Method and system for modifying the shape of a three-dimensional cycloidal gear.

Abstract

This invention provides a method and system for modifying the shape of a three-dimensional cycloidal gear, relating to the field of mechanical engineering. This method includes: converting geometric and stress information between a unit circle and the tooth profile polygon of a cycloidal gear using conformal mapping and a global scaling factor to optimize the stress distribution of the tooth end faces; constructing an elastohydrodynamic lubrication model under high-pressure operating conditions to analyze the fatigue characteristics of the tooth faces and evaluate the fatigue strength of the tooth faces; constructing a tooth profile model including an error term and performing synchronous optimization of the tooth end faces and tooth faces with the optimization goal of minimizing the sum of the contact force and offset, thereby realizing an integrated representation of tooth shape and error. This invention achieves comprehensive and accurate optimization of tooth shape and error, further improving the smoothness of gear meshing, durability, and operational stability. This invention brings higher efficiency, better quality, and lower energy consumption to industrial production, demonstrating broad application prospects and market value.

Description

TECHNICAL FIELD

[0001] The present invention relates to the technical field of mechanical engineering, and in particular, relates to a three-dimensional cycloidal gear tooth profile modification method and system. BACKGROUND ART

[0002] In mechanical transmission systems, the tooth profile design of cycloidal gears has received extensive attention and research in recent years as one of the key technologies for improving transmission efficiency, reducing noise, and enhancing durability. With the continuous advancement of industrial technology, especially the rapid development of high-precision manufacturing and automation control technologies, higher requirements are being placed on the tooth profile design of cycloidal gears. Against this background, advanced modification technologies such as equidistant modification, variable-distance modification, and rotation angle modification have emerged, becoming important means to optimize the contact characteristics of gears, reduce stress concentration, and improve transmission accuracy and durability.

[0003] The equidistant modification technology precisely adjusts the diameter of the pin teeth to ensure that equidistant contact of the cycloidal gear is achieved during the transmission process, effectively improving the stability and accuracy of the transmission system, and is particularly suitable for precision mechanical systems that have strict requirements for transmission accuracy. On the other hand, the variable-distance modification technology focuses on adapting to complex and highly variable load conditions in heavy machinery by changing the diameter of the pin tooth distribution circle and optimizing the relative positional relationship between gears, which greatly improves the load-bearing capacity and service life of the gears. In addition, the rotation angle modification technology realizes precise control over the tooth profile shape and meshing characteristics by finely adjusting the initial machining angle, providing more stable dynamic performance for high-speed gear systems.

[0004] Conventional tooth profile construction methods, such as methods based on homogeneous coordinate transformation, are widely used, but are insufficient to cope with complex tooth profile shapes, with low calculation efficiency and difficulty in intuitive representation. At the same time, the selection and optimization process of shape modification variables often depends on judgment based on engineer experience, and lacks systematic theoretical guidance and accurate calculation models, which may lead to performance fluctuations and instability in practical application of design results.

[0005] To overcome these drawbacks, in recent years, numerical calculation methods and simulation technologies have been widely used in the field of cycloidal gear tooth profile design. These technologies not only improve the accuracy and efficiency of design, but also provide more effective solutions for complex multi-variable and multi-objective optimization problems. However, for the design requirements of high precision and complex shapes, the prior art is still insufficient, and further research and development are required, especially in the processing of high-precision calculation and error correction.

[0006] To realize the accuracy, efficiency and intelligence of cycloidal gear tooth profile design, thorough exploration and innovation are required for high-precision calculation, error correction technology, multi-variable and multi-objective optimization algorithms, and the like. This provides strong technical support for the design and manufacture of key mechanical components such as RV reducers, and promotes the development of mechanical transmission systems toward higher performance, longer service life and lower noise. SUMMARY OF THE INVENTION PROBLEMS TO BE SOLVED BY THE INVENTION

[0007] Accordingly, embodiments of the present invention provide a three-dimensional cycloidal gear shape modification method and system for solving the problems of deformation and wear caused by stress concentration in the cycloidal gear design of the prior art, and the problem of contact fatigue caused by non-uniform contact stress under elastohydrodynamic lubrication conditions. MEANS FOR SOLVING THE PROBLEMS

