Cooperative Optimization Design Method, System and Equipment for Spiral Bevel Gear Tooth Surface and Micro-texture

Abstract

The present application discloses a co - optimization design method, system and device for the tooth surface and micro - texture of spiral bevel gears. The method constructs a differential surface model based on the target tooth surface, optimizes the machining parameters based on the differential surface model to obtain new machining parameters; based on the new machining parameters, the reference tooth surface and the target tooth surface, performs loaded contact analysis and sensitivity analysis on the tooth surface of the spiral bevel gear to obtain the target machining parameters, optimizes the tooth surface of the spiral bevel gear according to the target machining parameters to obtain the target tooth surface of the spiral bevel gear; determines the initial micro - texture parameters, and based on the initial micro - texture parameters, places micro - textures on the target tooth surface of the spiral bevel gear to construct a tooth surface of the spiral bevel gear containing micro - textures; constructs an objective function and constraint conditions for optimizing the micro - texture parameters, and performs loaded contact analysis on the tooth surface of the spiral bevel gear containing micro - textures to obtain the target micro - texture parameters that meet the objective function and constraint conditions. The present application can achieve the co - optimization design of the tooth surface and micro - texture of spiral bevel gears.

Description

Technical Field

[0001] The present application relates to the technical field of gear design, and particularly to a method, system and device for collaborative optimization design of spiral bevel gear tooth surfaces and micro-textures. Background Art

[0002] The contact characteristics of spiral bevel gears during transmission directly affect the meshing transmission quality of the gear pair. Traditional gear design mainly focuses on the geometric parameters of tooth profiles and tooth surfaces, while ignoring the influence of surface microstructures on transmission performance. In recent years, micro-texture technology has received attention due to its potential in improving gear meshing and interfacial tribological performance. Applying surface textures to the surfaces of gear pairs is worth trying, but most of the existing research on surface texturing of gear pairs focuses on cylindrical gears. Therefore, the existing related technical solutions have the following problems:

[0003] 1. The correlation between the textured structure and the contact transmission performance of spiral bevel gears is unclear and lacks rationality; 2. The current micro-texture design methods are mostly for ordinary gears, and insufficient consideration is given to the spatial surface characteristics of spiral bevel gears, making it difficult to achieve the collaborative optimization of tooth surface micro-textures and overall gear design parameters. Summary of the Invention

[0004] The present application aims to propose a method, system and device for collaborative optimization design of spiral bevel gear tooth surfaces and micro-textures, which can achieve the collaborative optimization design of spiral bevel gear tooth surfaces and micro-textures.

[0005] In a first aspect, an embodiment of the present application provides a method for collaborative optimization design of spiral bevel gear tooth surfaces and micro-textures, the method comprising:

[0006] Determine the initial machining parameters of the spiral bevel gear, and construct a first spiral bevel gear tooth surface equation in the gear fixed coordinate system based on the initial machining parameters, wherein the spiral bevel gear includes a large spiral bevel gear and a small spiral bevel gear;

[0007] Convert the first spiral bevel gear tooth surface equation in the gear fixed coordinate system into a second spiral bevel gear tooth surface equation in the meshing coordinate system;

[0008] Take the tooth surface of any one of the large spiral bevel gear and the small spiral bevel gear as the reference tooth surface, and construct the target tooth surface of the other spiral bevel gear based on the second spiral bevel gear tooth surface equation and ease-off;

[0009] Construct a differential surface model based on the target tooth surface, and optimize the machining parameters based on the differential surface model to obtain new machining parameters;

[0010] Based on the new machining parameters, the reference tooth surface and the target tooth surface, perform loaded contact analysis and sensitivity analysis on the spiral bevel gear tooth surface to obtain the target machining parameters, and optimize the spiral bevel gear tooth surface according to the target machining parameters to obtain the target spiral bevel gear tooth surface;

[0011] Determine the initial micro-texture parameters, and based on the initial micro-texture parameters, place micro-textures on the target spiral bevel gear tooth surface to construct a spiral bevel gear tooth surface with micro-textures;

[0012] Construct an objective function and constraint conditions for optimizing the micro-texture parameters, and perform loaded contact analysis on the spiral bevel gear tooth surface with micro-textures to obtain the target micro-texture parameters that meet the objective function and the constraint conditions.

[0013] Compared with the prior art, the first aspect of this application has the following beneficial effects:

[0014] This method determines the initial machining parameters of the spiral bevel gear, and constructs the first spiral bevel gear tooth surface equation in the gear fixed coordinate system based on the initial machining parameters, where the spiral bevel gear includes a large spiral bevel gear and a small spiral bevel gear; converts the first spiral bevel gear tooth surface equation in the gear fixed coordinate system into the second spiral bevel gear tooth surface equation in the meshing coordinate system; takes the tooth surface of any one of the large spiral bevel gear and the small spiral bevel gear as the reference tooth surface, and constructs the target tooth surface of the other spiral bevel gear based on the second spiral bevel gear tooth surface equation and ease-off; constructs a difference surface model based on the target tooth surface, and optimizes the machining parameters based on the difference surface model to obtain new machining parameters; based on the new machining parameters, the reference tooth surface and the target tooth surface, perform loaded contact analysis and sensitivity analysis on the spiral bevel gear tooth surface to obtain the target machining parameters, and optimize the spiral bevel gear tooth surface according to the target machining parameters to obtain the target spiral bevel gear tooth surface; determine the initial micro-texture parameters, and based on the initial micro-texture parameters, place micro-textures on the target spiral bevel gear tooth surface to construct a spiral bevel gear tooth surface with micro-textures; construct an objective function and constraint conditions for optimizing the micro-texture parameters, and perform loaded contact analysis on the spiral bevel gear tooth surface with micro-textures to obtain the target micro-texture parameters that meet the objective function and the constraint conditions. In this way, after optimizing the machining parameters based on the difference surface model, perform loaded contact analysis and sensitivity analysis on the spiral bevel gear tooth surface to obtain the target machining parameters, and thus obtain the target spiral bevel gear tooth surface, which can accurately model the spiral bevel gear tooth surface. Then, by placing micro-textures on the target spiral bevel gear tooth surface and performing loaded contact analysis on the spiral bevel gear tooth surface with micro-textures to optimize the micro-texture parameters, the correlation between the tooth surface micro-texture and the contact transmission performance of the spiral bevel gear is established, thereby realizing the collaborative optimization design of the spiral bevel gear tooth surface and the micro-texture.

[0015] In some embodiments, constructing a differential surface model based on the target tooth surface and optimizing machining parameters based on the differential surface model to obtain new machining parameters includes:

[0016] Constructing a differential surface model based on the target tooth surface as:

[0017] ;

[0018] Wherein, represents discrete tooth points on the target tooth surface, represents the th discrete tooth point on the initial surface, represents the tool height, represents the tool rotation angle, represents the meshing rotation angle, represents machining parameters, , represents the radial tool position, represents the tool point radius, represents the angular tool position, represents the vertical wheel position, represents the horizontal wheel position, represents the bed position, represents the root cone mounting angle, represents the tool rotation angle, represents the tool inclination angle, represents the normal vector corresponding to the th discrete tooth point on the initial surface, represents the normal distance between the th discrete tooth points between the target tooth surface and the initial surface;

[0019] Regarding the differential surface model as a least squares problem;

[0020] Using the L-M algorithm to solve the least squares problem to obtain new machining parameters.

