Sealing performance analysis method for elastic-plastic contact calculation based on finite element-boundary element coupling

Abstract

The invention relates to the field of sealing testing, in particular to a sealing performance analysis method based on elastic-plastic contact calculation of finite element-boundary element coupling, which comprises the following steps: establishing a finite element model of a sealing structure, and obtaining contact pressure distribution of a sealing contact interface; dividing the sealed contact interface into a plurality of fan-shaped areas, and processing each fan-shaped area into a rectangular area; generating a rough surface of which the surface height value has a specified statistical distribution rule for each rectangular region, performing equivalent contact simplification for the rough surface in the sealing contact process, and solving the microscopic contact state of the rough surface; and constructing a contact state matrix based on the microscopic contact state, and determining a leakage channel by using the contact state matrix. The problems that a traditional rough surface microcosmic contact finite element simulation method is low in calculation efficiency and elastic-plastic contact deformation convergence is difficult are solved, and the efficiency of microcosmic contact calculation and sealing performance analysis is greatly improved.

Description

Technical Field

[0001] The invention relates to the technical field of sealing test, and in particular to a sealing performance analysis method based on elastic-plastic contact calculation of finite element-boundary element coupling. Background Art

[0002] Sealing structures are widely used in high-end equipment in the fields of aerospace, weapons and ships, deep sea and ocean exploration. Once a sealing structure fails, the service life and reliability of the equipment will be significantly reduced. Although theoretical modeling can predict the leakage rate of sealing structures, some assumptions may be made in the model, making it difficult to match the actual working conditions. Although the experimental method can measure the leakage rate of sealing structures more accurately and directly, it requires the construction of a dedicated software and hardware system, which is costly. Summary of the invention

[0003] In view of the above problems, an embodiment of the present invention provides a sealing performance analysis method based on elastic-plastic contact calculation of finite element-boundary element coupling, comprising:

[0004] A finite element model of the sealing structure is established according to actual parameters, constraints and loads are applied to the finite element model, and the contact pressure distribution of the sealing contact interface in the sealing structure is obtained through simulation;

[0005] The sealing contact interface is divided into a plurality of sector-shaped regions, and each sector-shaped region is approximately treated as a rectangular region, wherein the contact pressure distribution in each rectangular region is uniform;

[0006] For each rectangular area, a conjugate gradient method is used to generate a rough surface whose surface height value has a specified statistical distribution law;

[0007] The equivalent contact simplification is performed on the rough surface in the sealing contact process to determine the equivalent contact surface of the rough surface. Based on the equivalent contact surface and with the contact pressure distribution as the boundary condition, the microscopic contact state of the rough surface is solved. The deformation stage is divided into a pure elastic stage and an elastic-plastic stage.

[0008] A contact state matrix is ​​constructed based on the microscopic contact state, so that the leakage channel is determined by using the contact state matrix, and the sealing performance is determined according to the state of the leakage channel.

[0009] Compared with the prior art, the beneficial effects of the present invention are: by simplifying the rough surface by equivalent contact and solving the microscopic contact state of the rough surface with the contact pressure distribution as the boundary condition, the problems of low calculation efficiency and difficulty in convergence of elastic-plastic contact deformation of the traditional rough surface microscopic contact finite element simulation method are solved, and the efficiency of microscopic contact calculation and sealing performance analysis is greatly improved.

[0010] Optionally, the process of establishing a finite element model of the sealing structure according to actual parameters includes:

[0011] Establish the finite element model of each part in the sealing structure according to the actual parameters, constrain the finite element model of each part according to the assembly relationship, and establish the overall finite element model of the sealing structure;

[0012] The bilinear isotropic hardening material model is used to simulate the stress-strain curve of the elastic-plastic material of the sealing structure. The material properties of each part in the overall finite element model are set, and the target surface and contact surface are defined respectively to determine the contact pair.