[0008] To solve the above problems, embodiments of the present invention provide a shape modification method for a three-dimensional cycloidal gear. This method, realizes the conversion of geometric information and stress information between the unit circle and the tooth profile polygon of the cycloidal gear through conformal mapping and a global scaling factor, so that the stress distribution on the tooth end face is optimized; constructs an elastohydrodynamic lubrication model under high-pressure operating conditions, analyzes the fatigue characteristics of the tooth surface, and evaluates the fatigue strength of the tooth surface; constructs a tooth profile model including an error term, takes minimizing the sum of contact force and offset as the optimization goal, performs synchronous optimization of the tooth end face and the tooth surface, and realizes the integrated representation of the tooth shape and the error, The mathematical formula of the above-mentioned tooth profile model including the error term is, JPEG2026536444000002.jpg27170 is the eccentricity, R b is the radius of the center circle of the pin teeth, z b is the number of pin teeth, δ d is the hysteresis angle, b, f, and d respectively represent the influence of the bending deformation of the input crankshaft on the contact characteristics, the influence of the bounce of the pin tooth end on the contact characteristics, and the influence of the meshing hysteresis angle on the contact characteristics, r u is the radius of the pin tooth circle, JPEG2026536444000003.jpg21170

[0009] JPEG2026536444000004.jpg22170 Here, a is a coefficient, r b is the radius of the distribution pitch circle of the pin teeth, z a represents the number of teeth of the cycloidal gear.

[0010] Preferably, for the simply connected polygon domain mapping, the calculation formula of the conformal mapping is, JPEG2026536444000005.jpg10170 Here, the original vertex ω of the polygon k corresponds to the vertex z after being mapped to the circle k , and at the point ω k , the tangential rotation angle of the polygon is (1-a k)π and a k is the vertex z of the polygon k These are complex parameters related to the mapping, where C and C1 are constants set according to the physical boundary conditions, n is the number of sides of the polygon, z represents a point on the complex plane to be mapped, and ω represents the mapping function.

[0011] Preferably, for a bounded multi-channel polygonal domain map, the formula for calculating the conformal map is as follows: The mapping values ​​of the interior points of a bounded multiconnected domain are calculated using the Cauchy integral formula, according to the boundary values ​​obtained by the Koebe iteration method of the bounded multiconnected domain. The formula for this calculation is: JPEG2026536444000006.jpg8170 Here, w is the value of the mapping function and represents a point on the complex plane after the mapping, z is the point on the complex plane to be mapped, ω(ηt) represents the value of the mapping function ω on the parameter curve η(t), η(t) is the parameter curve and describes a path on a bounded region J, η'(t) represents the derivative of the parameter curve η(t) with respect to t, and i is the imaginary unit. The value of the inverse circular mapping is calculated using Cauchy's integral formula, and the formula is as follows: JPEG2026536444000007.jpg9170 Here, z1 is the value of the inverse mapping function and represents a point mapped to the complex plane, w1 is a point on the complex plane to be inversely mapped, and ω (-1) (ξ(t)) is the inverse mapping function ω on the parameter curve ξ(t). (-1) The values ​​of ξ(t) are represented, ξ(t) is a parameter curve that describes a path on a bounded region J, and ξ'(t) represents the derivative of the parameter curve ξ(t) with respect to t.

[0012] Preferably, analyzing the fatigue characteristics of the tooth surface as described above and evaluating the fatigue strength of the tooth surface is, specifically, Step 1 involves inputting the initial operating status, tooth profile geometric information, and lubrication parameters, and selecting an appropriate mesh size. Step 2 involves selecting relaxation parameters, Step 3 involves solving the discrete Reynolds equation, and in the process of solving it, performing pressure iterations using the Gauss-Seidel method for low-pressure regions and the Jacobi method for high-pressure regions, depending on the pressure differences in the region. Step 4 updates pressure, viscosity, density and elastic deformation, Step 5 checks whether the pressure error conditions are simultaneously met. If they are met, it stores the updated parameters; otherwise, it executes step 2. Step 6 includes calculating the tangential and normal pressures of the contact surface based on the updated parameters, and evaluating the fatigue strength of the tooth surface in combination with the Findley model, i.e., calculating the fatigue index and fatigue probability distribution of the contact surface.

