A fast calculation method for assembly deformation of large rigidity parts based on boundary element algorithm

Abstract

The present invention discloses a method for fast calculation of assembly deformation of large rigidity parts based on boundary element algorithm. The method comprises the following steps: extracting the to-be-assembled surface and reference surface of the large rigidity assembly parts, and obtaining the point cloud models of the to-be-assembled surface and the reference surface, so as to obtain the initial differential surface point cloud model; obtaining the initial assembly state of the parts based on the rigid assembly method; quickly solving the differential surface point cloud model after assembly deformation based on the boundary element algorithm in the initial assembly state of the parts; and detecting the differential surface point cloud model after assembly deformation based on the density clustering algorithm. If the calculation is wrong, the adjacent surface solving algorithm is used to solve the adjacent surface sequence of the part, so as to update the differential surface point cloud model after assembly deformation and obtain the correct differential surface point cloud model after assembly deformation. The present invention takes into account the initial assembly state of the parts, effectively improves the accuracy of the assembly deformation calculation results, reduces the dimension of the problem, and greatly improves the calculation efficiency.

Description

Technical Field

[0001] The invention relates to a fast calculation method for assembly deformation, in particular to a fast calculation method for assembly deformation of large rigidity parts based on a boundary element algorithm. Background Art

[0002] At present, countries around the world are actively developing manufacturing industries. Compared with the world's advanced level, China's manufacturing industry is still large but not strong, and there is a clear gap in independent innovation capabilities, resource utilization efficiency, quality and efficiency. In order to adapt to the current development needs, it is necessary to develop a batch of precise, high-speed and efficient CNC machine tools and basic manufacturing equipment. If assembly simulation and tolerance analysis can be performed in the design stage of the product to check whether the tolerance parameters of the product meet the functional requirements, the product development cycle can be shortened and the development cost can be reduced. In order to perform high-precision tolerance analysis on high-rigidity parts, it is necessary to calculate the assembly deformation of the parts. Generally, parts with an elastic modulus greater than 172Gpa are defined as high-rigidity parts.

[0003] The assembly deformation of parts includes macro deformation and local surface deformation. Macro deformation is the volume deformation of an ideal assembly under the action of assembly force, and local surface deformation is the contact deformation of an assembly containing shape errors under the action of assembly force. Usually, macro deformation can be calculated by finite element method. When the rigidity of the parts is strong, the macro deformation generated during the assembly process is relatively small, and it is necessary to focus on the local surface deformation of the parts.

[0004] The finite element method is a commonly used numerical solution for the assembly deformation problem of parts. When solving the problem, the finite element method decomposes the entire problem area, and through the variational method, the error function is minimized and a stable solution is generated. Since the finite element method not only has high calculation accuracy, but also can adapt to various complex shapes, it has become an effective engineering analysis method. However, since tolerance analysis needs to obtain the statistical characteristics of the deformation results of part assembly, thousands of sample calculations are required. Although the use of the finite element method to calculate the contact deformation problem can obtain higher accuracy, it takes a certain amount of time. The boundary element method is a discrete boundary integral method. Compared with the finite element method, the boundary element method only needs to discretize the boundaries, which can reduce the dimension of the problem. However, since the boundary element method omits a lot of physical information, the assembly deformation results obtained by it may not meet the requirements of stable assembly.

[0005] In view of the above situation, for the assembly deformation calculation problem in the tolerance analysis of high-rigidity parts, it is necessary to ensure the accuracy of the calculation results of the assembly deformation of high-rigidity parts, and to improve the calculation efficiency of the assembly deformation problem of high-rigidity parts, which is impossible to achieve with traditional numerical calculation methods. Summary of the invention

[0006] In order to solve the problems existing in the background technology, the purpose of the present invention is to provide a fast calculation method for large stiffness part assembly deformation based on boundary element algorithm, which solves the problem that the calculation efficiency and calculation accuracy of part assembly deformation cannot be taken into account in the current tolerance analysis problem.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is:

[0008] The present invention comprises the following steps:

[0009] Step 1: Determine the material parameters of the high-rigidity assembly parts, the surface to be assembled and the reference surface, and use a three-coordinate measuring machine to obtain the point cloud model of the surface to be assembled and the reference surface of the parts;

[0010] Step 2: Use the differential surface algorithm to solve the point cloud model of the part's assembly surface and reference surface to obtain the initial differential surface point cloud model and the ideal plane of the part. Then use the convex hull algorithm to solve the differential surface point cloud model to obtain the differential surface convex hull. Then, determine the initial triangular contact surface of the part based on the intersection between the ray where the assembly force direction of the part is located and the differential surface convex hull.

