A method and apparatus for solving a sealed assembly completion state

Abstract

This application provides a method and apparatus for solving the completed state of a sealed assembly, relating to the field of sealing component design technology. It includes: acquiring the geometric model of an elastic component and its mating components and constructing an initial assembly configuration; discretizing the sealed assembly system using finite element methods and setting integration points in the elastic component; during the assembly iteration process, determining the corresponding projection point based on the integration point and the component combination it contains, and calculating the contact force at the integration point by combining material parameters, the projection point position, and the surface geometry information of the mating components; and unifying the contact force and the internal elastic force generated by the elastic component under the current configuration into a unified force balance relationship for nonlinear iterative solution until a preset convergence condition is met, thereby obtaining the completed state of the sealed assembly. This application can stably solve the completed state of a sealed assembly even with initial geometric interference, and improves the convergence and computational stability of the assembly simulation by uniformly handling the contact force and internal elastic force.

Description

Technical Field

[0001] This application relates to the field of sealing design technology, and in particular to a method and apparatus for solving the completed state of a sealing assembly. Background Technology

[0002] Rubber and plastic seals are widely used in various sealing structures, and their geometry and stress state after assembly have a significant impact on sealing performance. In seal assembly simulation analysis, the finite element method is typically used to simulate the assembly process between rubber and plastic parts or groove structures to obtain the assembled configuration and mechanical properties. Since the geometric modeling stage usually only establishes the initial morphological model of the sealing component, it is difficult to directly construct the deformed form after assembly. Radial interference is commonly observed between the rubber part and the mating components in the initial model. Therefore, the primary challenge in assembly simulation is how to handle the initial interference and obtain a stable assembled state.

[0003] Existing assembly simulation methods typically involve cutting the sidewalls of the groove during the modeling phase and axially offsetting the sealing components from their original assembly positions relative to the cut groove structure. During simulation, axial displacement is gradually applied to return the offset components to their original positions, thereby simulating the assembly process and analyzing the post-assembly morphology and mechanical properties. However, this type of method is prone to sharp-edge collisions between sealing components or between rubber parts and the bottom of the groove during simulation, leading to unstable contact calculations and even numerical divergence. Furthermore, the structural cutting during modeling and the displacement repositioning during simulation increase the overall operational complexity, prolong the simulation cycle, and reduce the computational efficiency of assembly simulation. Summary of the Invention

[0004] In view of this, this application provides a method and apparatus for solving the completed state of a sealed assembly, in order to solve the problems of difficult initial interference processing, easy calculation divergence and low efficiency in existing sealed assembly simulations.

[0005] Specifically, this application is implemented through the following technical solution:

[0006] The first aspect of this application provides a method for solving the completed state of a sealed assembly, the method comprising:

[0007] Obtain a geometric model that includes at least an elastic member and its mating members, and assemble them into an initial assembly configuration. Determine the component assembly based on the contact relationship between the elastic member and the mating members.

[0008] The elastic member and the mating member are discretized using finite element method to obtain finite element elements, and integration points are determined within each finite element element of the elastic member.

[0009] Based on the initial configuration, the current configuration of the sealing assembly is iteratively updated, and the specific iterative steps include at least:

[0010] Based on the integration point and the component combination where the integration point is located, determine the projection point corresponding to the integration point;

[0011] Obtain material parameters, and based on the material parameters, the integration point, the projection point, and the surface geometry information of the mating component, determine the contact force at the integration point. Based on the contact force and the internal elastic force generated by the elastic component under the current configuration, construct the overall force balance relationship and perform iterative solution to obtain the sealed assembly completed state.

[0012] A second aspect of this application provides a device for solving the completed state of a sealed assembly, the device comprising an acquisition module, a determination module, and an iteration module, wherein:

[0013] The acquisition module is used to acquire a geometric model that includes at least an elastic component and its mating components, and assemble them into an initial assembly configuration, and determine the component combination based on the contact relationship between the elastic component and the mating components;

[0014] The determining module is used to perform finite element discretization on the elastic component and the mating component to obtain finite element elements, and to determine the integration points in each finite element element of the elastic component.

[0015] The iteration module is used to iteratively update the current configuration of the sealing assembly based on the initial configuration, and the specific iteration steps include at least:

[0016] Based on the integration point and the component combination where the integration point is located, determine the projection point corresponding to the integration point;

[0017] Obtain material parameters, and based on the material parameters, the integration point, the projection point, and the surface geometry information of the mating component, determine the contact force at the integration point. Based on the contact force and the internal elastic force generated by the elastic component under the current configuration, construct the overall force balance relationship and perform iterative solution to obtain the sealed assembly completed state.

[0018] This application provides a method and apparatus for solving the completed state of a sealed assembly. Addressing the problems of difficulty in handling initial geometric interference, numerical divergence in contact calculations, and low computational efficiency in existing sealed assembly simulations, this method integrates the contact interaction between components and the deformation response of the elastic component into a force balance iterative process, achieving stable and efficient solutions for the completed state of the sealed assembly. Specifically, this application obtains a geometric model including at least the elastic component and its mating components, and determines the component combination based on the contact relationship between them, providing a clear component correspondence for subsequent contact analysis. Furthermore, the elastic component and its mating components are discretized using finite element methods, and integration points are set within the finite element elements of the elastic component to accurately characterize the deformation and stress state of the components at the continuous medium level. Furthermore, during the iterative update of the current configuration of the sealed assembly, starting from the initial assembly configuration, the corresponding projection point is determined based on the integration point and its component combination. The contact force at the integration point is calculated by combining material parameters and the surface geometry information of the mating components. This contact force, along with the internal elastic force generated by the elastic component under the current configuration, is used to construct the overall force balance relationship and iteratively solve it until the preset convergence condition is met, thereby obtaining the completed state of the sealed assembly. Through the above technical solution, this application can achieve stable solution of the assembly process even with initial geometric interference, coupling contact action and elastic deformation into the same force balance framework, effectively suppressing numerical divergence in the contact calculation process, and improving the convergence and overall computational efficiency of the sealed assembly simulation. Attached Figure Description

[0019] Figure 1 A flowchart of Embodiment 1 of the sealing assembly completion state solution method provided in this application;

[0020] Figure 2 This is a schematic diagram of the structure of Embodiment 1 of the sealing assembly completion state solving device provided in this application. Detailed Implementation

[0021] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application.