[0013] Preferably, analyzing the fatigue characteristics of the tooth surface is, specifically, By combining the Findley index and the Weibull distribution, the fatigue characteristics of the tooth surface were analyzed, and the probability of tooth surface fatigue failure P was determined. f This includes obtaining the following: JPEG2026536444000008.jpg22170

[0014] Preferably, the optimization target is Maximum f(b,f,d) = F c (b,f,d)+O s (b,f,d) Here, f(b,f,d) is the target function for optimization, and F c (b,f,d) represents the contact force caused by the error term, O s (b, f, d) represent the offset amount caused by the error term, and b, f, and d represent the effect on contact characteristics due to bending deformation of the input crankshaft, the effect on contact characteristics due to the rebound of the pin tooth ends, and the effect on contact characteristics due to the meshing hysteresis angle, respectively.

[0015] Embodiments of the present invention further provide a three-dimensional cycloidal gear shape modification system. This system is for realizing the three-dimensional cycloidal gear shape modification method described above, and specifically, A tooth end face stress optimization design module that uses conformal mapping and a global scaling factor to convert geometric information and stress information between a unit circle and the tooth profile polygon of a cycloidal gear, thereby optimizing the stress distribution at the tooth end face, This module optimizes tooth surface stress distribution for designing an elastohydrodynamic lubrication model under high-pressure operating conditions, analyzing tooth surface fatigue characteristics, and evaluating tooth surface fatigue strength. This includes a tooth end face and tooth surface synchronization optimization module to construct a tooth profile model that includes an error term, perform synchronized optimization of the tooth end face and tooth surface with the goal of minimizing the sum of the contact force and offset amount, and realize an integrated representation of tooth shape and error.

[0016] Embodiments of the present invention further provide an electronic device comprising a processor, memory, and a bus system, wherein the processor and the memory are connected via the bus system, the memory is for storing instructions, and the processor is for executing the instructions stored in the memory so that the three-dimensional cycloidal gear shape modification method described above is realized.

[0017] Embodiments of the present invention further provide a computer storage medium in which a computer software product is stored, and several instructions included in the computer software product cause a computer device to execute the three-dimensional cycloid gear shape modification method described above. [Effects of the Invention]

[0018] From the above technical aspects, it is clear that the present invention has the following beneficial effects. Embodiments of the present invention provide a method and system for modifying the shape of a three-dimensional cycloidal gear, achieving efficient coordinated optimization of tooth end faces and tooth surfaces by integrating conformal mapping, a global scaling factor, and an elastohydrodynamic lubrication model under high-pressure operating conditions. This method not only significantly improves computational efficiency (up to 4.75%) but also accurately adjusts and controls the stress distribution on the tooth end faces, ensures uniform contact force, and effectively slows the wear rate. At the same time, the constructed elastohydrodynamic lubrication model analyzes the fatigue characteristics of the tooth surfaces in detail, significantly improving the durability of the tooth surfaces. Furthermore, by constructing a tooth profile model that includes an error term, the aim is to minimize the sum of the contact force and offset, achieving comprehensive and accurate optimization of tooth shape and error, further improving the smoothness of gear meshing, durability, and operational stability. In summary, the present invention, centered on technological innovation, significantly enhances the overall performance of cycloidal gears, resulting in higher efficiency, better quality, and lower energy consumption in industrial production, demonstrating broad application prospects and market value. [Brief explanation of the drawing]

[0019] To more clearly describe the embodiments of the present invention or the technical aspects of the prior art, the drawings necessary for use in the embodiments are briefly described below. The features and advantages of the present invention will be more clearly understood by referring to the drawings, however, the drawings are illustrative and should not be understood as limiting the invention. Those skilled in the art can obtain other drawings from these drawings without any creative effort. [Figure 1] Figure 1 is a flowchart of a method for modifying the shape of a three-dimensional cycloidal gear provided by the embodiment. [Figure 2] Figure 2 is a schematic diagram of the tooth profile formation process of the cycloidal gear in the embodiment. [Figure 3] Figure 3 is a block diagram of a three-dimensional cycloidal gear shape modification system provided by the embodiment. [Modes for carrying out the invention]

[0020] To further clarify the object, technical aspects, and advantages of the embodiments of the present invention, the technical aspects of the embodiments of the present invention will be described clearly and completely below with reference to the drawings of the embodiments. Clearly, the embodiments described are some, but not all, embodiments of the present invention. Any other embodiments that can be obtained by those skilled in the art without creative work based on the embodiments of the present invention are all within the scope of the protection of the present invention.

