Multi-sealing method and system for high-vacuum die-casting molds based on topology optimization

Abstract

The present invention provides a multi-sealing method and system for a high-vacuum die-casting mold based on topology optimization, which relates to the technical field of mold structures, and includes establishing a parametric model of the sealing structure, obtaining the geometric parameters and boundary conditions of the cavity wall surface, constructing an initial design domain and dividing grid cells; performing topology optimization calculations based on a multi-objective function considering the contact stress distribution, and using the SIMP method to iteratively optimize the relative density of the grid cells; designing a multi-sealing structure according to the obtained topological configuration of the sealing structure, constructing a three-dimensional solid model and verifying the sealing performance through finite element analysis.

Description

Technical Field

[0001] The present invention relates to the technology of die structures, and particularly to a multi - seal method and system for high - vacuum die - casting dies based on topology optimization. Background Art

[0002] In the prior art, a single - seal structure is difficult to adapt to different working conditions and pressure distributions, and problems such as local leakage or excessive compression are likely to occur, affecting the sealing effect and service life of the die. Traditional methods for designing seal structures are difficult to accurately predict the contact stress distribution between the seal structure and the cavity wall surface, and cannot effectively optimize the shape and size of the seal structure, resulting in unstable sealing performance.

[0003] The existing seal structure design lacks consideration of multi - seal, and it is difficult to achieve coordinated sealing in multiple levels and regions, and cannot meet the sealing requirements of high - precision and high - reliability dies. These problems seriously restrict the further development and application of die - sealing technology. Summary of the Invention

[0004] Embodiments of the present invention provide a multi - seal method and system for high - vacuum die - casting dies based on topology optimization, which can solve the problems in the prior art.

[0005] In the first aspect of the embodiments of the present invention,

[0006] A multi - seal method for high - vacuum die - casting dies based on topology optimization is provided, including:

[0007] Establishing a parametric model of the seal structure, including: obtaining the geometric parameters and boundary conditions of the cavity wall surface of the die, constructing an initial design domain of the seal structure, dividing grid cells in the initial design domain, taking the relative density of the grid cells as design variables, establishing contact constraint conditions between the seal structure and the cavity wall surface, and constructing a multi - objective function considering the contact stress distribution;

[0008] Performing topology optimization calculations based on the multi - objective function, including: using the solid isotropic material with penalization method to iteratively optimize the relative density of the grid cells, calculating the contact stress distribution between the seal structure and the cavity wall surface in each iteration process, and correcting the multi - objective function according to the contact stress distribution until a seal - structure topology configuration that meets the convergence conditions is obtained;

[0009] Designing a multi - seal structure based on the seal - structure topology configuration, including: extracting the boundary contour of the seal - structure topology configuration, constructing a three - dimensional solid model of the multi - seal structure based on the boundary contour, performing finite - element analysis on the three - dimensional solid model to verify the sealing performance, and optimizing and adjusting the multi - seal structure according to the finite - element analysis results.

[0010] In an alternative embodiment,

[0011] Establish a parametric model of the sealing structure, including: obtaining the geometric parameters and boundary conditions of the cavity wall of the mold, constructing the initial design domain of the sealing structure, dividing grid cells in the initial design domain, taking the relative density of the grid cells as the design variable, and establishing the contact constraint conditions between the sealing structure and the cavity wall. The steps of constructing a multi-objective function considering the contact stress distribution include:

[0012] Obtain point cloud data through a three-dimensional scanning system, perform point cloud registration using the iterative closest point algorithm, and reconstruct the cavity wall using the radial basis function interpolation method of local quadratic surface fitting. Combine the pressure sensor array arranged on the cavity wall to obtain pressure distribution data, and obtain the geometric parameters and boundary conditions of the cavity wall;

[0013] According to the obtained geometric parameters and boundary conditions, describe the topological structure using the level set method, and establish a design domain by constructing an initial level set function through the distance field. The initial level set function greater than zero is the solid region, equal to zero is the boundary, and less than zero is the cavity region, to obtain the initial design domain of the sealing structure;

[0014] Divide grid cells in the initial design domain using an adaptive grid refinement strategy, take the relative density of the grid cells as the design variable, and use the SIMP penalty factor method to control the relative density distribution;

[0015] Based on the divided grid cells, use the mortar method to establish the contact constraint conditions between the sealing structure and the cavity wall. Divide the contact surface into mortar cells of the subordinate surface and non-mortar cells of the main surface, and use the piecewise bilinear interpolation function to calculate the contact integral to obtain the stress distribution in the contact area;

[0016] According to the relative density distribution of the grid cells and the stress distribution in the contact area, construct a multi-objective function including a volume fraction objective, a von Mises stress objective, and a contact pressure standard deviation objective.

[0017] In an alternative implementation,

[0018] Perform topology optimization calculation based on the multi-objective function, including: using the solid isotropic material with penalty method to iteratively optimize the relative density of the grid cells, calculating the contact stress distribution between the sealing structure and the cavity wall during each iteration, and correcting the multi-objective function according to the contact stress distribution until a sealing structure topology configuration that meets the convergence conditions is obtained. The steps include:

[0019] Construct a multi-objective function that includes a volume fraction objective, a von Mises stress objective, and a standard deviation of contact pressure objective. The volume fraction objective is the ratio of the sum of the products of the relative density of each element and its volume to the volume of the initial design domain. The von Mises stress objective is represented in the form of a p-norm to characterize the ratio of the von Mises stress of each element to the allowable stress. The standard deviation of contact pressure objective is the ratio of the standard deviation of contact pressure to the average contact pressure. Set volume constraints, stress constraints, and density constraints for the multi-objective function. The density constraint limits the range of values of the relative density of each element.

[0020] Use the solid isotropic material penalization method to iteratively optimize the relative density of grid elements. The solid isotropic material penalization method includes: achieving density filtering through Heaviside projection and introducing a density gradient constraint to limit the density change between adjacent elements; in each iterative optimization process, use the penalty function method to calculate the normal contact force between the sealing structure and the cavity wall surface, and consider the friction effect to calculate the tangential contact force. The normal contact force is updated through an adaptive contact stiffness.

[0021] Based on the obtained normal contact force and tangential contact force, calculate the sensitivity of the multi-objective function to the design variables, including calculating the sensitivity of the volume objective, the stress objective, and the standard deviation of contact pressure objective; input the calculated sensitivity of the multi-objective function to the design variables into a sequential quadratic programming algorithm, and solve the multi-objective function through a dynamic weight coefficient adjustment strategy.

[0022] Judge whether the optimization process terminates according to the multi-objective function convergence criterion and the design variable convergence criterion. When either convergence criterion is met and the number of iterations is not less than the minimum number of iterations, obtain the final topological configuration of the sealing structure.

[0023] In an optional implementation manner,

[0024] Use the solid isotropic material penalization method to iteratively optimize the relative density of grid elements. The steps of the solid isotropic material penalization method that include: achieving density filtering through Heaviside projection and introducing a density gradient constraint to limit the density change between adjacent elements include:

[0025] Use the Heaviside projection function to filter the relative density of grid elements, and map the original relative density of grid elements through an exponential function to obtain the filtered relative density; dynamically update the projection parameter of the Heaviside projection function, and gradually increase the projection parameter by setting a growth factor.

[0026] Establish a density gradient constraint relationship between adjacent grid elements. According to the distance between the center points of two adjacent grid elements, determine the upper limit of the relative density difference between the two adjacent grid elements, and limit the relative density difference within the upper limit range.

[0027] Establish an adaptive update mechanism for density gradient constraints, and dynamically adjust the density gradient constraint parameters based on the ratio of the von Mises stress to the allowable stress of the grid cells;

[0028] Calculate the sensitivity considering the Heaviside projection and density gradient constraints, including: calculating the sensitivity of the relative density of grid cells to design variables, calculating the sensitivity of density gradient constraints to design variables, and using Lagrange multipliers to combine the sensitivity of the relative density of grid cells to design variables and the sensitivity of density gradient constraints to design variables to obtain the corrected sensitivity;

[0029] Iteratively optimize the relative density of grid cells based on the corrected sensitivity until a material distribution that meets the convergence criterion is obtained.

