CN102779200A

CN102779200A - Analytical method for contact performance of junction surface containing microcosmic surface shape

Info

Publication number: CN102779200A
Application number: CN201110429057XA
Authority: CN
Inventors: 洪军; 杨国庆; 朱林波; 刘会静; 熊美华; 刘万普
Original assignee: Xian Jiaotong University
Current assignee: Xian Jiaotong University
Priority date: 2011-12-14
Filing date: 2011-12-14
Publication date: 2012-11-14
Anticipated expiration: 2031-12-14
Also published as: CN102779200B

Abstract

The invention discloses a method for analyzing the contact performance of a bonding surface including microscopic surface topography, which improves the grid division quality and solution efficiency, and improves the accuracy and reliability of rough surface contact performance prediction. Measure the actual surface through a laser confocal microscope or use the three-dimensional topography digital simulation method to obtain the rough surface, extract the height matrix of the 3D rough surface topography, and use the point cloud processing method to discretize the 3D rough surface into a height matrix file that can be easily extracted by finite element software , import it into the finite element software to generate the microscopic topography of each joint surface, use the translation and coordinate modification functions of the key points of the finite element software to establish a volume model considering the microscopic surface topography, and use the grid control method, The volume model is divided into hexahedral meshes, the finite element contact model of two 3D rough surfaces is constructed, the displacement and force load boundary conditions are gradually applied, and the contact characteristics of the joint surface are analyzed.

Description

A Method for Analyzing the Contact Performance of Bonding Surfaces Including Microscopic Surface Topography

技术领域 technical field

本发明涉及一种结合面接触性能仿真分析方法，特别是一种考虑两3D粗糙表面接触的结合面性能仿真分析方法，可用于分析微观粗糙表面的摩擦、磨损、接触刚度、接触热阻等接触性能。The invention relates to a method for simulation analysis of joint surface contact performance, especially a method for simulation analysis of joint surface performance considering the contact of two 3D rough surfaces, which can be used to analyze the contact of friction, wear, contact stiffness, contact thermal resistance, etc. of microscopic rough surfaces performance.

背景技术 Background technique

机械系统中存在大量的结合面，这些结合面的存在对机械系统整体特性有着很大影响，而结合面的接触实际是其粗糙表面的接触，粗糙表面形貌对结合面摩擦、磨损及其接触变形都有重要的影响。There are a large number of joint surfaces in the mechanical system. The existence of these joint surfaces has a great influence on the overall characteristics of the mechanical system, and the contact of the joint surface is actually the contact of its rough surface. The rough surface morphology has a great influence on the friction, wear and contact of the joint surface. Deformation has an important effect.

长期以来，国内外学者从理论层面上对粗糙表面的接触开展了大量的研究。在理论解析模型方面，构建了多种经典接触模型：GW模型、CEB模型、MB模型和KE模型等，但这些理论模型的建立都存在一定的假设条件，如所有微凸体都具有相同的峰顶曲率半径、微凸体接触时其变形相互独立，忽略微凸体之间的相互作用、不存在大变形、微凸体之间的接触全部是峰对峰正接触等。正是由于这些假设，使其无法贴合结合面间实际的微凸体接触状态，这极大影响了利用解析模型预测结合面性能的精度。For a long time, scholars at home and abroad have carried out a lot of research on the contact of rough surfaces from the theoretical level. In terms of theoretical analysis models, a variety of classical contact models have been constructed: GW model, CEB model, MB model and KE model, etc., but there are certain assumptions in the establishment of these theoretical models, such as all asperities have the same peak The radius of curvature of the top and the deformation of the asperities are independent of each other when they are in contact, the interaction between the asperities is ignored, there is no large deformation, and the contact between the asperities is all peak-to-peak positive contact, etc. It is precisely because of these assumptions that it cannot fit the actual asperity contact state between the bonding surfaces, which greatly affects the accuracy of using the analytical model to predict the performance of the bonding surface.

为了解决上述问题，近年来，有学者提出利用有限元数值模型模拟结合面间微观接触的方法，但其主要集中在单对微凸体的接触性能分析和光滑表面—粗糙表面的接触性能分析方面，尚未实现更贴合实际接触状态的两3D粗糙表面接触性能仿真分析。本发明从点云处理技术、体模型生成技术和网格划分技术三个方面入手，克服了现有技术瓶颈，提高了网格划分质量，构建了两3D粗糙表面接触模型，从而在一定程度上改善了结合面性能预测的准确性。In order to solve the above problems, in recent years, some scholars have proposed the method of using the finite element numerical model to simulate the microscopic contact between the bonding surfaces, but it mainly focuses on the analysis of the contact performance of a single pair of asperities and the analysis of the contact performance of a smooth surface-rough surface. However, the simulation analysis of the contact performance of two 3D rough surfaces that is more suitable for the actual contact state has not been realized. The present invention starts from three aspects of point cloud processing technology, volume model generation technology and grid division technology, overcomes the bottleneck of the existing technology, improves the quality of grid division, and constructs two 3D rough surface contact models, thus to a certain extent Improved accuracy of surface performance predictions.