[0013] Optionally, the process of applying constraints and loads to the finite element model to obtain the contact pressure distribution of the sealing contact interface in the sealing structure through simulation includes:

[0014] According to the actual working conditions, constraints and loads are imposed on the finite element model and the finite element analysis software is used to perform static solutions to extract the contact pressure of the sealing contact interface in the sealing structure. The contact pressure is fitted using simulation software to obtain the contact pressure distribution of the sealing contact interface in the sealing structure.

[0015] Optionally, the process of performing equivalent contact simplification on the rough surface in the sealing contact process to determine the equivalent contact surface of the rough surface includes:

[0016] For the two rough surfaces in the pure elastic stage, they are equivalently simplified to an equivalent elastic rough surface and a rigid ideal plane. The Young's modulus E of the equivalent elastic rough surface is * and Poisson's ratio ν * Satisfies the following expression:

[0017]

[0018] Among them, E1 and E2 represent the elastic modulus of the two rough surfaces before equivalent simplification, ν1 and ν2 represent the Poisson's ratio of the two rough surfaces before equivalent simplification;

[0019] Similarly, the two rough surfaces in the elastic-plastic deformation stage are equivalently simplified into an equivalent elastic-plastic rough surface and a rigid ideal plane.

[0020] Optionally, the process of solving the microscopic contact state of the rough surface based on the equivalent contact surface and using the contact pressure distribution as the boundary condition includes:

[0021] When two equivalent contact surfaces are squeezed and contacted with each other under load, the entire sealing structure tends to a stable state, that is, a state with minimum total residual potential energy. Therefore, based on the minimum potential energy theory, the problem of solving the microscopic contact state is transformed into the problem of calculating the minimum total residual potential energy:

[0022]

[0023] Among them, V * represents the total residual potential energy, represents the internal complementary energy of the underlying entity, u i * represents a given surface displacement, T i represents the surface force of the elastic body, Ω represents the force range of the elastic body surface; the rough surface is regarded as a frictionless linear semi-infinite elastic body, and the internal complementary energy of the solid under the surface is Numerically, it is similar to the elastic strain energy U E Equal, can be calculated by surface contact pressure and surface deformation;

[0024] When the rigid ideal plane and the elastic rough surface are squeezed against each other, the relative surface displacement between the rough surface and the rigid ideal plane is calculated from the initial contact gap distribution of the elastic body and the rigid body displacement. In this state, the total residual potential energy is expressed as follows:

[0025]

[0026] Where p(x,y) represents the contact pressure distribution, e u(x,y) represents the normal deformation of the rough surface, g0(x,y) represents the initial contact gap distribution of the contact interface, and δ represents the displacement of the rigid ideal plane;

[0027] According to Boussinesq theory, the deformation of an elastic body is related to the surface pressure distribution, so

[0028] e u(x,y)= ue G(x,y)*p(x,y)

[0029] in, ue G(x,y) represents the influence coefficient of the normal load on a point on the contact interface on the normal displacement of other points on the contact interface. The calculation expression is:

[0030]

[0031] At this time, there is only a single independent variable p(x, y) in the total residual potential energy calculation formula, and there is a unique contact pressure distribution that minimizes the total residual potential energy. The contact calculation of the rough surface is actually a process of finding the conditional extreme value of the quadratic functional. The minimum total residual potential energy can be solved by the CG-FFT method, and then the microscopic contact state can be obtained;

[0032] As the load increases, the stress in the local area of ​​the contact interface exceeds the yield limit of the sealing structure material, causing plastic strain and residual stress in the local area. The permanent surface deformation caused by plastic strain is the residual deformation. Therefore, in solving the elastic-plastic contact problem, it is necessary to calculate the microscopic contact state after superimposing the influence of the residual deformation and residual stress field on the rough surface.