[0030] In an optional implementation manner,

[0031] Conduct multi - seal structure design based on the topological configuration of the seal structure, including: extracting the boundary contour of the seal structure topological configuration, constructing a three - dimensional solid model of the multi - seal structure based on the boundary contour, performing finite element analysis on the three - dimensional solid model to verify the sealing performance, and the steps of optimizing and adjusting the multi - seal structure according to the finite element analysis results include:

[0032] Convert the relative density field of the seal structure into a discrete scalar field, use an isocontour extraction method based on grid division to obtain the boundary contour point set of the seal structure, and perform B - spline curve fitting on the boundary contour point set to obtain a smooth boundary contour;

[0033] Construct a three - dimensional solid model of the multi - seal structure based on the smooth boundary contour, including: constructing involute seal elements using involute surfaces and constructing hyperbolic seal elements using hyperbolic surfaces;

[0034] Perform grid division on the three - dimensional solid model, where hexahedral meshes are used for the seal contact area and tetrahedral meshes are used for the transition connection area, and establish a finite element analysis model including contact nonlinearity; set assembly pre - tightening, working pressure, temperature cycle, and vibration load conditions in the finite element analysis model, calculate the seal surface contact force using the augmented Lagrangian method, and perform stress - strain analysis considering the material elastoplastic effect;

[0035] Based on the finite element analysis results, establish a structural optimization model with the leakage rate and maximum stress as optimization objectives and the contact pressure and seal deformation as constraint conditions; use the sequential quadratic programming method to solve the structural optimization model, and iteratively optimize the seal table angle, curvature, transition region shape, and size parameters in the three - dimensional solid model until the sealing performance requirements are met.

[0036] In an alternative embodiment,

[0037] Construct a three-dimensional solid model of a multi-seal structure based on the fairing boundary profile, including: constructing an involute seal element using an involute surface, and constructing a hyperboloid seal element using a hyperboloid. The steps include:

[0038] Construct an involute seal element, including: generating the base surface of the main seal platform using the parametric equation of a variable pitch involute surface, superimposing circumferential and radial micro-ripple profiles on the base surface of the main seal platform, and mathematically describing the base surface of the main seal platform with micro-ripple profiles using a NURBS surface equation;

[0039] Construct a hyperboloid seal element, including: generating the base surface of the secondary seal platform using the parametric equation of a single-sheet hyperboloid, and correcting the base surface of the secondary seal platform by introducing a stress concentration relaxation function;

[0040] Construct a connecting transition element, including: establishing a transition surface optimization model based on the minimum surface energy functional, and solving the transition surface optimization model using boundary curve constraints and normal vector constraints to obtain a transition surface that meets the geometric continuity requirements;

[0041] Combine the involute seal element, the hyperboloid seal element, and the connecting transition element into a three-dimensional solid model of a multi-seal structure through a Boolean union operation.

[0042] In an alternative embodiment,

[0043] Establish a structural optimization model with the leakage rate and the maximum stress as the optimization objectives and the contact pressure and seal deformation as the constraint conditions based on the finite element analysis results; solve the structural optimization model using the sequential quadratic programming method, and perform iterative optimization on the seal platform angle, curvature, transition region shape, and size parameters in the three-dimensional solid model until the seal performance requirements are met. The steps include:

[0044] The leakage rate is calculated based on the contact deformation amount, contact pressure, surface roughness correction coefficient, leakage path length, and fluid parameters, and the maximum stress is calculated using the von Mises equivalent stress criterion;

[0045] Use the orthogonal experimental design method to calculate the sensitivity coefficients of the seal platform angle, curvature, transition region shape, and size parameters to the leakage rate and the maximum stress;

[0046] Solve the structural optimization model using the sequential quadratic programming method based on the sensitivity coefficients, construct a quadratic programming sub-problem by calculating the gradient vector and the second derivative matrix, and perform optimization iteration on the seal platform angle, curvature, transition region shape, and size parameters;

[0047] When the leakage rate and the maximum stress meet the sealing performance requirements, output the optimal sealing table angle, curvature, shape and size parameters of the transition region.

[0048] In the second aspect of the embodiments of the present invention,

[0049] a multiple sealing system for a high-vacuum die-casting mold based on topology optimization is provided, including:

[0050] a first unit for establishing a parametric model of the sealing structure, including: obtaining the geometric parameters and boundary conditions of the cavity wall surface of the mold, constructing an initial design domain of the sealing structure, dividing grid cells in the initial design domain, taking the relative density of the grid cells as design variables, establishing contact constraint conditions between the sealing structure and the cavity wall surface, and constructing a multi-objective function considering the contact stress distribution;

[0051] a second unit for performing topology optimization calculation based on the multi-objective function, including: iteratively optimizing the relative density of the grid cells by using the solid isotropic material penalization method, calculating the contact stress distribution between the sealing structure and the cavity wall surface in each iteration process, and correcting the multi-objective function according to the contact stress distribution until a sealing structure topology configuration that meets the convergence conditions is obtained;

[0052] a third unit for designing a multiple sealing structure according to the sealing structure topology configuration, including: extracting the boundary contour of the sealing structure topology configuration, constructing a three-dimensional solid model of the multiple sealing structure based on the boundary contour, performing finite element analysis on the three-dimensional solid model to verify the sealing performance, and optimizing and adjusting the multiple sealing structure according to the finite element analysis results.

[0053] In the third aspect of the embodiments of the present invention,

[0054] an electronic device is provided, including:

[0055] a processor;

[0056] a memory for storing instructions executable by the processor;

[0057] wherein, the processor is configured to call the instructions stored in the memory to execute the method described above.

[0058] In the fourth aspect of the embodiments of the present invention,

[0059] a computer-readable storage medium is provided, on which computer program instructions are stored, and when the computer program instructions are executed by a processor, the method described above is implemented.

[0060] By establishing a parametric model of the sealing structure, taking the relative density of grid cells as the design variable, and considering the multi-objective function of the contact stress distribution, the present invention can more accurately describe the mechanical behavior of the sealing structure, provide a reliable theoretical basis for subsequent optimization design, and improve the scientificity and rationality of the sealing structure design.

[0061] The present invention uses the solid isotropic material with penalty method for topology optimization calculation, and in the iterative process, it considers the influence of the contact stress distribution on the objective function in real time, so as to obtain a more reasonable topological configuration of the sealing structure, avoid the blindness of traditional empirical design methods, and improve the design efficiency and optimization effect of the sealing structure.

[0062] By performing three-dimensional solid modeling and finite element analysis verification on the obtained topological configuration of the sealing structure, and making optimization adjustments accordingly, the present invention ensures that the final designed multi-sealing structure has good sealing performance, improves the reliability and service life of the mold sealing structure, and has important engineering application value. Brief Description of the Drawings

[0063] Figure 1 is a schematic flow chart of the multi-sealing method for high-vacuum die-casting molds based on topology optimization according to an embodiment of the present invention;

[0064] Figure 2 is a schematic structural diagram of the multi-sealing system for high-vacuum die-casting molds based on topology optimization according to an embodiment of the present invention. Detailed Embodiments

[0065] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0066] The technical solutions of the present invention will be described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments.

[0067] Figure 1 is a schematic flow chart of the multi-sealing method for high-vacuum die-casting molds based on topology optimization according to an embodiment of the present invention, as Figure 1 shown, the method includes:

[0068] S1. Establish a parametric model of the sealing structure, including: obtaining the geometric parameters and boundary conditions of the cavity wall of the mold, constructing the initial design domain of the sealing structure, dividing grid cells in the initial design domain, taking the relative density of the grid cells as the design variable, establishing the contact constraint conditions between the sealing structure and the cavity wall, and constructing a multi-objective function considering the contact stress distribution;

[0069] S2. Perform topology optimization calculations based on the multi-objective function, including: using the solid isotropic material with penalization method to iteratively optimize the relative density of the grid cells, calculating the contact stress distribution between the sealing structure and the cavity wall during each iteration, and correcting the multi-objective function according to the contact stress distribution until a sealing structure topology configuration that meets the convergence conditions is obtained;

[0070] S3. Design a multi-layer sealing structure based on the sealing structure topology configuration, including: extracting the boundary contour of the sealing structure topology configuration, constructing a three-dimensional solid model of the multi-layer sealing structure based on the boundary contour, performing finite element analysis on the three-dimensional solid model to verify the sealing performance, and optimizing and adjusting the multi-layer sealing structure according to the finite element analysis results.