发明内容 Contents of the invention

本发明的主要目的是提供一种包含微观表面形貌的结合面接触性能分析方法，克服了两粗糙表面有限元接触模型构建中点云处理、体模型生成和网格划分技术瓶颈，提高了网格划分质量和求解效率，改善了粗糙表面接触性能预测的准确性和可靠性。The main purpose of the present invention is to provide a contact performance analysis method including microscopic surface topography, which overcomes the technical bottlenecks of point cloud processing, volume model generation and grid division in the construction of two rough surface finite element contact models, and improves the network efficiency. The quality of grid division and solution efficiency are improved, and the accuracy and reliability of rough surface contact performance prediction are improved.

本发明的技术方案是：Technical scheme of the present invention is:

一种包含微观表面形貌的结合面接触性能分析方法，包含下述步骤：A method for analyzing the contact performance of a bonding surface comprising microscopic surface topography, comprising the following steps:

1)通过激光共聚焦显微镜测量实际表面或利用三维形貌模拟方法获得高斯或非高斯粗糙表面，提取3D粗糙表面形貌的高度矩阵为Z(m，n)，其中m、n分别表示x、y方向取点的数目；1) The actual surface is measured by laser confocal microscope or Gaussian or non-Gaussian rough surface is obtained by three-dimensional topography simulation method, and the height matrix of 3D rough surface topography is extracted as Z(m, n), where m and n respectively represent x, The number of points in the y direction;

2)以步骤1)中获得的微观表面形貌为对象，选取适宜的间距，利用点云处理方法将3D粗糙表面离散成有限元软件容易提取的txt文件；2) Taking the microscopic surface topography obtained in step 1) as the object, selecting an appropriate spacing, and using the point cloud processing method to discretize the 3D rough surface into a txt file that can be easily extracted by finite element software;

3)利用步骤2)生成的三维点的txt文件，导入有限元软件中生成点云模型，利用有限元的双重循环命令，连接X/Y方向相邻四点，生成微观面片群，获得结合面每一连接表面的微观形貌；3) Use the txt file of the three-dimensional points generated in step 2), import it into the finite element software to generate a point cloud model, and use the double cycle command of the finite element to connect four adjacent points in the X/Y direction to generate a microscopic surface group and obtain a combined The microscopic topography of each connected surface;

4)以步骤3)生成的两组粗糙表面为基础，通过平面拉伸，并利用有限元软件关键点的平移和坐标修改功能，构建一组考虑连接表面微观表面形貌的体模型；4) Based on the two groups of rough surfaces generated in step 3), through plane stretching, and using the translation and coordinate modification functions of the key points of the finite element software, a group of volume models considering the microscopic surface topography of the connecting surface are constructed;

5)以步骤4)生成的体模型为基础，通过线网格控制的方法，对体模型进行六面体网格划分；5) based on the volume model generated in step 4), the volume model is divided into hexahedral meshes by means of line grid control;

6)以步骤5)生成的网格模型为基础，定义结合面接触对，固定下连接体下表面z方向的位移，通过上连接体上表面位移约束施加载荷边界条件，构建两3D粗糙表面接触的有限元接触模型，并进行结构静力求解，观测连接结合面的接触载荷和接触压力分布规律。6) Based on the mesh model generated in step 5), define the contact pair of the joint surface, fix the displacement of the lower surface of the lower connector in the z direction, and apply the load boundary condition through the displacement constraint on the upper surface of the upper connector to construct the contact between two 3D rough surfaces The finite element contact model of the model is used, and the static solution of the structure is carried out to observe the contact load and contact pressure distribution law of the connection joint surface.

所述的利用三维形貌模拟方法获得高斯粗糙表面，具体包含以下步骤：The Gaussian rough surface obtained by using the three-dimensional shape simulation method specifically includes the following steps:

1)利用白噪声发生器randn(m，n)产生白噪声序列η(m，n)，并计算其傅里叶变换A(m，n)：1) Use the white noise generator randn(m, n) to generate a white noise sequence η(m, n), and calculate its Fourier transform A(m, n):

$A A ((k k + + 11,, l l + + 11)) = = {Σ Σ}_{r r - - 00}^{m m - - 11} {Σ Σ}_{s the s - - 00}^{n no - - 11} η η ((r r + + 11,, s the s + + 11)) {e e}^{- - 22 πi πi ((kr kr / / m m + + ls ls / / n no))} \begin{matrix} k k = = 0,1,2 0,1,2 . . . . . . m m - - 11 \\ l l = = 0,1,2 0,1,2 . . . . . . n no - - 11 \end{matrix}$

2)利用给定自相关函数生成相关矩阵R(m，n)；假定自相关函数为f(x，y)，其中β_x、β_y分别为X、Y方向的自相关长度；2) Generate a correlation matrix R(m, n) using a given autocorrelation function; assume that the autocorrelation function is f(x, y), where β _x and β _y are the autocorrelation lengths in the X and Y directions, respectively;

$f f ((x x,, y the y)) = = exp exp ((- - 2.3 2.3 \sqrt{{((\frac{x x}{{β β}_{x x}}))}^{22} + + {((\frac{y the y}{{β β}_{y the y}}))}^{22}}))$