[0022] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used herein are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0023] It should be understood that although the terms first, second, third, etc., may be used in this application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0024] The following specific embodiments are given to illustrate the technical solution of this application in detail.

[0025] Figure 1 This is a flowchart of an embodiment of the sealing assembly completion state solution method provided in this application. Please refer to... Figure 1 The method provided in this embodiment may include:

[0026] S101. Obtain a geometric model that includes at least an elastic member and its mating members, and assemble them into an initial assembly configuration. Determine the component combination based on the contact relationship between the elastic member and the mating members.

[0027] Specifically, geometric models of each component in the sealed assembly are obtained. These geometric models are established based on product design data, and each component includes at least an elastic component and a mating component that mates with it. The elastic component is a rubber-plastic sealant used to achieve the sealing function, capable of significant elastic deformation during assembly. The mating component is a structural part that forms an assembly fit with the elastic component, including but not limited to grooves, piston rods, or support rings, which have higher structural stiffness than the elastic component. In one optional implementation, the geometric model may further include auxiliary structural components for defining the assembly position or assembly boundary, such as a housing, end cap, positioning step, or mounting groove end face. In another optional implementation, the geometric model may further include local geometric features related to contact analysis, such as guide surfaces, chamfered surfaces, or transition fillets, to more accurately describe the contact state and initial geometric interference that may occur in the elastic component during assembly.

[0028] Specifically, the geometric models of each component are established based on the product design dimensions and directly stacked according to the assembly positions shown in the design drawings to form the initial assembly configuration. In the initial assembly configuration, no load or displacement constraint is applied to any component, allowing geometric interference between the elastic component and the mating component in the radial direction, and axial insertion process during assembly is not considered.

[0029] Specifically, based on the geometry of the elastic component and the mating component, and their relative positional relationship in the designed assembled state, the component surfaces that will form contact between the elastic component and the mating component after assembly are pre-identified. These potentially contacting component surfaces are those that are adjacent to each other in the designed assembled state and have a contact or compression relationship after assembly; their selection is based on the CAD assembly model and engineering assembly experience. On this basis, using an elastic component and a mating component that contacts it in the assembled state as basic units, a description of the contact relationship between the elastic component and the mating component is established. This elastic component and the mating component constitute a component assembly, which defines the range of components allowed for contact detection and contact calculation in subsequent contact analysis.

[0030] It should be noted that, in one possible implementation, when the elastic member forms independent contact relationships with multiple different mating members in the assembled state, or when there are multiple independent contact areas in the same mating member, multiple component combinations can be established between the elastic member and the corresponding mating member according to the geometric proximity relationship and contact action characteristics in the assembled state, so as to define the contact analysis range corresponding to different contact action relationships respectively.

[0031] S102. Perform finite element discretization on the elastic member and the mating member to obtain finite element elements, and determine the integration points in each finite element element of the elastic member.

[0032] Specifically, based on the geometric characteristics of the components and their stress and deformation properties during assembly, the geometric domain of each component is divided into several spatial regions, and corresponding finite element elements are generated within each spatial region to describe the mechanical response behavior of the components during assembly. During the finite element discretization process, the mesh can be locally refined based on the engineer's experience. For example, for regions expected to undergo large elastic deformation or significant geometric changes, a relatively small element size is used for discretization; for regions with smaller deformation or gentler geometric changes, a relatively large element size is used, thereby reducing the overall computational scale while ensuring computational accuracy. The finite element is used to characterize the volumetric mechanical behavior of the components, and its outer surface naturally forms corresponding surface regions, serving as the geometric basis for contact relationships in subsequent contact analysis.

[0033] Furthermore, during the finite element discretization process, the discretization granularity of the finite element units can be determined by considering the geometric dimensions, volume, and mechanical properties of the elastic and mating components. For elastic components with relatively small volumes and large elastic deformations during assembly, a relatively high discretization density can be used; for mating components with large volumes, high structural stiffness, and small deformations, a relatively low discretization density can be used, thereby controlling the overall computational scale while ensuring the computational accuracy of critical areas. Optionally, the system can preset the total number of finite element units or the upper limit of the total degrees of freedom for finite element discretization, and uniformly coordinate and control the discretization granularity of different regions under this constraint. Specifically, in one implementation, each component or region is uniformly discretized using the same unit size to form an initial analysis model; in another implementation, while keeping the overall discretization scale basically unchanged, the unit size of each region is differentiated according to the contact response, deformation degree, or residual distribution of different regions during the assembly process, so that the discretization density of contact areas or high deformation areas is relatively increased, while the discretization density of non-critical areas is relatively decreased. The above method can balance the overall solution efficiency of the assembly process with the analysis accuracy of local contact behavior under limited computing resources, providing a stable and reliable discrete foundation for subsequent residual calculation and configuration update.

[0034] Specifically, after the finite element units are generated, integration points are set inside or on the surface of the finite element unit corresponding to the elastic component, according to the type of finite element unit and the numerical integration scheme adopted. These integration points are used to perform discrete approximate calculations of continuous physical quantities during the numerical solution process. The numerical integration scheme may include Gaussian integration or other equivalent numerical integration methods. In this embodiment, the integration points corresponding to the elastic component are preferably used as the main calculation object to characterize its elastic deformation during assembly and its contact response with the mating components.