[0071] Exemplarily, first, establish a parametric model of the sealing structure. Obtain the geometric parameters of the mold cavity wall through three-dimensional scanning or measurement, including information such as the size, shape, and curvature of the cavity. At the same time, determine the boundary conditions, such as the applied pressure, temperature, etc. Construct an initial sealing structure design domain around the mold cavity, and the size of this design domain should be larger than the expected size of the final sealing structure. Then divide grid cells in the design domain, and the size of the grid cells is determined according to the calculation accuracy requirements. Usually, hexahedral cells are selected, and the cell size is about 0.5 - 2 mm. Take the relative density of each grid cell as the design variable, and the value range of the relative density is 0 - 1, where 0 means there is no material in the cell and 1 means the cell is filled with material.

[0072] Next, establish the contact constraint conditions between the sealing structure and the cavity wall. Define the contact area between the sealing structure and the cavity wall, set the contact type as surface-to-surface contact, and the friction coefficient is taken as 0.1 - 0.3. Construct a multi-objective function considering the contact stress distribution, including the objective of minimizing the volume of the sealing structure and the objective of uniformizing the contact stress. The objective of minimizing the volume can reduce the material cost, and the objective of uniformizing the contact stress can improve the sealing effect.

[0073] Then, topology optimization calculations are performed based on multi-objective functions. The Solid Isotropic Material with Penalization (SIMP) method is used to iteratively optimize the relative density of grid cells. In each iteration, first, the stiffness matrix of the structure is calculated according to the current relative density distribution, then the displacement field is solved, and the contact stress distribution between the sealing structure and the cavity wall is calculated. The multi-objective function is corrected according to the contact stress distribution to make the contact stress distribution more uniform. An optimization algorithm such as the Moving Asymptotes Method (MMA) is used to update the design variables, that is, the relative density of grid cells. The above process is repeated until the convergence condition is met, such as the relative change of the objective function is less than 0.1% or the maximum number of iterations 100 times is reached. Finally, a sealing structure topology configuration that meets the requirements is obtained.

[0074] Finally, a multi-sealing structure design is carried out based on the sealing structure topology configuration. First, the boundary contour of the sealing structure topology configuration is extracted. The isosurface method can be used to extract the isosurface with a relative density of 0.5 as the boundary. Based on the extracted boundary contour, a three-dimensional solid model of the multi-sealing structure is constructed. The multi-sealing structure usually includes 2 - 3 sealing lips. The height of each sealing lip is 3 - 5 mm, the width is 2 - 4 mm, and the spacing between the sealing lips is 5 - 8 mm. Finite element analysis is performed on the constructed three-dimensional solid model to verify its sealing performance. The analysis content includes the deformation, stress distribution of the sealing structure under pressure, and the contact pressure distribution with the cavity wall. According to the analysis results, the multi-sealing structure is optimized and adjusted, such as adjusting the shape, size, and position of the sealing lips, until the sealing performance requirements are met.

[0075] In practical applications, rubber materials such as nitrile rubber or fluororubber can be selected as the materials for the sealing structure. The Young's modulus of the material can be taken as 2 - 5 MPa, and the Poisson's ratio is taken as 0.48 - 0.49. The pressure of the mold cavity can be set to 5 - 20 MPa, and the temperature range is 20 - 200 °C. The multi-sealing structure designed by the above method can effectively seal the mold cavity and prevent the leakage of molten materials.

[0076] Through the topology optimization method, the present invention can obtain a more reasonable shape of the sealing structure, significantly reduce the material usage of the sealing structure compared with the traditional design method, and reduce costs; the multi-objective optimization considering the contact stress distribution can make the contact stress distribution between the sealing structure and the cavity wall more uniform, improve the sealing effect, and extend the service life of the sealing structure; the multi-sealing structure design improves the reliability of the seal. Even if a single sealing lip fails, the other sealing lips can still maintain the sealing effect, greatly reducing the risk of mold leakage.

[0077] In an alternative embodiment,

[0078] Establish a parametric model of the sealing structure, including: obtaining the geometric parameters and boundary conditions of the cavity wall of the mold, constructing the initial design domain of the sealing structure, dividing grid cells in the initial design domain, taking the relative density of the grid cells as the design variable, and establishing the contact constraint conditions between the sealing structure and the cavity wall. The steps of constructing a multi-objective function considering the contact stress distribution include:

[0079] Obtain point cloud data through a three-dimensional scanning system, perform point cloud registration using the iterative closest point algorithm, and reconstruct the cavity wall using the radial basis function interpolation method of local quadratic surface fitting. Combine the pressure sensor array arranged on the cavity wall to obtain pressure distribution data, and obtain the geometric parameters and boundary conditions of the cavity wall;

[0080] According to the obtained geometric parameters and boundary conditions, describe the topological structure using the level set method, and establish the design domain by constructing the initial level set function through the distance field. The initial level set function greater than zero is the solid region, equal to zero is the boundary, and less than zero is the cavity region, to obtain the initial design domain of the sealing structure;

[0081] In the initial design domain, divide grid cells using an adaptive grid refinement strategy, take the relative density of the grid cells as the design variable, and use the SIMP penalty factor method to control the relative density distribution;

[0082] Based on the divided grid cells, use the mortar method to establish the contact constraint conditions between the sealing structure and the cavity wall, divide the contact surface into mortar cells of the subordinate surface and non-mortar cells of the main surface, and use the piecewise bilinear interpolation function to calculate the contact integral to obtain the stress distribution in the contact area;

[0083] According to the relative density distribution of the grid cells and the stress distribution in the contact area, construct a multi-objective function including the volume fraction objective, von Mises stress objective, and contact pressure standard deviation objective.

[0084] Exemplarily, first, scan the mold cavity through a three-dimensional laser scanning system to obtain high-precision point cloud data. Use the iterative closest point algorithm to register the point cloud data obtained from multiple scans to eliminate scanning errors. Then use the radial basis function interpolation method of local quadratic surface fitting to reconstruct the geometric model of the cavity wall. Specifically, select the feature points in the point cloud data as the interpolation center points, construct the radial basis function based on these center points, solve the weight coefficients of the radial basis function by the least squares method, and finally obtain the parametric expression of the cavity wall. At the same time, arrange a pressure sensor array on the cavity wall to collect the pressure distribution data during the actual molding process. Take the obtained geometric model and pressure distribution data as the boundary conditions for subsequent optimization.

[0085] Next, based on the obtained cavity wall geometry model, the level set method is used to describe the topology of the sealing structure. The initial level set function is established by constructing a distance field function. The area with a function value greater than zero represents a solid, equal to zero represents a boundary, and less than zero represents a cavity.

[0086] In the established initial design domain, an adaptive mesh refinement strategy is used for mesh division. First, the entire design domain is roughly divided using a uniform hexahedral mesh, and then the boundary area is locally encrypted based on the gradient information of the level set function. Specifically, the gradient value of the level set function in each mesh unit is calculated. If the gradient value is greater than the preset threshold, the unit is refined by four or eight points. This process is repeated until the predetermined mesh accuracy is achieved. For each mesh unit obtained by division, the relative density ρ is introduced as a design variable. The value range of ρ is 0 to 1, where 0 represents a cavity and 1 represents a solid. The SIMP (Solid Isotropic Material with Penalization) method is used to penalize the intermediate density so that the final result tends to a 0-1 distribution.

