A contact analysis method suitable for complex surfaces of any key parts

Abstract

The present invention relates to a contact analysis method applicable to complex surfaces of any key component, comprising the following steps: S1: obtaining surface m×n three-dimensional point set data through a measuring instrument and constructing a digital surface mesh model; S2: proposing a coarse contact state solution method with the minimum distance between the cross point sets of two surfaces as an iteration target; S3: establishing a three-dimensional mesh point set interpolation method based on linear interpolation; S4: solving the fine contact state based on a finer surface mesh and the relative position of the two surfaces at the coarse contact moment; solving the current problems of difficulty in obtaining complex surface expressions, unclear association rules between design parameters and contact states, and the inability of existing design methods to accurately analyze the contact states of complex surfaces, accurately describe the contact states of complex surfaces, and effectively assist in optimizing the design and manufacturing of key components.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical transmission and contact analysis, and relates to a contact analysis method applicable to the complex curved surfaces of any key parts, and is applicable to key parts in various major equipment, such as complex contact surfaces in transmission systems of aerospace, ships, automobiles, engineering machinery, etc. Background Art

[0002] In the design and manufacture of major equipment, contact analysis of complex curved surfaces on key components presents significant technical challenges. These components typically require high load capacity, long life, and high-precision operational performance, which is closely related to the mechanical behavior of the contact surfaces. Complex curved surfaces, such as the raceways and rolling elements of rolling bearings, high-precision robotic joints, and ultra-precision slideways, are often used in the transmission systems of major equipment, and their contact performance directly impacts the operational stability and reliability of the equipment.

[0003] With the development of high-end equipment in industries such as aerospace, shipbuilding, and new energy vehicles, the demands on contact surface design are becoming increasingly stringent. These demands not only meet the load-bearing capacity under extreme operating conditions, but also require controlling the error sensitivity of the contact surface, reducing noise, optimizing transmission errors, and other technical indicators. These high demands increase the complexity of contact surface design, and traditional contact analysis methods struggle to cope with this complexity. Especially under high-speed and heavy-load conditions, contact analysis of complex surfaces becomes even more difficult, and traditional methods fail to fully consider the following issues:

[0004] 1) Difficulty in Obtaining Complex Surface Expressions: Complex surfaces, such as spiral bevel gears and hypoid gears, have complex geometric forms that are difficult to accurately describe using simple mathematical expressions. Traditional methods typically rely on limited, simplified geometric models that fail to effectively capture the true shape of complex surfaces, resulting in an inability to accurately predict contact behavior and mechanical properties. This issue limits the accuracy and reliability of contact analysis, impacting the quality of equipment design and manufacturing.

[0005] 2) Insufficient accuracy of traditional analysis methods: Traditional discretization methods and rough contact estimation often lead to insufficient accuracy in contact analysis results for complex surfaces. This invention uses point cloud data acquired by high-precision 3D measuring instruments and a surface point set reconstruction algorithm to construct a high-precision digital surface mesh model, significantly improving the accuracy of contact analysis.

[0006] 3) Traditional analysis methods suffer from low computational efficiency and long calculation times: Traditional contact analysis relies on complex iterative optimization methods, resulting in high computational complexity and slow convergence. This invention optimizes the initial contact state using a minimum distance iteration method and reduces discretization errors through linear interpolation in subsequent analysis. This, combined with a refined surface mesh and coarse contact state, improves computational efficiency and shortens calculation time during contact analysis.

[0007] Therefore, given the shortcomings of existing design methods and the need for complex surface contact analysis, researchers in this field need to invent new contact analysis methods to overcome these shortcomings. These methods should be able to more accurately describe the contact state of complex surfaces, help optimize the design and manufacturing process, and thus improve the reliability, stability, and service life of equipment. Summary of the Invention

[0008] In view of this, the present invention provides a contact analysis method applicable to the complex surfaces of any key parts in order to solve the current problems of difficulty in obtaining complex surface expressions, unclear association rules between design parameters and contact states, and inability of existing design methods to accurately analyze the contact states of complex surfaces, accurately describe the contact states of complex surfaces, and help optimize the design and manufacturing of key components.