指定X、Y方向离散间距分别为Δ_x＝1μm、Δ_y＝1μm，在0≤x≤m/2，0≤y≤n/2区域内对自相关函数进行离散，获得自相关函数的离散矩阵R(m/2+1，n/2+1)，然后扩展为-m/2≤x≤m/2，-n/2≤y≤n/2区域内对应的自相关矩阵函数离散矩阵R(m，n)：Specify the discretization spacing in the X and Y directions as Δ _x = 1 μm and Δ _y = 1 μm, and discretize the autocorrelation function in the area of 0≤x≤m/2, 0≤y≤n/2 to obtain the discretization of the autocorrelation function Matrix R(m/2+1, n/2+1), and then expanded to -m/2≤x≤m/2, -n/2≤y≤n/2 corresponding autocorrelation matrix function discrete matrix in the region R(m,n):

R(k+1，l+1)＝f(k，l) k＝0，1，2...0.5m，l＝0，1，2...0.5nR(k+1, l+1)=f(k,l) k=0, 1, 2...0.5m, l=0, 1, 2...0.5n

R(0.5m+2+k，l+1)＝f(0.5m-k，l+1) k＝0，1，2...0.5m-2，l＝0，1，2...0.5nR(0.5m+2+k, l+1)＝f(0.5m-k, l+1) k＝0, 1, 2...0.5m-2, l＝0, 1, 2...0.5n

R(k+1，0.5n+l+2)＝f(k+1，0.5n-l) k＝0，1，2...0.5m，l＝0，1，2...0.5n-2R(k+1, 0.5n+l+2)＝f(k+1, 0.5n-l) k＝0, 1, 2...0.5m, l＝0, 1, 2...0.5n-2

R(0.5m+k+2，0.5n+l+2)＝f(0.5m-k，0.5n-l) k＝0，1，2...0.5m-2，l＝0，1，2...0.5n-2R(0.5m+k+2, 0.5n+l+2)＝f(0.5m-k, 0.5n-l) k＝0, 1, 2...0.5m-2, l＝0, 1, 2... 0.5n-2

3)对自相关函数矩阵R(m，n)进行傅里叶变换，获得模拟表面的功率谱密度P；3) Carry out Fourier transform to autocorrelation function matrix R (m, n), obtain the power spectral density P of simulated surface;

$P P ((11 + + k k,, 11 + + l l)) = = | | {Σ Σ}_{r r = = 00}^{m m - - 11} {Σ Σ}_{s the s = = 00}^{n no - - 11} R R ((r r + + 11,, s the s + + 11)) {e e}^{- - 22 πi πi ((kr kr / / m m + + ls ls / / n no))} | | \begin{matrix} k k = = 0,1,2 0,1,2 . . . . . . m m - - 11 \\ l l = = 0,1,2 0,1,2 . . . . . . n no - - 11 \end{matrix}$

4)由白噪声的功率谱密度为常数C，假设C＝1，计算白噪声到模拟高斯表面的传递函数H(m，n)：4) The power spectral density of the white noise is a constant C, assuming C=1, calculate the transfer function H(m, n) from the white noise to the simulated Gaussian surface:

$H h ((m m,, n no)) = = \sqrt{P P}$

5)利用频域点积(A.*H)取反傅里叶变换的方法获得高斯表面的初始高度矩阵序列z：5) Obtain the initial height matrix sequence z of the Gaussian surface by using the frequency domain dot product (A.*H) to take the inverse Fourier transform:

$z z ((k k + + 11,, l l + + 11)) = = \frac{11}{mn mn} {Σ Σ}_{r r = = 00}^{m m - - 11} {Σ Σ}_{s the s = = 00}^{n no - - 11} ((A A . . * * H h)) {e e}^{22 πi πi ((kr kr / / m m + + ls ls / / n no))} \begin{matrix} k k = = 0,1,2 0,1,2 . . . . . . m m - - 11 \\ l l = = 0,1,2 0,1,2 . . . . . . n no - - 11 \end{matrix}$

6)根据给定高度标准偏差σ与模拟表面z的实际标准偏差std2(z)，求白噪声功率谱密度常数C＝σ/std2(z)，从而模拟生成符合给定标准偏差等要求的高斯表面高度矩阵z：z＝z*C.6) Calculate the white noise power spectral density constant C=σ/std2(z) according to the standard deviation σ of the given height and the actual standard deviation std2(z) of the simulated surface z, so as to simulate and generate a Gaussian that meets the requirements of the given standard deviation, etc. Surface height matrix z: z=z*C.

所述的利用三维形貌模拟方法获得非高斯粗糙表面，具体包含以下步骤：The non-Gaussian rough surface obtained by using the three-dimensional shape simulation method specifically includes the following steps:

1)直接利用高斯粗糙表面的数字化模拟所生成的高度序列z，采用Pearson或Johnson非高斯变换系统进行非高斯变换，生成非高斯序列Z；1) Directly use the height sequence z generated by the digital simulation of the Gaussian rough surface, and use the Pearson or Johnson non-Gaussian transformation system to perform non-Gaussian transformation to generate a non-Gaussian sequence Z;

2)如果所生成的非高斯序列的偏斜度S_k与峰度K_u不满足精度要求，则采用新的白噪声序列，重复高斯粗糙表面高度序列的模拟及其非高斯转换，直到满足精度要求，完成非高斯粗糙表面的数字化模拟。2) If the skewness S _k and kurtosis K _u of the generated non-Gaussian sequence do not meet the accuracy requirements, use a new white noise sequence to repeat the simulation of the Gaussian rough surface height sequence and its non-Gaussian conversion until the accuracy is satisfied Requirements, to complete the digital simulation of non-Gaussian rough surface.

