A multi-tooth contact analysis method for point contact gear tooth surfaces

Abstract

The present invention relates to a multi-tooth contact analysis method suitable for point-contact gear tooth surfaces, comprising the following steps: S1: constructing an installation matrix, moving the three-dimensional point set data of the tooth surfaces of the large and small wheels to the meshing positions respectively, and constructing a tooth surface point set meshing model; S2: rotating the tooth surfaces of the large and small wheels respectively through a rotation matrix, and solving the rotation angle corresponding to the minimum distance between the cross point sets of the tooth surfaces of the large and small wheels; S3: using the rough contact angle as the initial value, interpolating the discrete points in the tooth surface grid based on the intelligent interpolation method of the contact area, and performing a fine contact solution; S4: performing local three-dimensional surface fitting of the simulated contact area based on a neural network, obtaining an accurate local three-dimensional surface expression, and constructing a universal gear pair meshing equation; S5: dynamically adjusting the contact ellipse by evaluating the probability of several front and rear teeth participating in meshing; and solving the problems that the traditional gear tooth contact analysis method cannot adapt to the solution of meshing equations of different gear pairs and the conventional gear tooth contact analysis method does not consider the overlap.

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 surfaces of point-contact gears, and in particular to a multi-tooth contact analysis method applicable to the tooth surfaces of point-contact gears of any gear pair. The method 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 a 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 gear pair performance and extending 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 typically derived and solved based on standard geometric assumptions or simplified meshing models. In practice, these methods often fail to adapt to the variability of different gear pair types. Due to differences in gear pair installation methods, the meshing equations used by different gear pairs during meshing vary significantly. Traditional methods typically optimize the meshing equations for a specific gear pair, making them difficult to adapt to gear pairs with varying geometries and operating conditions.

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

[0005] 3) Traditional multi-tooth gear contact analysis methods typically use complex iterative optimization algorithms to solve the contact ellipse. These methods require extensive nonlinear calculations and continuous error correction during the calculation process. While these methods can provide a certain degree of accuracy, the complex mathematical models and multiple iterations involved make the calculations extremely arduous, and the convergence rate of each iteration is slow. This often results in lengthy calculation times for gear pairs with high precision requirements or complex surfaces, making them difficult to quickly apply in practical engineering.

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

[0007] In view of this, the present invention provides a multi-tooth contact analysis method suitable for point contact gear tooth surfaces 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 actual 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 point contact gear tooth surfaces comprises the following steps:

[0010] S1: Based on 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 precisely scan the tooth surfaces of any gear pair of any type, acquiring m×n 3D point data for the gear and pinion tooth surfaces. An installation matrix is ​​constructed based on the actual installation data of the gear pair, and the Rodrigues coordinate transformation is used to move the gear and pinion tooth surfaces to the meshing position, enabling universal processing of any gear pair of any type.

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

[0013] The tooth surface point sets in the middle rows and columns of the large and small gear tooth surfaces are selected and formed into a cross point set through cross-intersection. This is used to estimate the initial contact position of the tooth surface. The rotation angle of the large and small gears is used as a variable, and the distance between the two tooth surface cross point sets is used as the target. The calculation is iterated continuously 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 coarse 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 perform fine contact solution;

[0015] Based on 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 to calculate the distance between the large and small wheel tooth surface point sets. With the point on the large and small wheel tooth surfaces corresponding to the minimum distance at each moment as the center, a pseudo-contact rectangular area with p rows above and below and q columns left and right is delineated. This area is interpolated using the intelligent interpolation method. By continuously rotating the large and small wheel tooth surfaces until the minimum tolerance requirement is met, the final contact area and contact point are determined;

[0016] S4: Based on the neural network, a local 3D surface fitting is performed on the simulated contact area to obtain an accurate local 3D surface expression and construct a universal gear pair meshing equation;

[0017] Based on the quasi-contact rectangular area that meets 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 the universal meshing equation and contact ellipse equation satisfied by the large and small wheels 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 the angles 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 the angles and the angles of several teeth rotated on the small wheel tooth surface, the meshing probability of the front and rear teeth is evaluated, and according to the meshing probability, the contact ellipse equation is adjusted to achieve multi-tooth contact analysis considering the degree of overlap.

[0020] Furthermore, in step S1, the high-precision three-dimensional measuring instrument is a three-coordinate measuring machine or a laser scanner, and the arbitrary 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 hypoid gear constructed 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 fixed, 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 matrix is ​​used to define the rotation angles of the large wheel and the small wheel respectively. The rotation matrix is ​​specifically as follows:

[0028]

[0029] in, represents the gear rotation angle, Indicates a small wheel, Represents the large wheel; the large wheel and 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 tooth surface cross point set, 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, are calculated by rotating the driven wheel and the large wheel. , solve the remaining five parameters of the small wheel meshing with each large wheel position.