[0009] In order to achieve the above object, the present invention provides the following technical solutions:

[0010] A contact analysis method applicable to complex surfaces of any key parts includes the following steps:

[0011] S1: Obtain surface m×n three-dimensional point set data through measuring instruments and construct a digital surface mesh model;

[0012] Using high-precision 3D measuring instruments to precisely scan complex surfaces, the 3D coordinate data of each position on the surface is obtained and recorded as a discrete 3D point set. Surface point set reconstruction algorithms are then used to reconstruct the discrete 3D point set to construct a digital surface mesh model (m×n format), where m and n are the number of rows and columns of the mesh, respectively.

[0013] S2: A rough contact state solution method is proposed with the minimum distance between the cross point sets of two surfaces as the iterative target;

[0014] A pair of cross points on the surface is selected, namely the middle row and middle column on the surface. These points are crossed to form a cross point set to estimate the rough contact position of the two surfaces. Then, the minimum distance iteration method is used to calculate the sum of the distances between each pair of points and gradually adjust the point set position until the contact points between the two surfaces reach the minimum distance. This process provides a preliminary contact state for further refined contact analysis and helps determine the relative position of the two surfaces in the initial contact stage, laying the foundation for subsequent refined contact analysis.

[0015] S3: Establish a three-dimensional grid point set interpolation method based on linear interpolation;

[0016] The linear interpolation method is used to interpolate the discrete points in the surface mesh, estimate the position of the midpoint between any two points on the surface, and generate a smoother and more refined three-dimensional interpolation model. In other words, the linear interpolation method is to achieve interpolation by taking a weighted average of the coordinates of adjacent grid points. The coordinates of each grid point and its surrounding neighboring points are weighted and averaged according to a certain weight to obtain the coordinates of the midpoint with a smooth transition in the area. This interpolation method can effectively estimate the midpoint between any two points in the surface mesh, fill the gaps in the mesh caused by discretization, thereby reducing the impact of discretization error and improving the accuracy of contact analysis.

[0017] S4: Solve the fine contact state based on the finer surface mesh and the relative position of the two surfaces at the coarse contact moment;

[0018] Based on the finer surface mesh obtained in step S3, combined with the relative positions of the two surfaces at the rough contact moment obtained in step S2, the contact state of the two surfaces is further solved through the refined contact algorithm; the contact stress between the two surfaces is accurately calculated using the Hertz contact theory; through the refined contact state solution method, combined with the machine learning algorithm and Hertz contact theory, the mechanical behavior of the two surfaces during the contact process is accurately simulated and predicted, providing the necessary data support for the subsequent optimization design of key parts of major equipment, ensuring the reliability and efficiency of surface contact.

[0019] Furthermore, in step S1, the high-precision three-dimensional measuring instrument is a laser scanner or a three-dimensional laser measuring instrument, and the discrete three-dimensional point set obtained represents the three-dimensional coordinates of each position on the surface; the surface point set reconstruction algorithm can analyze the distribution pattern of the discrete three-dimensional point set, and use fitting technology to infer the continuity and shape of the surface, eliminating the discontinuity effect caused by measurement errors or sparse point clouds; the digital surface mesh model performs noise filtering and error correction on the collected data to ensure that the final surface mesh can accurately represent the geometric contours of the actual component.

[0020] Furthermore, the specific calculation method of the minimum distance iteration method in step S2 is:

[0021]

[0022] Where, represents the i-th point of the cross point set of surface 1, Represents the jth point of the cross point set on surface 2. By gradually adjusting the relative positions of the cross point sets, the distance between each pair of points is gradually reduced, and finally the sum of the distances of all points between the cross point sets on the two surfaces is minimized. The specific adjustment process is: first calculate the sum of the distances between the current cross point sets, and adjust the positions of the point sets based on this result so that the distances gradually decrease; after each adjustment, recalculate the new distance between the point sets, and continue to adjust until the contact points between the two surfaces are minimized.

[0023] Furthermore, the linear interpolation method in step S3 is specifically as follows: a point in the surface grid Interpolation calculation is performed on the point, which has several neighboring points around it. , the coordinates of these neighboring points are , by taking a weighted average of the coordinates of these neighboring points, a new smooth point is obtained :

[0024]

[0025] in, is the weight coefficient of each neighboring point, which is usually determined by distance. The closer the point is, the greater its weight. In this way, the weighted average coordinate of each grid point can be obtained, thereby generating a continuous and smooth surface in the entire grid.