[0021] In some embodiments, performing a loaded contact analysis and a sensitivity analysis on the spiral bevel gear tooth surface based on the new machining parameters, the reference tooth surface, and the target tooth surface to obtain target machining parameters includes:

[0022] Obtaining the coordinates of two points to be contacted on the reference tooth surface and the target tooth surface;

[0023] Based on the coordinates of the two points to be contacted, constructing a contact condition equation;

[0024] Adding perturbations to the new machining parameters to obtain the initial contact point and the no-load transmission error;

[0025] Based on the initial contact point and the no-load transmission error, the contact condition equation is solved by the finite element method to obtain the contact position, the contact pressure distribution, and the contact deformation amount;

[0026] Based on the contact position, the contact pressure distribution, and the contact deformation amount, a contact performance evaluation index is determined;

[0027] Based on the contact performance evaluation index, the change of contact performance under different disturbances is analyzed, and a sensitivity analysis is performed on the change of contact performance to obtain highly sensitive machining parameters;

[0028] The contact deformation amount is superimposed on the target tooth surface to obtain a new target tooth surface;

[0029] Based on the new target tooth surface, the highly sensitive machining parameters are optimized to obtain optimized sensitive machining parameters;

[0030] Based on the optimized sensitive machining parameters and the new machining parameters, target machining parameters are determined.

[0031] In some embodiments, the constructing of the contact condition equation based on the coordinates of the two points to be contacted includes:

[0032] ;

[0033] Wherein, represents the input load, represents the normal pressure acting on the discrete small line segment , represents the main contact line segment, represents the position of the discrete normal pressure, represents the discrete small line segment, represents the radius of the normal pressure with respect to the axis of rotation, represents the geometric separation distance of the tooth surface calculated according to the coordinates of the two points to be contacted, represents the offset of the tooth surface contact point from the original position to the equilibrium position along the normal direction of the tooth surface, represents the equivalent Young's modulus of the gear pair, represents the equivalent radius of curvature of the gear pair, represents the machining parameter, represents the comprehensive bending and shear flexibility of the tooth, represents the coordinates of the deflection measurement point in the contact area, represents all discrete in the entire tooth surface area for integration.

[0034] In some embodiments, the implanting of micro-textures on the target spiral bevel gear tooth surface based on the initial micro-texture parameters to construct a spiral bevel gear tooth surface with micro-textures includes:

[0035] Construct a micro-texture equation based on the initial micro-texture parameters;

[0036] Place micro-textures on the tooth surface of the target spiral bevel gear according to the micro-texture equation, and construct a tooth surface of a spiral bevel gear with micro-textures.

[0037] In some embodiments, the placing micro-textures on the tooth surface of the target spiral bevel gear according to the micro-texture equation and constructing a tooth surface of a spiral bevel gear with micro-textures includes:

[0038] ;

[0039] ;

[0040] Wherein, represents the tooth surface of a spiral bevel gear with micro-textures, represents the tooth surface point coordinate in the x direction after considering micro-textures, represents the tooth surface point coordinate in the y direction after considering micro-textures, represents the tooth surface point coordinate in the z direction after considering micro-textures, represents the tooth surface point coordinate in the x direction without placing micro-textures, represents the tooth surface point coordinate in the y direction without placing micro-textures, represents the tooth surface point coordinate in the z direction without placing micro-textures, represents the tooth surface normal vector, represents the micro-texture equation, represents the tooth surface of the target spiral bevel gear, represents the tooth surface working area, represents the transition area, represents the tooth root area, represents the cutter height, represents the cutter rotation angle, represents the meshing rotation angle.

[0041] In some embodiments, the constructing the objective function and constraint conditions for optimizing the micro-texture parameters includes:

[0042] The objective function for constructing the optimized micro-texture parameters is:

[0043] ;

[0044] The constraint conditions for constructing the optimized micro-texture parameters are:

[0045] ;

[0046] Wherein, represents the small end, Indicates the tooth tip, Indicates the large end, Indicates the tooth root, Indicates the contact pattern, Indicates the micro-texture width, Indicates the oil film thickness, Indicates the oil film thickness without micro-texture, Indicates the amplitude of transmission error with micro-texture, Indicates the amplitude of transmission error without micro-texture, Indicates the stress gradient, Indicates the maximum allowable stress gradient.

[0047] In a second aspect, the embodiments of the present application further provide a system for collaborative optimization design of spiral bevel gear tooth surfaces and micro-textures, and the system includes:

[0048] A first tooth surface construction unit, configured to determine the initial machining parameters of a spiral bevel gear, and construct a first spiral bevel gear tooth surface equation in a gear fixed coordinate system based on the initial machining parameters, where the spiral bevel gear includes a large spiral bevel gear and a small spiral bevel gear;

[0049] A second tooth surface construction unit, configured to convert the first spiral bevel gear tooth surface equation in the gear fixed coordinate system into a second spiral bevel gear tooth surface equation in a meshing coordinate system;

[0050] A target tooth surface construction unit, configured to use the tooth surface of any one of the large spiral bevel gear and the small spiral bevel gear as a reference tooth surface, and construct the target tooth surface of the other spiral bevel gear based on the second spiral bevel gear tooth surface equation and ease-off;

[0051] A machining parameter optimization unit, configured to construct a differential surface model based on the target tooth surface, and optimize the machining parameters based on the differential surface model to obtain new machining parameters;

[0052] A gear tooth surface optimization unit, configured to perform loaded contact analysis and sensitivity analysis on the spiral bevel gear tooth surface based on the new machining parameters, the reference tooth surface, and the target tooth surface, obtain target machining parameters, and optimize the spiral bevel gear tooth surface according to the target machining parameters to obtain a target spiral bevel gear tooth surface;

[0053] A micro-texture placement unit, configured to determine initial micro-texture parameters, and place micro-textures on the target spiral bevel gear tooth surface based on the initial micro-texture parameters to construct a spiral bevel gear tooth surface with micro-textures;

[0054] The micro-texture parameter optimization unit is used to construct the objective function and constraint conditions for optimizing the micro-texture parameters, and perform a loaded contact analysis on the tooth surface of the spiral bevel gear with micro-textures to obtain the target micro-texture parameters that meet the objective function and the constraint conditions.

[0055] In a third aspect, an embodiment of the present application further provides an electronic device, including at least one control processor and a memory communicatively connected to the at least one control processor; the memory stores instructions executable by the at least one control processor, and when the instructions are executed by the at least one control processor, the at least one control processor is enabled to execute a method for collaborative optimization design of the tooth surface of a spiral bevel gear and micro-textures as described above.

[0056] In a fourth aspect, an embodiment of the present application further provides a computer-readable storage medium storing computer-executable instructions for causing a computer to execute a method for collaborative optimization design of the tooth surface of a spiral bevel gear and micro-textures as described above.

[0057] It can be understood that the beneficial effects of the above second aspect to the fourth aspect compared with the related art are the same as those of the above first aspect compared with the related art. For the relevant descriptions, reference can be made to the above first aspect and will not be elaborated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The above and / or additional aspects and advantages of the present application will become apparent and be readily understood from the following description of the embodiments in conjunction with the accompanying drawings, where:

[0059] Figure 1 is a schematic flowchart of an embodiment of a method for collaborative optimization design of the tooth surface of a spiral bevel gear and micro-textures provided by the present application;

[0060] Figure 2 is a schematic overall flowchart of the best embodiment of a method for collaborative optimization design of the tooth surface of a spiral bevel gear and micro-textures provided by the present application;

[0061] Figure 3 is a schematic diagram of a gear machining coordinate system in the best embodiment of a method for collaborative optimization design of the tooth surface of a spiral bevel gear and micro-textures provided by the present application;

[0062] Figure 4 is a schematic diagram of a blank discretization method in the best embodiment of a method for collaborative optimization design of the tooth surface of a spiral bevel gear and micro-textures provided by the present application;

[0063] Figure 5 is a schematic diagram of the installation position of a spiral bevel gear in the best embodiment of a method for collaborative optimization design of the tooth surface of a spiral bevel gear and micro-textures provided by the present application;

[0064] Figure 6 It is a schematic diagram of the complete conjugate surface, target tooth surface and correction principle in the best embodiment of the co - optimization design method of spiral bevel gear tooth surface and micro - texture provided by this application;

[0065] Figure 7 It is a schematic diagram of loaded contact analysis and tooth surface optimization in the best embodiment of the co - optimization design method of spiral bevel gear tooth surface and micro - texture provided by this application;

[0066] Figure 8 It is a schematic diagram of the square array texture of spiral bevel gears in the best embodiment of the co - optimization design method of spiral bevel gear tooth surface and micro - texture provided by this application;

[0067] Figure 9 It is a schematic diagram of the basic types of micro - textures in the best embodiment of the co - optimization design method of spiral bevel gear tooth surface and micro - texture provided by this application;

[0068] Figure 10 It is a schematic diagram of the structure of an embodiment of the co - optimization design system of spiral bevel gear tooth surface and micro - texture provided by this application. Detailed implementation manners

[0069] The embodiments of the present application will be described in detail below. The examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements with the same or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are only used to explain the present application and should not be construed as a limitation of the present application.