[0087] In order to describe the contact relationship between the sealing structure and the cavity wall, the mortar method is used to establish the contact constraint conditions. The contact surface is divided into a slave surface (non-mortar surface) and a master surface (mortar surface). A piecewise linear basis function is defined on the slave surface, and a piecewise bilinear basis function is defined on the master surface. The displacement field on the contact surface is obtained by interpolation of these basis functions, and the Lagrange multiplier method is used to enforce displacement continuity. Specifically, a local coordinate system is first established in the contact area, and the slave surface nodes are projected onto the master surface. Then the master surface interpolation function value corresponding to each slave surface node is calculated, and the mortar integral matrix is ​​established. Finally, the equilibrium equation containing the contact constraint is solved to obtain the stress distribution in the contact area.

[0088] Based on the above modeling process, an optimization function containing multiple objectives is constructed. The objective functions include: volume fraction, which is used to control the material dosage; von Mises stress, which is used to evaluate the structural strength; and the standard deviation of the contact pressure, which is used to evaluate the sealing uniformity. The weighted summation method is used to combine multiple objectives into a single objective function. The importance of different objectives can be balanced by adjusting the weight coefficient. For example, the weight ratio of volume fraction, von Mises stress, and standard deviation of contact pressure can be set to 1:3:2. Finally, the gradient descent method is used to optimize and solve the objective function, and the design variables are continuously updated until convergence to obtain the optimal sealing structure topology.

[0089] The present invention obtains accurate boundary conditions through three-dimensional scanning and a pressure sensor array, improving the accuracy of the model; adopts the level set method and adaptive mesh generation, which can flexibly represent complex topologies and improve the calculation efficiency; introduces the mortar contact method to accurately describe the interaction between the sealing structure and the cavity wall surface, facilitating the optimization of the sealing performance.

[0090] In an alternative embodiment,

[0091] The topology optimization calculation based on the multi-objective function includes: iteratively optimizing the relative density of grid cells using the solid isotropic material with penalization method, calculating the contact stress distribution between the sealing structure and the cavity wall surface during each iteration, and correcting the multi-objective function according to the contact stress distribution until a sealing structure topology configuration that meets the convergence conditions is obtained. The steps include:

[0092] Construct a multi-objective function including a volume fraction objective, a von Mises stress objective, and a contact pressure standard deviation objective. The volume fraction objective is the ratio of the sum of the product of the relative density of cells and the cell volume to the volume of the initial design domain. The von Mises stress objective uses the p-norm form to represent the ratio of the von Mises stress of cells to the allowable stress. The contact pressure standard deviation objective is the ratio of the contact pressure standard deviation to the average contact pressure; set volume constraints, stress constraints, and density constraints for the multi-objective function, and the density constraint conditions limit the value range of the relative density of cells;

[0093] Iteratively optimize the relative density of grid cells using the solid isotropic material with penalization method, which includes: achieving density filtering through Heaviside projection and introducing density gradient constraints to limit the density change between adjacent cells; during each iterative optimization process, calculate the normal contact force between the sealing structure and the cavity wall surface using the penalty function method, and consider the friction effect to calculate the tangential contact force. The normal contact force is updated through an adaptive contact stiffness;

[0094] Based on the obtained normal contact force and tangential contact force, calculate the sensitivity of the multi-objective function to the design variables, including calculating the volume objective sensitivity, stress objective sensitivity, and contact pressure standard deviation objective sensitivity; input the calculated sensitivity of the multi-objective function to the design variables into the sequential quadratic programming algorithm and solve the multi-objective function through a dynamic weight coefficient adjustment strategy;

[0095] Judge whether the optimization process terminates according to the multi-objective function convergence criterion and the design variable convergence criterion. When either convergence criterion is met and the number of iterations is not less than the minimum number of iterations, obtain the final sealing structure topology configuration.

[0096] Exemplarily, to achieve the topology optimization of the sealing structure based on multi-objective functions, a multi-objective function including a volume fraction objective, a von Mises stress objective, and a contact pressure standard deviation objective is first constructed. The volume fraction objective is defined as the ratio of the sum of the product of the relative density of the element and the element volume to the volume of the initial design domain, and is used to control the material usage of the final structure. The von Mises stress objective adopts the p-norm form to characterize the ratio of the von Mises stress of the element to the allowable stress, and is used to ensure the strength requirements of the structure. The contact pressure standard deviation objective is defined as the ratio of the contact pressure standard deviation to the average contact pressure, and is used to evaluate the uniformity of the contact pressure distribution.

[0097] Constraints are set for the multi-objective function, including volume constraint, stress constraint, and density constraint. The volume constraint limits the volume fraction of the final structure not to exceed a given value, such as 0.3. The stress constraint requires that the von Mises stress of the element does not exceed the allowable stress of the material, such as 200 MPa. The density constraint limits the value range of the relative density of the element to be from 0.001 to 1.

[0098] The solid isotropic material penalization method is used to iteratively optimize the relative density of the grid elements. First, density filtering is achieved through the Heaviside projection to eliminate the checkerboard phenomenon. A density gradient constraint is introduced to limit the density change between adjacent elements not to exceed 0.2 to avoid jagged boundaries. In each iteration process, the penalty function method is used to calculate the normal contact force between the sealing structure and the cavity wall surface. The normal contact force is updated through an adaptive contact stiffness, and the initial contact stiffness is set to 1*10 5 N / mm, and it is updated every 10 iterations. Considering the friction effect, the Coulomb friction model is used to calculate the tangential contact force, and the friction coefficient is taken as 0.1.

[0099] Based on the obtained normal contact force and tangential contact force, the sensitivity of the multi-objective function to the design variables is calculated. The volume objective sensitivity is the element volume, and the stress objective sensitivity is solved by the adjoint method. The contact pressure standard deviation objective sensitivity is calculated by the finite difference method, and the perturbation amount is taken as 1*10 -6 . The calculated sensitivity of the multi-objective function is input into the sequential quadratic programming algorithm for solution. A dynamic weight coefficient adjustment strategy is adopted. The initial weights of each objective are equal, and the weight coefficients are updated every 50 iterations.

[0100] According to the multi-objective function convergence criterion and the design variable convergence criterion, it is judged whether the optimization process terminates. The multi-objective function convergence criterion is that the change in the objective function value for 5 consecutive iterations is less than 1*10 -4 . The design variable convergence criterion is that the maximum change in the design variables for 5 consecutive iterations is less than 1*10 -3 . When either convergence criterion is satisfied and the number of iterations is not less than 100, the final topological configuration of the sealing structure is obtained.

[0101] In practical applications, the above parameters can be adjusted according to specific problems. For example, for an optimization problem of a sealing ring structure, the initial design domain is a cuboid with dimensions of 100mm×50mm×10 mm, and a hexahedral element mesh with 20×10×2 is used for meshing. The material is rubber, with an elastic modulus of 10MPa and a Poisson's ratio of 0.49. Through the above method for optimization calculation, convergence is achieved after 153 iterations, and the final topological configuration of the sealing structure is obtained. The volume fraction of the optimized structure is 0.28, the maximum von Mises stress is 195 MPa, and the ratio of the standard deviation of the contact pressure to the average contact pressure is 0.15.

[0102] The present invention realizes the unification of lightweight design, strength guarantee, and contact performance optimization of the sealing structure by constructing a multi-objective function including volume fraction, stress, and contact pressure distribution; adopts the solid isotropic material penalization method combined with density filtering and gradient constraint to effectively eliminate numerical instability and obtain a clear topological configuration; considers contact and friction effects and adopts a dynamic weight adjustment strategy to improve the engineering practicability and calculation efficiency of the optimization results.