[0026] Furthermore, in the fine contact state solution stage of step S4, the fine contact algorithm fixes the position of one of the surfaces and uses parameterized iterative increments to quickly adjust the relative position of the other surface, thereby gradually approaching the final contact state;

[0027] The calculation formula for the iterative increment is as follows:

[0028]

[0029] in, is the initial iteration increment, The minimum value of the distance between each point when the sum of the distances between all points on the cross point set on the two surfaces is minimized during the rough contact stage. The minimum distance between the points of the two surface points at this iteration ensures that the incremental adjustment is based on the proportional relationship between the minimum distance of the current iteration and the initial value, which can quickly guide the relative position between the two surfaces to gradually approach the actual contact state.

[0030] Through continuous iteration, when When the contact tolerance is less than the set minimum, it is determined that the two surfaces are in contact. The corresponding point is the contact point. At the contact point, a local grid point set is selected and the machine learning algorithm is used to fit the equation of one of the surfaces. The machine learning algorithm can effectively extract the geometric characteristics of the surface from these local grid point set data and accurately fit the mathematical expression of the surface where the point is located. The surface equation obtained by fitting is shown in the following formula, and the normal vector of the point is further calculated.

[0031]

[0032] Where, is the fitting equation of one of the surfaces;

[0033] Get the normal vector of the contact point After that, the two surface grid point sets are further calculated on the normal vector The distance in the direction; the difference vector between all points on the two surfaces is calculated along the normal vector Directional projection, calculate the normal vector of each point The displacement on is shown in the following formula:

[0034]

[0035] Where, is the position vector of the i-th point in surface 1 after interpolation, is the position vector of the j-th point in surface 2 after interpolation.

[0036] The beneficial effects of the present invention are:

[0037] 1. The contact analysis method disclosed in this invention, applicable to the complex surfaces of any key component, aims to address the problems of insufficient precision and low computational efficiency caused by traditional discretization methods and rough contact estimation in the contact analysis of key components of equipment with complex geometric shapes. The method first uses a high-precision three-dimensional measuring instrument to obtain three-dimensional point set data of the surface. This data is processed using a surface point set reconstruction algorithm to construct a high-precision digital surface mesh model. A preliminary contact state is then obtained by selecting a cross point set in the middle rows and columns of the surface and applying a minimum distance iteration method for optimization. The grid point coordinates are then interpolated using a weighted average method to generate a smoother surface model, significantly reducing the errors caused by discretization and providing a more accurate surface morphology for subsequent fine contact analysis. On this basis, the finer surface mesh and the relative positions of the two surfaces in the coarse contact state are used to further solve the fine contact state. This process accurately simulates and predicts the mechanical behavior during the contact process by optimizing the relative positions of the two surfaces. This contact analysis method can efficiently and accurately solve the difficult problems in complex surface contact analysis. It is widely used in the design, optimization and reliability analysis of key parts of major equipment, and provides effective technical support for improving the reliability, durability and performance of equipment.

[0038] 2. The contact analysis method disclosed in the present invention is applicable to the complex surfaces of any key parts. A digital model of the complex surface is obtained by a high-precision three-dimensional measuring instrument, and a surface point set reconstruction algorithm is used to eliminate measurement errors and discontinuities, thereby obtaining a more accurate surface mesh model. The linear interpolation method is used to further reduce the discretization error, generate a smooth three-dimensional surface, and significantly improve the accuracy of the contact analysis. By introducing the minimum distance iteration method and the coarse contact state solution strategy, the initial contact state between the two surfaces can be quickly estimated, avoiding redundant calculations in traditional methods and saving a lot of computing time. Especially in key components with complex geometric shapes, the number of iterative calculations required is reduced, and the computing efficiency is improved. It is applicable to a variety of complex surface components, such as robot joints, blades, rolling bearings, hydraulic cylinders, etc., and has broad application prospects. Whether it is machinery, aerospace, automotive industry, or high-precision manufacturing fields, it can provide reliable support for product design and optimization.