[0070] In the description of the present application, if the first, second, etc. are described, it is only for the purpose of distinguishing technical features and should not be construed as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features or implicitly indicating the sequence of the indicated technical features.

[0071] In the description of the present application, it should be understood that the orientation descriptions such as up, down, etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. It is only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present application.

[0072] In the description of the present application, it should be noted that unless otherwise clearly defined, words such as setting, installation, connection, etc. should be understood in a broad sense. Those skilled in the art can reasonably determine the specific meanings of the above words in the present application in combination with the specific content of the technical solution.

[0073] Since the existing related technical solutions have the following problems:

[0074] 1. The correlation between the textured structure and the contact transmission performance of spiral bevel gears is unclear and lacks rationality; 2. The current micro-texture design methods mostly target ordinary gears and insufficiently consider the spatial curved surface characteristics of spiral bevel gears, making it difficult to achieve the collaborative optimization of the tooth surface micro-texture and the overall design parameters of the gears.

[0075] To solve the above problems, this application proposes a method, system, and device for collaborative optimization design of the tooth surface and micro-texture of spiral bevel gears.

[0076] Referring to Figure 1 , the embodiment of this application provides a method for collaborative optimization design of the tooth surface and micro-texture of spiral bevel gears. The method includes the following steps:

[0077] Step S100: Determine the initial machining parameters of the spiral bevel gear, and construct the first spiral bevel gear tooth surface equation in the gear-fixed coordinate system based on the initial machining parameters, where the spiral bevel gear includes a large spiral bevel gear and a small spiral bevel gear;

[0078] Step S200: Convert the first spiral bevel gear tooth surface equation in the gear-fixed coordinate system into the second spiral bevel gear tooth surface equation in the meshing coordinate system;

[0079] Step S300: Take the tooth surface of any one of the large spiral bevel gear and the small spiral bevel gear as the reference tooth surface, and construct the target tooth surface of the other spiral bevel gear based on the second spiral bevel gear tooth surface equation and ease-off;

[0080] Step S400: Construct a differential surface model based on the target tooth surface, and optimize the machining parameters based on the differential surface model to obtain new machining parameters;

[0081] Step S500: Perform a loaded contact analysis and a sensitivity analysis on the spiral bevel gear tooth surface based on the new machining parameters, the reference tooth surface, and the target tooth surface to obtain the target machining parameters, and optimize the spiral bevel gear tooth surface according to the target machining parameters to obtain the target spiral bevel gear tooth surface;

[0082] Step S600: Determine the initial micro-texture parameters, and place micro-textures on the target spiral bevel gear tooth surface based on the initial micro-texture parameters to construct a spiral bevel gear tooth surface with micro-textures;

[0083] Step S700: Construct an objective function and constraint conditions for optimizing the micro-texture parameters, and perform a loaded contact analysis on the spiral bevel gear tooth surface with micro-textures to obtain the target micro-texture parameters that meet the objective function and constraint conditions.

[0084] In this embodiment, by determining the initial machining parameters of the spiral bevel gear and constructing the tooth surface equation of the first spiral bevel gear in the gear fixed coordinate system based on the initial machining parameters, where the spiral bevel gear includes a large spiral bevel gear and a small spiral bevel gear; converting the tooth surface equation of the first spiral bevel gear in the gear fixed coordinate system into the tooth surface equation of the second spiral bevel gear in the meshing coordinate system; taking the tooth surface of any one of the large spiral bevel gear and the small spiral bevel gear as the reference tooth surface, and constructing the target tooth surface of the other spiral bevel gear based on the tooth surface equation of the second spiral bevel gear and ease-off; constructing a difference surface model based on the target tooth surface, and optimizing the machining parameters based on the difference surface model to obtain new machining parameters; performing a loaded contact analysis and a sensitivity analysis on the tooth surface of the spiral bevel gear based on the new machining parameters, the reference tooth surface and the target tooth surface to obtain the target machining parameters, and optimizing the tooth surface of the spiral bevel gear according to the target machining parameters to obtain the target tooth surface of the spiral bevel gear; determining the initial micro-texture parameters, and placing micro-textures on the target tooth surface of the spiral bevel gear based on the initial micro-texture parameters to construct a tooth surface of the spiral bevel gear with micro-textures; constructing an objective function and constraint conditions for optimizing the micro-texture parameters, and performing a loaded contact analysis on the tooth surface of the spiral bevel gear with micro-textures to obtain the target micro-texture parameters that meet the objective function and constraint conditions. In this way, after optimizing the machining parameters based on the difference surface model, a loaded contact analysis and a sensitivity analysis are performed on the tooth surface of the spiral bevel gear to obtain the target machining parameters, and thus the target tooth surface of the spiral bevel gear is obtained, which can accurately model the tooth surface of the spiral bevel gear. Then, by placing micro-textures on the target tooth surface of the spiral bevel gear and performing a loaded contact analysis on the tooth surface of the spiral bevel gear with micro-textures to optimize the micro-texture parameters, the correlation between the tooth surface micro-texture and the contact transmission performance of the spiral bevel gear is established, thereby realizing the collaborative optimization design of the tooth surface of the spiral bevel gear and the micro-texture.

[0085] In some embodiments, constructing a difference surface model based on the target tooth surface and optimizing the machining parameters based on the difference surface model to obtain new machining parameters includes:

[0086] Constructing a difference surface model based on the target tooth surface is:

[0087] ;

[0088] Wherein, represents the discrete tooth points on the target tooth surface, represents the th discrete tooth point on the initial surface, represents the tool height, represents the tool rotation angle, represents the meshing rotation angle, represents the machining parameters, , represents the radial tool position, Denotes the cutter location point radius, Denotes the angular cutter location, Denotes the vertical wheel position, Denotes the horizontal wheel position, Denotes the bed position, Denotes the root cone mounting angle, Denotes the cutter rotation angle, Denotes the cutter rake angle, Denotes the th discrete tooth surface point of the initial surface corresponding normal vector, Denotes the normal distance between the th discrete tooth surface point of the target tooth surface and the initial tooth surface;

[0089] Regard the difference surface model as a least squares problem;

[0090] Use the L-M algorithm to solve the least squares problem to obtain new machining parameters.

[0091] In some embodiments, based on the new machining parameters, the reference tooth surface and the target tooth surface, perform a loaded contact analysis and a sensitivity analysis on the spiral bevel gear tooth surface to obtain the target machining parameters, including:

[0092] Obtain the coordinates of two points to be contacted on the reference tooth surface and the target tooth surface;

[0093] Based on the coordinates of the two points to be contacted, construct a contact condition equation;

[0094] Add perturbations to the new machining parameters to obtain the initial contact point and the no-load transmission error;

[0095] Based on the initial contact point and the no-load transmission error, use the finite element method to solve the contact condition equation to obtain the contact position, the contact pressure distribution, and the contact deformation;

[0096] Based on the contact position, the contact pressure distribution, and the contact deformation, determine the contact performance evaluation index;

[0097] Based on the contact performance evaluation index, analyze the change of contact performance under different perturbations, and perform a sensitivity analysis on the change of contact performance to obtain the highly sensitive machining parameters;

[0098] Superimpose the contact deformation on the target tooth surface to obtain a new target tooth surface;

[0099] Optimize the highly sensitive machining parameters based on the new target tooth surface to obtain the optimized sensitive machining parameters;

[0100] Based on the optimized sensitive machining parameters and the new machining parameters, determine the target machining parameters.