[0011] Step 3: According to the current triangular contact surface, determine the current initial assembly state of the part by the rigid assembly method;

[0012] Step 4: According to the material parameters of the part, the initial differential surface point cloud model is solved by using the boundary element algorithm in the current initial assembly state of the part to obtain the differential surface point cloud model after assembly deformation;

[0013] Step 5: Based on the ideal plane, the density clustering algorithm is used to detect the differential surface point cloud model after the current assembly deformation, and the number of contact convex bodies after clustering is obtained; if the number of contact convex bodies after clustering meets the stable assembly condition, the differential surface point cloud model after the current assembly deformation is calculated correctly; if not, the differential surface point cloud model after the current assembly deformation is calculated incorrectly, and the next step is performed;

[0014] Step 6: According to the differential surface convex hull, use the neighboring surface solving algorithm to solve the neighboring surface sequence of the initial triangular contact surface, take the triangles in the neighboring surface sequence as the updated triangular contact surface in turn and repeat steps 3-5 until the differential surface point cloud model after assembly deformation that meets the stable assembly conditions is obtained.

[0015] In step 5, all points in contact with the ideal plane in the differential surface point cloud model after the current assembly deformation are taken to form a contact point set, and then the contact point set is projected onto the xy plane to obtain a projection point set; then, the density clustering algorithm is used to cluster the projection points in the projection point set to obtain the number of contact convex bodies after clustering.

[0016] The stable assembly condition is that the number of contact convex bodies after clustering is greater than or equal to the preset number of contact convex bodies.

[0017] The preset number of contact protrusions is greater than or equal to 3.

[0018] In step 6, the adjacent face sequence of the initial triangular contact surface is solved by using the adjacent face solving algorithm according to the differential face convex hull, specifically:

[0019] S1: traverse each triangle in the differential surface convex hull, and for each triangle, determine whether the z-axis coordinate of the current triangle is less than the z-axis coordinate of the centroid of the initial differential surface point cloud model; if so, put the current triangle into the triangle sequence, otherwise, do not process it; after the traversal is completed, the final triangle sequence is obtained;

[0020] S2: Calculate the distance between the centroid of each triangle in the triangle sequence and the centroid of the initial triangle contact surface and record it as the centroid distance of each triangle, and the ratio of the area of ​​each triangle to the area of ​​the initial triangle contact surface and record it as the area ratio of each triangle. Divide the centroid distance of each triangle by the corresponding area ratio to obtain the centroid distance-area ratio of each triangle. Arrange each triangle in the triangle sequence in ascending order according to the centroid distance-area ratio of each triangle to obtain the adjacent face sequence of the initial triangle contact surface.

[0021] Due to the adoption of the above technical solution, the beneficial effects achieved by the present invention are:

[0022] The method of the present invention uses a boundary element algorithm that takes the initial assembly state of the parts into consideration, wherein the current initial assembly state of the parts is adjusted by a neighboring surface solution algorithm, and the assembly deformation result is calculated by the boundary element algorithm, thereby improving the calculation efficiency and calculation accuracy of the assembly deformation problem of large-rigidity parts.

[0023] The method of the present invention uses a density-based clustering algorithm to detect the calculation results of the rigidity part assembly deformation, thereby ensuring that the assembly results meet the stable assembly conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 The present invention is a flow chart of a method for rapidly calculating the assembly deformation of high-rigidity parts based on a boundary element algorithm.

[0025] Figure 2 This is a part drawing of an embodiment of the method for quickly calculating the assembly deformation of high-rigidity parts based on the boundary element algorithm of the present invention.

[0026] Figure 3 This is an assembly surface point cloud model diagram of an embodiment of the method for rapid calculation of assembly deformation of high-rigidity parts based on the boundary element algorithm of the present invention.

[0027] Figure 4It is a schematic diagram of the differential surface equivalent of an embodiment of the method for fast calculation of assembly deformation of large-rigidity parts based on the boundary element algorithm of the present invention.

[0028] Figure 5 It is a differential convex hull diagram of an embodiment of a method for fast calculation of assembly deformation of large-rigidity parts based on a boundary element algorithm of the present invention.