[0039] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0041] Figure 1 This is a flow chart of the contact analysis method applicable to any complex curved surface of a key component of the present invention;

[0042] Figure 2 for Figure 1 Schematic diagram of the reconstructed surface mesh in step S1;

[0043] Figure 3 for Figure 1 Schematic diagram of the cross point set distance in step S2;

[0044] Figure 4 for Figure 1 Schematic diagram of surface mesh interpolation in step S3;

[0045] Figure 5 for Figure 1 Schematic diagram of the projection of the distance between any two points in the normal vector direction during the fine contact stage in step S4. DETAILED DESCRIPTION

[0046] The following describes the embodiments of the present invention through specific examples. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. The present invention may also be implemented or applied through various other specific embodiments, and the details in this specification may be modified or altered based on different viewpoints and applications without departing from the spirit of the present invention.

[0047] like Figure 1 The contact analysis method shown in FIG. 1 is applicable to complex surfaces of any key parts and includes the following steps:

[0048] S1: Obtain surface m×n three-dimensional point set data through measuring instruments and construct a digital surface mesh model;

[0049] First, complex surfaces are precisely scanned using high-precision 3D measuring instruments, such as laser scanners or 3D laser measuring instruments. By emitting laser light and receiving the reflected signal, these high-precision devices can accurately measure the 3D coordinates of each point on the surface and convert this data into a point cloud. The resulting 3D point cloud is typically a discrete set of points, each representing a location on the surface and containing the precise coordinate information for that location. Because the surface itself can have complex geometric shapes, a simple discrete point set is difficult to directly analyze and therefore requires further processing and reconstruction.

[0050] These discrete 3D point sets are then processed and reconstructed using advanced surface point reconstruction algorithms. During the reconstruction process, the algorithms analyze the distribution patterns of the point sets to generate a more accurate and smooth digital surface model. Specifically, these algorithms use fitting techniques based on the spatial distribution characteristics of the collected discrete 3D point sets to infer the continuity and shape of the surface, thereby eliminating discontinuities caused by measurement errors or sparse point clouds.

[0051] After reconstruction, we finally get Figure 2 The digitized surface mesh point set shown is typically presented as an m×n grid, where m and n represent the number of rows and columns, respectively. Each grid point corresponds to a specific 3D coordinate, representing the shape and position of a small area on the surface. This gridding approach not only effectively discretizes complex surfaces but also provides highly accurate input data for subsequent contact analysis. This digitized surface mesh model enables in-depth study and analysis of the surface's geometric properties.

[0052] During this process, the generation of digital surface mesh models must ensure high precision, especially in contact analysis, where every detail can affect the final result. Therefore, the accuracy requirements are extremely high, and reasonable measurement equipment and algorithms must be used to ensure that the surface mesh can accurately reflect the geometry of the actual component. To further improve accuracy, the collected point cloud data is usually subjected to noise filtering and error correction to ensure that the final surface mesh can more accurately represent the geometric contours of the actual component. This precise digital surface mesh model provides a solid foundation for contact analysis, ensuring that subsequent calculations and optimization processes can be based on reliable data, thereby improving the reliability and durability of key components of major equipment during use.

[0053] S2: A rough contact state solution method is proposed with the minimum distance between the cross point sets of two surfaces as the iterative target;

[0054] First, a pair of cross point sets is selected on the surface. These point sets are typically composed of the points in the middle row and middle column of the surface. This cross-selected pair of points, known as a cross point set, effectively represents the general geometric characteristics of the surface. These point sets not only facilitate calculations but also provide a rough estimate of the contact position for subsequent contact analysis, helping us quickly determine the approximate contact area between the two surfaces. The purpose of selecting a cross point set is to simplify calculations while ensuring a representative initial contact estimate on complex surfaces.

[0055] Next, the minimum distance iteration method is used to iteratively optimize the pair of cross point sets. The core idea of ​​the minimum distance iteration method is to calculate the sum of the distances between each pair of points on the two cross point sets and gradually adjust the position of the point sets according to these distances until the distance between the point sets converges to the minimum value, thereby finding the initial contact state of the two surfaces. In each iteration, the calculation is as follows Figure 3 The sum of the distances between all points on the two surfaces shown is used as the optimization target.