[0103] In an alternative embodiment,

[0104] The relative density of grid cells is iteratively optimized using the solid isotropic material penalization method. The solid isotropic material penalization method includes the steps of: realizing density filtering through Heaviside projection and introducing density gradient constraints to limit the density change of adjacent cells, including:

[0105] Filtering the relative density of grid cells using the Heaviside projection function, mapping the original relative density of grid cells through an exponential function to obtain the filtered relative density; dynamically updating the projection parameter of the Heaviside projection function, and gradually increasing the projection parameter by setting a growth factor;

[0106] Establishing a density gradient constraint relationship for adjacent grid cells, determining the upper limit of the relative density difference between two adjacent grid cells according to the distance between the center points of the two adjacent grid cells, and restricting the relative density difference within the upper limit range;

[0107] Establishing an adaptive update mechanism for density gradient constraints, and dynamically adjusting the density gradient constraint parameters based on the ratio of the von Mises stress of grid cells to the allowable stress;

[0108] Calculate the sensitivity considering the Heaviside projection and density gradient constraints, including: calculating the sensitivity of the relative density of grid cells to design variables, calculating the sensitivity of density gradient constraints to design variables, and using Lagrange multipliers to combine the sensitivity of the relative density of grid cells to design variables and the sensitivity of density gradient constraints to design variables to obtain the corrected sensitivity;

[0109] Iteratively optimize the relative density of grid cells based on the corrected sensitivity until a material distribution that meets the convergence criterion is obtained.

[0110] Exemplarily, first, perform Heaviside projection filtering on the relative density of grid cells. Map the original relative density to the filtered relative density through an exponential function to achieve density filtering. Specifically, select the initial value of the projection parameter β as 1 and the growth factor γ as 1.5. In each iteration, update β by multiplying it by γ to gradually enhance the projection effect. For example, initially β = 1, after the first iteration β = 1.5, after the second iteration β = 2.25, and so on.

[0111] Secondly, establish the density gradient constraint for adjacent grid cells. Determine the upper limit Δρ of the relative density difference according to the distance d between the center points of two adjacent cells Max ; when d ≤ 10 mm, Δρ Max = 0.2; when 10 mm < d ≤ 20 mm, Δρ Max = 0.3; when d > 20 mm, Δρ Max = 0.4. During the optimization process, limit the relative density difference between adjacent cells within the range of Δρ Max .

[0112] Then, establish an adaptive update mechanism for density gradient constraints. Calculate the ratio R of the von Mises stress σ vm of each grid cell to the allowable stress σ allow as R = σ vm / σ allow ; when R < 0.5, reduce the density gradient constraint of this cell to increase Δρ Max by 10%; when R > 0.9, increase the density gradient constraint to decrease Δρ Max by 10%. This can dynamically adjust the density gradient constraint according to the stress distribution.

[0113] Next, calculate the sensitivity considering the Heaviside projection and density gradient constraints. First, calculate the sensitivity of the relative density of grid cells to design variables, and then calculate the sensitivity of density gradient constraints to design variables. Use the Lagrange multiplier method to combine the two to obtain the corrected sensitivity. The Lagrange multiplier is taken as 0.5 to achieve the balance of sensitivity.

[0114] Finally, the relative density of the grid cells is iteratively optimized based on the corrected sensitivity. The optimization criterion method is used for iterative calculation, and the iterative step size is 0.2. When the change rate of the objective function in 5 consecutive iterations is less than 0.1%, it is considered that the optimization converges, and the final material distribution result is obtained.

[0115] In practical applications, a cantilever beam structure can be selected for optimization. The length of the cantilever beam is 100 mm, the height is 20 mm, and the thickness is 2 mm. It is discretized into 5000 quadrilateral grid cells, and the initial relative density of each cell is 0.5. Through the above method for optimization, a lightweight structure that meets the stress constraints is finally obtained. The mass of the optimized cantilever beam is reduced by 35%, the maximum stress is reduced by 20%, and the structural stiffness is increased by 15%.

[0116] Through Heaviside projection and density gradient constraint, the present invention effectively suppresses the checkerboard phenomenon and mesh dependence, and improves the manufacturability of the optimization results; by introducing an adaptive update mechanism for density gradient constraint, the dynamic adjustment of the constraint strength is realized, and the flexibility and efficiency of the optimization are improved; iterative optimization is carried out using the corrected sensitivity, comprehensively considering the influence of various factors, making the optimization results more reasonable and reliable.

[0117] In an alternative embodiment,

[0118] Design a multi-seal structure based on the topological configuration of the seal structure, including: extracting the boundary contour of the topological configuration of the seal structure, constructing a three-dimensional solid model of the multi-seal structure based on the boundary contour, performing finite element analysis on the three-dimensional solid model to verify the sealing performance, and optimizing and adjusting the multi-seal structure according to the finite element analysis results, including the steps of:

[0119] Convert the relative density field of the seal structure into a discrete scalar field, use the contour line extraction method based on grid division to obtain the boundary contour point set of the seal structure, and perform B-spline curve fitting on the boundary contour point set to obtain a smooth boundary contour;

[0120] Construct a three-dimensional solid model of the multi-seal structure based on the smooth boundary contour, including: constructing an involute seal element using an involute surface, and constructing a hyperbolic seal element using a hyperbolic surface;

[0121] Perform mesh division on the three-dimensional solid model, where hexahedral meshes are used for the seal contact area and tetrahedral meshes are used for the transition connection area to establish a finite element analysis model including contact nonlinearity; set the assembly preload, working pressure, temperature cycle and vibration load conditions in the finite element analysis model, calculate the seal surface contact force using the augmented Lagrangian method, and perform stress-strain analysis considering the material elastoplastic effect;

[0122] Based on the finite element analysis results, a structural optimization model is established with the leakage rate and the maximum stress as the optimization objectives and the contact pressure and the sealing deformation as the constraint conditions; the sequential quadratic programming method is used to solve the structural optimization model, and the angles, curvatures, shapes of the transition regions and dimensional parameters of the sealing platforms in the three-dimensional solid model are iteratively optimized until the sealing performance requirements are met.

[0123] Exemplarily, first, the boundary contour of the topological configuration of the sealing structure is extracted. The relative density field of the sealing structure is obtained by the density method, and the relative density field is discretized into a scalar field with a 0-1 distribution. An isocontour extraction algorithm based on quadrilateral meshes is used to extract the boundary contour point set with a relative density of 0.5 as the threshold. The obtained boundary contour point set is fitted with a cubic B-spline curve, the number of control points is set to 20 - 30, and the curve knot vector is uniformly distributed. By adjusting the positions and weight coefficients of the control points, the maximum deviation between the fitted curve and the original point set is controlled within 0.1 mm, so as to obtain a smooth boundary contour.

[0124] Then, a three-dimensional solid model of the multi-sealing structure is constructed based on the smooth boundary contour. An involute surface is used to construct the first sealing element, the base circle radius of the involute surface is 50 mm, the pressure angle is 20 degrees, and the helix angle is 15 degrees. A hyperboloid is used to construct the second sealing element, the radius of curvature of the hyperboloid is 100 mm, and the taper angle is 10 degrees. A transition connection region is set between the two sealing elements, and the transition region is realized by a circular arc surface with a radius of 5 mm for smooth transition.

[0125] The three-dimensional solid model is subjected to finite element mesh division. Hexahedral meshes are used in the sealing contact region with a mesh size of 0.5 mm, and about 50,000 elements are divided in total. Tetrahedral meshes are used in the transition connection region with a mesh size of 1 mm, and about 30,000 elements are divided in total. A finite element analysis model including contact nonlinearity is established, and the friction coefficient between the sealing surfaces is set to 0.15.

[0126] In the finite element analysis model, the working conditions loads are applied: the assembly pre-tightening force is 2000 N, the working pressure is 10 MPa, the temperature cycle range is from -40 °C to 120 °C, the vibration load frequency is 100 Hz, and the acceleration is 10 g. The augmented Lagrangian method is used to solve the contact problem, and the contact convergence criterion is set to 0.001 mm. Considering the material elastoplastic effect, a bilinear constitutive model is adopted, the yield strength is 235 MPa, and the tangent modulus is 2000 MPa.

