in this invention includes: 101. Establish a finite element model of the design domain, which includes the jack's protruding structure and main structure. Set the pin holes on the protrusion and the fixing holes on the main body as undesignable areas. Assign initial density values ​​to all designable elements in the design domain to form an initial density field.

[0021] It is understood that the executing entity of this invention can be a topology optimization device with a jack hinged protrusion structure, or it can be a terminal or a server; the specific implementation is not limited here. This embodiment of the invention will be described using a server as an example.

[0022] Specifically, when establishing the finite element model of the design domain, the design domain is divided into a raised region and a main region. The raised region is the hinged raised structure of the jack, and the main region is the C5 structural component connected to the raised structure. The elements in the raised region where the pin holes for installing crescent-shaped parts are located and the elements in the main region where the bolt holes for fixing are located are marked as undesignable elements with a fixed density value of 1. The remaining elements are marked as designable elements. All designable elements are assigned the same initial density value, which is between 0 and 1, thus forming an initial density field.

[0023] It should be noted that the imported jack geometric model is divided into a raised area and a main body area. The raised area (hinged raised structure) has an overall dimension of 120mm in length, 80mm in width, and 60mm in height, and has a 24mm diameter pin hole for installing a crescent-shaped part. The main body area (C5 structural component connected to the raised structure) has an overall dimension of 220mm in length, 160mm in width, and 45mm in height, and has four evenly distributed bolt holes for overall fixation, with a bolt hole diameter of 14mm.

[0024] The entire design domain was meshed using 3D solid 8-node hexahedral elements, with a global average mesh size set to 2.4 mm. After meshing, the design domain contained 150,000 finite element elements and 168,000 nodes. The raised region contained 47,000 elements, and the main region contained 103,000 elements.

[0025] Identify and select specific area units that need to maintain structural integrity: Take 4500 elements within a 2.4mm range extending outward from the wall of the pin hole in the raised area and mark them as undesignable elements; 7500 elements extending outward from the walls of the four fixed bolt holes in the main area within a 2.4mm radius are designated as undesignable elements; the boundary nodes of the bolt hole walls are used to apply fixed displacement constraints later. The physical density of the aforementioned 12,000 undesignable units is directly set and locked to 1.0, so that it remains a solid material in subsequent optimization iterations.

[0026] All 138,000 elements within the design domain, excluding the undesignable elements, are marked as designable elements. A uniform initial relative density value of 0.5 is assigned to these 138,000 elements.

[0027] Thus, all 150,000 elements in the design domain have clear initial density properties (12,000 elements with a density of 1.0 and 138,000 elements with a density of 0.5), and a finite element model of the initial density field containing geometric features, mesh nodes and density distribution has been successfully constructed.

[0028] 102. Based on the initial density field or the subsequently obtained updated density field, perform finite element analysis to obtain the strain energy distribution and von Mises stress value of each element. Then, use the solid isotropic material penalty model to calculate the target compliance based on the strain energy, and solve the sensitivity of the target compliance to the density of each element. Then, perform density filtering on the sensitivity to obtain the filtered sensitivity.

[0029] Specifically, based on the initial density field or the subsequently obtained projected density field as the current density field, a finite element stiffness matrix is ​​constructed, where the elastic modulus of each element is obtained by interpolation from the current density value of the element through a solid isotropic material penalty model; loads and constraints under actual working conditions of the jack are applied, and the equilibrium equations are solved to obtain the nodal displacements of each element; the strain energy of each element is calculated based on the nodal displacements, and the von Mises stress value of each element is extracted; the sum of the strain energies of all elements is used as the target compliance, and the sensitivity of the target compliance to the density of each element is solved to obtain the initial sensitivity; density filtering is applied to the initial sensitivity, with the filtering radius being a preset multiple of the element size to eliminate the checkerboard effect, resulting in the filtered sensitivity. Furthermore, density filtering employs a dynamic filtering radius: based on the spatial distance between each cell location and the root of the protrusion, the closer the distance, the smaller the filtering radius; and the farther the distance, the larger the filtering radius. This ensures that the filtering radius of the root region is smaller than that of the main region, preserving the high-frequency topological details of that region. The filtering radius of the main region is larger than that of the root region, suppressing the checkerboard effect. The upper and lower limits of the dynamic filtering radius are preset according to the cell size. This dynamic filtering radius is directly used to perform convolution operations on the initial sensitivity to obtain the filtered sensitivity.