[0056] The specific calculation method is:

[0057]

[0058] Where, represents the i-th point of the cross point set of surface 1, Represents the jth point of the cross point set of surface 2.

[0059] At this point, the relative positions of the cross points are gradually adjusted to reduce the distance between each pair of points, ultimately minimizing the sum of the distances between all points on the two surfaces. This process essentially seeks the optimal relative position of the two surfaces during the initial contact phase, laying the foundation for detailed contact analysis.

[0060] The iterative process involves first calculating the sum of the distances between the current cross point sets and adjusting the point sets accordingly, gradually reducing the distance. After each adjustment, the distance between the new point sets is recalculated, and adjustments are continued until the number of contact points between the two surfaces is minimized. This optimization process provides a rough estimate of the contact area, ensuring that no potential contact areas are missed during contact state analysis.

[0061] The advantage of this minimum distance iteration method lies in its speed and efficiency. It can quickly provide a reliable initial contact state for subsequent more complex and detailed contact analysis. In addition, the iteratively optimized point set positions provide more accurate preliminary contact information for subsequent detailed contact analysis, ensuring that the contact analysis can be performed on an accurate geometric basis.

[0062] S3: Establish a three-dimensional grid point set interpolation method based on linear interpolation;

[0063] To further improve the accuracy of contact analysis, this step uses linear interpolation to interpolate the discrete points in the surface mesh, generating a smoother and more detailed 3D surface model. This interpolation method effectively estimates the intermediate position between any two points in the surface mesh, filling gaps in the mesh caused by discretization. This reduces the impact of discretization errors and improves the accuracy of contact analysis.

[0064] Specifically, linear interpolation achieves interpolation by taking a weighted average of the coordinates of neighboring grid points. The coordinates of each grid point and its surrounding neighbors are weighted and averaged, yielding the coordinates of the smoothest intermediate points within the region. This method is not only simple and efficient, but also produces relatively smooth transitions on surfaces. It is particularly well-suited for reducing errors caused by mesh discretization, thereby achieving more accurate 3D surface representations.

[0065] For example, suppose we have a point in the surface mesh Interpolation calculation is required, and there are several neighboring points around this point. , the coordinates of these neighboring points are By taking a weighted average of the coordinates of these neighboring points, we can get a new smooth point :

[0066]

[0067] in, is the weight coefficient for each neighboring point, usually determined by distance, with closer points having greater weights. In this way, we can obtain the weighted average coordinates of each grid point, thereby generating a continuous, smooth surface across the entire grid.

[0068] like Figure 4 As shown in the figure, the surface processed by linear interpolation exhibits a smoother geometry, avoiding the irregularities in the original discrete mesh model. The interpolation result shows the smooth transition between surface points after weighted averaging, and the resulting more accurate surface morphology. This interpolation result will serve as the basis for subsequent detailed contact analysis, providing a more accurate contact surface and enabling contact mechanics analysis to more precisely simulate the contact behavior between surfaces.

[0069] By applying this linear interpolation method, originally discretized 3D surface data is smoothed, effectively reducing the impact of discretization errors when calculating contact mechanics problems such as contact pressure and stress distribution, thereby improving the accuracy and reliability of the entire contact analysis process. Accurate surface morphology is crucial in contact analysis of complex surfaces, and linear interpolation provides an efficient and effective means to improve model accuracy, laying a solid foundation for subsequent detailed contact analysis.

[0070] S4: Solve the fine contact state based on the finer surface mesh and the relative position of the two surfaces at the coarse contact moment;

[0071] This process relies on a finer surface mesh and the relative positions of the two surfaces in a coarse contact state. This significantly reduces the computational effort required to iterate the relative positions of the two surfaces while ensuring accurate results. By introducing a refined contact state solution, we not only improve computational efficiency but also effectively avoid errors caused by coarse estimates, providing more reliable data for further contact analysis.

