Contact analysis method suitable for complex curved surface of any key component

Abstract

The invention relates to a contact analysis method suitable for a complex curved surface of any key component, and the method comprises the following steps: S1, obtaining m * n three-dimensional point set data of the curved surface through a measuring instrument, and constructing a digital curved surface mesh model; s2, proposing a rough contact state solving method taking the minimum distance between the cross point sets of the two curved surfaces as an iteration target; s3, establishing a three-dimensional grid point set interpolation method based on linear interpolation; s4, performing fine contact state solving based on the finer curved surface mesh and the relative position of the two curved surfaces at the coarse contact moment; the problems that an existing complex curved surface expression is difficult to obtain, the association rule of design parameters and the contact state is not clear, and an existing design method cannot accurately analyze the contact state of the complex curved surface, cannot accurately describe the contact state of the complex curved surface and cannot well help optimization design and manufacturing of key parts are solved.

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 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, the contact analysis of complex curved surfaces of key components poses important technical challenges. These equipment usually require high load-bearing capacity, long life, and high-precision operating performance, which is closely related to the mechanical behavior between contact surfaces. Complex curved surfaces, such as the raceways and rolling elements of rolling bearings, high-precision robot joints, and ultra-precision slides, are often used in the transmission systems of major equipment, and their contact performance directly affects the operating stability and reliability of the equipment.

[0003] With the development of high-end equipment such as aerospace, ships, and new energy vehicles, the demand for contact surface design is getting higher and higher. It is required not only to meet the load-bearing capacity under extreme working conditions, but also to control the error sensitivity on the contact surface, reduce noise, optimize transmission errors and other technical indicators. These high requirements increase the complexity of contact surface design, and traditional contact analysis methods are difficult to cope with this complexity. Especially under high-speed and heavy-load conditions, contact analysis of complex surfaces becomes more difficult, and traditional methods fail to fully consider the following issues:

[0004] 1) It is difficult to obtain complex surface expressions: Complex surfaces such as spiral bevel gears and hypoid gears have complex geometric shapes and are difficult to accurately describe with simple mathematical expressions. Traditional methods usually rely on limited simplified geometric models and cannot effectively capture the true shape of complex surfaces, resulting in the inability to accurately predict contact behavior and mechanical properties. This problem limits the accuracy and reliability of contact analysis, affecting 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 of complex surface contact analysis results. The present invention uses point cloud data obtained by high-precision three-dimensional measuring instruments and adopts surface point set reconstruction algorithms to construct a high-precision digital surface mesh model, which greatly improves the accuracy of contact analysis.

[0006] 3) Traditional analysis methods have low computational efficiency and long computational time: In traditional contact analysis, due to the use of complex iterative optimization methods, the amount of calculation is large and the convergence speed is slow. The present invention optimizes the initial contact state through the minimum distance iteration method, and reduces the discretization error through linear interpolation in subsequent analysis. At the same time, it combines fine surface meshes with coarse contact states to improve the computational efficiency in the contact analysis process and shorten the computational time.

[0007] Therefore, based on the shortcomings of existing design methods and the needs of complex surface contact analysis, researchers in this field need to invent new contact analysis methods to overcome the above defects. 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 problems that the current complex surface expressions are difficult to obtain, the correlation between design parameters and contact states is unclear, and the existing design methods are unable to accurately analyze the contact states of complex surfaces, cannot accurately describe the contact states of complex surfaces, and cannot help optimize the design and manufacture 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 the surface m×n three-dimensional point set data through measuring instruments and construct a digital surface mesh model;

[0012] Use high-precision 3D measuring instruments to accurately scan complex surfaces, obtain 3D coordinate data of each position on the surface, record it as a discrete 3D point set, and use the surface point set reconstruction algorithm 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 with the minimum distance between the cross point sets of two surfaces as the iteration target is proposed;

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

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

[0016] The discrete points in the surface mesh are interpolated by linear interpolation to estimate the position of the middle point between any two points on the surface, generating a smoother and more precise three-dimensional interpolation model. That is, the linear interpolation method realizes interpolation by weighted averaging the coordinates of the adjacent grid points. The coordinates of each grid point and its surrounding neighboring points are weighted averaged according to a certain weight to obtain the coordinates of the middle point with a smooth transition in the area. Such an interpolation method can effectively estimate the middle position between any two points in the surface mesh, fill the gaps in the mesh caused by discretization, thereby reducing the influence of discretization errors and improving the accuracy of contact analysis.