[0030] It should be noted that the current density field (initially consisting of 12,000 undesignable elements with a density of 1.0 and 138,000 designable elements with a density of 0.5) is used as the benchmark, with the elastic modulus of high-strength cast steel ZG35CrMo being 210 GPa and Poisson's ratio being 0.3. Using a solid isotropic material penalty model (penalty factor set to 3), the current interpolated elastic modulus of each element is calculated (the initial interpolated elastic modulus of the designable elements is 26.25 GPa).

[0031] Full constraints are applied to the undesignable element boundary nodes of the four fixed bolt hole walls in the main region; a downward concentrated vertical load of 25 kN under actual working conditions is applied to the nodes inside the pin holes in the protruding region. The global stiffness matrix is ​​assembled and the equilibrium equations are solved to obtain the displacement vectors of each node. The strain energy distribution of each element is extracted based on the nodal displacements, and the von Mises stress value of each element is calculated.

[0032] The strain energies of all 150,000 elements are summed to obtain the overall target compliance of the structure (approximately 18.5 J in the initial state). Based on the derivative relationship between compliance and element density, the partial derivative of the target compliance with respect to each element density is solved one by one to obtain the initial sensitivity values ​​of 138,000 designable elements.

[0033] To eliminate the checkerboard effect and preserve details in key areas, a dynamic filtering radius strategy based on spatial distance is adopted: Using the root of the protrusion (the center of the transition plane where the protrusion intersects with the main body) as a reference point, calculate the spatial distance from the centroid of each unit to this reference point; The upper and lower limits of the dynamic filtration radius are set to 1.5 to 4.0 times the unit size (2.4 mm), i.e., 3.6 mm to 9.6 mm. The filtration radius in the raised root area (within the range of 0 mm to 20 mm) is linearly set to 3.6 mm to 4.8 mm; the filtration radius at the far end of the main body area (greater than 80 mm) gradually increases to 9.6 mm. The initial sensitivity of each cell is calculated using a neighborhood-weighted average convolution based on the dynamic filtering radius to eliminate abrupt changes in sensitivity between adjacent cells and output the filtered sensitivity.

[0034] 103. Using the P-norm to approximate the maximum von Mises stress, calculate the sensitivity of stress constraint to each element density, and then weight and combine this sensitivity with the filtered sensitivity to form a corrected sensitivity.

[0035] Specifically, using the filtered sensitivity and the von Mises stress value of each element as input, the maximum von Mises stress is approximated using the P-norm to construct a stress constraint function. This constraint function summarizes the von Mises stress of all elements in the design domain into a scalar value, ensuring that the maximum stress does not exceed the allowable stress of the material during the optimization process. The sensitivity of the stress constraint function to the density of each element is solved using the adjoint method to obtain the stress constraint sensitivity of each element. The filtered sensitivity and the currently calculated stress constraint sensitivity are weighted and summed according to preset weighting coefficients to form the corrected sensitivity.

[0036] Furthermore, the preset weighting coefficients are dynamically adjusted based on the ratio of the maximum von Mises stress to the allowable stress of the material within the design domain of the current iteration step: when this ratio is greater than the first preset threshold, the weighting coefficient of the stress constraint sensitivity increases, and the weighting coefficient of the filtered sensitivity decreases accordingly; when this ratio is less than the second preset threshold, the weighting coefficient of the stress constraint sensitivity decreases, and the weighting coefficient of the filtered sensitivity increases accordingly; the first preset threshold is greater than the second preset threshold, which ensures that stress constraints are prioritized in stress-critical areas and compliance is prioritized to be reduced in stress-safe areas. The dynamically adjusted weighting coefficients are directly used for weighted summation to form the corrected sensitivity.

[0037] It should be noted that the allowable stress of the high-strength cast steel material (ZG35CrMo) for the jack is set to 350 MPa. The von Mises stress distribution of the 150,000 elements obtained in step 102 is extracted, and the highest local stress extracted in the current iteration step is located in the transition region at the root of the protrusion, with a value of 420 MPa.