[0072] During the detailed contact state solution phase, we fix the position of one surface and use parameterized iterative increments to quickly adjust the relative position of the other surface, gradually approaching the final contact state. This process, by controlling the size of the iterative increment, not only ensures calculation accuracy but also accelerates the iterative convergence speed, greatly improving overall computational efficiency. The formula for calculating the iterative increment is as follows:

[0073]

[0074] in, is the initial iteration increment, The minimum value of the distance between each point when the sum of the distances between all points on the cross point set on the two surfaces is minimized during the rough contact stage. The minimum distance between the points on the two surfaces at this iteration is the minimum distance between them. This formula ensures that at each iteration, the incremental adjustment is based on the proportional relationship between the minimum distance of the current iteration and the initial value, which can quickly guide the relative position of the two surfaces to gradually approach the actual contact state.

[0075] Through continuous iteration, when When the contact tolerance is less than the set minimum, it is determined that the two surfaces are in contact. The corresponding point is the contact point. At the contact point, a local grid point set is selected and the machine learning algorithm is used to fit the equation of one of the surfaces. The machine learning algorithm can effectively extract the geometric characteristics of the surface from these local grid point set data and accurately fit the mathematical expression of the surface at the point. The surface equation obtained by fitting is shown in the following formula, and the normal vector of the point can be further calculated.

[0076]

[0077] Where, is the fitting equation of one of the surfaces.

[0078] Get the normal vector of the contact point After that, the two surface grid point sets are further calculated on the normal vector The distance in the direction. Figure 5 As shown, the difference vector between all points on the two surfaces is drawn along the normal vector Directional projection, calculate the normal vector of each point The displacement on is shown in the following formula:

[0079]

[0080] Where, is the position vector of the i-th point in surface 1 after interpolation, is the position vector of the j-th point in surface 2 after interpolation.

[0081] Next, we use Hertz contact theory to accurately calculate the contact stress between the two surfaces. Hertz contact theory is a classic contact mechanics model widely used to describe contact problems between elastic objects. In Hertz theory, the contact stress distribution is closely related to parameters such as the contact area, normal force, and the material's elastic modulus. By using Hertz theory, we can obtain information such as the contact pressure distribution, contact stress, and stress concentration within the contact region between the two surfaces, providing a detailed mechanical model for contact analysis.

[0082] Through the above-mentioned sophisticated contact state solution method, combined with machine learning algorithms and Hertz contact theory, it is possible to accurately simulate and predict the mechanical behavior of two surfaces during contact, providing accurate mechanical data support for the design and optimization of key parts of major equipment.

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A contact analysis method applicable to complex curved surfaces of any key parts, characterized in that: The following steps are involved: S1: Obtain surface m×n three-dimensional point set data through measuring instruments and construct a digital surface mesh model; Using high-precision 3D measuring instruments to precisely scan complex surfaces, the 3D coordinate data of each position on the surface is obtained and recorded as a discrete 3D point set. Surface point set reconstruction algorithms are then used to reconstruct the discrete 3D point set to construct a digital surface mesh model (m×n format), where m and n are the number of rows and columns of the mesh, respectively. S2: A rough contact state solution method is proposed with the minimum distance between the cross point sets of two surfaces as the iterative target; A pair of cross points on the surface is selected, namely the middle row and middle column on the surface. These points are crossed to form a cross point set to estimate the rough contact position of the two surfaces. Then, the minimum distance iteration method is used to calculate the sum of the distances between each pair of points and gradually adjust the point set position until the contact points between the two surfaces reach the minimum distance. This process provides a preliminary contact state for further refined contact analysis and helps determine the relative position of the two surfaces in the initial contact stage, laying the foundation for subsequent refined contact analysis. S3: Establish a three-dimensional grid point set interpolation method based on linear interpolation; The linear interpolation method is used to interpolate the discrete points in the surface mesh, estimate the position of the midpoint between any two points on the surface, and generate a smoother and more refined three-dimensional interpolation model. The linear interpolation method achieves interpolation by taking a weighted average of the coordinates of adjacent grid points. The coordinates of each grid point and its surrounding neighboring points are weighted and averaged according to the weight to obtain the coordinates of the midpoint with a smooth transition in the area. This interpolation method can effectively estimate the midpoint between any two points in the surface mesh, fill the gaps in the mesh caused by discretization, thereby reducing the impact of discretization error and improving the accuracy of contact analysis. S4: Solve the fine contact state based on the finer surface mesh and the relative position of the two surfaces at the coarse contact moment; Based on the finer surface mesh obtained in step S3, combined with the relative positions of the two surfaces at the rough contact moment obtained in step S2, the contact state of the two surfaces is further solved through the refined contact algorithm; the contact stress between the two surfaces is accurately calculated using the Hertz contact theory; through the refined contact state solution method, combined with the machine learning algorithm and Hertz contact theory, the mechanical behavior of the two surfaces during the contact process is accurately simulated and predicted, providing the necessary data support for the subsequent optimization design of key parts of major equipment, ensuring the reliability and efficiency of surface contact.