[0017] S4: Solve the fine contact state based on a 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 fine contact algorithm; the contact stress between the two surfaces is accurately calculated using the Hertz contact theory; through the fine contact state solution method, combined with the machine learning algorithm and the Hertz contact theory, the mechanical behavior of the two surfaces in 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 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 law of the discrete three-dimensional point set, and use the 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 contour of the actual component.

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

[0021]

[0022] In the formula, 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. By gradually adjusting the relative position of the cross point set, 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 position of the point set according to this result, so that the distance gradually decreases; after each adjustment, recalculate the distance between the new point sets, and continue to adjust until the contact points between the two surfaces are minimized.

[0023] Further, the linear interpolation method in step S3 is specifically 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 :

[0024]

[0025] in, It is the weight coefficient of each neighboring point, which is usually determined by the 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 solving 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 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 of all points between the cross point sets on the two surfaces is minimized in the rough contact stage. The minimum distance between the points of the two surface point sets at the iteration moment ensures that the incremental adjustment is based on the proportional relationship between the minimum distance of the current iteration and the initial value at each iteration, which can quickly guide the relative position between the two surfaces to gradually approach the actual contact state;

[0030] Through continuous iteration, When the contact tolerance is less than the set minimum, the two surfaces are considered to be 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] In the formula, is the fitting equation of one of the surfaces;

[0033] Get the normal vector of the contact point After that, the two surface mesh points 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 for each point The displacement on is shown in the following formula:

[0034]

[0035] In the formula, 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 the present invention is applicable to complex surfaces of any key parts, and is intended to solve the problems of insufficient accuracy and low computational efficiency caused by traditional discretization methods and rough contact estimation in the contact analysis of key parts of equipment with complex geometric shapes. The method first obtains the three-dimensional point set data of the surface through a high-precision three-dimensional measuring instrument, processes the data in combination with the surface point set reconstruction algorithm, and constructs a high-precision digital surface mesh model. Then, the cross point set of the middle row and column on the surface is selected and optimized by the minimum distance iteration method to obtain the preliminary contact state. Then, the grid point coordinates are interpolated by weighted averaging to generate a smoother surface model, which significantly reduces the error caused by discretization and provides a more accurate surface morphology for subsequent fine contact analysis. On this basis, the fine contact state is further solved by using a finer surface mesh and the relative position of the two surfaces under the rough contact state. This process accurately simulates and predicts the mechanical behavior during the contact process by optimizing the relative position of the two surfaces. This contact analysis method can efficiently and accurately solve the difficult problems in contact analysis of complex surfaces. 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. The digital model of the complex surface is obtained by a high-precision three-dimensional measuring instrument, and the surface point set reconstruction algorithm is used to eliminate the measurement error and discontinuity, so as to obtain 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, the redundant calculation in the traditional method is avoided, and a lot of calculation time is saved. Especially in the key parts with complex geometric shapes, the number of iterative calculations required is reduced, and the calculation efficiency is improved. It is applicable to a variety of complex surface parts, 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 field, it can provide reliable support for product design and optimization.

[0039] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can 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 in conjunction with the accompanying drawings, wherein:

[0041] Figure 1 It is a flow chart of the contact analysis method applicable to any complex curved surface of key parts 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 distance between the cross points 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 fine contact stage in step S4 in the direction of the normal vector. DETAILED DESCRIPTION

[0046] The following describes the embodiments of the present invention through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention.

[0047] like Figure 1 A contact analysis method applicable to complex surfaces of any key parts is shown, comprising the following steps:

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

[0049] First, use high-precision 3D measuring instruments, such as laser scanners or 3D laser measuring instruments, to accurately scan complex surfaces. These high-precision devices can accurately measure the 3D coordinates of each point on the surface by emitting lasers and receiving reflected signals, and convert these data into point cloud data. The acquired 3D point cloud is usually a discrete 3D point set, each point represents a position on the surface and contains the precise coordinate information of the position. Since the surface itself may have a complex geometric shape, a simple discrete point set is difficult to use directly for analysis, so it needs to be further processed and reconstructed.

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

[0051] After reconstruction, we finally get Figure 2 The digitized surface grid point set shown is usually presented as an m×n grid, where m and n represent the number of rows and columns of the grid, respectively. Each grid point corresponds to a specific three-dimensional coordinate, representing the shape and position of a small area on the surface. This gridding method can not only effectively discretize complex surfaces, but also provide high-precision input data for subsequent contact analysis. Through this digitized surface grid model, the geometric characteristics of the surface can be deeply studied and analyzed.