[0035] S103. Based on the initial configuration, the current configuration of the sealing assembly is iteratively updated. The specific iterative steps include at least:

[0036] S1031. Based on the integration point and the component combination where the integration point is located, determine the projection point corresponding to the integration point.

[0037] Specifically, the projection point is the point on the candidate contact surface of the mating component that is geometrically closest to the integration point and satisfies the preset contact determination condition. It is used to characterize the geometric position where the integration point makes contact under the current configuration. By dynamically determining the corresponding projection point for each integration point during the iteration process, subsequent contact force calculations can be based on the actual geometric relationships under the current configuration, thus providing a geometric basis for the gradual elimination of assembly interference and the solution of the assembly completion state.

[0038] Optionally, in one possible implementation, before iteratively updating the current configuration of the sealing assembly, the method further includes:

[0039] Based on the subordinate relationship between the integration points and the component combination, the integration points are filtered to obtain a filtered set of integration points, and subsequent iterative updates are performed only on the filtered set of integration points.

[0040] Specifically, after finite element discretization and setting integration points in the elastic components, a dependency relationship is established between each integration point and its corresponding component combination based on the aforementioned determined component combinations. Specifically, if an integration point is located within the geometric region of the elastic component corresponding to a component combination in the initial configuration, and this geometric region belongs to the pre-determined contact surface range within the component combination, then the integration point is determined to belong to that component combination. Conversely, if an integration point is not located within the geometric region of the elastic component corresponding to any component combination, then the integration point is determined not to belong to any component combination. Based on this, only integration points belonging to at least one component combination are retained as a filtered set of integration points, and the relevant calculation operations in the subsequent iterative update process are performed only on this filtered set of integration points; integration points not belonging to any component combination do not participate in the subsequent iterative update. Through this method, the subsequent calculation process only targets integration points with the geometric possibility of participating in the interaction between components, thereby reducing the number of integration points involved in the calculation, reducing the computational scale, and improving the solution efficiency without affecting the correctness of the solution results.

[0041] It should be noted that, based on the above-mentioned selection of integration points according to the component combination hierarchy, the set of selected integration points can be further dynamically updated by considering the geometric position of the integration points in the current configuration. For example, during the iteration process, integration points whose distance exceeds a preset threshold can be temporarily removed based on the distance relationship between the integration point and its corresponding mating component surface. These points are only reinstated into the set of integration points for calculation in subsequent iterations when they enter a geometric neighborhood where contact is possible. This approach can further reduce the number of integration points involved in the calculation during the iteration process while maintaining the accuracy of contact determination, thereby improving the overall solution efficiency.

[0042] Optionally, in one possible implementation, determining the projection point corresponding to the integration point based on the integration point and the component combination where the integration point is located includes:

[0043] (1) Obtain the spatial coordinates of the integration point under the current configuration, and determine the search domain based on the component combination where the integration point is located, with the integration point as the center.

[0044] Specifically, by obtaining the spatial coordinates of the integration point under the current configuration and combining them with the component combination relationship to which the integration point belongs, a search domain is defined within the neighborhood of the integration point. This ensures that subsequent geometric judgments are performed only within the geometric range of components that may interact with the integration point. By introducing this search domain, a global search within the entire geometric range of the mating components can be avoided, thereby improving the stability and computational efficiency of the geometric judgments and providing a reliable geometric basis for subsequently determining the projection point corresponding to the integration point.

[0045] Optionally, in one possible implementation, determining the search domain based on the component combination containing the integration point, centered on the integration point, includes:

[0046] A) Based on the component combination to which the integration point belongs, determine the opposing component that forms a component combination with the component where the integration point is located.

[0047] Specifically, the opposing component is a component or an effective geometric part of a component selected from the mating components to form an opposing geometric constraint relationship with the elastic component in the assembly direction, thereby constituting the geometric constraint boundary of the elastic component. The integration point is only set on the elastic component; therefore, for any integration point, the opposing component corresponding to that integration point can be selected from the corresponding mating components according to its component combination, so that subsequent geometric judgments are performed only within the geometric range corresponding to the opposing component.

[0048] B) Based on the geometric relationship between the integration point and the opposing component, determine the maximum radial interference dimension formed between the integration point and the opposing component during the assembly process.

[0049] Specifically, based on the geometric relationship between the integration point and the opposing component, the maximum radial interference dimension formed between the integration point and the opposing component during the assembly process is determined. This maximum radial interference dimension characterizes the maximum radial overlap or intrusion that the elastic component may produce relative to the opposing component during the initial assembly configuration and subsequent iterations.

[0050] In an alternative embodiment, the maximum radial interference dimension can be predetermined based on the design dimensions of the assembly structure, for example, based on the difference between the free external dimensions of the elastic member and the mating internal dimensions of the opposing member.

[0051] In one optional embodiment, the maximum radial interference dimension can be determined by detecting the geometric distance between the relevant position on the surface of the elastic member and the surface of the opposing member under the initial assembly configuration, such as calculating the minimum distance from the integration point on the surface of the elastic member to the opposing member, and taking the maximum negative value as the maximum radial interference dimension.

[0052] In an optional embodiment, the maximum radial interference size can also be set as a preset proportional value related to the cross-sectional size of the elastic member, taking into account the design experience of the sealing structure. The maximum radial interference size determined by any of the above methods can be used to characterize the interference range that needs to be effectively identified and eliminated; this application does not limit this.

[0053] C) Determine the diameter value of the search domain based on the maximum radial interference size.

[0054] Specifically, after obtaining the maximum radial interference size, the diameter of the search domain is determined based on this maximum radial interference size, ensuring that the search domain covers the entire spatial range where the integration point may interfere with the opposing component during assembly. Preferably, the diameter of the search domain is set to be greater than the radial range corresponding to the maximum radial interference size to avoid potential interference areas not being identified due to insufficient search range, thereby affecting the integrity and stability of subsequent contact calculations.