[0040] Furthermore, 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 engaged with the large wheel is calculated according to the degree of overlap. 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] Adjust the angle of several teeth before and after the big wheel Substitute them into the general meshing equation respectively and solve to get the rotation angle of the small wheel meshing with it at this position, which is recorded as ,by and The deviation of the tooth is used as an indicator to evaluate the probability of several teeth participating in the meshing; the load distribution law under the multi-tooth meshing state is analyzed, and the results are combined with the contact ellipse equation to dynamically adjust the deformation degree during the 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] Where, 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 disclosed multi-tooth contact analysis method for point-contact gear tooth surfaces uses a neural network to perform local three-dimensional surface fitting of the contact region. Using the Rodrigues coordinate transformation, it adjusts gear pairs of arbitrary geometry to meshing positions, enabling universal processing of different gear pairs (such as hypoid gears, bevel gears, cylindrical gears, and variable-thickness gears). Traditional methods are often designed for specific gear pairs and are difficult to apply universally. This method, by adapting to gear pairs of varying geometries, broadens its scope of application.

[0049] 2. The disclosed multi-tooth contact analysis method for point-contact gear tooth surfaces employs an intelligent interpolation method to interpolate the simulated contact region of a tooth surface point set to improve computational accuracy. This ensures accurate description of the contact characteristics of complex tooth surfaces while meeting minimum tolerance requirements. This method also offers significant advantages in computational efficiency. By initially estimating the rough contact angle and then gradually reducing the increments to achieve the final solution, it significantly reduces the number of iterations and overcomes the computational complexity and slow convergence of traditional iterative algorithms.

[0050] 3. The multi-tooth contact analysis method disclosed in this invention, applicable to point-contact gear tooth surfaces, comprehensively considers the impact of overlap on gear pair performance by evaluating the probability of multiple gears engaging simultaneously. By dynamically adjusting the contact ellipse equation, the probability of front and rear teeth engaging in meshing is reflected based on changes 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 engaging in meshing. This entire method effectively improves the computational efficiency of multi-tooth contact while ensuring solution accuracy, and is applicable to contact analysis of various gear transmissions.

[0051] 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

[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 with reference to the accompanying drawings, in which:

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

[0054] Figure 2 For the present invention Figure 1 Schematic diagram of the coordinate system installed 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 the 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 The comparison chart of the contact analysis results in step S5; 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. 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.

[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, a 3D scan of the gear tooth surfaces is performed using precision measuring equipment (such as a three-dimensional coordinate measuring machine or laser scanner) to obtain data for both the gear and pinion tooth surfaces. The scan results in an m×n 3D point set, where m is the number of rows and n is the number of columns. Each point contains a 3D coordinate value (x, y, z). To ensure data accuracy, the scanned point set data undergoes preprocessing, 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 and the tooth surface point set data of the large wheel and the small wheel are moved to the initial meshing position. Figure 2 As shown, taking the most general hypoid gear as an example, the installation matrix of the hypoid gear is constructed 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 fixed, 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 and small wheels respectively through the rotation matrix to find the rotation angle corresponding to the minimum distance between the cross point sets of the tooth surfaces of the large and small wheels;

[0071] From the tooth surface point sets of the large and small wheels, the tooth surface point sets corresponding to the middle rows and columns of the tooth surfaces are selected. These points form two sets of cross points, which are used to preliminarily estimate the contact area of ​​the tooth surfaces. The rotation angles of the large and small wheels 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 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 tooth surface cross point set, Represents the coordinates of the cross point set of the tooth surface after rotation.

[0077] Define a distance function between the gear teeth and the pinion teeth, using the minimum distance between the two cross-point sets as the objective function, and express it as a function of rotation angle. Use the rotation matrix to adjust the angles of the gear teeth, respectively. The adjustment range can be set based on 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, record the coarse contact angle at that time, which serves as the initial value for the subsequent fine contact analysis.

[0078] S3: Using the coarse 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 perform fine contact solution;

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

[0080] For the rectangular area of ​​​​presumed contact, an intelligent interpolation algorithm is applied to 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 a more uniform point cloud data, thereby optimizing the accuracy of the contact calculation.

[0081] Based on the rough contact angle, the rotation angle increments are gradually reduced, the relative positions of the large and small wheels are continuously adjusted, and the minimum distance between each point within 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 points are determined.

