Multi-tooth contact analysis method suitable for point contact gear tooth surface

Abstract

The invention relates to a multi-tooth contact analysis method suitable for the tooth surface of a point contact gear, and the method comprises the steps: S1, constructing an installation matrix, moving the tooth surface three-dimensional point set data of a large gear and a small gear to a meshing position, and constructing a tooth surface point set meshing model; s2, rotating the gear tooth surfaces of the large gear and the small gear through the rotation matrix, and solving a rotation angle corresponding to the minimum distance between the cross point sets of the gear tooth surfaces of the large gear and the small gear; s3, by taking the coarse contact angle as an initial value, performing interpolation on discrete points in a tooth surface grid based on an intelligent interpolation method of a contact area, and performing fine contact solution; s4, performing three-dimensional curved surface local fitting on the to-be-contacted area based on a neural network to obtain an accurate local three-dimensional curved surface expression, and constructing a universal gear pair meshing equation; s5, dynamically adjusting a contact ellipse by evaluating the probability that a plurality of teeth participate in meshing before and after; the problems that a traditional gear tooth contact analysis method cannot adapt to different gear pair meshing equation solutions and a conventional gear tooth contact analysis method does not consider the contact ratio are solved.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical transmission and contact analysis, and relates to a multi-tooth contact analysis method applicable to the tooth surface of a point-contact gear, and in particular to a multi-tooth contact analysis method applicable to the tooth surface of a point-contact gear of any gear pair, and is applicable to various gear transmissions, such as multi-tooth contact analysis of hypoid gears, bevel gears, cylindrical gears, variable-thickness gears and the like. Background Art

[0002] In the gear transmission system, the meshing performance of the gear pair directly affects key indicators such as transmission efficiency, noise, and vibration. With the continuous development of gear transmission technology, the traditional single-tooth contact analysis method can no longer meet the precise analysis requirements of modern gear pairs under complex loads. In recent years, multi-tooth contact analysis has gradually become a hot topic in gear meshing research, especially in the design and manufacture of high-speed, heavy-load, and high-precision gear transmissions. Accurate multi-tooth contact analysis methods have become the key to improving the performance of gear pairs and extending their service life. Although many scholars have made significant progress in gear tooth contact analysis, the existing gear tooth contact analysis methods still face the following difficulties:

[0003] 1) Traditional multi-tooth gear contact analysis methods are usually derived and solved based on standard geometric assumptions or simplified meshing models. These methods are often unable to adapt to the changes of different types of gear pairs in practical applications. Due to the differences in the installation methods of gear pairs, the meshing equations of different gear pairs during the meshing process are significantly different. The meshing equation solution process of traditional methods is usually optimized for a specific gear pair, and it is difficult to adapt to gear pairs with different geometric shapes and working conditions.

[0004] 2) Conventional multi-tooth gear contact analysis methods are mostly based on the contact assumption under ideal conditions, ignoring the impact of overlap on the meshing process. These methods usually only consider the contact of a single tooth pair, and fail to fully reflect the actual contact state when multiple teeth are simultaneously engaged. In the actual transmission process, multiple tooth surfaces participate in meshing together, resulting in a more complex distribution of contact pressure and load, and the contact order and contact area between different tooth pairs will change as the meshing process progresses.

[0005] 3) Traditional multi-tooth gear contact analysis methods usually use complex iterative optimization algorithms to solve the contact ellipse. These methods require a large number of nonlinear operations and continuous error correction during the calculation process. Although these methods can provide a certain degree of accuracy, due to the involvement of complex mathematical models and multiple iterations, the amount of calculation is very large, and the convergence speed of each iteration is slow. This means that when facing gear pairs with high precision requirements or complex surfaces, traditional methods often require long calculations and are difficult to quickly apply in actual engineering.

[0006] Therefore, based on the shortcomings of the existing multi-tooth gear contact analysis methods for gear pairs, researchers in this field should invent new design methods to overcome the above-mentioned defects. Summary of the invention

[0007] In view of this, the present invention provides a multi-tooth contact analysis method suitable for the tooth surface of point contact gears in order to solve the problems that the multi-tooth gear contact analysis method in the above-mentioned existing gear pairs is difficult to adapt to the meshing equations of different gear pairs, the traditional gear contact analysis does not fully consider the overlap, and the calculation amount is large and the convergence speed is slow, which affects its application in practical engineering.