[0101] In this embodiment, contact performance evaluation indexes are obtained through contact performance analysis, and then sensitivity analysis is carried out based on the contact performance evaluation indexes, so that highly sensitive machining parameters can be obtained. Only these highly sensitive machining parameters need to be optimized again, and non-highly sensitive machining parameters do not need to be optimized again, which improves the efficiency of machining parameter optimization and enables the accurate modeling of the spiral bevel gear tooth surface in the later stage.

[0102] In some embodiments, based on the coordinates of two points to be contacted, a contact condition equation is constructed, including:

[0103] ;

[0104] Among them, represents the input load, represents the normal pressure acting on the discrete small line segment ; represents the main contact line segment, represents the position of the discrete normal pressure, represents the discrete small line segment, represents the radius of the normal pressure with respect to the axis of rotation, represents the geometric separation distance of the tooth surface calculated according to the coordinates of the two points to be contacted, represents the offset of the tooth surface contact point from the original position to the equilibrium position along the normal direction of the tooth surface, represents the equivalent Young's modulus of the gear pair, represents the equivalent radius of curvature of the gear pair, represents the machining parameter, represents the comprehensive bending and shear flexibility of the tooth, represents the coordinates of the deflection measurement point in the contact area, represents integrating all discrete in the entire tooth surface area.

[0105] In some embodiments, based on the initial micro-texture parameters, micro-textures are placed on the tooth surface of the target spiral bevel gear to construct a spiral bevel gear tooth surface with micro-textures, including:

[0106] Based on the initial micro-texture parameters, a micro-texture equation is constructed;

[0107] According to the micro-texture equation, micro-textures are placed on the tooth surface of the target spiral bevel gear to construct a spiral bevel gear tooth surface with micro-textures.

[0108] In this embodiment, by placing micro-textures on the tooth surface of the target spiral bevel gear, a good data foundation is laid for the later loading contact analysis.

[0109] In some embodiments, according to the micro-texture equation, micro-textures are placed on the tooth surface of the target spiral bevel gear to construct a spiral bevel gear tooth surface with micro-textures, including:

[0110] ;

[0111] ;

[0112] where, represents the spiral bevel gear tooth surface with micro-textures, represents the tooth point coordinate in the x direction after considering the micro-textures, represents the tooth point coordinate in the y direction after considering the micro-textures, represents the tooth point coordinate in the z direction after considering the micro-textures, represents the tooth point coordinate in the x direction without micro-textures, represents the tooth point coordinate in the y direction without micro-textures, represents the tooth point coordinate in the z direction without micro-textures, represents the tooth point normal vector, represents the micro-texture equation, represents the target spiral bevel gear tooth surface, represents the tooth surface working area, represents the transition area, represents the tooth root area, represents the cutter height, represents the cutter rotation angle, represents the meshing rotation angle.

[0113] In some embodiments, an objective function and constraint conditions for optimizing the micro-texture parameters are constructed, including:

[0114] The objective function for optimizing the micro-texture parameters is:

[0115] ;

[0116] The constraint conditions for optimizing the micro-texture parameters are:

[0117] ;

[0118] where, represents the small end, represents the tooth tip, represents the large end, represents the tooth root, represents the contact pattern, represents the micro-texture width, represents the oil film thickness, represents the oil film thickness without micro-textures, Denote the amplitude of transmission error with micro-texture inserted Denote the amplitude of transmission error without micro-texture inserted Denote the stress gradient Denote the maximum allowable stress gradient

[0119] In this embodiment, by constructing the objective function and constraint conditions for optimizing the micro-texture parameters, the optimized target micro-texture parameters conform to the objective function and constraint conditions, so that the load-carrying capacity of the optimized spiral bevel gear is the best

[0120] For the convenience of those skilled in the art to understand, the following provides a set of best embodiments

[0121] This embodiment aims to solve some problems existing in the prior art: the correlation between the textured structure and the contact transmission performance of spiral bevel gears is unclear and lacks rationality; the current micro-texture design methods mostly target ordinary gears and insufficiently consider the spatial curved surface characteristics of spiral bevel gears, making it difficult to achieve the collaborative optimization of the tooth surface micro-texture and the overall design parameters of the gear. This embodiment proposes a collaborative optimization design method for the tooth surface and micro-texture of spiral bevel gears based on loaded contact analysis. Referring to Figure 2 , the technical solution of this embodiment specifically includes the following steps

[0122] Step 1. Establish the tooth surface equation of the spiral bevel gear

[0123] Through the numerical simulation of spiral bevel gear machining, an accurate tooth surface equation of the spiral bevel gear is established, providing input for the loaded contact analysis of the spiral bevel gear and the construction of the gear model with micro-texture. The specific implementation method is as follows

[0124] Step 1.1. Based on the established cutter disc equation, the gear machining coordinate system is as Figure 3 shown. From the numerical simulation of the spiral bevel gear machining process and the meshing principle, the tooth surface equation of the spiral bevel gear is derived. Among them, the spiral bevel gear includes a large spiral bevel gear (i.e., the large wheel) and a small spiral bevel gear (i.e., the small wheel).

[0125] is the coordinate system fixed to the cutter disc (i.e., the gear fixed coordinate system), and the cutter disc equation in the coordinate system can be expressed as

[0126] (1);

[0127] Among them, denotes the cutter disc radius denotes the tool pressure angle. In the case of considering tool modification, it needs to be remapped by establishing a hypothetical straight tool, and the establishment of the hypothetical straight tool is a well-known technology in the art, which is not specifically described in this embodiment Denote the cutter surface parameters, Denote the cutter rotation angle, Denote the cutter height, Denote the small spiral bevel gear, Denote the large spiral bevel gear.

[0128] The tooth surface equation of the spiral bevel gear can be derived from the relative relationship between the cutter and the blank during the machining process, and can be written based on the universal motion concept as:

[0129] (2);

[0130] Among them, Denote the equation of the cutter surface cluster, Denote the coordinate transformation matrix, Denote the workpiece, Denote the cutter, whose specific form is related to the specific machining method, Denote the radial tool position, Denote the radius of the tool point, Denote the angular tool position, Denote the vertical wheel position, Denote the horizontal wheel position, Denote the bed position, Denote the root cone mounting angle, Denote the cutter rotation angle, Denote the cutter inclination angle, Denote the swing angle of the cradle, Denote the cutter normal vector.

[0131] The tooth surface of the spiral bevel gear is enveloped by a cylindrical cutter and satisfies the following meshing equation:

[0132] (3);

[0133] Among them, Denote the tooth surface equation of the spiral bevel gear (i.e., the tooth surface equation of the first spiral bevel gear), Denote the value of the cutter normal vector in the machining coordinate system, Denote the relative velocity between the cutter and the blank.

[0134] Step 1.2. Solve the tooth surface equation.

[0135] Equation (3) can be solved by discretizing the blank to obtain regular tooth points, providing a basis for subsequent topology optimization. The specific implementation process is as follows:

[0136] Figure 4In (a), it is the motion trajectory of the boundary points of the simulated tool profile. The dividing lines (i.e., the root region) of the working area, transition area, and root fillet of the tooth surface are obtained from Equation (2) in Step 1.1, projected onto the two-dimensional drawing of the gear blank, and the two-dimensional projection area of the spiral bevel gear blank is divided and evenly discretized, as shown in Figure 4 Figure (b).