[0055] Furthermore, the diameter of the search domain is not arbitrarily increased; its upper limit can be determined by constraining the local geometric feature scale of the opposing component, thus limiting the search domain to the local geometric region corresponding to the integration point. This avoids introducing discontinuous geometric feature surfaces due to an excessively large contact search range. In this embodiment, the upper limit of the search domain diameter can be determined based on the minimum radius of curvature of the opposing component surface, the local geometric feature size, or its distance to the geometric boundary. Specifically, the maximum radius value corresponding to the upper limit of the search domain diameter... The following constraints must be satisfied:

[0056] ;

[0057] in, The minimum radius of curvature of the opposing component surface in the neighborhood of the integration point is the minimum characteristic scale used to reflect the geometric changes in this region. To characterize the local geometric feature dimensions of opposing components, and to limit the search domain from crossing different geometric feature surfaces; , A pre-set scaling factor, based on assembly accuracy requirements or numerical stability needs, is used to suppress excessive scaling of the search domain while ensuring complete coverage of the potential contact area. It should be noted that in other embodiments or optional implementations, the upper limit of the search domain diameter can be further limited by combining the displacement change scale of adjacent iterations during assembly, or by simultaneously constraining both geometric feature scale and displacement change scale, to further improve the stability of the contact search.

[0058] Specifically, by using the above method, the search domain is always limited to the local geometric feature scale of the opposing component, thereby avoiding the problem of projection point jump caused by the search domain crossing different geometric feature regions while ensuring the integrity of contact recognition, and improving the continuity and stability of contact search during nonlinear iteration.

[0059] D) Construct the search domain with the integration point as the center of the sphere and the diameter value as the diameter.

[0060] Specifically, after determining the diameter value of the search domain, for each integration point involved in the contact calculation, a corresponding spherical search domain is constructed with the integration point as the center and the diameter value corresponding to the integration point as the diameter, so that each integration point corresponds to an independent search domain, which is used to limit the geometric judgment range related to the integration point.

[0061] Specifically, during the nonlinear iteration process, the geometric shape of the component is updated gradually with the nodal displacement. The integration point, as the numerical integration position within the finite element, remains unchanged in the local coordinate system of the element, while its spatial coordinates in the global coordinate system are updated synchronously with the update of the element nodal coordinates. That is, in each iteration, the spatial position of the integration point is obtained by interpolating the current nodal coordinates through the element shape function, rather than regenerating the integration point, thereby ensuring the continuity of the integration point during the deformation process of the component.

[0062] Specifically, in the geometric judgment process, contact-related geometric detection and judgment operations are only performed on the geometric regions of opposing components that fall within the spherical search domain. This limits the contact search to the contact neighborhood of the integration point in the previous iteration step, thereby avoiding frequent jumps between contact projection points on different geometric feature surfaces, reducing the computational overhead of global search, and improving the continuity and stability of contact calculation in the nonlinear iteration process.

[0063] It should be noted that the diameter of the search domain is fixed after being determined based on the maximum radial interference size before the calculation begins. The size of the search domain is not dynamically adjusted during subsequent nonlinear iterations to ensure the consistency of the search range and the stability of the calculation process.

[0064] It should be noted that in this embodiment, the search domain is constructed using a specified offset method, and the offset is set to zero to ensure that the geometric contact relationship is consistent with the actual physical contact relationship, and to avoid introducing additional calculation errors by artificially enlarging or shrinking the contact area.

[0065] (2) Determine the projection point corresponding to the integration point based on the search domain and the component combination.

[0066] Specifically, surface elements of opposing components in the component assembly are screened based on the search domain. Only surface elements whose geometric regions fall within the search domain are selected as candidate surface elements for subsequent calculations, thus avoiding a global search across the entire geometric range of the opposing components. Subsequently, for each candidate surface element, the local projection point of the integration point on that surface element is calculated. Specifically, let the spatial coordinates of the integration point in the current configuration be... The candidate surface unit is determined by its parameter coordinates. Its spatial position in the global coordinate system can be described as follows:

[0067] ;

[0068] in, Let be the shape function of the surface unit. These are the spatial coordinates of the node corresponding to the surface element in the current configuration. This represents the number of nodes in the surface unit. The spatial coordinates of the integration point in the current configuration are also given. Given quantities, find the parametric coordinates that minimize the squared distance from the integration point to any point on the surface element. That is, minimizing the objective function Thus, the corresponding local projection point is determined. The aforementioned minimization problem is a nonlinear least squares problem, which can be solved in this embodiment using Newton's iteration method or an equivalent numerical iteration method.

[0069] Furthermore, after obtaining the local projection points of the integration point on each candidate surface unit, the distance metric between the integration point and each projection point is calculated, and among the projection points corresponding to all candidate surface units, the projection point whose geometric relationship is closest to the contact state of the integration point is selected as the final projection point corresponding to the integration point.

[0070] S1032. Obtain material parameters. Based on the material parameters, the integration point, the projection point, and the surface geometry information of the mating component, determine the contact force at the integration point. Based on the contact force and the internal elastic force generated by the elastic component under the current configuration, construct the overall force balance relationship and perform iterative solution to obtain the sealed assembly completed state.

[0071] Specifically, based on the integration point and its corresponding projection point, and combined with the surface geometry information of the mating component, it is determined whether contact occurs between the integration point and the mating component. If contact occurs, the penetration amount at the integration point is determined based on the integration point, the projection point, and the geometric information on the surface unit where the projection point is located. Furthermore, the contact force at the integration point is calculated by combining the material parameters. Subsequently, the contact force at the integration point is assembled into the overall force balance relationship according to the finite element discretization relationship, and iteratively solved together with the internal elastic force generated by the elastic component under the current configuration, thereby obtaining the displacement update result of the elastic component under the current iteration step.