[0021] Example 1 To address the problems of deformation and wear due to stress concentration in conventional cycloidal gear design, and contact fatigue due to non-uniform contact stress under elastofluid lubrication conditions, the present invention proposes a method for modifying the shape of a three-dimensional cycloidal gear, as shown in Figure 1. This method is Step S1 involves converting geometric and stress information between the unit circle and the tooth profile polygon of the cycloid gear using conformal mapping and a global scaling factor, thereby optimizing the stress distribution at the tooth end face. Step S2 involves constructing an elasto-hydrodynamic lubrication model under high-pressure operating conditions, analyzing the fatigue characteristics of the tooth surface, and evaluating the fatigue strength of the tooth surface. Step S3 includes constructing a tooth profile model that includes an error term, performing synchronous optimization of the tooth end face and tooth surface with the goal of minimizing the sum of the contact force and offset amount, and realizing an integrated representation of tooth shape and error.

[0022] As can be seen from the above technical aspects, the present invention proposes a method for modifying the shape of a three-dimensional cycloidal gear. First, stress analysis is performed on the tooth end face using conformal mapping and global scaling factor technology to achieve efficient conversion of geometric information and stress information between the unit circle and the tooth profile polygon. Subsequently, machining and operating error terms are introduced and combined with a neural network agent model, a genetic algorithm, and a Bayesian optimization least-squares boosting agent model to optimize the tooth end face stress design, ensuring a uniform stress distribution and reducing wear. Next, to address the problem of non-uniform contact stress on the tooth surface, an elastohydrodynamic lubrication model under high-pressure operating conditions is constructed, and the system's operating parameters are adjusted and controlled using a pattern search optimization method to rapidly analyze and optimize the fatigue characteristics of the tooth surface. Finally, synchronized optimization of the tooth end face and tooth surface is performed, with the optimization goal being to minimize the sum of the contact force and offset. Using a response surface optimization method, and in combination with finite element analysis, the integrated representation of tooth shape and error is verified and optimized to achieve a uniform distribution of contact force between the tooth end face and tooth surface, further improving the overall performance and service life of the cycloidal gear.

[0023] In this embodiment, in step S1, the conversion of geometric information and stress information between the unit circle and the tooth profile polygon of the cycloid gear is achieved by conformal mapping and a global scaling factor, so that the stress distribution on the tooth end face is optimized.

[0024] Here, for a simply connected polygonal domain map, the formula for calculating a conformal map is: JPEG2026536444000009.jpg10170 Here, the original vertex ω of the polygon k This is the vertex z after it has been mapped to a circle. k Corresponding to point ω k In this case, the tangent rotation angle of the polygon is (1-a k )π and a k is the vertex z of the polygon k These are complex parameters related to the mapping, where C and C1 are constants set according to the physical boundary conditions, n is the number of sides of the polygon, z represents a point on the complex plane to be mapped, and ω represents the mapping function.

[0025] For a bounded multi-channel polygonal domain map, the formula for calculating the conformal map is as follows: The mapping values ​​of the interior points of a bounded multiconnected domain are calculated using the Cauchy integral formula, according to the boundary values ​​obtained by the Koebe iteration method of the bounded multiconnected domain. The formula for this calculation is: JPEG2026536444000010.jpg9170 Here, w is the value of the mapping function and represents a point on the complex plane after the mapping, z is the point on the complex plane to be mapped, ω(η(t)) represents the value of the mapping function ω on the parameter curve η(t), η(t) is the parameter curve and describes a path on a bounded region J, η'(t) represents the derivative of the parameter curve η(t) with respect to t, and i is the imaginary unit. The value of the inverse circular mapping is calculated using Cauchy's integral formula, and the formula is as follows: JPEG2026536444000011.jpg9170 Here, z1 is the value of the inverse mapping function and represents a point mapped to the complex plane, w1 is a point on the complex plane to be inversely mapped, and ω (-1) (ξ(t)) is the inverse mapping function ω on the parameter curve ξ(t). (-1) The values ​​of ξ(t) are represented, ξ(t) is a parameter curve that describes a path on a bounded region J, and ξ'(t) represents the derivative of the parameter curve ξ(t) with respect to t.