所述的利用点云处理方法将3D粗糙表面离散成有限元软件容易提取的高度矩阵文件，具体包含以下步骤：The use of the point cloud processing method to discretize the 3D rough surface into a height matrix file that is easily extracted by finite element software specifically includes the following steps:

1)对于实测或模拟表面，可以在水平方向按照一定的规律，生成包含3列的点文件，其中每一行的三个数据代表一个点坐标，第1、2、3列分别表示对应点的x、y、z坐标；1) For the measured or simulated surface, a point file containing 3 columns can be generated in the horizontal direction according to certain rules, in which the three data in each row represent a point coordinate, and the 1st, 2nd, and 3rd columns respectively represent the x of the corresponding point , y, z coordinates;

2)通过Ultraedit软件将点的格式修改为有限元软件识别的点创建命令，从而方便有限元软件读取此类型的txt点文件，直接生成点云模型。2) Modify the point format to the point creation command recognized by the finite element software through the Ultraedit software, so that the finite element software can read this type of txt point file and directly generate the point cloud model.

所述的利用有限元软件关键点的平移和坐标修改功能，构建一组考虑微观表面相貌的体模型，具体包含以下步骤：The use of the translation and coordinate modification functions of the key points of the finite element software to construct a group of volume models considering the microscopic surface appearance specifically includes the following steps:

1)分别将两组微观表面沿Z正方向与反方向拉伸，生成具有一定高度的两组微六面体群；1) Stretch the two groups of microscopic surfaces along the Z positive direction and the opposite direction to generate two groups of microhexahedron groups with a certain height;

2)修改每一组微六面体群的点坐标，使得每一组六面体群中连接表面的对面顶点具有相同的Z坐标值，形成光滑表面；2) Modify the point coordinates of each group of micro-hexahedron groups, so that the opposite vertices of the connected surfaces in each group of hexahedron groups have the same Z coordinate value, forming a smooth surface;

3)调节某一连接体的Z向位置，确保两连接表面有局部点刚发生初始接触。3) Adjust the Z-direction position of a connecting body to ensure that there are local points on the two connecting surfaces where initial contact occurs.

所述的通过线网格控制的方法对体模型进行六面体网格划分，具体包含以下步骤：The described method of controlling the volume model by the method of hexahedral meshing specifically includes the following steps:

1)网格单元数量的控制：在上述构建的体模型中选择厚度方向的所有线条，控制线条高度方向的网格大小或网格层数，同时通过控制水平方向网格的大小，精确控制网格的数量；1) Control of the number of grid units: select all the lines in the thickness direction in the volume model constructed above, control the grid size or the number of grid layers in the height direction of the lines, and precisely control the grid size by controlling the size of the grid in the horizontal direction. number of grids;

2)对同一个微六面体中，若四条高度方向的线条，高度相差悬殊，对其高度方向的网格大小进行适当调整，使高度值大的网格数目与高度值小的线条对应网格数目相差偶数，从而保证顺利生成高质量的六面体网格；2) For the same micro-hexahedron, if the heights of the four lines in the height direction are very different, adjust the grid size in the height direction appropriately, so that the number of grids with a large height value corresponds to the number of grids with a small height value The difference is even, so as to ensure the smooth generation of high-quality hexahedral mesh;

3)指定网格单元类型与材料属性，生成六面体扫描网格。3) Specify the grid element type and material properties to generate a hexahedral scanning grid.

本发明提出一种考虑两3D粗糙表面接触的结合面性能仿真分析方法，从点云处理技术、体模型生成技术和网格划分技术三个方面入手，克服了现有技术瓶颈，提高了网格划分质量和求解效率，构建了两3D粗糙表面接触模型，从而在一定程度上解决了求解问题中的难收敛性、改善了结合面性能预测的准确性和可靠性。以此，可有效指导结合面的设计、加工和装配，使其满足结合面性能要求，从而保障机械装备整体性能。The present invention proposes a simulation analysis method for joint surface performance considering the contact of two 3D rough surfaces, starting from three aspects of point cloud processing technology, volume model generation technology and grid division technology, which overcomes the bottleneck of the existing technology and improves the grid quality. The quality and solution efficiency are divided, and the contact model of two 3D rough surfaces is constructed, which solves the difficulty of convergence in the solution problem to a certain extent, and improves the accuracy and reliability of the performance prediction of the joint surface. In this way, the design, processing and assembly of the joint surface can be effectively guided to meet the performance requirements of the joint surface, thereby ensuring the overall performance of the mechanical equipment.