[0008] In order to achieve the above object, the present invention provides the following technical solutions:

[0009] A multi-tooth contact analysis method applicable to the tooth surface of a point contact gear comprises the following steps:

[0010] S1: According to the actual installation data of the gear pair, the installation matrix is ​​constructed, and the m×n three-dimensional point set data of the tooth surface of the large wheel and the small wheel are moved to the meshing position respectively to construct the tooth surface point set meshing model;

[0011] High-precision 3D measuring instruments are used to accurately scan the tooth surfaces of different types of arbitrary gear pairs, and m×n 3D point set data of the large and small gear tooth surfaces are obtained. The installation matrix is ​​constructed according to the actual installation data of the gear pair, and the large and small gear tooth surfaces are moved to the meshing position using Rodriguez coordinate transformation, thus realizing universal processing of different types of arbitrary gear pairs.

[0012] S2: Rotate the tooth surfaces of the large wheel and the small wheel respectively through the rotation matrix to solve the rotation angle corresponding to the minimum distance between the cross point sets of the tooth surfaces of the large wheel and the small wheel;

[0013] Select the tooth surface point sets in the middle row and middle column on the tooth surface of the large wheel and the small wheel, and form a cross point set by crossing to estimate the initial contact position of the tooth surface. Take the rotation angle of the large wheel and the small wheel as the variable, and the distance between the cross point sets of the two tooth surfaces as the target. Continuously iterate the calculation until the minimum distance between the cross point sets is obtained. The corresponding rotation angle at this time is the rough contact angle.

[0014] S3: Using the rough contact angle as the initial value, the discrete points in the tooth surface mesh are interpolated based on the intelligent interpolation method of the contact area to solve the fine contact;

[0015] According to the rough contact angle obtained in step S2 and the distribution characteristics of the tooth surface point set in step S1, combined with the minimum distance between the two tooth surface point sets, the increment is gradually reduced, the distance between the large wheel and small wheel tooth surface point sets is calculated, and the point on the large wheel and small wheel tooth surfaces corresponding to the minimum distance at each moment is used as the center to delineate the quasi-contact rectangular area of ​​each of p rows above and below and q columns on the left and right, and the intelligent interpolation method is used to interpolate the area, and the final contact area and contact point are determined by continuously rotating the large wheel and small wheel tooth surfaces until the minimum tolerance requirement is met;

[0016] S4: Based on the neural network, the three-dimensional surface of the simulated contact area is locally fitted to obtain the accurate local three-dimensional surface expression and construct the general gear pair meshing equation;

[0017] Based on the quasi-contact rectangular area that satisfies the minimum tolerance in step S3, the geometric characteristics of the local grid point set in the area are extracted through a neural network, and the three-dimensional surface expression of the area is accurately fitted to construct a universal meshing equation and a contact ellipse equation satisfied by the large wheel and the small wheel at the meshing point F;

[0018] S5: Dynamically adjust the contact ellipse by evaluating the probability of several front and rear teeth participating in meshing;

[0019] Based on the precise meshing point data solved in step S4, the angles of several teeth on the large wheel tooth surface are rotated, and the rotation angles of the small wheel when the large wheel tooth surface meshes with the small wheel at this angle are calculated respectively; by comparing the difference between the rotation angle of the small wheel when the large wheel tooth surface meshes with the small wheel at this angle and the angle of several teeth rotated on the small wheel tooth surface, the probability of the front and rear teeth participating in the meshing is evaluated, and according to the probability of participating in the meshing, the contact ellipse equation is adjusted, thereby realizing multi-tooth contact analysis considering the overlap.

[0020] Furthermore, in step S1, the high-precision three-dimensional measuring instrument is a three-coordinate measuring machine or a laser scanner, and any gear pair is one of a hypoid gear, a bevel gear, a cylindrical gear, and a variable thickness gear.

[0021] Furthermore, in step S1, any gear pair is a hypoid gear, and the installation matrix of the constructed hypoid gear is:

[0022]

[0023] in, is the offset distance of the hypoid gear, is the shaft angle of the hypoid gear;

[0024] Keep the small wheel tooth surface unchanged, and transform the driven wheel large wheel tooth surface so that the large and small wheels are in the correct meshing position, as shown below:

[0025]

[0026] in, is the original coordinate of the big wheel, is the coordinate of the large wheel after transformation.