[0026] Global Scaling Factor: In geometric calculations, to determine the mean radius of a two-dimensional polygon P based on its geometric center, the present invention employs a structured method. The polygon P consists of n vertices, and the coordinates of each vertex are (x i ,y i It is expressed as ), where i is 1 to n. The mean radius of the polygon is r. avg The formal steps for calculating this are as follows: First, the horizontal and vertical coordinates of all the vertices of the polygon are organized into a single two-dimensional matrix. Although this matrix is ​​not directly required for the calculation, this step embodies the concept of data integration. Next, according to the coordinates of the vertices, the geometric center (C) of the polygon is determined. x ,C y ) is calculated. The coordinates of the geometric center are given by the arithmetic mean of the vertex coordinates, i.e., JPEG2026536444000012.jpg7170 Then, each vertex of the polygon (x i ,y i Regarding this vertex, from this vertex to the geometric center (C x ,C y Euclidean distance d to ) i This is calculated using the following formula: JPEG2026536444000013.jpg10170 Finally, the average Euclidean distance from all vertices to the geometric center is taken to determine the average radius r of the polygon. avg This can be obtained. That is, JPEG2026536444000014.jpg14170 This method provides an important reference criterion for geometric transformations such as polygon scaling, namely the mean radius r. avg This is provided, which reflects the average extent of the polygon's spread around its geometric center.

[0027] Specifically, the tooth end face optimization according to the present invention includes the following: Using conformal mapping and a global scaling factor, the interconversion of geometric information and stress information between the unit circle and the tooth profile polygon of the cycloidal gear is achieved, thereby improving computational efficiency. Machining and operating error terms (e.g., bending deformation of the input crankshaft, bounce at the end of the pin teeth, and meshing hysteresis angle) are introduced into the tooth end face model to construct a tooth profile model that includes the error terms. Using a neural network agent model and a pattern search method, in combination with a genetic algorithm and a least-squares boosting agent model of Bayesian optimization, the optimal combination of error parameters before and after contact force fluctuations is found, thereby achieving a uniform distribution of tooth end face stress. In combination with a response surface optimization method, the maximum allowable error value is determined, and the finite element method is used to verify that the transition of the contact force after optimization is smoother.

[0028] In this embodiment, in step S2, an elastohydrodynamic lubrication model is constructed under high-pressure operating conditions, the fatigue characteristics of the tooth surface are analyzed, and the fatigue strength of the tooth surface is evaluated.

[0029] Specifically, considering the problem of non-uniform contact stress on tooth surfaces under elastohydrodynamic lubrication conditions, the present invention constructs an elastohydrodynamic lubrication model for high-pressure operating conditions and analyzes the evolutionary laws of tooth surface fatigue in combination with the Findley index and Weibull distribution. By using a pattern search optimization method and adjusting and controlling the system's operating parameters, rapid analysis and optimization of contact surface fatigue characteristics under various operating conditions are achieved, resulting in a slower wear rate.

[0030] The elastofluid lubrication model used in the present invention under high-pressure operating conditions is: JPEG2026536444000015.jpg22170, P t η is called the fracture pressure, and η is viscosity. o This is the initial viscosity, P a =0.7P t , P b =1.4P t Therefore, c0, c1, c2, c3, α, and α2 are all coefficients. In this embodiment, tooth surface analysis is performed according to the above model, and the data is fitted using a Gaussian model according to the experimental measurement data, and the conclusion formula is obtained. JPEG2026536444000016.jpg29170

[0031] Furthermore, the fatigue characteristics of the tooth surface will be analyzed, and the fatigue strength of the tooth surface will be evaluated. Specifically, Step 1 involves inputting the initial operating status, tooth profile geometric information, and lubrication parameters, and selecting an appropriate mesh size. Step 2 involves selecting relaxation parameters, Step 3 involves solving the discrete Reynolds equation, and in the process of solving it, performing pressure iterations using the Gauss-Seidel method for low-pressure regions and the Jacobi method for high-pressure regions, depending on the pressure differences in the region. Step 4 updates pressure, viscosity, density and elastic deformation, Step 5 checks whether the pressure error conditions are simultaneously met. If they are met, it stores the updated parameters; otherwise, it executes step 2. Step 6 includes calculating the tangential and normal pressures of the contact surface based on the updated parameters, and evaluating the fatigue strength of the tooth surface in combination with the Findley model, i.e., calculating the fatigue index and fatigue probability distribution of the contact surface.