附图说明 Description of drawings

图1各向同性高斯表面及其高度分布(β_x＝β_y＝3，μ＝0，σ＝1.6，点数256×256)Figure 1 Isotropic Gaussian surface and its height distribution (β _x = β _y = 3, μ = 0, σ = 1.6, number of points 256×256)

图2各向异性高斯表面及其高度分布(β_x＝2，β_y＝100，μ＝0，σ＝1.6，点数256×256)Figure 2 Anisotropic Gaussian surface and its height distribution (β _x = 2, β _y = 100, μ = 0, σ = 1.6, points 256×256)

图3各向同性非高斯表面及其高度分布(β_x＝β_y＝5，μ＝0，σ＝1.6，S_k＝-1，K_u＝4.5，点数128×128)Figure 3 Isotropic non-Gaussian surface and its height distribution (β _x = β _y = 5, μ = 0, σ = 1.6, S _k = -1, K _u = 4.5, points 128×128)

图4各向异性非高斯表面及其高度分布(β_x＝2，β_y＝100，μ＝0，σ＝1.6，S_kz＝0.5，K_uz＝3.5，点数256×256)Figure 4 Anisotropic non-Gaussian surface and its height distribution (β _x = 2, β _y = 100, μ = 0, σ = 1.6, S _kz = 0.5, Ku _uz = 3.5, points 256×256)

图5构成结合面的点云(128×128×2)Figure 5 The point cloud (128×128×2) that constitutes the combined surface

图6连接表面的面片群Figure 6. Groups of patches on connected surfaces

图7上下连接表面的体拉伸、上下连接体群的顶点坐标修改以及连接体的Z轴平移Figure 7 Body stretching of the upper and lower connecting surfaces, vertex coordinate modification of the upper and lower connecting body groups, and Z-axis translation of the connecting body

图8考虑两粗糙表面接触的六面体网格模型图Figure 8 The hexahedral mesh model considering the contact between two rough surfaces

图9载荷不断增大对应的上连接体Z向应力变化规律Fig. 9 The change law of the Z-direction stress of the upper connecting body corresponding to the increasing load

图10载荷不断增大对应的上连接体等效应力变化规律Figure 10 Changes in the equivalent stress of the upper connector corresponding to the increasing load

图11载荷不断增大对应的结合面接触应力与接触区域变化规律Fig. 11 The change law of the contact stress and contact area of the joint surface corresponding to the increasing load

具体实施方式 Detailed ways

以满足一定的自相关函数、标准偏差、偏斜度与峰度等统计特征的3D高斯和非高斯粗糙表面的数字化模拟为例，对本发明的微观表面形貌获取方法进行说明；以一组高斯表面形貌接触为例，采用ANSYS有限元软件，对本发明的结合面接触性能模型构建和分析方法进行说明。Taking the digital simulation of 3D Gaussian and non-Gaussian rough surfaces satisfying certain statistical characteristics such as autocorrelation function, standard deviation, skewness and kurtosis as an example, the microscopic surface topography acquisition method of the present invention is described; a group of Gaussian Taking surface topography contact as an example, ANSYS finite element software is used to describe the method for building and analyzing the contact performance model of the joint surface of the present invention.

1.微观表面形貌获取：1. Acquisition of microscopic surface topography:

利用三维形貌模拟方法获得高斯或非高斯粗糙表面，提取3D粗糙表面形貌的高度矩阵为Z(m，n)，其中m、n分别表示x、y方向取点的数目，具体步骤如下：The Gaussian or non-Gaussian rough surface is obtained by using the three-dimensional topography simulation method, and the height matrix of the 3D rough surface topography is extracted as Z(m, n), where m and n represent the number of points in the x and y directions respectively. The specific steps are as follows:

(1)利用三维形貌模拟方法获得高斯粗糙表面，步骤如下：(1) Using the three-dimensional shape simulation method to obtain a Gaussian rough surface, the steps are as follows:

1)利用白噪声发生器randn(m，n)产生白噪声序列η(m，n)，且获得其傅里叶变换 1) Use the white noise generator randn(m, n) to generate a white noise sequence η(m, n), and obtain its Fourier transform

$n no)) : : A A ((k k + + 11,, l l + + 11)) = = {Σ Σ}_{r r - - 00}^{m m - - 11} {Σ Σ}_{s the s - - 00}^{n no - - 11} η η ((r r + + 11,, s the s + + 11)) {e e}^{- - 22 πi πi ((kr kr / / m m + + ls ls / / n no))} \begin{matrix} k k = = 0,1,2 0,1,2 . . . . . . m m - - 11 \\ l l = = 0,1,2 0,1,2 . . . . . . n no - - 11 \end{matrix}$

2)利用给定自相关函数生成相关矩阵R(m，n)；假定自相关函数为f，其中β_x、β_y分别为X、Y方向的自相关长度；2) Generate a correlation matrix R(m, n) using a given autocorrelation function; assume that the autocorrelation function is f, where β _x and β _y are the autocorrelation lengths in the X and Y directions, respectively;

$H h ((m m,, n no)) = = \sqrt{P P}$

6)根据给定高度标准偏差σ与模拟表面z的实际标准偏差std2(z)，求白噪声功率谱密度常数C＝σ/std2(z)，从而模拟生成符合给定标准偏差等要求的高斯表面高度矩阵z：z＝z*C。6) Calculate the white noise power spectral density constant C=σ/std2(z) according to the standard deviation σ of the given height and the actual standard deviation std2(z) of the simulated surface z, so as to simulate and generate a Gaussian that meets the requirements of the given standard deviation, etc. Surface height matrix z: z=z*C.