[0127] Based on the finite element analysis results, a structural optimization model is established. With the leakage rate less than 1×10 -6 Pa·m 3Taking the minimum contact pressure of the sealing surface being greater than 20 MPa and the maximum sealing deformation being less than 0.2 mm as the constraint conditions, and the / s and the maximum stress being less than 200 MPa as the optimization objectives. The sequential quadratic programming method is used for optimization and solution. The design variables include: the inclination angle of the sealing platform (5 - 15 degrees), the curvature radius of the transition region (3 - 8 mm), the width of the sealing platform (2 - 5 mm), etc. Through 15 - 20 iterations of optimization, a structural scheme that meets the sealing performance requirements is finally obtained.

[0128] The present invention adopts a topological configuration extraction and multiple sealing element construction method, which can quickly obtain an initial structural scheme with good sealing performance, significantly improve the design efficiency, and shorten the design cycle by more than 50%. By establishing a refined finite element model considering various working conditions and combining with structural optimization design, the sealing structure can maintain stable sealing performance under various working conditions, the leakage rate is reduced by 80%, and the service life is increased by more than 1 time.

[0129] In an alternative embodiment,

[0130] Constructing a three-dimensional solid model of the multiple sealing structure based on the fairing boundary contour, including: the steps of constructing an involute sealing element by using an involute surface and constructing a hyperboloid sealing element by using a hyperboloid surface include:

[0131] Constructing an involute sealing element, including: generating the basic surface of the main sealing platform by using the parametric equation of a variable pitch involute surface, superimposing the circumferential and radial micro-ripple morphologies on the basic surface of the main sealing platform, and mathematically describing the basic surface of the main sealing platform with the micro-ripple morphology by using the NURBS surface equation;

[0132] Constructing a hyperboloid sealing element, including: generating the basic surface of the secondary sealing platform by using the parametric equation of a single-sheet hyperboloid, and correcting the basic surface of the secondary sealing platform by introducing a stress concentration relaxation function;

[0133] Constructing a connecting transition element, including: establishing an optimization model of the transition surface based on the minimum surface energy functional, and solving the optimization model of the transition surface by using boundary curve constraints and normal vector constraints to obtain a transition surface that meets the geometric continuity requirements;

[0134] Combining the involute sealing element, the hyperboloid sealing element and the connecting transition element into a three-dimensional solid model of the multiple sealing structure through a Boolean union operation.

[0135] Exemplarily, first, an involute sealing element is constructed using an involute surface. Specifically, the parametric equation of the variable pitch involute surface is used to generate the base surface of the main sealing platform. The parametric equation of the variable pitch involute surface can be expressed as a function of parameters u and v, where u represents the radial parameter and v represents the circumferential parameter. By adjusting the coefficients in the equation, the shape of the involute surface can be controlled. For example, the value range of u can be set from 0 to 1, and the value range of v can be set from 0 to 2π to generate an involute surface with a radius ranging from 10 mm to 20 mm and a height of 5 mm.

[0136] On the generated base surface of the main sealing platform, the circumferential and radial micro-ripple morphologies are superimposed. The circumferential ripple can be described by a sine function, with a wavelength set to 0.5 mm and an amplitude of 0.02 mm. The radial ripple can be described by an exponential function, with the wavelength gradually increasing from the inner diameter to the outer diameter and the amplitude remaining unchanged at 0.01 mm. By superimposing these two ripples on the base surface, the main sealing platform surface with micro-topography is obtained.

[0137] Then, the main sealing platform surface with micro-ripple morphology is mathematically described using the NURBS surface equation (Non-Uniform Rational B-Spline surface equation). The NURBS surface can accurately represent complex free-form surfaces. The control point grid is set to 20×20, the order is 3, and the weight factors are all 1. By using the least squares fitting method, the control point coordinates of the NURBS surface are solved to obtain the NURBS expression of the main sealing platform surface.

[0138] Next, a hyperboloid sealing element is constructed. The parametric equation of a single-sheet hyperboloid is used to generate the base surface of the secondary sealing platform. The single-sheet hyperboloid equation contains two shape parameters a and b, and the opening size of the hyperboloid can be controlled by adjusting these two parameters. For example, setting a = 15 mm and b = 10 mm generates a hyperboloid with a height of 8 mm as the base surface of the secondary sealing platform.

[0139] To relieve stress concentration, a stress concentration relief function is introduced to correct the base surface of the secondary sealing platform. The stress concentration relief function can be in the form of a power exponential function to perform a smooth transition on the surface in the edge region of the hyperboloid. Specifically, the width of the relief region can be set to 2 mm and the power exponent to 2. By combining the relief function with the original hyperboloid equation, the corrected secondary sealing platform surface equation is obtained.

[0140] Then, a connection transition element is constructed. Based on the minimum surface energy functional, an optimization model for the transition surface is established. The surface energy functional includes an area term, a bending term, and a torsion term, and can be expressed in the form of a double integral of surface parameters u and v. The variational method is used to transform the functional problem into a partial differential equation solving problem.

[0141] During the solution process, it is necessary to apply boundary curve constraints and normal vector constraints. The boundary curve constraint requires that the transition surface precisely coincides with the boundary curves of the primary sealing platform and the secondary sealing platform. The normal vector constraint requires that the normal vectors of the transition surface at the boundary smoothly transition with the normal vectors of the adjacent surfaces. Substitute these constraint conditions into the partial differential equation and use the finite difference method for numerical solution to obtain a transition surface that meets the geometric continuity requirements.

[0142] Finally, the involute sealing element, hyperboloid sealing element, and connecting transition element are combined into a three-dimensional solid model of the multi-seal structure through Boolean union operations. First, convert the three elements into B-rep (Boundary Representation) models, and then use the union operation in Boolean operations to merge them. There may be overlapping surfaces and gaps in the merged model, which need to be repaired. Use a gap repair algorithm with a tolerance of 0.001 mm to perform topological inspection and repair on the model, and finally obtain a complete three-dimensional solid model of the multi-seal structure.

[0143] The present invention uses variable pitch involute surfaces and single-sheet hyperboloids to construct the primary and secondary sealing platforms respectively, giving full play to the geometric characteristics of the two surfaces and improving the sealing performance and load-bearing capacity of the sealing structure; introducing microscopic corrugated topography and stress concentration mitigation functions on the surface of the sealing element can improve the distribution of sealing contact stress, reduce the leakage risk, and extend the sealing life; constructing the connecting transition element based on the minimum surface energy method ensures the geometric continuity of the overall model, which is beneficial to improving the overall performance and reliability of the sealing structure.

[0144] In an alternative embodiment,

[0145] The steps of establishing a structural optimization model with the leakage rate and maximum stress as the optimization objectives and the contact pressure and seal deformation as the constraint conditions based on the finite element analysis results; using the sequential quadratic programming method to solve the structural optimization model and iteratively optimizing the sealing platform angle, curvature, transition region shape, and size parameters in the three-dimensional solid model until the sealing performance requirements are met include:

[0146] The leakage rate is calculated based on the contact deformation amount, contact pressure, surface roughness correction coefficient, leakage path length, and fluid parameters, and the maximum stress is calculated using the von Mises equivalent stress criterion;

[0147] Use the orthogonal experimental design method to calculate the sensitivity coefficients of the sealing platform angle, curvature, transition region shape, and size parameters to the leakage rate and maximum stress;

[0148] Based on the sensitivity coefficients, use the sequential quadratic programming method to solve the structural optimization model, construct a quadratic programming sub-problem by calculating the gradient vector and second derivative matrix, and perform optimization iterations on the sealing platform angle, curvature, transition region shape, and size parameters.

[0149] When the leakage rate and the maximum stress meet the sealing performance requirements, output the optimal sealing table angle, curvature, transition region shape and size parameters.

[0150] Exemplarily, first, establish a structural optimization model based on the finite element analysis results. This model takes the leakage rate and the maximum stress as the optimization objectives and the contact pressure and the sealing deformation as the constraint conditions. Among them, the leakage rate is calculated based on the contact deformation amount, the contact pressure, the surface roughness correction coefficient, the leakage path length and the fluid parameters, and the maximum stress is calculated using the von Mises equivalent stress criterion. Specifically, the modified Reynolds equation can be used to calculate the leakage rate, considering the influence of factors such as contact deformation, contact pressure distribution, and surface roughness.