[0027] Furthermore, in step S2, the rotation matrices are used to define the rotation angles of the large wheel and the small wheel, respectively. The rotation matrices are specifically as follows:

[0028]

[0029] in, represents the gear rotation angle, Indicates a small wheel. Represents the big wheel; the big wheel and the small wheel are transformed using the rotation matrix to simulate the gear rotation process, as shown below:

[0030]

[0031] in, represents the original coordinates of the cross point set on the tooth surface, Represents the coordinates of the cross point set on the tooth surface after rotation.

[0032] Furthermore, the intelligent interpolation algorithm in step S3 can adjust the interpolation weight according to the tooth surface geometry to generate more uniform point cloud data, thereby optimizing the accuracy of contact calculation.

[0033] Furthermore, in step S4, the expressions of the large wheel and the small wheel in the same coordinate system are as follows:

[0034] ,

[0035] in, is the local three-dimensional surface expression of the small wheel, is the local three-dimensional surface expression of the large wheel;

[0036] At the meshing point F, the large wheel and the small wheel should satisfy the following equation:

[0037]

[0038] in, and Respectively represent the unit normal vectors of the small wheel and the large wheel in the global coordinate system;

[0039] The general meshing equations have Six unknowns, including five independent equations, through the rotation angle of the driven wheel , solve the remaining five parameters of the small wheel meshing with each large wheel position.

[0040] Further, in step S5, at each rotation angle of the large wheel, the corresponding angle of the small wheel when the front and rear teeth are meshed with the large wheel is calculated according to the overlap degree, and the angle of the front and rear teeth is calculated. It is expressed as follows:

[0041]

[0042] in, The angle corresponding to the target tooth at this moment is, is the number of front and rear teeth, is the number of gear teeth, Indicates a small wheel. It means big wheel;

[0043] Set the angle of several teeth on the front and rear of the large wheel Substitute them into the general meshing equation respectively and solve to obtain the rotation angle of the small wheel meshing with it at this position, which is recorded as ,by and The deviation of the front and rear teeth is used as an indicator to evaluate the probability of several teeth participating in meshing; the load distribution law under multi-tooth meshing state is analyzed, and the results are combined with the contact ellipse equation to dynamically adjust the deformation degree during solution. , optimize the contact analysis effect of gear pairs.

[0044] Further, in step S5, after obtaining the parameters of a series of meshing points, the rotation angles of the large wheel and the small wheel during the meshing process are and , the transmission error can be obtained according to the expression of transmission error, as shown below:

[0045]

[0046] In the formula, and are the initial rotation angles of the small wheel and the large wheel, is the number of gear teeth on the pinion, is the number of gear teeth of the large wheel; the accuracy of this method is verified by finite element analysis of hypoid gears.

[0047] The beneficial effects of the present invention are:

[0048] 1. The multi-tooth contact analysis method for point contact gear tooth surfaces disclosed in the present invention performs local fitting of three-dimensional surfaces in the contact area through a neural network, and uses Rodriguez coordinate transformation to adjust gear pairs of any geometric shape to the meshing position, thereby realizing universal processing of different types of gear pairs (such as hypoid gears, bevel gears, cylindrical gears, variable thickness gears, etc.). Traditional methods are often designed for specific gear pairs and are difficult to be universal. However, the present invention broadens its application scope by adapting to gear pairs of different geometries.

[0049] 2. The multi-tooth contact analysis method for point contact gear tooth surfaces disclosed in the present invention uses an intelligent interpolation method to interpolate the quasi-contact area of ​​the tooth surface point set in order to improve the calculation accuracy, ensuring that the contact characteristics of the complex tooth surface are accurately described on the basis of meeting the minimum tolerance requirements. At the same time, this method also has significant advantages in computational efficiency. Through the preliminary estimation of the rough contact angle, the final solution is gradually reduced by incremental solution, which significantly reduces the number of iterations and overcomes the problems of large computational complexity and slow convergence speed of traditional iterative algorithms.