[0032] By combining the Findley index and the Weibull distribution, the fatigue characteristics of the tooth surface were analyzed, and the probability of tooth surface fatigue failure P was determined. f We obtain the following: JPEG2026536444000017.jpg30170

[0033] In this embodiment, in step S3, a tooth profile model including an error term is constructed, and synchronous optimization of the tooth end face and tooth surface is performed with the goal of minimizing the sum of the contact force and offset amount, thereby realizing an integrated representation of tooth shape and error.

[0034] Specifically, this invention constructs a tooth profile model that includes an error term, taking into account the operating error term. Using a response surface optimization method, it optimizes the contact force distribution of a single tooth profile, ensuring synchronous optimization between the tooth end face and the tooth surface. The optimization goal is to minimize the sum of the contact force and offset, thereby achieving an integrated representation of the tooth shape and error. Synchronous optimization ensures a more uniform contact force distribution between the tooth end face and tooth surface, slowing the wear rate. In combination with finite element analysis, the performance of the tooth end face and tooth surface structure after synchronous optimization in actual operation is verified, ensuring the achievement of the optimization goal.

[0035] Here, the mathematical expression for the tooth profile model, including the error term (considering input crankshaft bending deformation error, pin tooth end bounce error, and hysteresis angle error), is: JPEG2026536444000018.jpg18170JPEG2026536444000019.jpg44170

[0036] JPEG2026536444000020.jpg9170r b is the radius of the pin tooth distribution pitch circle, z a ∠O represents the number of teeth on a cycloid gear. b O u K is defined as the terminal angle, φ ec It is represented by φ ec =arccot[(R b / r b -cosφ Hb ) / sinφ Hb Figure 2 shows the tooth formation process of a cycloidal gear. Specifically, a cartate epitrochoid (the tooth profile of a cycloidal gear) refers to the trajectory of a point within a rolling circle when a movable circle undergoes pure rolling motion around a fixed circle. The specific process is as follows: Fixed Cartesian coordinate system XO a At Y, the pitch circle of the cycloid gear (radius r a ) is fixed, and thereafter the circle r a This refers to the distribution pitch circle of the pin teeth (radius r b ) thereafter, b It is called, O a A circle r centered on a It performs pure rolling motion around the center O, and the distance between the two centers of the circle is e. A rotating arm of length e is centered at O a Around φ Ha When rotated by this much, the center of the pin tooth circle O u and O b The rotation angle of the line connecting the two points is φ ba It becomes a degree. Point P is on circle r a O is the instantaneous velocity center when it is in pure rolling motion. u After connecting and P, the line and the pin tooth circle (i.e., circle r) u The intersection point K with ) is the point at the corresponding angle on the cycloid gear.

[0037] Furthermore, the optimization goal of the present invention is, Maximum f(b,f,d) = F c (b,f,d)+O s (b, f, d) Here, f(b,f,d) is the target function for optimization, and F c(b,f,d) represents the contact force caused by the error term, O s (b, f, d) represent the offset amount caused by the error term, and b, f, and d represent the effect on contact characteristics due to bending deformation of the input crankshaft, the effect on contact characteristics due to the rebound of the pin tooth ends, and the effect on contact characteristics due to the meshing hysteresis angle, respectively.

[0038] Example 2 As shown in Figure 3, the present invention provides a three-dimensional cycloidal gear shape modification system, which is for realizing the three-dimensional cycloidal gear shape modification method of the above-described embodiment 1, and specifically, A tooth end face stress optimization design module 100 is provided to optimize the stress distribution at the tooth end face by converting geometric information and stress information between the unit circle and the tooth profile polygon of the cycloidal gear using conformal mapping and a global scaling factor, and A tooth surface stress distribution optimization design module 200 is used to construct an elastohydrodynamic lubrication model under high-pressure operating conditions, analyze the fatigue characteristics of tooth surfaces, and evaluate the fatigue strength of tooth surfaces. The system includes a tooth profile model that incorporates an error term, and performs synchronized optimization of the tooth end face and tooth surface with the goal of minimizing the sum of the contact force and offset amount, thereby achieving an integrated representation of tooth shape and error. This includes a tooth end face and tooth surface synchronized optimization module 300.

[0039] The three-dimensional cycloidal gear shape modification system of this embodiment is for realizing the three-dimensional cycloidal gear shape modification method described above. Therefore, for specific embodiments of the three-dimensional cycloidal gear shape modification system, one can refer to the embodiment portion of the three-dimensional cycloidal gear shape modification method described above. For example, the tooth end face stress optimization design module 100, the tooth surface stress distribution optimization design module 200, and the tooth end face and tooth surface synchronization optimization module 300 are for realizing steps S1, S2, and S3 in the three-dimensional cycloidal gear shape modification method described above, respectively. Therefore, for specific embodiments, one can refer to the descriptions of the corresponding partial embodiments. To avoid redundancy, this will not be repeated here.