[0038] To aggregate the discrete stresses across the entire field into a differentiable scalar, the P-norm is used to approximate the maximum von Mises stress, with the P-norm parameter set to 8. This function is then used to perform condensed calculations on the stress values ​​of all elements across the entire field, constructing a scalar constraint function that reflects the overall stress state of the structure.

[0039] Using the constructed stress constraint function as the objective, the corresponding adjoint equation is established. Combining the global nodal displacement and stiffness matrices obtained in step 102, the adjoint method is used to solve the partial derivatives of the stress constraint function with respect to the density of 138,000 designable elements, efficiently solving for the stress constraint sensitivity of each designable element.

[0040] To prevent drastic weight changes from causing iterative oscillations, a smooth adjustment strategy is set: the first threshold is preset to 1.05, and the second threshold is preset to 0.85.

[0041] The ratio of the current maximum von Mises stress to the allowable stress, i.e., the ratio of 420 MPa to 350 MPa, is calculated and the result is 1.20.

[0042] Because the ratio of 1.20 is greater than the first preset threshold of 1.05, the system determines that the local stress exceeds the limit. The weighting coefficient of the stress constraint sensitivity is smoothly interpolated to the upper limit of 0.70, and the weighting coefficient of the filtered compliance sensitivity is smoothly interpolated to the lower limit of 0.30.

[0043] For 138,000 designable elements, the filtered compliance sensitivity is multiplied by 0.30 and then weighted and summed with the stress constraint sensitivity multiplied by 0.70 to calculate the corrected sensitivity for each element, which is used to guide the density iteration in the next stage.

[0044] 104. Based on the modified sensitivity, the density value of each element in the design domain is updated using the optimal criterion method. During the update process, draft angle constraints and minimum wall thickness constraints are applied. The draft angle constraint is achieved by limiting the density difference between adjacent elements in the draft direction to not exceed the preset gradient upper limit. The minimum wall thickness constraint is controlled by incrementally increasing the threshold parameter of the Heaviside projection. After the update, a new density field is obtained.

[0045] Specifically, using the modified sensitivity as input, the optimal criterion method is used to determine the density update direction and magnitude of each cell. The Lagrange multiplier is solved using the bisection method to satisfy the preset volume fraction constraint, resulting in the initial updated density field. Based on the initial updated density field, a draft angle constraint is applied: for each column of adjacent cells in the draft direction, if the density difference between them exceeds the preset gradient upper limit, the density value of the higher density cell is adjusted towards the lower density cell, so that the density change gradient in this direction is always within the gradient upper limit, resulting in a density field that meets the draft angle requirement. Based on the density field that meets the draft angle requirement, a minimum wall thickness constraint is applied: by setting the threshold parameter of the Heaviside projection and gradually increasing this parameter in subsequent iterations, the intermediate density cells in the current density field gradually separate towards 0 or 1, thereby suppressing the generation of fragmented features smaller than the minimum wall thickness, and finally obtaining a new density field that simultaneously satisfies the draft angle constraint and the minimum wall thickness constraint.

[0046] Furthermore, the draft angle constraint is achieved in the following way: taking the pre-set draft direction as the reference direction, the density gradient value between each column of adjacent cells in this direction is calculated; when the density gradient value exceeds the preset gradient upper limit, a density reduction operation is performed on the cell with the higher density value in the column, and the reduction amount is equal to the product of the excess part and the cell spacing, until the density gradient value between all adjacent cells in the column does not exceed the gradient upper limit; after processing all columns, a density field that meets the draft angle requirement is obtained.

[0047] It should be noted that, using the corrected sensitivity of the 138,000 designable elements calculated in step 103 as input, the upper limit of the volume fraction constraint of the structure is set to 0.40. The optimal criterion method is used, and the Lagrange multipliers are solved by the bisection method to determine the density update direction and magnitude of each element, and the initial updated density field is calculated.

[0048] The draft direction is set along the height of the jack (extending from the main structure towards the top of the protrusion). Based on a 2.4mm grid cell size, the upper limit of the gradient of the density difference between adjacent cells is preset to 0.15.