[0033] Optionally, the process of constructing a contact state matrix based on the microscopic contact state, and then determining the leakage channel using the contact state matrix includes:

[0034] According to the microscopic contact state, the contact points and non-contact points in the sealing contact interface are determined, and the sealing contact interface is projected onto a two-dimensional plane, and the contact points are assigned a value of 0 and the non-contact points are assigned a value of 1, thereby constructing a contact state matrix;

[0035] Traverse each point in the contact state matrix from the entrance of the sealed contact interface to the exit direction. During the traversal process, if the current point and the points adjacent to the current point are both non-contact points, record the coordinates of the current point and the points adjacent to the current point into the connected unit set;

[0036] After the traversal is completed, the points in the connected unit set are reassigned to 2 in the contact state matrix. When the points assigned to 2 connect the inlet and outlet of the sealed contact interface, the sealed contact interface leakage is determined. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The drawings described herein are used to provide a further understanding of the present invention, constitute a part of the present application, and do not constitute a limitation of the present invention. In the drawings:

[0038] Figure 1 It is a principle block diagram of the sealing performance analysis method of the present invention based on elastic-plastic contact calculation of finite element-boundary element coupling;

[0039] Figure 2 A schematic diagram of a rectangular area obtained by approximate processing according to an embodiment of the present invention;

[0040] Figure 3 A simplified schematic diagram of equivalent contacts provided by an embodiment of the present invention;

[0041] Figure 4 A four-connected grid model provided by an embodiment of the present invention;

[0042] Figure 5 A schematic diagram of a contact state matrix provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments and the accompanying drawings. Here, the illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0044] See also Figure 1 , a sealing performance analysis method based on elastic-plastic contact calculation of finite element-boundary element coupling is provided in an embodiment of the present invention, comprising:

[0045] Step 1: Establish a finite element model of the sealing structure according to actual parameters, apply constraints and loads to the finite element model, and obtain the contact pressure distribution of the sealing contact interface in the sealing structure through simulation.

[0046] During implementation, the finite element modeling of the sealing structure can establish the finite element model of each part in the sealing structure according to the actual parameters, and constrain the finite element model of each part according to the assembly relationship to establish the overall finite element model of the sealing structure;

[0047] The parameters and boundary conditions of the finite element model are as follows: a bilinear isotropic hardening material model is used to simulate the stress-strain curve of the elastic-plastic material of the sealing structure (as shown in the following expression); the material properties of each part in the overall finite element model are set; and the target surface and contact surface are defined respectively to determine the contact pair; specifically, two-dimensional surface elements TARGE170 and CONTA173 can be selected as contact surface elements, and constraints and loads can be applied according to actual working conditions.

[0048]

[0049] During implementation, the macro contact pressure distribution can be obtained by applying constraints and loads to the finite element model according to the actual working conditions, and then using the Ansys19.2 finite element analysis software to perform static solutions, extracting the contact pressure of the sealing contact interface in the sealing structure, and importing the obtained contact pressure into the Matlab software. The contact pressure is fitted using the cftool command in the simulation software Matlab to obtain the contact pressure distribution of the sealing contact interface.

[0050] Step 2: Divide the sealing contact interface into a plurality of sector-shaped regions, and approximate each sector-shaped region as a rectangular region, wherein the contact pressure in each rectangular region is evenly distributed.

[0051] In practice, the contact pressure distribution of the sealing contact interface is uneven. When the boundary element is used to perform microscopic contact calculation of the sealing contact interface, the uniform load condition is usually required. In order to solve this problem, the macroscopic sealing contact interface is divided into multiple sector areas, and each sector area is approximated as a rectangular area, in which the contact pressure distribution in each rectangular area is uniform, such as Figure 2As shown, the macroscopic contact pressure of each sector area is calculated as the boundary condition for the subsequent microscopic contact calculation of the rectangular area.

[0052] Step 3: For each rectangular area, a conjugate gradient method is used to generate a rough surface whose surface height values ​​have a specified statistical distribution law.

[0053] In practice, the rough surface has obvious self-affine property. According to this property, the rough surface can be characterized by numerical methods. The conjugate gradient method can generate a rough surface with a specified statistical distribution law of surface height values.

[0054] Step 4: Perform equivalent contact simplification on the rough surface during the sealing contact process to determine the equivalent contact surface of the rough surface, and solve the microscopic contact state of the rough surface based on the equivalent contact surface and using the contact pressure distribution as the boundary condition.