[0137] Due to the uniform discretization of the tooth surface area, there is:

[0138] (4);

[0139] In the formula, , , represents the components along the x, y, and z axes in the gear-fixed coordinate system, represents the distance of the discrete point from the axis of rotation of the gear blank, represents the distance of the discrete point from the apex of the pitch cone of the gear blank. Regular tooth surface points are obtained by combining Equation (2), Equation (3), and Equation (4).

[0140] Step 2. Tooth surface design scheme.

[0141] Taking the transmission error, contact pattern position, and contact pattern size requirements as constraint conditions, the initial machining parameters are determined. The machining parameters of the pinion can be determined, or the machining parameters of the gear can be determined. If the machining parameters of the pinion are determined, the tooth surface of the gear is taken as the reference; if the machining parameters of the gear are determined, the tooth surface of the pinion is taken as the reference.

[0142] Step 2.1. Spiral bevel gear contact analysis model: The installation position of the spiral bevel gear is shown in Figure 5. The tooth surface equation in the gear-fixed coordinate system is transformed to the meshing coordinate system so that the pinion and gear of the gear pair are represented by a unified coordinate system. For a tooth surface contact point at a certain moment, there are the following formulas:

[0143] (5);

[0144] Among them, represents the tooth surface equation of the spiral bevel gear in the meshing coordinate system (i.e., the tooth surface equation of the second spiral bevel gear), represents the transformation matrix from the gear-fixed coordinate system to the meshing coordinate system, represents the shaft angle, represents the rotation angle of the gear pair from the initial position to the meshing position, i.e., the meshing rotation angle. According to the differential geometry continuous contact condition of the surface, there are the following formulas:

[0145] (6);

[0146] Among them, represents the radial vector of the contact point on the pinion, represents the radial vector of the contact point on the gear, represents the normal vector of the contact point on the pinion, represents the normal vector of the contact point on the gear.

[0147] 2.2. Solving machining parameters.

[0148] 2.2.1. Constructing the target tooth surface based on ease-off. Specifically, based on the reference tooth surface of the pinion, transmission error, and contact pattern constraints, the target tooth surface of the pinion is constructed. The ease-off in this embodiment is a prior art and will not be described in detail in this embodiment.

[0149] To construct the target tooth surface of the pinion, that is, the optimized tooth surface of the pinion , first, a reference surface needs to be constructed . Based on the determined machining parameters, through step 1, the spiral bevel gear tooth surface of the gear is obtained . and need to satisfy the constraint: having the same motion law relative to the gear tooth surface . Therefore, according to the line contact principle, the fully conjugate surface of the gear is obtained, that is . When the pinion tooth surface and the gear tooth surface are fully conjugate, assuming a symmetric parabolic transmission error is preset, the meshing angle of the gear and the meshing angle of the pinion satisfy:

[0150] (7);

[0151] Among them, represents the meshing rotation angle of the pinion, represents the meshing rotation angle of the gear, represents the meshing rotation angle at the design reference point of the gear, represents the meshing rotation angle at the design reference point of the pinion, represents the number of teeth of the pinion, represents the number of teeth of the gear, represents the amplitude of the no-load transmission error at the meshing conversion point. From equation (5), the rotation angle when any point on the gear tooth surface enters the meshing position can be solved, and the corresponding meshing rotation angle of the pinion can be obtained by solving equation (7). Further, substituting and into equation (6), the pinion tooth surface that is fully conjugate to the gear and satisfies the symmetric parabolic transmission error can be obtained . It is necessary to preset the contact trace and modification along the meshing line direction for the pinion. As shown in Figure 6, the surface For any point on the surface of the pinion, the coordinate values (L, R) in the rotational projection section still need to satisfy Equation (4).

[0152] When optimizing the tooth surface contact performance, usually only the pinion tooth surface is optimized. Therefore, the optimized surface of the gear is identical to However, the gear tooth surface can also be optimized. Therefore, the optimized surface of the pinion is identical to In this embodiment, the tooth surface contact performance of the pinion is optimized as an example. Therefore, the target tooth surface of the pinion is constructed in Step 2.2.1. It should be noted that in this embodiment, the tooth surface contact performance of the gear can also be optimized, that is, the target tooth surface of the gear can be constructed in the same way of ease-off in Step 2.2.1. In the tooth surface contact performance optimization, the optimization methods of the gear and the pinion are basically the same, and will not be repeated in this embodiment. According to the mapping relationship between the ease-off surface and the transmission error and contact performance, the optimized tooth surfaces of the gear pair can be obtained from the preset no-load transmission error amplitude , contact path and major axis of the instantaneous contact ellipse and .

[0153] 2.2.2. Solving machining parameters

[0154] The initial machining parameters of the gear and the pinion are obtained from the blank parameters of the gear pair and the principle of local conjugation, and the surface of the gear is established and the initial surface of the pinion . And they are input into Step 2.2.1 to obtain the optimized tooth surface of the pinion (which is also called the target tooth surface in the text because it is the optimization target of the subsequent optimization algorithm) . Based on the target tooth surface of the pinion and the initial surface of the pinion , a differential surface model is constructed:

[0155] (8);

[0156] where represents the discrete tooth points on the target tooth surface, represents the normal distance between the target tooth surface and the initial surface at the th discrete tooth point. Equation (8) can be regarded as a least squares problem:

[0157] (9);

[0158] Based on the L-M algorithm, the new machining parameters are obtained.

[0159] 2.3. Tooth surface model update.

[0160] Input the machining parameters output in 2.2 into Step 1 to obtain the updated tooth surface equation of the spiral bevel gear.

[0161] Step 3: Spiral bevel gear loaded contact model.

[0162] Based on the contact condition equation, establish the loaded contact model of the spiral bevel gear, solve it by combining the finite element method, and obtain the loaded contact imprint (which can be obtained through the contact position and pressure distribution) and the tooth surface deformation. By changing the machining parameters, explore their influence on the contact performance, and conduct a sensitivity analysis to screen the machining parameters that have a greater impact on the contact performance. According to the sensitivity analysis results, formulate a tooth surface optimization strategy, and loop through Step 2 to finally obtain the tooth surface design scheme with the optimal contact performance of the gear pair under specific working conditions.

[0163] 3.1. Spiral bevel gear loaded contact analysis.

[0164] When the and coordinates and the no-load transmission error are known, the loaded contact analysis process is shown in Figure 7. and are the two points to be contacted on the pinion tooth surface and the gear tooth surface respectively. After applying a load to the spiral bevel gear pair, it is necessary to eliminate the tooth geometry clearance and balance the load. Segment the main contact line , and set the length of each discrete small line segment to . The contact condition equation is expressed as:

[0165] (10);

[0166] Among them, represents the input load, represents the normal pressure acting on the discrete small line segment , represents the main contact line segment, represents the position of the discrete normal pressure, represents the discrete small line segment, represents the radius of the normal pressure with respect to the axis of rotation, represents the geometric separation distance of the tooth surface calculated according to the coordinates of the two points to be contacted, represents the offset of the tooth surface contact point along the tooth surface normal direction from the original position to the equilibrium position, represents the equivalent Young's modulus of the gear pair, , represents the equivalent radius of curvature of the gear pair, , denotes the Poisson's ratio, and the subscripts 1 and 2 denote the pinion and the gear respectively, denotes the machining parameters, denotes the comprehensive bending and shear flexibility of the tooth, denotes the coordinates of the deflection measurement points in the contact area, denotes all discrete in the entire tooth surface area for integration.