[0082] S4: Based on the neural network, a local 3D surface fitting is performed on the simulated contact area to obtain an accurate local 3D surface expression and construct a universal gear pair meshing equation;

[0083] The grid point set within the quasi-contact rectangular region determined in step S3 is input into the neural network model. A neural network model suitable for local tooth surface fitting is designed and trained. The nonlinear fitting capability of the neural network is utilized to extract the geometric features of the point set within the quasi-contact region and generate a local three-dimensional surface expression. The expressions for the large and small wheels in the same coordinate system can then 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 Represent the unit normal vectors of the small wheel and the large wheel in the global coordinate system respectively.

[0089] The general meshing equations have Six unknowns, including five independent equations, are calculated by rotating the driven wheel and the large wheel. , we can solve the remaining five parameters of the small wheel meshing with each large wheel position.

[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 engaged with the large wheel is calculated according to the degree of overlap. 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] Adjust the angle of several teeth before and after the big wheel Substitute them into the general meshing equation respectively and solve to get 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 point satisfies 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] Where, and are the initial rotation angles of the small wheel and the large wheel respectively, 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 results of this method and the finite element results is within 10%.

[0102] This method requires only two tooth surface point sets and installation data for any gear pair. Through analytical methods, it rapidly obtains a series of meshing point locations, contact ellipses, and transmission errors for any gear pair considering multi-tooth contact. This method is highly universal, significantly reducing redundant calculations in tooth surface contact analysis while maintaining solution accuracy. By dynamically adjusting the contact ellipse equation, it accurately describes the meshing characteristics of multi-tooth meshing.

[0103] 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 multi-tooth contact analysis method suitable for point contact gear tooth surfaces, characterized in that: The steps include: S1: Based on 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 precisely scan the tooth surfaces of any gear pair of any type, acquiring m×n 3D point data for the gear and pinion tooth surfaces. An installation matrix is ​​constructed based on the actual installation data of the gear pair, and the Rodrigues coordinate transformation is used to move the gear and pinion tooth surfaces to the meshing position, enabling universal processing of any gear pair of any type. S2: Rotate the tooth surfaces of the large and small wheels respectively through the rotation matrix to find the rotation angle corresponding to the minimum distance between the cross point sets of the tooth surfaces of the large and small wheels; The tooth surface point sets in the middle rows and columns of the large and small gear tooth surfaces are selected and formed into a cross point set through cross-intersection. This is used to estimate the initial contact position of the tooth surface. The rotation angle of the large and small gears is used as a variable, and the distance between the two tooth surface cross point sets is used as the target. The calculation is iterated continuously 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 coarse 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 perform fine contact solution; Based on 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 to calculate the distance between the large and small wheel tooth surface point sets. With the point on the large and small wheel tooth surfaces corresponding to the minimum distance at each moment as the center, a pseudo-contact rectangular area with p rows above and below and q columns left and right is delineated. This area is interpolated using the intelligent interpolation method. By continuously rotating the large and small wheel tooth surfaces until the minimum tolerance requirement is met, the final contact area and contact point are determined; S4: Based on the neural network, a local 3D surface fitting is performed on the simulated contact area to obtain an accurate local 3D surface expression and construct a universal gear pair meshing equation; Based on the quasi-contact rectangular area that meets 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 the universal meshing equation and contact ellipse equation satisfied by the large and small wheels 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 the angles 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 the angles and the angles of several teeth rotated on the small wheel tooth surface, the meshing probability of the front and rear teeth is evaluated, and according to the meshing probability, the contact ellipse equation is adjusted to achieve multi-tooth contact analysis considering the degree of overlap.

2. The multi-tooth contact analysis method applicable to point contact gear tooth surfaces according to claim 1, characterized in that: In step S1, the high-precision three-dimensional measuring instrument is a three-coordinate measuring machine or a laser scanner, and the arbitrary 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 point contact gear tooth surfaces according to 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 fixed, 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 big wheel, is the coordinate of the large wheel after transformation.

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

5. The multi-tooth contact analysis method applicable to point contact gear tooth surfaces according to 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 point contact gear tooth surfaces according to 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, are calculated by rotating the driven wheel and the large 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 point contact gear tooth surfaces according to 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 engaged with the large wheel is calculated according to the degree of overlap. 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; Adjust the angle of several teeth before and after the big wheel Substitute them into the general meshing equation respectively and solve to get the rotation angle of the small wheel meshing with it at this position, which is recorded as ,by and The deviation of the tooth is used as an indicator to evaluate the probability of several teeth participating in the meshing; the load distribution law under the multi-tooth meshing state is analyzed, and the results are combined with the contact ellipse equation to dynamically adjust the deformation degree during the solution. , optimize the contact analysis effect of gear pairs.

8. The multi-tooth contact analysis method applicable to point contact gear tooth surfaces according to 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: Where, 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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