[0050] 3. The multi-tooth contact analysis method disclosed in the present invention is applicable to the tooth surface of point-contact gears. By evaluating the probability of multiple gears meshing at the same time, it fully considers the influence of the overlap on the performance of the gear pair. By dynamically adjusting the contact ellipse equation, the probability of the front and rear teeth participating in the meshing is reflected according to the change in the actual contact area, thereby accurately describing the load distribution and contact pressure characteristics during multi-tooth meshing. The contact ellipse is dynamically adjusted by evaluating the probability of several front and rear teeth participating in the meshing. The whole set of methods effectively improves the calculation efficiency of multi-tooth contact while ensuring the solution accuracy, and is suitable for contact analysis of various gear transmissions.

[0051] 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

[0052] 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:

[0053] Figure 1 It is a flow chart of the multi-tooth contact analysis method applicable to the tooth surface of a point contact gear of the present invention;

[0054] Figure 2 For the present invention Figure 1 Schematic diagram of the installation coordinate system in step S1;

[0055] Figure 3 For the present invention Figure 1 Schematic diagram of coarse contact solution in step S2;

[0056] Figure 4 For the present invention Figure 1 Schematic diagram of the intelligent interpolation method based on the contact area in step S3;

[0057] Figure 5 For the present invention Figure 1 Schematic diagram of geometric conditions at the meshing point in step S4;

[0058] Figure 6 For the present invention Figure 1 Schematic diagram of the contact ellipse boundary points in step S5;

[0059] Figure 7 For the present invention Figure 1 A comparison chart of the contact analysis results in step S5; wherein Figure 7 (a) is the analysis result of this method, Figure 7 (b) is the finite element analysis result. DETAILED DESCRIPTION

[0060] 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.

[0061] like Figure 1 A multi-tooth contact analysis method suitable for point contact gear tooth surfaces is shown, comprising the following steps:

[0062] S1: By installing the matrix, the m×n three-dimensional point set data of the tooth surface of the large wheel and the small wheel are moved to the meshing position respectively to construct the tooth surface point set meshing model;

[0063] First, the gear pair tooth surface is scanned in three dimensions by precision measuring equipment (such as a three-dimensional coordinate measuring machine or a laser scanner) to obtain the tooth surface data of the large and small wheels. The scanning result is m×n three-dimensional point set data, where m is the number of rows of the tooth surface point set, n is the number of columns, and each point contains a three-dimensional coordinate value (x, y, z). To ensure the accuracy of the data, the tooth surface point set data obtained by scanning is preprocessed, including denoising, data resampling, and point cloud alignment to eliminate measurement errors.

[0064] According to the actual installation data of the gear pair, the installation matrix is ​​constructed to move the tooth surface point set data of the large wheel and the small wheel to the initial meshing position. Figure 2 As shown, taking the most general hypoid gear as an example, the installation matrix of the constructed hypoid gear is as follows

[0065]

[0066] in, is the offset distance of the hypoid gear, is the shaft angle of the hypoid gear.

[0067] Keep the small wheel tooth surface unchanged, and transform the driven wheel large wheel tooth surface so that the large and small wheels are in the correct meshing position, as shown below:

[0068]

[0069] in, is the original coordinate of the big wheel, is the coordinate of the large wheel after transformation.

[0070] S2: Rotate the tooth surfaces of the large wheel and the small wheel respectively through the rotation matrix to solve the rotation angle corresponding to the minimum distance between the cross point sets of the tooth surfaces of the large wheel and the small wheel;

[0071] From the tooth surface point sets of the large wheel and small wheel, the tooth surface point sets corresponding to the rows and columns in the middle of the tooth surface are selected. These points form two sets of cross point sets for preliminary estimation of the contact area of ​​the tooth surface. The rotation angles of the large wheel and small wheel are defined using rotation matrices. The rotation matrices are as follows:

[0072]

[0073] in, represents the gear rotation angle, Indicates a small wheel. Indicates a large wheel.

[0074] like Figure 3 As shown, the large wheel and the small wheel are transformed using rotation matrices to simulate the gear rotation process, as shown below:

[0075]

[0076] in, represents the original coordinates of the cross point set on the tooth surface, Represents the coordinates of the cross point set on the tooth surface after rotation.