[0167] Based on the finite element method, the contact condition equation is solved to obtain the contact position, contact pressure distribution and contact deformation. By applying the vector rotation algorithm (the vector rotation algorithm is a well-known technology in the art and is not specifically described in this embodiment), the no-load transmission error can be effectively obtained. From the contact position and contact pressure distribution, by applying the contact pattern visualization technology, the distance between the pattern and the tooth surface boundary is used as one of the important evaluation indexes of the contact performance. Given the pressure distribution and contact deformation, the maximum contact stress can also be calculated. The maximum contact stress on the tooth surface and the amplitude of the loaded transmission error are also used as evaluation indexes of the contact performance. Combined with the distance between the pattern and the tooth surface boundary, it provides a scientific basis for the optimization of the tooth surface.

[0168] 3.2. Tooth surface optimization strategy.

[0169] By introducing small perturbations into the initial machining parameters, comparing the changes in the tooth surface contact performance under different perturbation conditions, deeply analyzing the influence of each machining parameter on the tooth surface contact performance, and conducting a sensitivity analysis. According to the results of the sensitivity analysis, the key machining parameters that have a greater impact on the tooth surface contact performance are screened out. Combining the multi-objective optimization requirements such as tooth surface contact stress and transmission error, targeted tooth surface optimization strategies are formulated for these key machining parameters. To improve the optimization calculation efficiency and comprehensively consider the multi-objective optimization requirements such as tooth surface contact stress and transmission error, the following optimization strategy is specially formulated: The highly sensitive machining parameters that have a more significant impact on the target are selected as the optimization variables, while the remaining machining parameters are kept consistent with the initial machining parameters in 2.2.2. Subsequently, the expected tooth surface deformation is superimposed on the target tooth surface constructed in step 2.2.1 to form a new target tooth surface. The problem of approximating the target tooth surface is transformed into a least squares problem, and the L-M algorithm is used to accurately solve the machining parameters (i.e., obtain the target machining parameters). Through this series of optimization measures, the purpose of optimizing the loaded contact performance of the tooth surface is finally achieved to obtain the target spiral bevel gear tooth surface.

[0170] Step 4, Micro-texture design and topology optimization method for spiral bevel gears.

[0171] After the operations of Step 1, Step 2, and Step 3, the spiral bevel gear pair without micro-texture features that meets the requirements has been successfully designed. Based on the constraints of oil film formation conditions and contact performance, optimize the geometric parameters of the micro-texture (such as depth, spacing, and shape, etc.) to promote the stable formation of the lubricating film and reduce the impact on the load-carrying capacity; establish a tooth surface micro-texture model and place it on the tooth surface of the spiral bevel gear to form a spiral bevel gear model that comprehensively considers tooth surface modification and micro-texture; input the tooth surface loaded contact performance obtained in Step 3; apply the topology optimization method to optimize the distribution and size of the micro-texture to further improve the load-carrying capacity and lubrication effect of the tooth surface.

[0172] 4.1. Micro-texture placement and gear model construction.

[0173] According to the bionic similarity principle, select the micro-texture with anti-wear and anti-friction functions. Based on the results of the bearing contact analysis of the gear after preliminary modification (that is, the optimized target spiral bevel gear tooth surface equation obtained through Steps 1 to 3 without adding micro-texture), then select the micro-texture placement area and micro-texture parameters on the tooth surface. The micro-texture in this embodiment adopts a square array of pits, and the parameters of the square array texture include width , depth , axial spacing , circumferential spacing , depth-to-diameter ratio and density . Among them,

[0174] (11);

[0175] (12);

[0176] On the normal direction of the gear, construct the micro-texture as shown in Figure 8. Consider establishing the micro-texture equation as:

[0177] (13);

[0178] Map the micro-texture to the tooth surface of the spiral bevel gear with ideal contact performance (that is, the target spiral bevel gear tooth surface obtained in Step 3) to obtain the mathematical model of the spiral bevel gear tooth surface containing the micro-texture:

[0179] (14);

[0180] (15);

[0181] Among them, represents the tooth surface of the spiral bevel gear containing the micro-texture, represents the tooth surface point coordinates in the x direction considering the micro-texture, Denote the tooth surface point coordinates in the y direction after considering micro-textures. Denote the tooth surface point coordinates in the z direction after considering micro-textures. Denote the tooth surface point coordinates in the x direction without micro-textures implanted. Denote the tooth surface point coordinates in the y direction without micro-textures implanted. Denote the tooth surface point coordinates in the z direction without micro-textures implanted. Denote the tooth surface normal vector. Denote the micro-texture equation. Denote the tooth surface of the target spiral bevel gear, that is, the tooth surface without micro-textures implanted. The equation differentiates the tooth surface area, as shown in Figure 8. Denote the working area of the tooth surface. Denote the transition area. Denote the tooth root area. The tooth surface without micro-textures implanted refers to the tooth surface of a spiral bevel gear with ideal contact performance. The tooth surface point coordinates, tooth root area, working area of the tooth surface, and transition area without micro-textures implanted can be calculated in the same way as in Step 1.2, and will not be described repeatedly here.

[0182] 4.2. Determination of initial micro-texture parameters.

[0183] Refer to Figure 9 , Figure 9 In which (a), (b), (c), and (d) are all basic micro-texture types. Define different basic micro-texture types and select the texture type. When selecting micro-texture parameters, it is necessary to ensure that they meet the oil film formation conditions and at the same time minimize the weakening effect on the gear load-carrying capacity. Taking the square array of pits as an example, the preliminary selection of its parameters should follow the following principles:

[0184] 1) Width : During the transmission process of spiral bevel gears, due to the unique curved surface contact of spiral bevel gears, the area of the instantaneous contact region is very small. If the micro-texture size is too small, it cannot effectively store lubricating oil and abrasive debris; if the size is too large, it will cause lubricating oil to escape, increase the contact stress, and weaken the load-carrying capacity of the gear pair. Select the length of the minor semi-axis of the contact ellipse as the initial design value of the micro-texture width .

[0185] 2) Depth : The depth of the micro-texture has a significant impact on the lubrication performance of the specimen surface. Too shallow a depth will damage the boundary layer and cannot store lubricating oil and abrasive debris; too deep a depth will make it difficult to form a high hydrodynamic pressure and cannot effectively improve the lubrication performance. Select 100μm as the initial design value of the micro-texture depth .

[0186] 3) Density :The micro-texture density has a significant impact on the performance of the surface micro-texture and the contact stress of the contact surface. Research shows that when the micro-texture density is in the range of 10% to 30%, the micro-texture can effectively play the role of friction reduction and anti-wear. 30% is selected as the initial design value of the micro-texture density of the initial design value.

[0187] (16);

[0188] 4.3. Topological optimization.

[0189] Taking the square array of pits as an example, topological optimization is carried out based on the variable density method. The optimization region is discretized with a finite number of grid cells, and a density value of 0 or 1 is assigned to each grid cell, where 0 means the grid cell does not contain material and 1 means the grid cell is filled with material. Through the binary material distribution method, the structural distribution of the optimization region is discretely simulated, and then the refined material layout design is realized. To make the optimized spiral bevel gear have the best load-carrying capacity, the maximization of the contact footprint is taken as the objective function, that is, the distances of the contact footprint from the large end, small end, tooth tip, and tooth root are minimized. The load transmission error TE , no stress concentration at the texture edge, no stress concentration at the texture edge are used as constraints. No stress concentration in the tooth surface area can also be expressed as the distances from the contact footprint to the small end, tooth tip, large end, and tooth root are non-negative numbers.

[0190] The mathematical model of topological optimization is expressed as follows:

[0191] Objective function:

[0192] (17);

[0193] Constraint conditions:

[0194] (18);

[0195] Among them, represents the small end, represents the tooth tip, represents the large end, represents the tooth root, represents the contact footprint, represents the distances from the contact footprint to the small end, tooth tip, large end, and tooth root, represents the width of the micro-texture, represents the oil film thickness, represents the oil film thickness without the micro-texture, and this value can be obtained by fluid calculation and analysis through the equivalent point contact model, represents the amplitude of the transmission error with the micro-texture, represents the amplitude of the transmission error without the micro-texture, represents the stress gradient, Represents the maximum allowable stress gradient [1].