[0072] Optionally, in one possible implementation, determining the contact force at the integration point based on the material parameters, the integration point, the projection point, and the surface geometry information of the mating component includes:

[0073] (1) Calculate the penetration amount based on the integration point, the projection point and the geometric information on the surface unit where the projection point is located.

[0074] Specifically, based on the spatial position of the integration point in the current configuration, the spatial position of the projection point on the surface of the mating component, and the geometric information of the surface unit where the projection point is located, the normal penetration degree of the integration point relative to the surface of the mating component is calculated, and the normal penetration degree is used as the penetration amount at the integration point.

[0075] Optionally, in one possible implementation, calculating the penetration amount based on the integration point, the projection point, and the geometric information on the surface unit where the projection point is located includes:

[0076] A) Based on the geometric information of the surface of the opposing component where the projection point is located, determine the surface normal direction corresponding to the projection point.

[0077] Specifically, the surface of the opposing component, after finite element discretization, is composed of multiple surface elements, and the projection point is located on one of these surface elements. Based on the geometric description of this surface element, the local tangential direction of the surface element at the projection point is obtained, and the normal direction perpendicular to the surface element is determined based on this local tangential direction. In an optional implementation, the local tangential direction can be obtained from the geometric parameterization relationship of the surface element or calculated from the nodal coordinates of the surface element. Preferably, the surface normal direction is represented by the unit normal vector of the surface element at the projection point, used to characterize the normal geometric direction of the mating component surface at that location.

[0078] B) Based on the spatial position of the integration point and the projection point, construct the relative displacement vector between the integration point and the projection point, and generate the normal relative displacement of the integration point relative to the projection point based on the relative displacement vector and the surface normal direction.

[0079] Specifically, let the spatial position vector of the integration point in the current configuration be... The spatial position vector of the projection point on the surface of the opposing component is: Then the relative displacement vector of the integration point with respect to the projection point can be expressed as: Based on this, the relative displacement vector is directed along the surface normal direction at the projection point. By projecting, the normal relative displacement of the integration point with respect to the projected point is obtained, where Let be the unit surface normal vector at the projection point.

[0080] C) Determine the penetration amount at the integration point based on the spatial positions of the integration point and the projection point and the relative displacement of the normal.

[0081] Specifically, the penetration amount δ is defined as the displacement component of the integration point relative to the projection point in the surface normal direction, and its mathematical expression is:

[0082] ;

[0083] Wherein, δ represents the geometric penetration degree of the integration point along the normal direction of the opposing member surface; when δ is greater than zero, it indicates that the integration point penetrates the opposing member surface in the current configuration; when δ is less than or equal to zero, it indicates that no penetration has occurred or that the components are in a critical contact state. The penetration amount serves as the basic geometric parameter for subsequent contact force calculations, reflecting the degree of contact interference between the elastic member and the mating member.

[0084] (2) Calculate the contact force at the integration point based on the penetration amount and the material parameters.

[0085] Specifically, after obtaining the penetration amount at the integration point, a mechanical response calculation is performed on the penetration amount based on the material parameters to determine the contact force at the integration point. The material parameters characterize the mechanical properties of the components involved in the contact in the contact direction, and the contact force reflects the contact action experienced at the integration point under the current configuration and iteration steps.

[0086] Optionally, in one possible implementation, the contact force at the integration point includes a first contact force along the surface normal direction at the projection point, and a second contact force along the surface tangential direction perpendicular to the surface normal direction; the calculation of the contact force at the integration point based on the penetration amount and the material parameters includes:

[0087] A) Calculate the first contact force based on the penetration amount and the material parameters.

[0088] Specifically, the integration point is located on the surface of the elastic member, and the projection point is located on the surface of the opposing member that forms a mating relationship with the elastic member. During the contact analysis, the integration point is allowed to geometrically penetrate the projection point in the normal direction to improve the numerical stability of the nonlinear iterative process. Based on this, the contact force at the integration point is decomposed along the surface normal and surface tangential directions at the projection point. The contact force along the surface normal direction is defined as the first contact force, used to characterize the positive compressive force between the members; the contact force along the surface tangential direction is defined as the second contact force, used to characterize the tangential constraint between the members due to friction.

[0089] Specifically, the contact force model used to establish the relationship between the first contact force and the penetration amount can be implemented using contact numerical algorithms such as the penalty function method, the Lagrange multiplier method, or the augmented Lagrange method. In this embodiment, the augmented Lagrange contact algorithm is preferably used to construct the first contact force model, so as to improve the numerical stability and convergence performance of the nonlinear iterative process while ensuring that the penetration amount is controlled.

[0090] Specifically, under the augmented Lagrange contact algorithm, a virtual normal contact elastic constraint is established at the integration point to characterize the mechanical response relationship between the integration point and its corresponding projection point in the normal direction. The first contact force at the integration point along the surface normal direction at the projection point... It can be represented as:

[0091] ;

[0092] in, The penetration amount at the integration point. For normal contact stiffness, These are Lagrange multipliers used to record and accumulate the normal contact constraint forces formed in the previous iteration. During the iterative calculation process, these Lagrange multipliers... It updates dynamically with each iteration step, allowing the constraint penetration amount to gradually converge to a preset range without significantly increasing the normal contact stiffness, thereby improving the stability and accuracy of contact calculation.