[0055] In practice, according to the Johnson hypothesis, the purely elastic contact problem between two rough surfaces is equivalent to the contact problem between an elastic rough surface with equivalent three-dimensional surface morphology and equivalent material properties and a rigid ideal plane. Figure 3 As shown; Young's modulus E of the equivalent elastic rough surface * and Poisson's ratio ν * Satisfies the following expression:

[0056]

[0057] Among them, E1 and E2 represent the elastic modulus of the two rough surfaces before equivalent simplification, ν1 and ν2 represent the Poisson's ratio of the two rough surfaces before equivalent simplification;

[0058] Similarly, the two rough surfaces in the elastic-plastic deformation stage are equivalently simplified into an equivalent elastic-plastic rough surface and a rigid ideal plane.

[0059] In practice, when two equivalent contact surfaces are squeezed and contacted with each other under load, the entire sealing structure tends to a stable state, that is, a state with the minimum total residual potential energy. Therefore, based on the minimum potential energy theory, the problem of solving the microscopic contact state is transformed into the problem of calculating the minimum total residual potential energy:

[0060]

[0061] Among them, V * represents the total residual potential energy, represents the internal complementary energy of the underlying entity, u i * represents a given surface displacement, T irepresents the surface force of the elastic body, Ω represents the force range of the elastic body surface; the rough surface is regarded as a frictionless linear semi-infinite elastic body, and the internal complementary energy of the solid under the surface is Numerically, it is similar to the elastic strain energy U E Equal, can be calculated by surface contact pressure and surface deformation;

[0062] When the rigid ideal plane and the elastic rough surface are squeezed against each other, the relative surface displacement between the rough surface and the rigid ideal plane is calculated from the initial contact gap distribution of the elastic body and the rigid body displacement. In this state, the total residual potential energy is expressed as follows:

[0063]

[0064] Where p(x,y) represents the contact pressure distribution, e u(x,y) represents the normal deformation of the rough surface, g0(x,y) represents the initial contact gap distribution of the contact interface, and δ represents the displacement of the rigid ideal plane;

[0065] According to Boussinesq theory, the deformation of an elastic body is related to the surface pressure distribution, so

[0066] e u(x,y)= ue G(x,y)*p(x,y)

[0067] in, ue G(x,y) represents the influence coefficient of the normal load on a point on the contact interface on the normal displacement of other points on the contact interface. The calculation expression is:

[0068]

[0069] At this time, there is only a single independent variable p(x, y) in the total residual potential energy calculation formula, and there is a unique contact pressure distribution that minimizes the total residual potential energy. The contact calculation of the rough surface is actually a process of finding the conditional extreme value of the quadratic functional. The minimum total residual potential energy can be solved by the CG-FFT method, and then the microscopic contact state can be obtained;

[0070] As the load increases, the stress in the local area of ​​the contact interface exceeds the yield limit of the sealing structure material, causing plastic strain and residual stress in the local area. The permanent surface deformation caused by plastic strain is the residual deformation. Therefore, in the solution of elastic-plastic and plastic contact problems, it is necessary to superimpose the influence of residual deformation and residual stress field on the rough surface, that is, to simplify the elastic-plastic contact problem into a linear elastic contact problem and then calculate the microscopic contact state.

[0071] Step five, constructing a contact state matrix based on the microscopic contact state, thereby using the contact state matrix to determine the leakage channel, and determining the sealing performance according to the state of the leakage channel.

[0072] In practice, in order to solve the leakage channel, the contact points and non-contact points in the sealed contact interface are determined according to the microscopic contact state, the sealed contact interface is projected onto a two-dimensional plane, and the contact points are assigned a value of 0 and the non-contact points are assigned a value of 1, thereby constructing a contact state matrix, such as Figure 5 As shown;

[0073] Traverse each point in the contact state matrix from the entrance of the sealed contact interface to the exit direction. During the traversal process, if the current point and the points adjacent to the current point are both non-contact points, record the coordinates of the current point and the points adjacent to the current point into the connected unit set;

[0074] After the traversal is completed, the points in the connected unit set are reassigned to 2 in the contact state matrix. When the points assigned to 2 connect the inlet and outlet of the sealed contact interface, the sealed contact interface leakage is determined.