[0196] Step 5, iterative optimization: Loop through Step 3, by adjusting the contact imprint and transmission error curve, select different types of micro-textures, and execute Step 4 to establish a spiral bevel gear model with implanted micro-textures, obtain the optimal parameters under the current micro-texture type, and obtain the collaborative design of the spiral bevel gear tooth surface and micro-texture with the optimal contact performance at the gear pair interface under specific working conditions.

[0197] Compared with the prior art, the technical solution of this embodiment has the following advantages:

[0198] (1) Explore the correlation between the characteristic parameters such as the shape, size, density, and distribution form of the bionic micro-texture on the tooth surface and the loaded contact analysis of the spiral bevel gear tooth surface, and provide a basis for the reasonable design of micro-texture parameters.

[0199] (2) Ensure the rationality of the tooth surface and micro-texture design, meet the actual performance requirements, reduce the number of design iterations, and improve the design efficiency.

[0200] Refer to Figure 10 , this application embodiment also provides a collaborative optimization design system for the spiral bevel gear tooth surface and micro-texture. This system includes a first tooth surface construction unit 100, a second tooth surface construction unit 200, a target tooth surface construction unit 300, a machining parameter optimization unit 400, a gear tooth surface optimization unit 500, an implanted micro-texture unit 600, and a micro-texture parameter optimization unit 700, where:

[0201] The first tooth surface construction unit 100 is used to determine the initial machining parameters of the spiral bevel gear and construct the first spiral bevel gear tooth surface equation in the gear fixed coordinate system, where the spiral bevel gear includes a large spiral bevel gear and a small spiral bevel gear;

[0202] The second tooth surface construction unit 200 is used to convert the first spiral bevel gear tooth surface equation in the gear fixed coordinate system into the second spiral bevel gear tooth surface equation in the meshing coordinate system;

[0203] The target tooth surface construction unit 300 is used to use the tooth surface of any one of the large spiral bevel gear and the small spiral bevel gear as the reference tooth surface, and construct the target tooth surface of the other spiral bevel gear based on the second spiral bevel gear tooth surface equation and ease-off;

[0204] The machining parameter optimization unit 400 is used to construct a differential surface model based on the target tooth surface and optimize the machining parameters based on the differential surface model to obtain new machining parameters;

[0205] The gear tooth surface optimization unit 500 is used to perform loaded contact analysis and sensitivity analysis on the spiral bevel gear tooth surface based on new machining parameters, a reference tooth surface, and a target tooth surface, obtain target machining parameters, and optimize the spiral bevel gear tooth surface according to the target machining parameters to obtain a target spiral bevel gear tooth surface;

[0206] The micro-texture unit 600 is configured to determine initial micro-texture parameters and, based on the initial micro-texture parameters, implant micro-textures on the target spiral bevel gear tooth surface to construct a spiral bevel gear tooth surface with micro-textures;

[0207] The micro-texture parameter optimization unit 700 is used to construct an objective function and constraint conditions for optimizing micro-texture parameters, and perform loaded contact analysis on the spiral bevel gear tooth surface with micro-textures to obtain target micro-texture parameters that meet the objective function and constraint conditions.

[0208] It should be noted that since the spiral bevel gear tooth surface and micro-texture collaborative optimization design system in this embodiment is based on the same inventive concept as the above-mentioned spiral bevel gear tooth surface and micro-texture collaborative optimization design method, the corresponding content in the method embodiment also applies to this system embodiment and will not be elaborated here.

[0209] This application embodiment also provides an electronic device, including: at least one control processor and a memory for communicatively connecting with at least one control processor.

[0210] The memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. In addition, the memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one magnetic disk storage device, a flash memory device, or other non-transitory solid-state storage devices. In some embodiments, the memory may optionally include a memory remotely disposed relative to the processor, and these remote memories may be connected to the processor through a network. Examples of the above networks include, but are not limited to, the Internet, an enterprise intranet, a local area network, a mobile communication network, and combinations thereof.

[0211] The non-transitory software programs and instructions required to implement the spiral bevel gear tooth surface and micro-texture collaborative optimization design method of the above embodiment are stored in the memory and, when executed by the processor, execute the spiral bevel gear tooth surface and micro-texture collaborative optimization design method in the above embodiment. For example, execute the Figure 1 method steps S100 to step S700 described above.

[0212] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, that is, they may be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0213] The embodiments of the present application also provide a computer-readable storage medium. The computer-readable storage medium stores computer-executable instructions. When the computer-executable instructions are executed by one or more control processors, the one or more control processors can be enabled to execute a method for collaborative optimization design of the tooth surface of a spiral bevel gear and micro-texture in the above method embodiments. For example, execute the functions of method steps S100 to S700 described above. Figure 1

[0214] Those of ordinary skill in the art can understand that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and their appropriate combinations. Some physical components or all physical components can be implemented as software executed by a processor, such as a central processing unit, a digital signal processor, or a microprocessor, or implemented as hardware, or implemented as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include a computer storage medium (or non-transitory medium) and a communication medium (or transitory medium). As is well known to those of ordinary skill in the art, the term computer storage medium includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information, such as computer-readable instructions, data structures, program modules, or other data. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cassette, tape, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store the desired information and can be accessed by a computer. In addition, as is well known to those of ordinary skill in the art, a communication medium typically includes computer-readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave or other transmission mechanism, and can include any information delivery medium.

[0215] The above is a specific description of the preferred embodiments of the present application. However, the embodiments of the present application are not limited to the above embodiments. Those skilled in the art can make various equivalent deformations or substitutions without departing from the spirit of the embodiments of the present application. These equivalent deformations or substitutions are all included within the scope defined by the claims of the embodiments of the present application.

[0216] The embodiments of the present application have been described in detail above with reference to the accompanying drawings. However, the present application is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present application within the scope of knowledge possessed by those of ordinary skill in the art to which the present application pertains.

Claims

1. A method for collaborative optimization design of spiral bevel gear tooth surface and micro texture, characterized in that: The method comprises: Determine initial processing parameters of the spiral bevel gear, and construct a first spiral bevel gear tooth surface equation in a gear fixed coordinate system based on the initial processing parameters, wherein the spiral bevel gear includes a large spiral bevel gear and a small spiral bevel gear; Convert the tooth surface equation of the first spiral bevel gear in the gear fixed coordinate system into the tooth surface equation of the second spiral bevel gear in the meshing coordinate system; Taking the tooth surface of any one of the large spiral bevel gear and the small spiral bevel gear as a reference tooth surface, and constructing a target tooth surface of the other spiral bevel gear based on the tooth surface equation and ease-off of the second spiral bevel gear; Constructing a difference surface model based on the target tooth surface, and optimizing machining parameters based on the difference surface model to obtain new machining parameters; Based on the new processing parameters, the reference tooth surface and the target tooth surface, a loading contact analysis and a sensitivity analysis are performed on the tooth surface of the spiral bevel gear to obtain the target processing parameters, and the tooth surface of the spiral bevel gear is optimized according to the target processing parameters to obtain the target spiral bevel gear tooth surface; Determining initial micro-texture parameters, and based on the initial micro-texture parameters, placing micro-texture on the target spiral bevel gear tooth surface to construct a spiral bevel gear tooth surface containing micro-texture; An objective function and constraint conditions for optimizing micro-texture parameters are constructed, and a loading contact analysis is performed on the tooth surface of the spiral bevel gear containing micro-texture to obtain target micro-texture parameters that meet the objective function and the constraint conditions, wherein: The objective function for optimizing microtexture parameters is constructed as follows: ； The constraints for constructing the optimized microtexture parameters are: ； in, Represents little endian, Indicates the tooth top, Indicates big endian, Indicates tooth root, Indicates contact marks, represents the microtexture width, Indicates the oil film thickness, represents the oil film thickness without micro-texture, represents the amplitude of the transmission error of the inserted microtexture, represents the transmission error amplitude without micro-texture, represents the stress gradient, Represents the maximum allowable stress gradient.