[0093] It should be noted that the normal contact stiffness is the mechanical constraint strength of the component assembly in the normal direction, and its value can be set according to material properties, mesh scale, and numerical convergence requirements. In one implementation, the normal contact stiffness... The normal contact stiffness can be set within a preset range to improve numerical convergence performance while ensuring contact accuracy. Preferably, in the initial iteration stage, the normal contact stiffness can be set to a larger value to enhance the normal constraint effect. When convergence difficulties occur in the nonlinear iteration process, the normal contact stiffness can be appropriately reduced according to the calculation state to avoid numerical instability caused by excessive contact stiffness. In this embodiment, the normal contact stiffness... The value is set empirically, and values ​​within the range of 0.1 to 1 can meet the calculation accuracy requirements. From a convergence perspective, the normal contact stiffness can be pre-set. If the normal stiffness is set to 1, and subsequent simulations do not converge, the normal stiffness can be gradually reduced as needed.

[0094] B) Calculate the second contact force based on the spatial position of the integration point and the projection point in the current iteration step, the first contact force, and the material parameters.

[0095] Specifically, based on the relative displacement changes of the integration point and the projection point in space, the relative motion state of the component assembly in the tangential direction is determined, and the assembly is judged to be in an adhesive or sliding state. The second contact force is used to characterize the tangential constraint effect between components due to friction, so as to consider both normal compression and tangential friction during the contact analysis, thereby more realistically reflecting the stress state and deformation behavior of the rubber components during assembly.

[0096] Optionally, in one possible implementation, calculating the second contact force based on the spatial position of the integration point and the projection point in the current iteration step, the first contact force, and the material parameters includes:

[0097] (1) In the current iteration step, based on the spatial position of the integration point and the projection point, determine the relative motion state of the integration point with respect to the projection point in the tangential direction of the surface.

[0098] Specifically, in the contact analysis process, the tangential relative motion state is used to characterize whether relative slippage occurs in the component assembly along the tangential direction of the surface. In different implementations, the tangential relative motion state can be determined based on relative displacement information, equivalent velocity information, or historical contact states. For example, the motion state of the contact pair can be determined by analyzing the relative position change trend of the integration point and the projection point along the tangential direction of the surface in adjacent iteration steps, or based on the tangential relative motion velocity derived from this position change.

[0099] Specifically, in this embodiment, the relative position vector between the integration point and its corresponding projection point in the current iteration step is calculated; and the relative position vector between the same integration point and its corresponding projection point in the previous iteration step is calculated. By subtracting the relative position vectors obtained in the above two iteration steps, the relative displacement vector of the integration point relative to the projection point between adjacent iteration steps is obtained. Based on this, the relative displacement vector is projected onto the tangential plane of the surface at the projection point to obtain the tangential relative displacement vector, which is used to characterize the relative motion of the integration point in the tangential direction of the surface. When the tangential relative displacement shows a continuous accumulation trend between adjacent iteration steps, and its direction of change indicates that the integration point has a significant relative motion with respect to the projection point in the tangential direction of the surface, the contact pair is determined to be in a sliding state; when the tangential relative displacement remains within a preset range between adjacent iteration steps, or does not show a continuous accumulation trend, the contact pair is determined to be in an adhesive state. In this way, without introducing additional contact history variables, the stability of the tangential relative motion state can be determined solely based on the geometric positional relationship between the integration point and the projection point in adjacent iteration steps. Furthermore, the tangential relative displacement vector can be combined with the iteration step size to obtain equivalent tangential relative motion velocity information when needed, for use in the subsequent second contact force model.

[0100] (2) Calculate the second contact force based on the first contact force, the material parameters and the relative motion state in the tangential direction of the surface.

[0101] Specifically, when the contact pair is determined to be in a sliding state, a friction constraint needs to be introduced in the tangential direction of the surface to calculate the second contact force. In different implementations, the second contact force can be calculated based on the Coulomb friction model, a regularized friction model, or a continuous friction model combining stick-slip transition conditions; this application does not limit this. In this embodiment, a second contact force calculation method based on the Coulomb friction assumption is preferred.

[0102] Specifically, based on the spatial positions of the integration point and the projection point in adjacent iteration steps, the tangential relative displacement vector of the integration point relative to the projection point is determined. Combined with the current iteration step size, this tangential relative displacement vector is equivalently represented as a tangential relative velocity vector, reflecting the instantaneous motion trend of the integration point in the tangential direction of the surface. Based on this, the second contact force at the integration point along the tangential direction of the surface... It can be represented as:

[0103] ;

[0104] in: The coefficient of friction, The first contact force calculated along the surface normal direction at the integration point. Let be the equivalent relative velocity vector of the integration point with respect to the projection point in the tangential direction of the surface. The unit direction vector of the tangential relative motion is used to determine the direction of the second contact force in the tangential plane of the surface.

[0105] It should be noted that the coefficient of friction is used to characterize the tangential friction characteristics between a rubber component and an opposing component under lubricated or semi-lubricated contact conditions. Its value can be determined based on material test results, empirical parameters, or a preset friction model. This application does not impose any limitations on this.

[0106] In summary, by using the above method, in the nonlinear iterative solution process, a friction constraint consistent with the tangential relative motion state can be introduced on the basis of the first contact force, so that the second contact force is updated in real time with the contact state, thereby more accurately reflecting the real stress state and deformation behavior of the rubber component during assembly or compression.

[0107] Specifically, after obtaining the contact force at the integration point, the contact force and the internal elastic force generated by the elastic member under the current configuration are integrated into the overall force balance relationship to describe the mechanical equilibrium relationship of the structural system under the current configuration. In this embodiment, the overall force balance relationship can be expressed in the following residual form:

[0108] ;

[0109] in, Let be the displacement vector of each node in the structural system. This refers to the internal elastic force vector generated by material deformation in the elastic member under the current configuration. Let be the equivalent contact force vector introduced by the contact action at the integration point. Wherein, The internal force vector of the elastic member is calculated from the material constitutive relation under the current configuration, and its magnitude and direction vary with the nodal displacement. The status is updated dynamically.