利用上述给定的自相关函数，x、y方向的自相关函数均取3μm，模拟表面的x、y方向取点为256×256、表面的标准偏差为1.6μm，模拟获得的各向同性高斯表面形貌及其高度分布如图1所示。x、y方向的自相关函数分别取2μm、100μm，模拟获得的高斯表面形貌表现出各向异性，具有一定的纹理，如图2所示。Using the given autocorrelation function above, the autocorrelation function in the x and y directions is set to 3 μm, the points in the x and y directions of the simulated surface are 256×256, and the standard deviation of the surface is 1.6 μm. The simulated isotropic Gaussian The surface morphology and its height distribution are shown in Fig. 1. The autocorrelation functions in the x and y directions are respectively set at 2 μm and 100 μm, and the simulated Gaussian surface topography shows anisotropy and a certain texture, as shown in Figure 2.

(2)利用三维形貌模拟方法获得非高斯粗糙表面，步骤如下：(2) Obtain a non-Gaussian rough surface using the three-dimensional shape simulation method, the steps are as follows:

利用上述给定的自相关函数，x、y方向的自相关函数均取5μm，模拟表面的x、y方向取点为128×128、表面的均值、标准偏差、偏斜度与峰度分别为0、1.6μm、-1与4.5，模拟获得的各向同性非高斯表面形貌及其高度分布如图3所示。若x、y方向的自相关函数分别取2μm、100μm，模拟表面的x、y方向取点为256×256、表面的标准偏差、偏斜度与峰度分别为1.6μm、0.5与3.5，模拟获得的各向异性非高斯表面形貌呈现出一定的纹理，如图2所示。Using the given autocorrelation function above, the autocorrelation function in the x and y directions is taken as 5 μm, the points in the x and y directions of the simulated surface are 128×128, and the mean value, standard deviation, skewness and kurtosis of the surface are respectively 0, 1.6 μm, -1 and 4.5, the simulated isotropic non-Gaussian surface morphology and its height distribution are shown in Figure 3. If the autocorrelation functions in the x and y directions are respectively 2 μm and 100 μm, the points in the x and y directions of the simulated surface are 256×256, and the standard deviation, skewness and kurtosis of the surface are 1.6 μm, 0.5 and 3.5 respectively. The obtained anisotropic non-Gaussian surface topography presents a certain texture, as shown in Figure 2.

2.微观形貌的离散与信息存储2. Discretization and information storage of microscopic topography

利用步骤1微观形貌的获取方法，获得两128×128点数的高斯粗糙表面(上下表面标准偏差分别为0.8μm与1.6μm)，x、y方向间距选取1μm，利用点云处理方法将3D粗糙表面离散成有限元软件容易提取的txt文件，具体步骤如下：Using the microscopic topography acquisition method in step 1, two 128×128-point Gaussian rough surfaces (standard deviations of the upper and lower surfaces are 0.8 μm and 1.6 μm respectively), the spacing in the x and y directions are selected as 1 μm, and the 3D rough surfaces are processed by point cloud processing. The surface is discretized into a txt file that can be easily extracted by finite element software. The specific steps are as follows:

2)通过Ultraedit软件将点的格式修改为有限元软件识别的点创建命令“k，，X，Y，Z”(k相当于ANSYS中的点创建命令；“，，”两个逗号间省略了点的代号；X、Y、Z分别表示点的坐标值，通过逗号隔开)，从而方便ANSYS软件读取这种类型的txt点文件直接生成点云模型。2) Use the Ultraedit software to modify the point format to the point creation command "k,, X, Y, Z" recognized by the finite element software (k is equivalent to the point creation command in ANSYS; ",," is omitted between the two commas The code of the point; X, Y, and Z represent the coordinate values of the point respectively, separated by commas), so that it is convenient for ANSYS software to read this type of txt point file and directly generate a point cloud model.

3.微观表面形貌的面模型构建3. Surface model construction of microscopic surface topography

将步骤2生成的三维点的txt文件，导入ANSYS软件中生成点云模型(如图5所示)，利用ANSYS的双重循环命令(*do，...，*end)，连接X/Y方向相邻四点，生成微观面片群，获得结合面每一连接表面的微观形貌(如图6所示)。Import the txt file of the three-dimensional points generated in step 2 into ANSYS software to generate a point cloud model (as shown in Figure 5), and use the double cycle command (*do,...,*end) of ANSYS to connect the X/Y direction For four adjacent points, a group of microscopic facets is generated, and the microscopic topography of each connected surface of the joint surface is obtained (as shown in Figure 6).

4.微观表面形貌的体模型构建4. Construction of volume model of microscopic surface topography

以步骤3生成的两组粗糙表面为基础，通过平面拉伸，结合ANSYS关键点的平移和坐标修改功能，构建一组考虑连接表面微观表面形貌的体模型，上下连接表面的拉伸、上下连接体群顶点Z坐标的修改以及连接体群的Z轴平移如图7所示，具体步骤如下：Based on the two sets of rough surfaces generated in step 3, through plane stretching, combined with the translation and coordinate modification functions of ANSYS key points, a set of volume models considering the microscopic surface topography of the connecting surface is constructed. The stretching of the upper and lower connecting surfaces, the upper and lower The modification of the Z-coordinates of the vertices of the connector group and the Z-axis translation of the connector group are shown in Figure 7, and the specific steps are as follows:

1)分别将上、下两组微观表面沿Z轴的正、反方向拉伸，生成具有一定厚度(厚度大于两粗糙表面的最大轮廓高度，此处约为12μm)的两组微六面体群；1) Stretch the upper and lower groups of microscopic surfaces along the positive and negative directions of the Z axis to generate two groups of microhexahedron groups with a certain thickness (thickness greater than the maximum contour height of the two rough surfaces, here about 12 μm);

2)分别修改上、下两组微六面体群的上、下表面的顶点坐标，分别使得上、下两组六面体群中的上、下表面的顶点具有相同的Z坐标值，形成光滑表面；2) modifying the vertex coordinates of the upper and lower surfaces of the upper and lower two groups of micro-hexahedron groups respectively, so that the vertices of the upper and lower surfaces in the upper and lower two groups of hexahedron groups have the same Z coordinate value, forming a smooth surface;

3)调节上一连接体的Z向位置，确保两连接表面有局部点刚好发生初始接触。3) Adjust the Z-direction position of the previous connecting body to ensure that there are local points on the two connecting surfaces that just make initial contact.

5.体模型网格划分5. Volume model meshing

以步骤4生成的体模型为基础，通过线网格控制的方法，对体模型进行六面体网格划分；Based on the volume model generated in step 4, the volume model is divided into hexahedral meshes through the method of line grid control;

1)网格单元数量的控制：在上述构建的体模型中选择厚度方向的所有线条，控制线条高度方向的网格大小或网格层数，同时通过控制水平方向网格的大小，精确控制网格的数量，如图8的网格数量为127×127×4×2；1) Control of the number of grid units: select all the lines in the thickness direction in the volume model constructed above, control the grid size or the number of grid layers in the height direction of the lines, and precisely control the grid size by controlling the size of the grid in the horizontal direction. The number of grids, as shown in Figure 8, the number of grids is 127×127×4×2;

2)对同一个微六面体中，由于四条高度方向的线条，高度相差不大，在高度方向统一定义4层网格单元；2) For the same microhexahedron, due to the four lines in the height direction, the height difference is not large, and 4 layers of grid units are uniformly defined in the height direction;

3)指定网格单元类型为Solid45，上下材料为45钢，生成六面体扫描网格，如图8所示。3) Specify the grid unit type as Solid45, and the upper and lower materials are 45 steel to generate a hexahedral scanning grid, as shown in Figure 8.

6.结合面接触特性分析6. Analysis of the contact characteristics of the joint surface

以步骤5生成的网格模型为基础，定义结合面接触对，固定下端体模型下表面z方向的位移，通过上端体模型上表面位移约束施加载荷边界条件(-0.5，0.8，11，1.4，...，2.3，2.6μm)，构建两3D粗糙表面接触的有限元接触模型，并对两粗糙表面的接触中微凸体的变形、Z向应力与等效应力以及结合面的接触压力与接触区域进行了分析。其中图9所示为载荷增大时对应的上连接体Z向应力变化规律，图10所示为载荷增大时对应的上连接体等效应力变化规律，图11所示为载荷增大时对应的结合面接触压力与接触区域的变化规律。Based on the mesh model generated in step 5, define the contact pair of the combined surface, fix the displacement of the lower surface of the lower body model in the z direction, and apply load boundary conditions (-0.5, 0.8, 11, 1.4, ..., 2.3, 2.6μm), construct a finite element contact model of two 3D rough surfaces in contact, and analyze the deformation of asperities, Z-direction stress and equivalent stress, as well as the contact pressure and The contact area was analyzed. Among them, Figure 9 shows the change law of the stress in the Z direction of the upper connector corresponding to the increase of the load, Figure 10 shows the change law of the equivalent stress of the upper connector corresponding to the increase of the load, and Figure 11 shows the change law of the equivalent stress of the upper connector when the load increases. The corresponding change law of the contact pressure and contact area of the joint surface.

Claims

1. a faying face contact performance analytical approach that comprises the microcosmic surface pattern is characterized in that, comprises following step:

1) measure real surface through laser confocal microscope or utilize the three-dimensional appearance analogy method to obtain Gauss or non-Gauss's rough surface, the height matrix that extracts the 3D rough surface morphology be Z (m, n), wherein m, n represent that respectively x, y direction get number a little;

2) be object with the microcosmic surface pattern that obtains in the step 1), choose suitable spacing, utilize some cloud disposal route that the 3D rough surface is separated into the txt file that finite element software extracts easily;

3) utilize step 2) txt file of the three-dimensional point that generates, import in the finite element software and generate point cloud model, utilize the dual loop command of finite element, connect adjacent 4 points of X/Y direction, generate microcosmic dough sheet crowd, each connects the microscopic appearance on surface to obtain faying face;

4) two groups of rough surfaces that generate with step 3) are basis, through planar stretch, and utilize translation and the coordinate modify feature of finite element software key point, make up the phantom type of one group of consideration connection surface microscopic surface topography;

5) the phantom type that generates with step 4) is the basis, through the method for gauze lattice control, the phantom type is carried out hexahedral mesh divide;

6) grid model that generates with step 5) is the basis; The contact of definition faying face is right; The fixing displacement of connector lower surface z direction down through to last connector upper surface displacement constraint imposed load boundary condition, makes up the finite element contact model of two 3D rough surfaces contact; And carry out structural static and find the solution, observation connects the contact load and the contact pressure regularity of distribution of faying face.