2. The contact analysis method applicable to complex curved surfaces of any key parts as claimed in claim 1, characterized in that: In step S1, the high-precision three-dimensional measuring instrument is a laser scanner or a three-dimensional laser measuring instrument. The obtained discrete three-dimensional point set represents the three-dimensional coordinates of each position on the surface. The surface point set reconstruction algorithm can analyze the distribution pattern of the discrete three-dimensional point set and use fitting technology to infer the continuity and shape of the surface, eliminating the discontinuity effect caused by measurement error or sparse point cloud. The digital surface mesh model can filter noise and correct errors in the collected data to ensure that the final surface mesh can accurately represent the geometric contours of the actual component.

3. The contact analysis method applicable to complex curved surfaces of any key parts as claimed in claim 1, characterized in that: The specific calculation method of the minimum distance iteration method in step S2 is: Where, represents the i-th point of the cross point set of surface 1, Represents the jth point of the cross point set on surface 2. By gradually adjusting the relative positions of the cross point sets, the distance between each pair of points is gradually reduced, and finally the sum of the distances of all points between the cross point sets on the two surfaces is minimized. The specific adjustment process is: first calculate the sum of the distances between the current cross point sets, and adjust the positions of the point sets based on this result so that the distances gradually decrease; after each adjustment, recalculate the new distance between the point sets, and continue to adjust until the contact points between the two surfaces are minimized.

4. The contact analysis method applicable to complex curved surfaces of any key parts as claimed in claim 3, characterized in that: The linear interpolation method in step S3 is as follows: a point in the surface mesh Interpolation calculation is performed on the point, which has several neighboring points around it. , the coordinates of these neighboring points are , by taking a weighted average of the coordinates of these neighboring points, a new smooth point is obtained : in, is the weight coefficient of each neighboring point, which is usually determined by distance. The closer the point is, the greater its weight. In this way, the weighted average coordinate of each grid point can be obtained, thereby generating a continuous and smooth surface in the entire grid.

5. The contact analysis method applicable to complex curved surfaces of any key parts as claimed in claim 4, characterized in that: In the fine contact state solution stage of step S4, the fine contact algorithm fixes the position of one of the surfaces and uses parameterized iterative increments to quickly adjust the relative position of the other surface, thereby gradually approaching the final contact state; The calculation formula for the iterative increment is as follows: in, is the initial iteration increment, The minimum value of the distance between each point when the sum of the distances between all points on the cross point set on the two surfaces is minimized during the rough contact stage. The minimum distance between the points of the two surface points at this iteration ensures that the incremental adjustment is based on the proportional relationship between the minimum distance of the current iteration and the initial value, which can quickly guide the relative position between the two surfaces to gradually approach the actual contact state. Through continuous iteration, when When the contact tolerance is less than the set minimum, it is determined that the two surfaces are in contact. The corresponding point is the contact point. At the contact point, a local grid point set is selected and the machine learning algorithm is used to fit the equation of one of the surfaces. The machine learning algorithm can effectively extract the geometric characteristics of the surface from these local grid point set data and accurately fit the mathematical expression of the surface where the point is located. The surface equation obtained by fitting is shown in the following formula, and the normal vector of the point is further calculated. Where, is the fitting equation of one of the surfaces; Get the normal vector of the contact point After that, the two surface grid point sets are further calculated on the normal vector The distance in the direction; the difference vector between all points on the two surfaces is calculated along the normal vector Directional projection, calculate the normal vector of each point The displacement on is shown in the following formula: Where, is the position vector of the i-th point in surface 1 after interpolation, is the position vector of the j-th point in surface 2 after interpolation.

Images