[0029] Figure 6 This is a diagram of the stable assembly detection results of the fast calculation method for assembly deformation of high-rigidity parts based on the boundary element algorithm of the present invention. DETAILED DESCRIPTION

[0030] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0031] like Figure 1 As shown, the present invention comprises the following steps:

[0032] Step 1: Determine the material parameters of the high-rigidity assembly parts and the surface to be assembled and the reference surface. The material parameters are specifically elastic modulus, Poisson's ratio, etc., and use a three-coordinate measuring instrument to obtain the point cloud model of the surface to be assembled and the reference surface of the parts; the high-rigidity assembly parts of this embodiment are as follows: Figure 2 As shown in (a) and (b), part 1 is a high-rigidity reference part, and part 2 is a high-rigidity part to be assembled; the point cloud model of the surface to be assembled in this embodiment is as follows Figure 3 The upper surface of the large stiffness reference part, that is, the upper surface of part 1, is used as the reference surface. The geometric center of the upper surface of part 1 is the origin of the coordinate system. The direction parallel to the length of part 1 is the x-axis of the coordinate system. The direction parallel to the width of part 1 is the y-axis of the coordinate system. The direction perpendicular to the upper surface of part 1 is the z-axis of the coordinate system.

[0033] Step 2: If Figure 4 As shown, the contact problem is simplified, and the differential surface algorithm is used to solve the point cloud model of the surface to be assembled and the reference surface of the part to obtain the initial differential surface point cloud model and the ideal plane of the part. Then, the convex hull algorithm is used to solve the differential surface point cloud model to obtain the differential surface convex hull. The differential surface convex hull of this embodiment is shown in FIG. Figure 5 As shown. Then, the initial triangular contact surface of the part is determined according to the intersection between the ray where the assembly force direction of the part is located and the convex hull of the differential surface;

[0034] Step 3: According to the current triangular contact surface, determine the current initial assembly state of the part by the rigid assembly method;

[0035] Step 4: According to the material parameters of the part, the initial differential surface point cloud model is quickly solved by using the boundary element algorithm in the current initial assembly state of the part to obtain the differential surface point cloud model after assembly deformation;

[0036] In order to obtain the number of contact convex bodies c after the part assembly simulation, the point cloud data of contact needs to be divided into different contact clusters, which is a typical clustering problem. Considering that the contact clusters have irregular shapes, uneven distribution and certain noise, the number of contact convex bodies c is solved by a density-based clustering algorithm.

[0037] Step 5: Based on the ideal plane, the density clustering algorithm is used to detect the differential surface point cloud model after the current assembly deformation, and the number of contact convex bodies after clustering is obtained; if the number of contact convex bodies after clustering meets the stable assembly condition, the differential surface point cloud model after the current assembly deformation is calculated correctly; if not, the differential surface point cloud model after the current assembly deformation is calculated incorrectly, and the next step is performed;

[0038] In step 5, all points in the differential surface point cloud model after the current assembly deformation that are in contact with the ideal plane are taken to form a contact point set, that is, all points in the contact point set are in the ideal plane, and the contact point set is recorded as P D ={d i ∈R 3 , 1≤i≤n D}, where n D is the total number of contact points, and then the contact point set is projected onto the xy plane to obtain the projection point set.

[0039] Then, the density clustering algorithm is used to cluster the projection points in the projection point set to obtain the number of contact convex bodies after clustering. In the specific implementation, the neighborhood radius ε and the minimum number of included objects MinPts of the density clustering algorithm are set according to the actual size of the part assembly surface.

[0040] Step 6: According to the differential surface convex hull, use the neighboring surface solving algorithm to solve the neighboring surface sequence of the initial triangular contact surface, and use the triangles in the neighboring surface sequence as the updated triangular contact surface in turn and repeat steps 3-5 until the differential surface point cloud model after assembly deformation that meets the preset stable assembly conditions is obtained.

[0041] The stable assembly condition is that the number of contact convex bodies after clustering is greater than or equal to the preset number of contact convex bodies.

[0042] The preset number of contact protrusions is greater than or equal to 3. In this embodiment, the preset number of contact protrusions is set to 3.

[0043] In step 6, based on the differential surface convex hull, the adjacent surface solving algorithm is used to solve the adjacent surface sequence of the initial triangular contact surface, specifically:

[0044] S1: traverse each triangle in the differential surface convex hull, and for each triangle, determine whether the z-axis coordinate of the current triangle is less than the z-axis coordinate of the centroid of the initial differential surface point cloud model; if so, put the current triangle into the triangle sequence, otherwise, do not process it; after the traversal is completed, the final triangle sequence is obtained;

[0045] S2: Calculate the distance between the centroid of each triangle in the triangle sequence and the centroid of the initial triangle contact surface and record it as the centroid distance of each triangle, and the ratio of the area of ​​each triangle to the area of ​​the initial triangle contact surface and record it as the area ratio of each triangle. Divide the centroid distance of each triangle by the corresponding area ratio to obtain the centroid distance-area ratio of each triangle. Arrange each triangle in the triangle sequence in ascending order according to the centroid distance-area ratio of each triangle to obtain the adjacent face sequence of the initial triangle contact surface.