[0049] All element columns were traversed along the draft direction. In a certain vertical element column, the density values ​​of two adjacent elements were detected to be 0.85 and 0.60, respectively, with a density difference of 0.25 exceeding the gradient limit of 0.15. A pruning method combining upward scaling (filling) and smooth transition was adopted to adjust the lower density elements to 0.70, eliminating reverse draft undercuts while avoiding a sudden reduction in the overall structural volume. After correction, the Lagrange multipliers were readjusted to ensure that the overall volume fraction was strictly maintained at 0.40, outputting a density field that met the draft angle requirements.

[0050] Geometric control based on Heaviside projection is applied to the density field after draft adjustment. The preset minimum wall thickness is 7.2 mm (corresponding to 3 element widths).

[0051] In the current iteration, the threshold parameter of the Heaviside projection is increased from 2.0 in the previous step to 2.5, increasing the separation penalty for intermediate densities. By increasing the steepness of the projection function, intermediate density cells distributed between 0.2 and 0.8 are forced to converge towards 0 (void) or 1 (solid), forcibly eliminating small ribs and fragmented pores smaller than 7.2 mm, ultimately obtaining a new density field that simultaneously satisfies draft angle constraints and minimum wall thickness constraints.

[0052] 105. Apply Heaviside projection to the new density field to make the intermediate density converge to 0 or 1, and obtain the projected density field. Then repeat the above operation until the change in density field is less than the convergence threshold and the density field is basically stable for several consecutive iterations. The converged binarized density field is obtained as the initial topology shape. Finally, post-process the initial topology shape: delete isolated material elements that are not connected to the fixed boundary, and add rounded corner features at all sharp transition positions to output a castable jack hinge protrusion structure topology.

[0053] Specifically, a Heaviside projection is applied to the new density field. By setting a projection threshold parameter, all intermediate density values ​​in the new density field converge to a value of 0 or 1, resulting in the projected density field. The convergence condition is then determined: the absolute average of the density changes of all elements between the projected density field and the projected density field output in the previous iteration is calculated. If this absolute average is less than a preset convergence threshold and this condition is met for multiple consecutive iterations, convergence is confirmed, the iteration stops, and the current projected density field is used as the converged binarized density field, which is the initial topological shape. If the convergence condition is not met, the current projected density field is used as the input for the next iteration, and the aforementioned operation is repeated. The converged binarized density field is then post-processed: isolated material elements not connected to the fixed boundary are identified and deleted, and rounded corners with a preset radius of curvature are added to sharp transition points between all adjacent materials. The final output is a jack hinge protrusion structure topology that can be directly used for casting mold manufacturing.

[0054] It should be noted that the Heaviside projection function is applied to the new density field output in step 104. The projection truncation parameter is set to 0.5, and the kurtosis parameter is increased to 20, which accelerates the separation of the intermediate density values ​​between 0 and 1 in the 138,000 designable elements towards the two extremes, resulting in the binarized density field after projection in the current iteration step.

[0055] Extract the projected density field output from the 65th iteration and compare it with that from the 64th iteration: calculate the absolute value of the density change of each of the 150,000 elements and average it. The calculated absolute average value is 0.0008. The preset convergence threshold is 0.001.

[0056] Table 1

[0057] Since the density change in three consecutive iterations is less than 0.001, the system determines that the topology has stabilized and stops the loop iteration. At this point, the overall compliance has stabilized and converged to 16.2 J, and the maximum von Mises stress has decreased from the initial 420 MPa and stabilized at 310 MPa (below the allowable value of 350 MPa). The density field output in step 67 is used as the initial topology binarized mesh.

[0058] Geometric repair is performed on the converged binarized mesh: boundary smoothing is performed on the gray stray blocks at the edges to ensure the continuity of the stress path; at the intersection of the protrusion root and the main body and the edge of the internal hole, a transition fillet feature with a radius of 5mm is uniformly added to eliminate stress concentration and output a smooth castable topology.

[0059] 106. Import the topology of the castable jack hinge protrusion structure into the casting process simulation software, establish a three-dimensional casting model, set the gating system and riser positions, and perform simulation of the filling and solidification processes to obtain the predicted results of shrinkage porosity distribution inside the casting. Based on the predicted results of shrinkage porosity distribution, identify the location and volume of the shrinkage porosity area. If the shrinkage porosity area appears in key stress-bearing parts such as the root of the protrusion or the wall of the pin hole, perform local thickening treatment on the castable topology. The thickening amount is set according to the shrinkage porosity risk level until the shrinkage porosity volume ratio of the key parts is lower than the preset threshold, and obtain the corrected topology. Perform finite element static analysis on the corrected topology again to verify whether its compliance and maximum von Mises stress are within the allowable deviation range of the initial optimization results. If the deviation exceeds the preset range, return to perform the above operation and re-optimize the density field corresponding to the corrected topology as the initial density field. If the deviation is within the range, output the corrected topology as the final topology of the jack hinge protrusion structure.