[0052] In this process, the generation of digital surface mesh models must ensure high accuracy, especially in contact analysis, where every detail may affect the final result. Therefore, the accuracy requirements are particularly 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. In order to further improve the 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 contour of the actual component. This precise digital surface mesh model provides a solid foundation for contact analysis, ensuring that the subsequent calculation and optimization process can be based on reliable data, thereby improving the reliability and durability of key parts of major equipment during use.

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

[0054] First, select a pair of cross point sets on the surface. These point sets are usually composed of points in the middle row and middle column on the surface. This pair of point sets selected by cross method is called cross point set, which can effectively represent the general geometric characteristics of the surface. These point sets are not only easy to calculate, but also can provide a rough estimate of the contact position for subsequent contact analysis, helping us to quickly determine the approximate contact area of ​​the two surfaces. The purpose of selecting a cross point set is to simplify the calculation while ensuring a representative preliminary estimate of contact on a complex surface.

[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 find the initial contact state of the two surfaces by calculating the sum of the distances between each pair of points on the two cross point sets and gradually adjusting the positions of the point sets according to these distances until the distance between the point sets converges to the minimum value. Figure 3 The sum of the distances of all points between the cross point sets on the two surfaces shown is used as the optimization target.

[0056] The specific calculation method is:

[0057]

[0058] In the formula, 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 time, by gradually adjusting the relative position of the cross point set, the distance between each pair of points is gradually reduced, and finally the sum of the distances between all points on the two surfaces is minimized. This process is actually looking for the best relative position of the two surfaces in the initial contact stage, laying the foundation for fine contact analysis.

[0060] The specific iterative process includes: first, calculate the sum of the distances between the current cross point sets, and adjust the position of the point sets based on this result so that the distance gradually decreases. After each adjustment, the distance between the new point sets is recalculated and adjusted again until the contact points between the two surfaces are minimized. Through this optimization process, we can obtain a rough contact area to ensure that no potential contact areas are missed during contact state analysis.

[0061] The advantage of this minimum distance iteration method is its speed and efficiency. It can provide a reliable initial contact state for subsequent more complex and detailed contact analysis in a short time. In addition, the point set position after iterative optimization provides 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] In order to further improve the accuracy of contact analysis, this step uses linear interpolation to interpolate the discrete point set in the surface mesh, thereby generating a smoother and more detailed three-dimensional surface model. Through the interpolation method, we can effectively estimate the middle position between any two points in the surface mesh, fill the gaps in the mesh caused by discretization, and thus reduce the impact of discretization errors and improve the accuracy of contact analysis.

[0064] Specifically, the linear interpolation method implements interpolation by weighted averaging the coordinates of neighboring 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 middle point with a smooth transition in the area. This method is not only simple and efficient, but also can achieve a smoother transition on the surface. It is particularly suitable for reducing the error caused by mesh discretization, thereby obtaining a more accurate three-dimensional surface representation.

[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 of each neighboring point, which is usually determined by distance. The closer the point is, the greater the weight. In this way, we can get the weighted average coordinates of each grid point, thereby generating a continuous and smooth surface in the entire grid.

[0068] like Figure 4 As shown in the figure, the surface processed by the linear interpolation method will present a smoother geometric shape, avoiding the irregularities in the original discrete mesh model. The interpolation result shows the smooth transition of each point on the surface after weighted averaging, and the resulting more accurate surface morphology. The interpolation result will serve as the basic data for subsequent detailed contact analysis, providing a more accurate contact surface, so that the contact mechanics analysis can more finely simulate the contact behavior between surfaces.

[0069] Through the application of this linear interpolation method, the originally discretized three-dimensional surface data is smoothed, which can effectively reduce the impact of discrete 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. In complex surface contact analysis, accurate surface morphology is crucial, and linear interpolation provides an efficient and effective means to improve the accuracy of the model, providing a solid foundation for subsequent fine contact analysis.

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

[0071] This process is based on a finer surface mesh and the relative position of the two surfaces in a coarse contact state, which greatly reduces the amount of iterative calculation of the relative position of the two surfaces while ensuring the accuracy of the solution. By introducing a fine contact state solution method, we not only improve the calculation efficiency, but also effectively avoid the errors caused by rough estimation, providing more reliable data for further contact analysis.