2. The spiral bevel gear tooth surface and micro-texture collaborative optimization design method according to claim 1, characterized in that: The step of constructing a difference surface model based on the target tooth surface and optimizing machining parameters based on the difference surface model to obtain new machining parameters includes: The difference surface model constructed based on the target tooth surface is: ； in, represents the discrete tooth surface points on the target tooth surface, Represents the first discrete tooth surface points, Indicates the tool height, Indicates the tool rotation angle, represents the meshing angle, Indicates the processing parameters, , Indicates radial tool position, Indicates the tool position radius, Indicates the angular tool position. Indicates the vertical wheel position, Indicates the horizontal wheel position, Indicates bed space, represents the root cone installation angle, Indicates the knife turning angle, Indicates the blade inclination angle, The initial surface The normal vector corresponding to the discrete tooth surface point is The distance between the target tooth surface and the initial surface Normal distance of discrete tooth surface points; The difference surface model is regarded as a least squares problem; The LM algorithm is used to solve the least squares problem and obtain new processing parameters.

3. The spiral bevel gear tooth surface and micro-texture collaborative optimization design method according to claim 1, characterized in that: The step of performing loading contact analysis and sensitivity analysis on the spiral bevel gear tooth surface based on the new processing parameters, the reference tooth surface and the target tooth surface to obtain the target processing parameters includes: Acquire coordinates of two to-be-contacted points on the reference tooth surface and the target tooth surface; Based on the coordinates of the two points to be contacted, a contact condition equation is constructed; Adding disturbance to the new processing parameters to obtain an initial contact point and a no-load transfer error; Based on the initial contact point and the no-load transfer error, the contact condition equation is solved by using a finite element method to obtain a contact position, a contact pressure distribution, and a contact deformation; Determining a contact performance evaluation index based on the contact position, the contact pressure distribution, and the contact deformation; Based on the contact performance evaluation index, the contact performance changes under different disturbances are analyzed, and the sensitivity analysis of the contact performance changes is performed to obtain highly sensitive processing parameters; superimposing the contact deformation onto the target tooth surface to obtain a new target tooth surface; Optimizing the highly sensitive machining parameters based on the new target tooth surface to obtain optimized sensitive machining parameters; Based on the optimized sensitive processing parameters and the new processing parameters, target processing parameters are determined.

4. The method for collaborative optimization design of spiral bevel gear tooth surface and micro texture according to claim 3, characterized in that: The step of constructing a contact condition equation based on the coordinates of the two points to be contacted comprises: ； in, represents the input load, Indicates that it acts on discrete small line segments The positive pressure on represents the main contact line segment, represents the location of the discrete positive pressure, represents a discrete small line segment, It represents the radius of the normal pressure on the rotating axis, represents the tooth surface geometric separation distance calculated according to the coordinates of the two contact points, It represents the displacement of the tooth surface contact point from the original position to the equilibrium position along the normal direction of the tooth surface. represents the equivalent Young's modulus of the gear pair, represents the equivalent radius of curvature of the gear pair, Indicates the processing parameters, represents the combined bending and shear flexibility of the gear teeth, represents the coordinates of the deflection measurement points in the contact area, Represents all discrete Find the integral.

5. The method for collaborative optimization design of spiral bevel gear tooth surface and micro texture according to claim 1, characterized in that: The method of inserting micro texture on the tooth surface of the target spiral bevel gear based on the initial micro texture parameter to construct the tooth surface of the spiral bevel gear containing micro texture comprises: Based on the initial micro-texture parameters, constructing a micro-texture equation; According to the micro-texture equation, micro-texture is placed on the tooth surface of the target spiral bevel gear to construct the tooth surface of the spiral bevel gear containing micro-texture.

6. The method for collaborative optimization design of spiral bevel gear tooth surface and micro texture according to claim 5, characterized in that: According to the micro-texture equation, micro-texture is placed on the tooth surface of the target spiral bevel gear to construct the tooth surface of the spiral bevel gear containing micro-texture, including: ； ； in, represents the spiral bevel gear tooth surface with micro texture, represents the coordinates of the tooth surface points in the x direction after considering the microtexture, represents the coordinates of the tooth surface points in the y direction after considering the microtexture, represents the coordinates of the tooth surface point in the z direction after considering the microtexture, represents the coordinates of the tooth surface point in the x direction without micro-texture, represents the coordinates of the tooth surface point in the y direction without micro-texture, represents the coordinates of the tooth surface point in the z direction without micro-texture, represents the normal vector of the tooth surface point, represents the microtexture equation, represents the target spiral bevel gear tooth surface, Indicates the working area of ​​the tooth surface, Indicates the transition area. represents the tooth root area, Indicates the tool height, Indicates the tool rotation angle, Represents the engagement angle.

7. A spiral bevel gear tooth surface and micro-texture collaborative optimization design system, characterized in that: The system comprises: A first tooth surface construction unit, used for determining initial processing parameters of the spiral bevel gear, and constructing a first spiral bevel gear tooth surface equation in a gear fixed coordinate system based on the initial processing parameters, wherein the spiral bevel gear includes a large spiral bevel gear and a small spiral bevel gear; A second tooth surface construction unit, used for converting the tooth surface equation of the first spiral bevel gear in the gear fixed coordinate system into the tooth surface equation of the second spiral bevel gear in the meshing coordinate system; a target tooth surface construction unit, configured to use the tooth surface of any one of the large spiral bevel gear and the small spiral bevel gear as a reference tooth surface, and to construct a target tooth surface of the other spiral bevel gear based on the tooth surface equation of the second spiral bevel gear and ease-off; A machining parameter optimization unit, used for constructing a difference surface model based on the target tooth surface, and optimizing machining parameters based on the difference surface model to obtain new machining parameters; A gear tooth surface optimization unit, configured to perform a loading contact analysis and a sensitivity analysis on the spiral bevel gear tooth surface based on the new processing parameters, the reference tooth surface and the target tooth surface to obtain target processing parameters, and optimize the spiral bevel gear tooth surface according to the target processing parameters to obtain a target spiral bevel gear tooth surface; Inserting a micro-texture unit to determine initial micro-texture parameters, and inserting micro-texture on the tooth surface of the target spiral bevel gear based on the initial micro-texture parameters to construct a spiral bevel gear tooth surface containing micro-texture; The micro-texture parameter optimization unit is used to construct an objective function and constraint conditions for optimizing the micro-texture parameters, and perform a loading contact analysis on the tooth surface of the spiral bevel gear containing micro-texture to obtain target micro-texture parameters that meet the objective function and the constraint conditions, wherein: The objective function for optimizing microtexture parameters is constructed as follows: ； The constraints for constructing the optimized microtexture parameters are: ； in, Represents little endian, Indicates the tooth top, Indicates big endian, Indicates tooth root, Indicates contact marks, represents the microtexture width, Indicates the oil film thickness, represents the oil film thickness without micro-texture, represents the amplitude of the transmission error of the inserted microtexture, represents the transmission error amplitude without micro-texture, represents the stress gradient, Represents the maximum allowable stress gradient.

8. An electronic device, characterized in that: It includes at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions that can be executed by the at least one control processor, and the instructions are executed by the at least one control processor so that the at least one control processor can execute the method for collaborative optimization design of spiral bevel gear tooth surface and micro-texture as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the method for collaborative optimization design of spiral bevel gear tooth surface and micro-texture as described in any one of claims 1 to 6.

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