[0046] Figure 6 It is a projection diagram of contact convex bodies obtained after assembly of this embodiment. The numbers 1 to 7 in the figure represent convex bodies that come into contact after the parts are deformed during assembly. Therefore, the number of contact convex bodies after clustering in this embodiment is c=7, which meets the stable assembly condition.

Claims

1. A fast calculation method for assembly deformation of large rigidity parts based on boundary element algorithm, It is characterized in that The following steps are involved: Step 1: Determine the material parameters of the high-rigidity assembly parts, the surface to be assembled and the reference surface, and use a three-coordinate measuring machine to obtain the point cloud model of the surface to be assembled and the reference surface of the parts; Step 2: Use the differential surface algorithm to solve the point cloud model of the part's assembly surface and reference surface to obtain the initial differential surface point cloud model and the ideal plane of the part. Then use the convex hull algorithm to solve the differential surface point cloud model to obtain the differential surface convex hull. Then, determine the initial triangular contact surface of the part based on the intersection between the ray where the assembly force direction of the part is located and the differential surface convex hull. Step 3: According to the current triangular contact surface, determine the current initial assembly state of the part by the rigid assembly method; Step 4: According to the material parameters of the part, the initial differential surface point cloud model is solved by using the boundary element algorithm in the current initial assembly state of the part to obtain the differential surface point cloud model after assembly deformation; Step 5: Based on the ideal plane, the density clustering algorithm is used to detect the differential surface point cloud model of the current assembly after deformation, and the number of contact convex bodies after clustering is obtained; If the number of contact convex bodies after clustering meets the stable assembly condition, the differential surface point cloud model after the current assembly deformation is calculated correctly; if not, the differential surface point cloud model after the current assembly deformation is calculated incorrectly, and the next step is performed; Step 6: According to the differential surface convex hull, use the neighboring surface solving algorithm to solve the neighboring surface sequence of the initial triangular contact surface, take the triangles in the neighboring surface sequence as the updated triangular contact surface in turn and repeat steps 3-5 until the differential surface point cloud model after assembly deformation that meets the stable assembly conditions is obtained.

2. According to claim 1, a fast calculation method for assembly deformation of large rigidity parts based on boundary element algorithm, It is characterized in that In step 5, all points in contact with the ideal plane in the differential surface point cloud model after the current assembly deformation are taken to form a contact point set, and then the contact point set is projected onto the xy plane to obtain a projection point set; then, the density clustering algorithm is used to cluster the projection points in the projection point set to obtain the number of contact convex bodies after clustering.

3. According to the method of fast calculation of high stiffness parts assembly deformation based on boundary element algorithm in claim 1, It is characterized in that The stable assembly condition is that the number of contact convex bodies after clustering is greater than or equal to the preset number of contact convex bodies.

4. According to claim 3, a fast calculation method for assembly deformation of large rigidity parts based on boundary element algorithm, It is characterized in that The preset number of contact protrusions is greater than or equal to 3.

5. According to the method of fast calculation of high stiffness parts assembly deformation based on boundary element algorithm in claim 1, It is characterized in that In step 6, the adjacent face sequence of the initial triangular contact surface is solved by using the adjacent face solving algorithm according to the differential face convex hull, specifically: S1: traverse each triangle in the differential surface convex hull, and for each triangle, determine whether the z-axis coordinate of the current triangle is less than the z-axis coordinate of the centroid of the initial differential surface point cloud model; if so, put the current triangle into the triangle sequence, otherwise, do not process it; after the traversal is completed, the final triangle sequence is obtained; S2: Calculate the distance between the centroid of each triangle in the triangle sequence and the centroid of the initial triangle contact surface and record it as the centroid distance of each triangle, and the ratio of the area of ​​each triangle to the area of ​​the initial triangle contact surface and record it as the area ratio of each triangle. Divide the centroid distance of each triangle by the corresponding area ratio to obtain the centroid distance-area ratio of each triangle. Arrange each triangle in the triangle sequence in ascending order according to the centroid distance-area ratio of each triangle to obtain the adjacent face sequence of the initial triangle contact surface.

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