[0077] Define the distance function between the large wheel and small wheel tooth surfaces, take the minimum distance between the two cross point sets as the objective function, and express it as a function of the rotation angle. Use the rotation matrix to adjust the angles of the large wheel and small wheel tooth surfaces respectively, and the adjustment range can be set according to the actual meshing conditions of the gear pair. By continuously calculating the distance between the two cross point sets, when the distance between the two cross point sets reaches the minimum value, record the coarse contact angle at this time as the initial value for the subsequent fine contact analysis.

[0078] S3: Using the rough contact angle as the initial value, the discrete points in the tooth surface mesh are interpolated based on the intelligent interpolation method of the contact area to solve the fine contact;

[0079] like Figure 4As shown in the figure, according to the distribution characteristics of the rough contact angle and the tooth surface point set, a quasi-contact rectangular area centered on the corresponding point of the two tooth surfaces with the minimum distance between the tooth surfaces is selected. This area includes grid points in p rows above and below and q columns on the left and right, which is used to more accurately calculate the contact state of the tooth surface.

[0080] For the quasi-contact rectangular area, the intelligent interpolation algorithm is applied to interpolate the grid points to improve the accuracy and distribution density of the point set. The intelligent interpolation algorithm can adjust the interpolation weight according to the tooth surface geometry to generate more uniform point cloud data, thereby optimizing the accuracy of contact calculation.

[0081] On the basis of the rough contact angle, the increment of the rotation angle is gradually reduced, the relative position of the large wheel and the small wheel is continuously adjusted, and the minimum distance between each point in the rectangular area of ​​the two tooth surfaces in simulated contact is calculated. When the minimum distance meets the set tolerance requirements, the final contact area and contact point are determined.

[0082] S4: Based on the neural network, the three-dimensional surface of the simulated contact area is locally fitted to obtain the accurate local three-dimensional surface expression and construct the general gear pair meshing equation;

[0083] The grid point set in the quasi-contact rectangular area determined in step S3 is input into the neural network model, and a neural network model suitable for local fitting of the tooth surface is designed and trained. The nonlinear fitting ability of the neural network is used to extract the geometric features of the point set in the quasi-contact area and generate a local three-dimensional surface expression. The expression of the large wheel and the small wheel in the same coordinate system can be expressed as follows:

[0084] ,

[0085] in, is the local three-dimensional surface expression of the small wheel, is the local three-dimensional surface expression of the large wheel.

[0086] like Figure 5 As shown, at the meshing point F, the large wheel and the small wheel should satisfy the following equation:

[0087]

[0088] in, and Respectively represent the unit normal vectors of the small wheel and the large wheel in the global coordinate system.

[0089] The general meshing equations have Six unknowns, including five independent equations, through the rotation angle of the driven wheel , the remaining five parameters of the small wheel meshing with each large wheel position can be solved.

[0090] S5: Dynamically adjust the contact ellipse by evaluating the probability of several front and rear teeth participating in meshing;

[0091] According to the contact point position and contact area data obtained in step S3 and step S4, the rotation process of the large wheel and the small wheel is simulated. At each rotation angle of the large wheel, the corresponding angle of the small wheel when the front and rear teeth are meshed with the large wheel is calculated according to the overlap degree. It can be expressed as follows:

[0092]

[0093] in, The angle corresponding to the target tooth at this moment is, is the number of front and rear teeth, is the number of gear teeth, Indicates a small wheel. Indicates a large wheel.

[0094] Set the angle of several teeth on the front and rear of the large wheel Substitute them into the general meshing equation respectively and solve to obtain the rotation angle of the small wheel meshing with it at this position, which is recorded as .by and The deviation amount is used as an indicator to evaluate the probability of several front and rear teeth participating in meshing.

[0095] Analyze the load distribution law under multi-tooth meshing state, combine the results with the contact ellipse equation, and dynamically adjust the deformation degree during solution , optimize the contact analysis effect of the gear pair. Figure 6 As shown, the tooth surface position vectors of the small wheel and the large wheel at the meshing point at this moment are obtained. , Then. At this time, the contact ellipse boundary points satisfy the position vectors of the two tooth surfaces , The distance in the direction of the common normal is , 0.00635mm is the diameter of red particles in the tooth surface rolling test, as shown below:

[0096]

[0097] in, is the normal vector at the meshing point of the large gear tooth surface at this meshing moment, which is a constant.