[0110] Specifically, the internal elastic force vector It can be calculated using the finite element method, i.e., based on nodal displacements. Calculate the strain of each element, then obtain the stress by combining the material constitutive relation, and finally obtain the internal force vector of each node by summing the element forces. The contact force vector The contact force is composed of contact forces at multiple integration points. The first and second contact forces calculated at each integration point are mapped to equivalent nodal forces through their corresponding shape functions and assembled into the overall contact force vector, which can be expressed as:

[0111] ;

[0112] in, Number the integration points. Let be the shape function matrix corresponding to the integration point. This is its transpose matrix, used to convert the contact forces at the integration points into nodal forces. and The first The first contact force along the surface normal direction and the second contact force along the surface tangential direction at each integration point.

[0113] Specifically, the nodal displacement vectors are solved step by step using a nonlinear iterative method. During the iteration process, each step involves updating the node displacements. Recalculate and And form a new residual vector. Until the residual vector If the changes satisfy the preset convergence condition in adjacent iteration steps, the mechanical state of the sealing structure can be considered to have reached equilibrium, thus obtaining the assembled state of the rubber-plastic seal. In this embodiment, the preset convergence condition can be determined by the norm of the residual vector, the increment of nodal displacement, or the magnitude of the change in contact force, to ensure that the penetration amount is within the allowable range and the contact force and internal force are stable in the assembled state, thereby ensuring the accuracy of the overall mechanical response.

[0114] Optionally, in one possible implementation, the iterative solution includes at least:

[0115] (1) In the current iteration step, based on the contact force at the integration point and the internal elastic force generated by the elastic member in the current configuration, an overall force balance relationship is constructed, and the residual is calculated based on the overall force balance relationship.

[0116] Specifically, in each iteration step, the internal elastic force vector is... With the equivalent contact force vector Perform synthesis to construct the overall force balance residual vector. The residual vector is used to characterize the mechanical imbalances at each degree of freedom of the structural system that have not yet reached mechanical equilibrium under the current iteration step. The magnitude of the residual vector reflects the degree to which the overall force balance relationship is satisfied under the current configuration, providing a basis for subsequent iteration judgments. The specific calculation methods, assembly processes, and expressions of the contact forces and internal elastic forces in the overall force balance relationship have been explained in the foregoing embodiments and will not be repeated here.

[0117] (2) Determine whether the residual is less than the preset tolerance value. If yes, complete the iteration; otherwise, update the current configuration of the sealing assembly and return to the iterative solution step of determining the projection point corresponding to the integral point based on the integral point and the component combination where the integral point is located.

[0118] Specifically, the corresponding residual vectors are calculated in adjacent iteration steps, and the magnitudes of the residual vectors are compared. When the magnitude of the residual vector is less than a preset tolerance value, it is determined that the contact force introduced by the contact action and the elastic force inside the elastic component in the structural system under the current iteration state have reached a state of mechanical equilibrium at the overall structural scale. In this embodiment, the preset tolerance value can be set according to material properties, contact stiffness, and numerical stability requirements. For example, in the assembly simulation of rubber and plastic seals, the residual tolerance value can be selected as 0.5% of the overall force residual relative to the characteristic load, so as to ensure calculation accuracy while taking into account iterative convergence efficiency. This embodiment does not limit this. Under the above conditions, it is considered that the seal has been assembled under the current configuration. At this time, the structural system no longer produces significant displacement updates or mechanical response changes, thereby enabling the evaluation of the morphology and mechanical properties of the assembled seal.

[0119] This application provides a method and apparatus for solving the completed state of a sealed assembly. The method involves acquiring a geometric model including at least an elastic component and its mating components, assembling them into an initial assembly configuration, and determining the component combination based on the contact relationship between the elastic component and the mating components. Further, the elastic component and mating components are discretized using finite element methods (FEM) to obtain finite element elements, and integration points are determined within each finite element element of the elastic component. Based on this, the current configuration of the sealed assembly is iteratively updated according to the initial assembly configuration. In each iteration, the corresponding projection point is determined based on the integration point and its component combination. The contact force at the integration point is determined by combining material parameters, the integration point, the projection point, and the surface geometry information of the mating components. The contact force and the internal elastic force generated by the elastic component under the current configuration are then assembled into an overall force balance relationship for iterative solution until the solution result of the overall force balance relationship in adjacent iterations satisfies a preset convergence condition, thereby obtaining the completed state of the sealed assembly. Through the above technical solution, this application can reliably solve the completed assembly state of a seal even when there is interference in the initial geometry. During the assembly iteration process, the contact force and the internal force generated by the elastic component are uniformly introduced into the overall force balance relationship, thereby effectively preventing numerical divergence in the contact calculation and improving the stability, convergence and computational efficiency of the assembly simulation process.

[0120] Corresponding to the aforementioned embodiment of the sealing assembly completion state solution method, this application also provides an embodiment of the sealing assembly completion state solution apparatus.

[0121] Figure 2This is a schematic diagram of the structure of Embodiment 1 of the sealing assembly completion state solving device provided in this application. Please refer to... Figure 2 The apparatus provided in this embodiment includes an acquisition module 201, a determination module 202, and an iteration module 203, wherein:

[0122] The acquisition module 201 is used to acquire a geometric model including at least an elastic component and its mating components, and assemble them into an initial assembly configuration, and determine the component combination based on the contact relationship between the elastic component and the mating components;

[0123] The determining module 202 is used to perform finite element discretization on the elastic component and the mating component to obtain finite element elements, and to determine the integration points in each finite element element of the elastic component.