[0075] Specifically, in the process of traversing each point in the contact state matrix, a four-connected grid model can be used to analyze the connectivity state, such as Figure 4 As shown in the figure, assuming that the coordinate (I, J) is a non-contact point, first determine whether the point adjacent to the point (I, J) is a non-contact point. If the point at (I+1, J) is also a non-contact point, then transfer the search mark from (I, J) to (I+1, J), and store the coordinates of the points at (I+1, J) and (I+1, J) in the connected unit set. Repeat the above process until the sealed contact interface exit is traversed. After that, reassign the points in the connected unit set to 2 in the contact state matrix. See Figure 5 The point with a value of 0 represents the sealing contact part, the point with a value of 1 is surrounded by the contact point and has no contribution to the leakage, and the point with a value of 2 connects the inlet and outlet of the sealing contact interface to form a leakage channel.

[0076] The core idea of ​​the solution provided by the embodiment of the present invention is to use finite element to solve the contact stress distribution of the macroscopic finite element model, and use it as a boundary condition to solve the microscopic contact state of the cover, and then solve the leakage channel to evaluate the sealing performance of the sealing structure. It solves the problems of low calculation efficiency and difficulty in convergence of elastic-plastic contact deformation of the traditional rough surface microscopic contact finite element simulation method, and is an effective method for macroscopic sealing structure to realize microscopic contact state calculation and quantitative analysis of sealing performance.

[0077] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A sealing performance analysis method based on elastic-plastic contact calculation of finite element-boundary element coupling, characterized in that: The method comprises: A finite element model of the sealing structure is established according to actual parameters, constraints and loads are applied to the finite element model, and the contact pressure distribution of the sealing contact interface in the sealing structure is obtained through simulation; The sealing contact interface is divided into a plurality of sector-shaped regions, and each sector-shaped region is approximately treated as a rectangular region, wherein the contact pressure distribution in each rectangular region is uniform; For each rectangular area, a conjugate gradient method is used to generate a rough surface whose surface height value has a specified statistical distribution law; The equivalent contact simplification is performed on the rough surface in the sealing contact process to determine the equivalent contact surface of the rough surface. Based on the equivalent contact surface and with the contact pressure distribution as the boundary condition, the microscopic contact state of the rough surface is solved. The sealing contact process is divided into a pure elastic stage and an elastoplastic stage. A contact state matrix is ​​constructed based on the microscopic contact state, so that the leakage channel is determined by using the contact state matrix, and the sealing performance is determined according to the state of the leakage channel.

2. The sealing performance analysis method based on elastic-plastic contact calculation of finite element-boundary element coupling according to claim 1, characterized in that: The process of establishing a finite element model of a sealing structure based on actual parameters includes: Establish the finite element model of each part in the sealing structure according to the actual parameters, constrain the finite element model of each part according to the assembly relationship, and establish the overall finite element model of the sealing structure; The bilinear isotropic hardening material model is used to simulate the stress-strain curve of the elastic-plastic material of the sealing structure. The material properties of each part in the overall finite element model are set, and the target surface and contact surface are defined respectively to determine the contact pair.

3. The sealing performance analysis method based on elastic-plastic contact calculation of finite element-boundary element coupling according to claim 1, characterized in that: The process of applying constraints and loads to the finite element model and obtaining the contact pressure distribution of the sealing contact interface in the sealing structure through simulation includes: According to the actual working conditions, constraints and loads are imposed on the finite element model and the finite element analysis software is used to perform static solutions to extract the contact pressure of the sealing contact interface in the sealing structure. The contact pressure is fitted using simulation software to obtain the contact pressure distribution of the sealing contact interface in the sealing structure.