[0098] After obtaining the parameters of a series of meshing points, the rotation angles of the large and small wheels during the meshing process are and , the transmission error can be obtained according to the expression of transmission error, as shown below

[0099]

[0100] In the formula, and are the initial rotation angles of the small wheel and the large wheel, is the number of pinion gear teeth, is the number of teeth on the large wheel gear.

[0101] The accuracy of this method is verified by finite element analysis of a hypoid gear. The results are as follows: Figure 7 As shown, Figure 7 (a) is the analysis result of this method, Figure 7 (b) is the finite element analysis result. It can be seen that the deviation between the result of this method and the finite element result is within 10%.

[0102] This method only requires two tooth surface point set data and installation data of any gear pair to quickly obtain a series of meshing point positions and contact ellipses, as well as transmission errors of any gear pair considering multi-tooth contact through analytical methods. This method has high universality, greatly reduces the redundant calculation of tooth surface contact analysis while ensuring the accuracy of the solution, and accurately describes the meshing characteristics of multi-tooth meshing by dynamically adjusting the contact ellipse equation.

[0103] 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 multi-tooth contact analysis method suitable for point contact gear tooth surfaces, characterized in that: The steps include: S1: According to the actual installation data of the gear pair, the installation matrix is ​​constructed, and the m×n three-dimensional point set data of the tooth surface of the large wheel and the small wheel are moved to the meshing position respectively to construct the tooth surface point set meshing model; High-precision 3D measuring instruments are used to accurately scan the tooth surfaces of different types of arbitrary gear pairs, and m×n 3D point set data of the large and small gear tooth surfaces are obtained. The installation matrix is ​​constructed according to the actual installation data of the gear pair, and the large and small gear tooth surfaces are moved to the meshing position using Rodriguez coordinate transformation, thus realizing universal processing of different types of arbitrary gear pairs. S2: Rotate the tooth surfaces of the large wheel and the small wheel respectively through the rotation matrix to solve the rotation angle corresponding to the minimum distance between the cross point sets of the tooth surfaces of the large wheel and the small wheel; Select the tooth surface point sets in the middle row and middle column on the tooth surface of the large wheel and the small wheel, and form a cross point set by crossing to estimate the initial contact position of the tooth surface. Take the rotation angle of the large wheel and the small wheel as the variable, and the distance between the cross point sets of the two tooth surfaces as the target. Continuously iterate the calculation until the minimum distance between the cross point sets is obtained. The corresponding rotation angle at this time is the rough contact angle. S3: Using the rough contact angle as the initial value, the discrete points in the tooth surface mesh are interpolated based on the intelligent interpolation method of the contact area to solve the fine contact; According to the rough contact angle obtained in step S2 and the distribution characteristics of the tooth surface point set in step S1, combined with the minimum distance between the two tooth surface point sets, the increment is gradually reduced, the distance between the large wheel and small wheel tooth surface point sets is calculated, and the point on the large wheel and small wheel tooth surfaces corresponding to the minimum distance at each moment is used as the center to delineate the quasi-contact rectangular area of ​​each of p rows above and below and q columns on the left and right, and the intelligent interpolation method is used to interpolate the area, and the final contact area and contact point are determined by continuously rotating the large wheel and small wheel tooth surfaces until the minimum tolerance requirement is met; S4: Based on the neural network, the three-dimensional surface of the simulated contact area is locally fitted to obtain the accurate local three-dimensional surface expression and construct the general gear pair meshing equation; Based on the quasi-contact rectangular area that satisfies the minimum tolerance in step S3, the geometric characteristics of the local grid point set in the area are extracted through a neural network, and the three-dimensional surface expression of the area is accurately fitted to construct a universal meshing equation and a contact ellipse equation satisfied by the large wheel and the small wheel at the meshing point F; S5: Dynamically adjust the contact ellipse by evaluating the probability of several front and rear teeth participating in meshing; Based on the precise meshing point data solved in step S4, the angles of several teeth on the large wheel tooth surface are rotated, and the rotation angles of the small wheel when the large wheel tooth surface meshes with the small wheel at this angle are calculated respectively; by comparing the difference between the rotation angle of the small wheel when the large wheel tooth surface meshes with the small wheel at this angle and the angle of several teeth rotated on the small wheel tooth surface, the probability of the front and rear teeth participating in the meshing is evaluated, and according to the probability of participating in the meshing, the contact ellipse equation is adjusted, thereby realizing multi-tooth contact analysis considering the overlap.