2. a kind of faying face contact performance analytical approach that comprises the microcosmic surface pattern according to claim 1, the described three-dimensional appearance analogy method of utilizing obtains Gauss's rough surface, specifically comprises following steps:

1) utilize white noise generator randn (m, n) produce white noise sequence η (m, n), and obtain its Fourier transform A (m, n);

2) utilize given autocorrelation function generate correlation matrix R (m, n); Suppose autocorrelation function be f (x, y), β wherein _x, β _yBe respectively the auto-correlation length of X, Y direction;

Specify X, the discrete spacing of Y direction to be respectively Δ _x=1 μ m, Δ _y=1 μ m, at 0≤x≤m/2,0≤y≤n/2 disperses to autocorrelation function in the zone; (m/2+1 n/2+1), expands to-m/2≤x≤m/2 the discrete matrix R of acquisition autocorrelation function then; The autocorrelation matrix function discrete matrix R of correspondence in-n/2≤y≤n/2 zone (m, n):

R(k+1,l+1)=f(k,l) k=0,1,2...0.5m，l=0,1,2...0.5n

R(0.5m+2+k,l+1)=f(0.5m-k,l+1) k=0,1,2...0.5m-2，l=0,1,2...0.5n

R(k+1,0.5n+l+2)=f(k+1,0.5n-l) k=0,1,2...0.5m，l=0,1,2...0.5n-2

R(0.5m+k+2,0.5n+l+2)=f(0.5m-k,0.5n-l) k=0,1,2...0.5m-2，l=0,1,2...0.5n-2

3) (m n) carries out Fourier transform, obtains the power spectrum density P of simulating surface to autocorrelation function matrix R;

4) power spectrum density by white noise is a constant C, supposes C=1, calculate white noise to the transfer function H on simulation Gauss surface (m, n):

5) utilize frequency domain dot product (A.*H) negate Fourier transform method to obtain the elemental height matrix sequence z on Gauss surface:

6), ask white noise power spectrum density constant C=σ/std2 (z), thereby simulation generates the Gauss's surface elevation matrix z:z=z*C. that meets requirements such as given standard deviation according to the actual standard deviation std2 (z) of assigned altitute standard deviation and simulating surface z

3. a kind of faying face contact performance analytical approach that comprises the microcosmic surface pattern according to claim 1, the described three-dimensional appearance analogy method of utilizing obtains non-Gauss's rough surface, specifically comprises following steps:

1) directly utilizes the height sequence z that digitized simulation generated of Gauss's rough surface, adopt Pearson or the non-Gaussian transformation of Johnson system to carry out non-Gaussian transformation, generate non-gaussian sequence Z;

2) if the measure of skewness S of the non-gaussian sequence that is generated _kWith kurtosis K _uDo not satisfy accuracy requirement, then adopt new white noise sequence, repeat the simulation and the non-Gauss conversion thereof of Gauss's rough surface height sequence,, accomplish the digitized simulation of non-Gauss's rough surface up to satisfying accuracy requirement.

4. a kind of faying face contact performance analytical approach that comprises the microcosmic surface pattern according to claim 1, described utilization point cloud disposal route is separated into the height matrix file that finite element software extracts easily with the 3D rough surface, specifically comprises following steps:

1) for actual measurement or simulating surface, can generate the dot file that comprises 3 row in the horizontal direction according to certain rules, wherein three data of each row are represented a point coordinate, and the 1st, 2,3 row are represented x, y, the z coordinate of corresponding point respectively;

2) be the some establishment order of finite element software identification through Ultraedit software with the form modifying of putting, thereby make things convenient for finite element software to read the txt dot file of this type, directly generate point cloud model.

5. a kind of faying face contact performance analytical approach that comprises the microcosmic surface pattern according to claim 1; Described translation and the coordinate modify feature that utilizes the finite element software key point; Make up one group of phantom type of considering the microcosmic surface appearance, specifically comprise following steps:

1) respectively two groups of microcosmic surfaces is stretched along Z positive dirction and opposite direction, generate two groups of little hexahedron crowds with certain altitude;

2) revise the point coordinate that each organizes little hexahedron crowd, make connect the surface among each group hexahedron crowd vertex of surface is had identical Z coordinate figure, form smooth surface;

3) Z that regulates a certain connector guarantees that to the position two connection surfaces have partial points that initial contact has just taken place.

6. a kind of faying face contact performance analytical approach that comprises the microcosmic surface pattern according to claim 1, described method through the control of gauze lattice is carried out the hexahedral mesh division to the phantom type, specifically comprises following steps:

1) control of grid cell quantity: in the phantom type of above-mentioned structure, select all lines of thickness direction, control the sizing grid or the grid number of plies of lines short transverse, pass through the size of controlling level direction grid simultaneously, accurately the quantity of control mesh;

2) in same little hexahedron; If the lines of four short transverses; Highly differ greatly; Sizing grid to its short transverse is suitably adjusted, and makes the little corresponding grid number of lines of big grid number of height value and height value differ even number, thereby guarantees to generate smoothly high-quality hexahedral mesh;

3) specify grid cell type and material properties, generate hexahedron scanning grid.