[0060] Furthermore, the local thickening process specifically includes: taking the protrusion root region and the pin hole wall region as key stress-bearing parts, extracting the shrinkage volume ratio of the region; when the shrinkage volume ratio exceeds a preset threshold, increasing the material thickness along the outer surface normal direction of the region, the thickening amount being equal to the product of the shrinkage volume ratio of the region and the reference thickness divided by the material density correction coefficient, until the shrinkage volume ratio of the region is lower than the preset threshold, thus obtaining the corrected topology.

[0061] It should be noted that the 3D topological model of the jack hinge protrusion obtained from post-processing in step 105 was imported into the casting process simulation software. The casting material was set as ZG35CrMo cast steel, and the pouring temperature was set as 1560℃. A sprue was arranged on the side of the main structure, and a 22mm diameter heat-generating dark riser was set on the side of the thick root of the protrusion. Numerical simulation of the filling and solidification process was performed to obtain the predicted results of internal defects in the casting after solidification.

[0062] Simulation results indicate that local shrinkage porosity is predicted at the junction of the protrusion root and the pin hole wall. The extracted shrinkage porosity volume percentage in this region is 4.8%, exceeding the preset threshold of 1.5% for this location.

[0063] The local thickness was increased in the normal direction: the baseline wall thickness of the area was extracted as 18mm, the thickening correction factor was set to 0.8, and the calculated thickening thickness was 1.08mm (shrinkage rate 4.8% multiplied by the baseline thickness 18mm and divided by the factor 0.8). The material thickness was increased by 1.08mm along the normal direction of the protrusion root and the outer surface of the hole wall. After resimulation, the shrinkage volume ratio of the key parts decreased to 0.9%, meeting the requirements, and the corrected topology model was generated.

[0064] A finite element static analysis was performed again on the modified topology (with a 25kN vertical load and fixed constraints) to verify the performance deviation: Table 2

[0065] Secondary verification shows that the compliance and maximum stress deviation of the modified structure are both within the allowable deviation range of 5.0%, and there is no need to restart the topology optimization iteration. The modified topology is output as the topology of the jack hinge protrusion structure.

[0066] The present invention also provides a topology optimization device for a jack hinge protrusion structure. The topology optimization device for the jack hinge protrusion structure includes a memory and a processor. The memory stores computer-readable instructions. When the computer-readable instructions are executed by the processor, the processor performs the steps of the topology optimization method for the jack hinge protrusion structure in the above embodiments.

[0067] The present invention also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when the instructions are executed on a computer, cause the computer to perform the steps of the topology optimization method for the jack hinge protrusion structure.

[0068] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0069] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0070] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A topology optimization method for a jack hinged protrusion structure, characterized in that, include: A finite element model of the design domain is established, wherein the design domain is divided into an undesignable region and a designable region, and initial density values ​​are assigned to the designable elements in the designable region to form an initial density field. Finite element analysis is performed based on the initial density field or the updated density field during the iteration process to obtain the strain energy and stress value of each designable unit. The target compliance is calculated based on the strain energy. The initial sensitivity of the target compliance to the density value of the designable unit is solved, and the initial sensitivity is filtered to obtain the filtered sensitivity. The stress constraint sensitivity of the stress constraint to the density value of the designable unit is calculated based on the stress value, and the stress constraint sensitivity is combined with the filtered sensitivity to form a corrected sensitivity. The density value of the designable unit is updated using an optimization algorithm based on the modified sensitivity, and casting process constraints are applied during the update process to obtain the updated density field. The casting process constraints include at least draft angle constraints and minimum wall thickness constraints. Numerical projection is applied to the updated density field to make the density values ​​converge to binary. It is then determined whether the convergence condition is met. If the convergence condition is not met, the process returns to the step of performing finite element analysis based on the initial density field or the updated density field during the iteration process. If the convergence condition is met, the updated density field that meets the convergence condition is taken as the initial topological shape, and the initial topological shape is post-processed to output the topological model.