2. The multi-tooth contact analysis method applicable to the tooth surface of a point contact gear as claimed in claim 1, characterized in that: In step S1, the high-precision three-dimensional measuring instrument is a three-dimensional coordinate measuring machine or a laser scanner, and any gear pair is one of a hypoid gear, a bevel gear, a cylindrical gear, and a variable thickness gear.

3. The multi-tooth contact analysis method applicable to the tooth surface of a point contact gear as claimed in claim 1, characterized in that: In step S1, any gear pair is a hypoid gear, and the installation matrix of the constructed hypoid gear is: in, is the offset distance of the hypoid gear, is the shaft angle of the hypoid gear; Keep the small wheel tooth surface unchanged, and transform the driven wheel large wheel tooth surface so that the large and small wheels are in the correct meshing position, as shown below: in, is the original coordinate of the large wheel, is the coordinate of the large wheel after transformation.

4. The multi-tooth contact analysis method applicable to the tooth surface of a point contact gear as claimed in claim 3, characterized in that: In step S2, the rotation matrices are used to define the rotation angles of the large wheel and the small wheel respectively. The rotation matrices are specifically as follows: in, represents the gear rotation angle, Indicates a small wheel. Represents the big wheel; the big wheel and the small wheel are transformed using the rotation matrix to simulate the gear rotation process, as shown below: in, represents the original coordinates of the cross point set on the tooth surface, Represents the coordinates of the cross point set on the tooth surface after rotation.

5. The multi-tooth contact analysis method applicable to the tooth surface of a point contact gear as claimed in claim 4, characterized in that: In step S3, the intelligent interpolation algorithm can adjust the interpolation weight according to the tooth surface geometry to generate more uniform point cloud data, thereby optimizing the accuracy of contact calculation.

6. The multi-tooth contact analysis method applicable to the tooth surface of a point contact gear as claimed in claim 5, characterized in that: In step S4, the expressions of the large wheel and the small wheel in the same coordinate system are as follows: , in, is the local three-dimensional surface expression of the small wheel, is the local three-dimensional surface expression of the large wheel; At the meshing point F, the large wheel and the small wheel should satisfy the following equation: in, and Respectively represent the unit normal vectors of the small wheel and the large wheel in the global coordinate system; The general meshing equations have Six unknowns, including five independent equations, through the rotation angle of the driven wheel , solve the remaining five parameters of the small wheel meshing with each large wheel position.

7. The multi-tooth contact analysis method applicable to the tooth surface of a point contact gear as claimed in claim 6, characterized in that: In step S5, at each rotation angle of the large wheel, the corresponding angle of the small wheel when the front and rear teeth are meshed with the large wheel is calculated according to the overlap degree, and the angles of the front and rear teeth are calculated. It is expressed as follows: in, The angle corresponding to the target tooth at this moment is, is the number of front and rear teeth, is the number of gear teeth, Indicates a small wheel. It means big wheel; Set the angle of several teeth on the front and rear of the large wheel Substitute them into the general meshing equation respectively and solve to obtain the rotation angle of the small wheel meshing with it at this position, which is recorded as ,by and The deviation of the front and rear teeth is used as an indicator to evaluate the probability of several teeth participating in meshing; the load distribution law under multi-tooth meshing state is analyzed, and the results are combined with the contact ellipse equation to dynamically adjust the deformation degree during solution. , optimize the contact analysis effect of gear pairs.

8. The multi-tooth contact analysis method applicable to the tooth surface of a point contact gear as claimed in claim 7, characterized in that: In step S5, after obtaining the parameters of a series of meshing points, the rotation angles of the large wheel and the small wheel during the meshing process are and , the transmission error is obtained according to the expression of transmission error, as shown below: In the formula, and are the initial rotation angles of the small wheel and the large wheel, is the number of gear teeth on the pinion, is the number of gear teeth of the large wheel; the accuracy of this method is verified by finite element analysis of hypoid gears.

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