[0072] In the detailed contact state solution stage, we fix the position of one of the surfaces and use parameterized iterative increments to quickly adjust the relative position of the other surface, thereby gradually approaching the final contact state. This process controls the size of the iterative increment, which not only ensures the calculation accuracy, but also speeds up the convergence of the iteration, greatly improving the overall calculation efficiency. The calculation formula for 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 of all points between the cross point sets on the two surfaces is minimized in the rough contact stage. The minimum distance between the points of the two surface points at this iteration is the minimum value. The design of 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 between the two surfaces to gradually approach the actual contact state.

[0075] Through continuous iteration, When the contact tolerance is less than the set minimum, the two surfaces are considered to be 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, as shown in the following formula, can be further calculated for the normal vector of the point

[0076]

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

[0078] Get the normal vector of the contact point After that, the two surface mesh points 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 taken along the normal vector Directional projection, calculate the normal vector for each point The displacement on is shown in the following formula:

[0079]

[0080] In the formula, 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, the contact stress between the two surfaces is accurately calculated using Hertz contact theory. Hertz contact theory is a classic contact mechanics model that is widely used to describe contact problems between elastic objects. In Hertz theory, the contact stress distribution is closely related to parameters such as contact area, normal force, and elastic modulus of the material. By using Hertz theory, we can obtain information such as contact pressure distribution, contact stress, and stress concentration in the contact area 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 solution of the present invention rather than to limit it. 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 solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A contact analysis method applicable to complex surfaces of any key parts, characterized in that: The following steps are involved: S1: Obtain the surface m×n three-dimensional point set data through measuring instruments and construct a digital surface mesh model; Use high-precision 3D measuring instruments to accurately scan complex surfaces, obtain 3D coordinate data of each position on the surface, record it as a discrete 3D point set, and use the surface point set reconstruction algorithm 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 with the minimum distance between the cross point sets of two surfaces as the iteration target is proposed; A pair of cross point sets on the surface, i.e., the middle row and middle column on the surface, are selected. These points are formed into a cross point set by crossing, which is used to estimate the rough contact position of the two surfaces. Then, the minimum distance iteration method is used to gradually adjust the point set position by calculating the sum of the distances between each pair of points until the contact points between the two surfaces reach the minimum distance. This process provides a preliminary contact state for further fine contact analysis, and helps determine the relative position of the two surfaces in the initial contact stage, laying the foundation for subsequent fine 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 middle point between any two points on the surface, and generate a smoother and more precise three-dimensional interpolation model. The linear interpolation method realizes interpolation by weighted averaging 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 middle point with a smooth transition in the area. This interpolation method can effectively estimate the middle position between any two points in the surface mesh, fill the gaps in the mesh caused by discretization, and thus reduce the influence of discretization errors and improve the accuracy of contact analysis. S4: Solve the fine contact state based on a 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 fine contact algorithm; the contact stress between the two surfaces is accurately calculated using the Hertz contact theory; through the fine contact state solution method, combined with the machine learning algorithm and the Hertz contact theory, the mechanical behavior of the two surfaces in 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 any complex curved surface of a key component 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, and 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 law of the discrete three-dimensional point set, and use the 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 any complex curved surface of key parts as claimed in claim 1, characterized in that: The specific calculation method of the minimum distance iteration method in step S2 is: In the formula, 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. By gradually adjusting the relative position of the cross point set, 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 position of the point set according to this result, so that the distance gradually decreases; after each adjustment, recalculate the distance between the new point sets, and continue to adjust until the contact points between the two surfaces are minimized.

4. The contact analysis method applicable to any complex curved surface of a key component 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, It is the weight coefficient of each neighboring point, which is usually determined by the 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 any complex curved surface of a key component as claimed in claim 4, characterized in that: Step S4: In the fine contact state solving stage, 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 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 of all points between the cross point sets on the two surfaces is minimized in the rough contact stage. The minimum distance between the points of the two surface point sets at the iteration moment ensures that the incremental adjustment is based on the proportional relationship between the minimum distance of the current iteration and the initial value at each iteration, which can quickly guide the relative position between the two surfaces to gradually approach the actual contact state; Through continuous iteration, When the contact tolerance is less than the set minimum, the two surfaces are considered to be 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. In the formula, is the fitting equation of one of the surfaces; Get the normal vector of the contact point After that, the two surface mesh points 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 for each point The displacement on is shown in the following formula: In the formula, is the position vector of the i-th point in surface 1 after interpolation, is the position vector of the jth point in surface 2 after interpolation.

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