2. The topology optimization method for the jack hinged protrusion structure according to claim 1, characterized in that, The casting connection structure is a hinged protrusion structure of a jack. The undesignable area includes the units containing the pin holes and fixing holes used for assembly, and the unit density value of the undesignable area is fixed at 1.

3. The topology optimization method for the jack hinged protrusion structure according to claim 1, characterized in that, The step of performing finite element analysis based on the initial density field or the updated density field during the iteration process to obtain the strain energy and stress value of each designable element includes: The elastic modulus of each of the designable elements is calculated using a solid isotropic material penalty model; By applying loads and boundary constraints, the equilibrium equations are solved to obtain the nodal displacements; The strain energy of each designable unit is calculated based on the nodal displacement, and the von Mises stress is extracted as the stress value.

4. The topology optimization method for the jack hinged protrusion structure according to claim 1, characterized in that, The filtering of the initial sensitivity includes: Calculate the spatial distance from the designable unit to the preset reference position; The filter radius of the designable unit is dynamically adjusted based on the spatial distance. The smaller the spatial distance, the smaller the filter radius. The filtered sensitivity is obtained by calculating the initial sensitivity based on the filter radius.

5. The topology optimization method for the jack hinged protrusion structure according to claim 1, characterized in that, The calculation of the stress constraint sensitivity to the density value of the designable unit based on the stress value includes: The stress values ​​of the designable unit are approximated as the global maximum stress using the P-norm function, and a stress constraint function is constructed. The stress constraint sensitivity is obtained by solving the sensitivity of the stress constraint function to the density value of the designable element using the adjoint method.

6. The topology optimization method for the jack hinged protrusion structure according to claim 1, characterized in that, The step of combining the stress constraint sensitivity with the filtered sensitivity to form a modified sensitivity includes: The stress constraint sensitivity and the filtered sensitivity are weighted and summed using a preset weighting coefficient, wherein the preset weighting coefficient is dynamically adjusted based on the ratio of the maximum stress in the current design domain to the allowable stress of the material. When the ratio is greater than a first preset threshold, the preset weight coefficient of the stress constraint sensitivity is increased; when the ratio is less than a second preset threshold, the preset weight coefficient of the stress constraint sensitivity is decreased, and the first preset threshold is greater than the second preset threshold.

7. The topology optimization method for the jack hinged protrusion structure according to claim 1, characterized in that, The optimization algorithm is the optimal criterion method, and the update process combines the bisection method to solve for the volume fraction constraint. The draft angle constraint in the casting process constraint includes: calculating the density gradient value between adjacent designable units in the draft direction; if the density gradient value exceeds a preset gradient upper limit, reducing the density value of the designable unit with the higher density value until the density gradient value does not exceed the preset gradient upper limit. The minimum wall thickness constraint in the casting process constraint includes: gradually increasing the threshold parameter used for the numerical projection during the update process to suppress the generation of features smaller than the preset wall thickness size.

8. The topology optimization method for the jack hinged protrusion structure according to claim 1, characterized in that, The numerical projection is a Heaviside projection; The determination of whether the convergence condition is met includes: calculating the absolute average of the density changes of all the designable units between the currently obtained updated density field and the previously obtained updated density field; if the absolute average is less than a preset convergence threshold, it is determined that the convergence condition is met.

9. The topology optimization method for the jack hinged protrusion structure according to claim 1, characterized in that, It also includes the steps of verifying and correcting the topology model: The topological model is imported into the simulation model to perform solidification process simulation and obtain the predicted results of shrinkage distribution. Based on the predicted shrinkage distribution, the shrinkage region and its shrinkage volume ratio are extracted. If the shrinkage volume ratio is higher than a preset threshold, the topology model is locally thickened to obtain a corrected topology model. The modified topology model is re-verified by finite element static analysis. If its mechanical performance deviation is within the allowable range, the modified topology model is output as the final result.

10. The topology optimization method for the jack hinged protrusion structure according to claim 9, characterized in that, The local thickening treatment specifically involves increasing the material thickness along the normal direction of the outer surface of the shrinkage area, with the amount of thickening being positively correlated with the product of the shrinkage volume fraction and the reference thickness.

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