[0124] The iteration module 203 is used to iteratively update the current configuration of the sealing assembly based on the initial configuration, and the specific iteration steps include at least:

[0125] Based on the integration point and the component combination where the integration point is located, determine the projection point corresponding to the integration point;

[0126] Obtain material parameters, and based on the material parameters, the integration point, the projection point, and the surface geometry information of the mating component, determine the contact force at the integration point. Based on the contact force and the internal elastic force generated by the elastic component under the current configuration, construct the overall force balance relationship and perform iterative solution to obtain the sealed assembly completed state.

[0127] The apparatus of this embodiment can be used to perform... Figure 1 The steps of the method embodiment shown are similar in principle and process, and will not be repeated here.

[0128] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0129] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0130] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for solving the completed state of a sealed assembly, characterized in that, Includes the following steps: Obtain a geometric model that includes at least an elastic member and its mating members, and assemble them into an initial assembly configuration. Determine the component assembly based on the contact relationship between the elastic member and the mating members. The elastic member and the mating member are discretized using finite element method to obtain finite element elements, and integration points are determined within each finite element element of the elastic member. Based on the initial configuration, the current configuration of the sealing assembly is iteratively updated, and the specific iterative steps include at least: Based on the integration point and the component combination where the integration point is located, determine the projection point corresponding to the integration point; Obtain material parameters, and based on the material parameters, the integration point, the projection point, and the surface geometry information of the mating component, determine the contact force at the integration point. Based on the contact force and the internal elastic force generated by the elastic component under the current configuration, construct the overall force balance relationship and perform iterative solution to obtain the sealed assembly completed state. The step of determining the projection point corresponding to the integration point based on the integration point and the component combination where the integration point is located includes: Obtain the spatial coordinates of the integration point under the current configuration, and determine the search domain based on the component combination where the integration point is located, with the integration point as the center. The projection point corresponding to the integration point is determined based on the search domain and the component combination; The step of determining the search domain based on the component combination where the integration point is located, centered on the integration point, includes: Based on the component combination to which the integration point belongs, determine the opposing component that forms a component combination with the component where the integration point is located; Based on the geometric relationship between the integration point and the opposing component, the maximum radial interference size formed between the integration point and the opposing component during the assembly process is determined; The diameter value of the search domain is determined based on the maximum radial interference size; The search domain is constructed with the integration point as the center of the sphere and the diameter value as the diameter. The determination of the contact force at the integration point based on the material parameters, the integration point, the projection point, and the surface geometry information of the mating component includes: The penetration amount is calculated based on the integration point, the projection point, and the geometric information on the surface unit where the projection point is located. Calculate the contact force at the integration point based on the penetration amount and the material parameters; The contact force at the integration point includes a first contact force along the surface normal direction at the projection point, and a second contact force along the surface tangential direction perpendicular to the surface normal direction; the calculation of the contact force at the integration point based on the penetration amount and the material parameters includes: Calculate the first contact force based on the penetration amount and the material parameters; Based on the spatial position of the integration point and the projection point in the current iteration step, the first contact force, and the material parameters, calculate the second contact force; The calculation of the second contact force based on the spatial position of the integration point and the projection point in the current iteration step, the first contact force, and the material parameters includes: In the current iteration step, based on the spatial position of the integration point and the projection point, the relative motion state of the integration point with respect to the projection point in the tangential direction of the surface is determined; The second contact force is calculated based on the first contact force, the material parameters, and the relative motion state in the tangential direction of the surface.

2. The method of claim 1, wherein, The calculation of penetration based on the integration point, the projection point, and the geometric information on the surface unit where the projection point is located includes: Based on the geometric information of the surface of the opposing component where the projection point is located, the surface normal direction corresponding to the projection point is determined; Based on the spatial position of the integration point and the projection point, a relative displacement vector between the integration point and the projection point is constructed. Based on the relative displacement vector and the surface normal direction, the normal relative displacement of the integration point relative to the projection point is generated. The penetration amount at the integration point is determined based on the spatial positions of the integration point and the projection point, as well as the relative displacement in the normal direction.

3. The method of claim 1, wherein, The iterative solution includes at least: In the current iteration step, based on the contact force at the integration point and the internal elastic force generated by the elastic member under the current configuration, an overall force balance relationship is constructed, and the residual is calculated based on the overall force balance relationship. Determine whether the residual is less than the preset tolerance value. If so, complete the iteration; otherwise, update the current configuration of the sealing assembly and return to the iterative solution step of determining the projection point corresponding to the integration point based on the integration point and the component combination where the integration point is located. When the residual corresponding to the solution result of the overall force balance relationship in the adjacent iteration step is lower than the preset tolerance value, the current configuration of the sealing assembly is determined to be the sealing assembly completion state.

4. The method of claim 1, wherein, Before iteratively updating the current configuration of the sealed assembly, the method further includes: Based on the subordinate relationship between the integration points and the component combination, the integration points are filtered to obtain a filtered set of integration points, and subsequent iterative updates are performed only on the filtered set of integration points.

5. A sealed assembly completion state solver apparatus, characterized by, The apparatus is used to execute the sealing assembly completion state solution method according to any one of claims 1-4; the apparatus includes an acquisition module, a determination module, and an iteration module, wherein: The acquisition module is used to acquire a geometric model that includes at least an elastic component and its mating components, and assemble them into an initial assembly configuration, and determine the component combination based on the contact relationship between the elastic component and the mating components; The determining module is used to perform finite element discretization on the elastic component and the mating component to obtain finite element elements, and to determine the integration points in each finite element element of the elastic component. The iteration module is used to iteratively update the current configuration of the sealing assembly based on the initial configuration, and the specific iteration steps include at least: Based on the integration point and the component combination where the integration point is located, determine the projection point corresponding to the integration point; Obtaining material parameters, determining the contact force at the integral point based on the material parameters, the integral point, the projection point and the surface geometric information of the matching component, and constructing the overall force balance relationship and performing iterative solution based on the contact force and the internal elastic force generated by the elastic component in the current configuration to obtain the sealing assembly completed state.

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