[0151] Next, use the orthogonal experimental design method to calculate the sensitivity coefficients of the sealing table angle, curvature, transition region shape and size parameters to the leakage rate and the maximum stress. Select key parameters such as the sealing table angle, the radius of curvature, the length and width of the transition region, and design an orthogonal experimental table. Calculate the leakage rate and the maximum stress under different parameter combinations through finite element analysis, and use the range analysis method to calculate the sensitivity coefficients of each parameter. For example, for a certain sealing structure, the orthogonal experimental design is carried out, and the sensitivity coefficients of the sealing table angle, the radius of curvature, the length and width of the transition region to the leakage rate are 0.45, 0.30, 0.15, 0.10 respectively, and the sensitivity coefficients to the maximum stress are 0.40, 0.35, 0.15, 0.10 respectively.

[0152] Then, solve the structural optimization model using the sequential quadratic programming method based on the sensitivity coefficients. Construct a quadratic programming sub-problem by calculating the gradient vector and the second derivative matrix, and perform optimization iterations on the sealing table angle, curvature, transition region shape and size parameters. Specifically, first determine the initial design point and the search direction, and calculate the gradient vectors of the objective function and the constraint function. Then construct the Lagrangian function and calculate the approximate value of its Hessian matrix. Construct a quadratic programming sub-problem based on the gradient vector and the Hessian matrix, solve to obtain the search direction and the step size. Update the design variables along the search direction, and repeat the above process until convergence. For example, the initial design parameters of a certain sealing structure are: the sealing table angle is 30°, the radius of curvature is 5 mm, the length of the transition region is 2 mm, and the width is 1 mm. After 10 iterations of optimization, the final optimized parameters are: the sealing table angle is 35°, the radius of curvature is 6 mm, the length of the transition region is 2.5 mm, and the width is 1.2 mm.

[0153] Finally, when the leakage rate and the maximum stress meet the sealing performance requirements, output the optimal sealing table angle, curvature, transition region shape and size parameters. For example, the leakage rate of the optimized sealing structure is reduced to 5×10 -7mL / s, the maximum stress is reduced to 200 MPa, meeting the sealing performance requirements. At this time, the optimal design parameters are output: the sealing table angle is 35°, the curvature radius is 6 mm, the transition region length is 2.5 mm, and the width is 1.2 mm.

[0154] By establishing a structural optimization model with the leakage rate and the maximum stress as the optimization objectives, the present invention comprehensively considers the sealing performance and the structural strength, and can effectively improve the comprehensive performance of the sealing structure; the sensitivity coefficient is calculated by using the orthogonal experimental design method, which can quickly identify the key parameters affecting the sealing performance and improve the optimization efficiency; the optimization solution is carried out based on the sequential quadratic programming method, which can efficiently search for the optimal solution and ensure the convergence and stability of the optimization result at the same time.

[0155] Figure 2 is a schematic structural diagram of a multi-sealing system for a high-vacuum die-casting mold based on topology optimization according to an embodiment of the present invention, as Figure 2 shown, the system includes:

[0156] The first unit is used to establish a parametric model of the sealing structure, including: obtaining the geometric parameters and boundary conditions of the cavity wall surface of the mold, constructing the initial design domain of the sealing structure, dividing grid units in the initial design domain, using the relative density of the grid units as the design variable, establishing the contact constraint condition between the sealing structure and the cavity wall surface, and constructing a multi-objective function considering the contact stress distribution;

[0157] The second unit is used to perform topology optimization calculation based on the multi-objective function, including: using the solid isotropic material penalization method to iteratively optimize the relative density of the grid units, calculating the contact stress distribution between the sealing structure and the cavity wall surface during each iteration, and correcting the multi-objective function according to the contact stress distribution until a sealing structure topology configuration that meets the convergence conditions is obtained;

[0158] The third unit is used to design a multi-sealing structure according to the sealing structure topology configuration, including: extracting the boundary contour of the sealing structure topology configuration, constructing a three-dimensional solid model of the multi-sealing structure based on the boundary contour, performing finite element analysis on the three-dimensional solid model to verify the sealing performance, and optimizing and adjusting the multi-sealing structure according to the finite element analysis result.

[0159] In the third aspect of the embodiment of the present invention,

[0160] A kind of electronic device is provided, including:

[0161] A processor;

[0162] A memory for storing instructions executable by the processor;

[0163] Wherein, the processor is configured to call the instructions stored in the memory to execute the method described above.

[0164] In the fourth aspect of the embodiments of the present invention,

[0165] a computer-readable storage medium is provided, on which computer program instructions are stored, and when the computer program instructions are executed by a processor, the foregoing method is implemented.

[0166] The present invention may be a method, an apparatus, a system, and / or a computer program product. The computer program product may include a computer-readable storage medium on which computer-readable program instructions for executing various aspects of the present invention are loaded.

[0167] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-sealing method for high-vacuum die-casting molds based on topology optimization, characterized in that Including: Establish a parametric model of the sealing structure, including: obtaining the geometric parameters and boundary conditions of the cavity wall surface of the mold, constructing the initial design domain of the sealing structure, dividing grid elements in the initial design domain, taking the relative density of the grid elements as design variables, establishing the contact constraint conditions between the sealing structure and the cavity wall surface, and constructing a multi-objective function considering the contact stress distribution, including: constructing a multi-objective function containing a volume fraction objective, a von Mises stress objective, and a contact pressure standard deviation objective according to the relative density distribution of the grid elements and the stress distribution in the contact area; the volume fraction objective is the ratio of the sum of the products of the relative density of the elements and the element volume to the volume of the initial design domain, the von Mises stress objective is represented in the form of a p-norm to characterize the ratio of the von Mises stress of the elements to the allowable stress, and the contact pressure standard deviation objective is the ratio of the contact pressure standard deviation to the average contact pressure; setting volume constraints, stress constraints, and density constraints for the multi-objective function, and the density constraint conditions limit the value range of the relative density of the elements. Perform topology optimization calculation based on the multi-objective function, including: using the solid isotropic material penalization method to iteratively optimize the relative density of the grid elements, calculating the contact stress distribution between the sealing structure and the cavity wall surface during each iteration, and correcting the multi-objective function according to the contact stress distribution until a sealing structure topology configuration that meets the convergence conditions is obtained. Carry out the design of a multi-layer sealing structure based on the sealing structure topology configuration, including: extracting the boundary contour of the sealing structure topology configuration, constructing a three-dimensional solid model of the multi-layer sealing structure based on the boundary contour, performing finite element analysis on the three-dimensional solid model to verify the sealing performance, and optimizing and adjusting the multi-layer sealing structure according to the finite element analysis results, including: establishing a structure optimization model with the leakage rate and the maximum stress as the optimization objectives and the contact pressure and the sealing deformation as the constraint conditions based on the finite element analysis results; using the sequential quadratic programming method to solve the structure optimization model, and iteratively optimizing the sealing table angle, curvature, transition region shape, and size parameters in the three-dimensional solid model until the steps to meet the sealing performance requirements include: the leakage rate is calculated based on the contact deformation amount, contact pressure, surface roughness correction coefficient, leakage path length, and fluid parameters, and the maximum stress is calculated using the von Mises equivalent stress criterion; using the orthogonal experimental design method to calculate the sensitivity coefficients of the sealing table angle, curvature, transition region shape, and size parameters to the leakage rate and the maximum stress; solving the structure optimization model using the sequential quadratic programming method based on the sensitivity coefficients, constructing a quadratic programming sub-problem by calculating the gradient vector and the second derivative matrix, and performing optimization iteration on the sealing table angle, curvature, transition region shape, and size parameters; when the leakage rate and the maximum stress meet the sealing performance requirements, output the optimal sealing table angle, curvature, transition region shape, and size parameters.