4. The sealing performance analysis method based on elastic-plastic contact calculation of finite element-boundary element coupling according to claim 1, characterized in that: The process of determining the equivalent contact surface of the rough surface in the sealing contact process includes: For the two rough surfaces in the pure elastic stage, they are equivalently simplified to an equivalent elastic rough surface and a rigid ideal plane. The Young's modulus E of the equivalent elastic rough surface is * and Poisson's ratio ν * Satisfies the following expression: Among them, E1 and E2 represent the elastic modulus of the two rough surfaces before equivalent simplification, ν1 and ν2 represent the Poisson's ratio of the two rough surfaces before equivalent simplification; Similarly, the two rough surfaces in the elastic-plastic deformation stage are equivalently simplified into an equivalent elastic-plastic rough surface and a rigid ideal plane.

5. The sealing performance analysis method based on elastic-plastic contact calculation of finite element-boundary element coupling according to claim 4, characterized in that: The process of solving the microscopic contact state of the rough surface based on the equivalent contact surface and using the contact pressure distribution as the boundary condition includes: When two equivalent contact surfaces are squeezed and contacted with each other under load, the entire sealing structure tends to a stable state, that is, a state with minimum total residual potential energy. Therefore, based on the minimum potential energy theory, the problem of solving the microscopic contact state is transformed into the problem of calculating the minimum total residual potential energy: Among them, V * represents the total residual potential energy, represents the internal complementary energy of the underlying entity, represents a given surface displacement, T i represents the surface force of the elastic body, Ω represents the force range of the elastic body surface; the rough surface is regarded as a frictionless linear semi-infinite elastic body, and the internal complementary energy of the solid under the surface is Numerically, it is similar to the elastic strain energy U E Equal, can be calculated by surface contact pressure and surface deformation; When the rigid ideal plane and the elastic rough surface are squeezed against each other, the relative surface displacement between the rough surface and the rigid ideal plane is calculated from the initial contact gap distribution of the elastic body and the rigid body displacement. In this state, the total residual potential energy is expressed as follows: Where p(x,y) represents the contact pressure distribution, e u(x,y) represents the normal deformation of the rough surface, g0(x,y) represents the initial contact gap distribution of the contact interface, and δ represents the displacement of the rigid ideal plane; According to Boussinesq theory, the deformation of an elastic body is related to the surface pressure distribution, so e u(x,y)= ue G(x,y)*p(x,y) in, ue G(x,y) represents the influence coefficient of the normal load on a point on the contact interface on the normal displacement of other points on the contact interface. The calculation expression is: At this time, there is only a single independent variable p(x, y) in the total residual potential energy calculation formula, and there is a unique contact pressure distribution that minimizes the total residual potential energy. The contact calculation of the rough surface is actually a process of finding the conditional extreme value of the quadratic functional. The minimum total residual potential energy can be solved by the CG-FFT method, and then the microscopic contact state can be obtained; As the load increases, the stress in the local area of ​​the contact interface exceeds the yield limit of the sealing structure material, causing plastic strain and residual stress in the local area. The permanent surface deformation caused by plastic strain is the residual deformation. Therefore, in solving the elastic-plastic contact problem, it is necessary to calculate the microscopic contact state after superimposing the influence of the residual deformation and residual stress field on the rough surface.

6. The sealing performance analysis method based on elastic-plastic contact calculation of finite element-boundary element coupling according to claim 5, characterized in that: The process of constructing a contact state matrix based on the microscopic contact state and determining the leakage channel using the contact state matrix includes: According to the microscopic contact state, the contact points and non-contact points in the sealing contact interface are determined, and the sealing contact interface is projected onto a two-dimensional plane, and the contact points are assigned a value of 0 and the non-contact points are assigned a value of 1, thereby constructing a contact state matrix; Traverse each point in the contact state matrix from the entrance of the sealed contact interface to the exit direction. During the traversal process, if the current point and the points adjacent to the current point are both non-contact points, record the coordinates of the current point and the points adjacent to the current point into the connected unit set; After the traversal is completed, the points in the connected unit set are reassigned to 2 in the contact state matrix. When the points assigned to 2 connect the inlet and outlet of the sealed contact interface, the sealed contact interface leakage is determined.

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