2. The method according to claim 1, wherein Establish a parametric model of the sealing structure, including: obtaining the geometric parameters and boundary conditions of the cavity wall of the mold, constructing the initial design domain of the sealing structure, dividing grid elements in the initial design domain, taking the relative density of the grid elements as the design variable, establishing the contact constraint conditions between the sealing structure and the cavity wall, and constructing a multi-objective function considering the contact stress distribution, which includes the following steps: Obtain point cloud data through a three-dimensional scanning system, perform point cloud registration using the iterative closest point algorithm, and reconstruct the cavity wall using the radial basis function interpolation method of local quadratic surface fitting. Combine the pressure sensor array arranged on the cavity wall to obtain pressure distribution data, and obtain the geometric parameters and boundary conditions of the cavity wall; According to the obtained geometric parameters and boundary conditions, describe the topological structure using the level set method, and establish a design domain by constructing an initial level set function through the distance field. The initial level set function greater than zero is the solid region, equal to zero is the boundary, and less than zero is the cavity region, so as to obtain the initial design domain of the sealing structure; Adopt an adaptive grid refinement strategy to divide grid elements in the initial design domain, take the relative density of the grid elements as the design variable, and use the SIMP penalty factor method to control the relative density distribution; Based on the divided grid elements, use the mortar method to establish the contact constraint conditions between the sealing structure and the cavity wall, divide the contact surface into the mortar elements of the subordinate surface and the non-mortar elements of the main surface, and use the piecewise bilinear interpolation function to calculate the contact integral to obtain the stress distribution in the contact area.

3. The method according to claim 1, wherein Perform topology optimization calculation based on the multi-objective function, including: using the solid isotropic material with penalization method to iteratively optimize the relative density of the grid elements, calculating the contact stress distribution between the sealing structure and the cavity wall during each iteration process, and correcting the multi-objective function according to the contact stress distribution until the topological configuration of the sealing structure that meets the convergence conditions is obtained, which includes the following steps: Use the solid isotropic material with penalization method to iteratively optimize the relative density of the grid elements. The solid isotropic material with penalization method includes: realizing density filtering through the Heaviside projection, introducing density gradient constraints to limit the density change of adjacent elements; during each iterative optimization process, use the penalty function method to calculate the normal contact force between the sealing structure and the cavity wall, and consider the friction effect to calculate the tangential contact force, and update the normal contact force through the adaptive contact stiffness; Based on the obtained normal contact force and tangential contact force, calculate the sensitivity of the multi-objective function to the design variables, including calculating the volume objective sensitivity, stress objective sensitivity, and contact pressure standard deviation objective sensitivity; input the calculated sensitivity of the multi-objective function to the design variables into the sequential quadratic programming algorithm, and solve the multi-objective function through the dynamic weight coefficient adjustment strategy; Judge whether the optimization process terminates according to the multi-objective function convergence criterion and the design variable convergence criterion. When either convergence criterion is met and the number of iterations is not less than the minimum number of iterations, obtain the final topological configuration of the sealing structure.

4. The method according to claim 3, wherein The relative density of grid cells is iteratively optimized using the solid isotropic material with penalization method, and the solid isotropic material with penalization method includes the steps of: achieving density filtering through Heaviside projection, and introducing density gradient constraints to limit the density change of adjacent cells, including: Filtering the relative density of grid cells using the Heaviside projection function, mapping the original relative density of grid cells through an exponential function to obtain the filtered relative density; dynamically updating the projection parameter of the Heaviside projection function, and gradually increasing the projection parameter by setting a growth factor; Establishing the density gradient constraint relationship between adjacent grid cells, determining the upper limit of the relative density difference between two adjacent grid cells according to the distance between the center points of the two adjacent grid cells, and restricting the relative density difference within the upper limit range; Establishing an adaptive update mechanism for density gradient constraints, and dynamically adjusting the density gradient constraint parameters based on the ratio of the von Mises stress to the allowable stress of grid cells; Calculating the sensitivity considering Heaviside projection and density gradient constraints, including: calculating the sensitivity of the relative density of grid cells to design variables, calculating the sensitivity of density gradient constraints to design variables, and combining the sensitivity of the relative density of grid cells to design variables and the sensitivity of density gradient constraints to design variables using Lagrange multipliers to obtain the corrected sensitivity; Iteratively optimizing the relative density of grid cells based on the corrected sensitivity until a material distribution that meets the convergence criterion is obtained.

5. The method according to claim 1, characterized in that, Conducting multi-seal structure design based on the topology configuration of the seal structure, including: extracting the boundary contour of the seal structure topology configuration, constructing a three-dimensional solid model of the multi-seal structure based on the boundary contour, performing finite element analysis on the three-dimensional solid model to verify the sealing performance, and optimizing and adjusting the multi-seal structure according to the finite element analysis results, including the steps of: Converting the relative density field of the seal structure into a discrete scalar field, obtaining the boundary contour point set of the seal structure using the contour extraction method based on grid division, and performing B-spline curve fitting on the boundary contour point set to obtain a smooth boundary contour; Constructing a three-dimensional solid model of the multi-seal structure based on the smooth boundary contour, including: constructing an involute seal element using an involute surface, and constructing a hyperbolic seal element using a hyperboloid; Performing mesh division on the three-dimensional solid model, where hexahedral meshes are used for the seal contact area and tetrahedral meshes are used for the transition connection area to establish a finite element analysis model including contact nonlinearity; setting assembly preload, working pressure, temperature cycle, and vibration load conditions in the finite element analysis model, calculating the seal surface contact force using the augmented Lagrangian method, and considering the material elastoplastic effect for stress-strain analysis.

6. The method according to claim 5, wherein Constructing a three-dimensional solid model of the multi-seal structure based on the smooth boundary contour, including: constructing an involute seal element using an involute surface, and constructing a hyperbolic seal element using a hyperboloid, including the steps of: Construct an involute seal element, including: generating the base surface of the main seal platform using the parametric equation of the variable pitch involute surface, superimposing the circumferential and radial micro-ripple morphologies on the base surface of the main seal platform, and mathematically describing the base surface of the main seal platform with the micro-ripple morphology using the NURBS surface equation; Construct a hyperboloid seal element, including: generating the base surface of the secondary seal platform using the parametric equation of the single-sheet hyperboloid, and introducing a stress concentration mitigation function to correct the base surface of the secondary seal platform; Construct a connection transition element, including: establishing a transition surface optimization model based on the minimum surface energy functional, solving the transition surface optimization model using boundary curve constraints and normal vector constraints, and obtaining a transition surface that meets the geometric continuity requirements; Combine the involute seal element, the hyperboloid seal element, and the connection transition element into a three-dimensional solid model of a multi-seal structure through a Boolean union operation.

7. A multi-sealing system for a high-vacuum die-casting mold based on topology optimization, which is used to implement the method described in any one of the preceding claims 1-6, characterized in that, Including: The first unit is used to establish a parametric model of the seal structure, including: obtaining the geometric parameters and boundary conditions of the cavity wall surface of the mold, constructing the initial design domain of the seal structure, dividing grid elements in the initial design domain, using the relative density of the grid elements as design variables, establishing the contact constraint conditions between the seal structure and the cavity wall surface, and constructing a multi-objective function considering the contact stress distribution; The second unit is used to perform topology optimization calculations based on the multi-objective function, including: using the solid isotropic material with penalization method to iteratively optimize the relative density of the grid elements, calculating the contact stress distribution between the seal structure and the cavity wall surface during each iteration, and correcting the multi-objective function according to the contact stress distribution until a seal structure topology configuration that meets the convergence conditions is obtained; The third unit is used to design a multi-seal structure based on the seal structure topology configuration, including: extracting the boundary contour of the seal structure topology configuration, constructing a three-dimensional solid model of the multi-seal structure based on the boundary contour, performing finite element analysis on the three-dimensional solid model to verify the sealing performance, and optimizing and adjusting the multi-seal structure according to the finite element analysis results.

8. An electronic device, characterized in that, Including: A processor; A memory for storing instructions executable by the processor; Wherein, the processor is configured to call the instructions stored in the memory to execute the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, the method according to any one of claims 1 to 6 is implemented.

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