[0040] Example 3 Embodiments of the present invention provide an electronic device. This electronic device includes a processor, memory, and a bus system, the processor and memory being connected via the bus system, the memory being for storing instructions, and the processor being for executing the instructions stored in the memory so that the three-dimensional cycloid gear shape modification method described above is realized.

[0041] Example 4 An embodiment of the present invention provides a computer storage medium. This computer storage medium stores a computer software product, and several instructions contained in the computer software product cause a computer device to execute the above-described three-dimensional cycloid gear shape modification method.

[0042] Those skilled in the art will understand that embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-compatible storage media (including, but not limited to, magnetic disk memory, CD-ROM, optical memory, etc.) containing computer-compatible program code.

[0043] This application is described with reference to flowcharts and / or block diagrams of methods, devices (systems) and computer program products according to embodiments of this application. Each flow and / or block in the flowcharts and / or block diagrams, and combinations of flows and / or blocks in the flowcharts and / or block diagrams, should be understood to be realized by computer program instructions. These computer program instructions are provided to a general-purpose computer, a dedicated computer, an embedded processor or other programmable data processing device processor to form a device, and instructions executed by the computer or other programmable data processing device processor form a device for realizing the functions specified in one or more flows of the flowchart and / or one or more blocks of the block diagram.

[0044] These computer program instructions may be stored in computer-readable memory that can guide a computer or other programmable data processing device to operate in a particular manner, and the instructions stored in this computer-readable memory form a product including an instruction unit. This instruction unit implements the functions specified in one or more flows of a flowchart and / or one or more blocks of a block diagram. These computer program instructions may be loaded into a computer or other programmable data processing device, and by executing a series of operational steps on the computer or other programmable data processing device, a process implemented on the computer is formed, and the instructions executed on the computer or other programmable data processing device provide steps for implementing the functions specified in one or more flows of a flowchart and / or one or more blocks of a block diagram.

[0045] Clearly, the embodiments described above are merely examples to clarify the explanation and do not limit the embodiments. Those skilled in the art can make various other forms of changes and modifications based on the above description. It is not necessary, nor is it possible, to comprehensively list all embodiments here, but the obvious changes and modifications that can be derived therefrom still fall within the scope of protection of the present invention.

Claims

1. A method for modifying the shape of a three-dimensional cycloidal gear, The objective is to optimize the stress distribution at the tooth end face by converting geometric and stress information between the unit circle and the tooth profile polygon of the cycloidal gear using conformal mapping and a global scaling factor. To construct an elastohydrodynamic lubrication model under high-pressure operating conditions, analyze the fatigue characteristics of tooth surfaces, and evaluate the fatigue strength of tooth surfaces, This involves constructing a tooth profile model that includes an error term, optimizing the tooth end face and tooth surface synchronously with the goal of minimizing the sum of the contact force and offset amount, and achieving an integrated representation of tooth shape and error. The formula for the tooth profile model, including the error term mentioned above, is: A method for modifying the shape of a three-dimensional cycloidal gear, characterized by the features described above.

2. Here, a is a coefficient, and r b is the radius of the pin tooth distribution pitch circle, z a This represents the number of teeth on the cycloid gear. The method for modifying the shape of a three-dimensional cycloidal gear according to feature 1.

3. For a simply connected polygonal domain map, the formula for calculating the conformal map is: Here, the original vertex ω of the polygon k corresponds to the vertex z after being mapped to a circle k , and at point ω k , the tangent rotation angle of the polygon is (1-a k )π, a k is a complex parameter related to the vertex z of the polygon k , C and C １ are constants set according to physical boundary conditions, n represents the number of sides of the polygon, z represents a point on the complex plane to be mapped, and ω represents the mapping function The method for modifying the shape of a three-dimensional cycloidal gear according to feature 1.

4. For a bounded multi-channel polygonal domain map, the formula for calculating the conformal map is as follows: The mapping values ​​of internal points in a bounded, multiconnected domain are calculated using the Cauchy integral formula, according to the boundary values ​​obtained by the Koebe iteration method. The formula for this calculation is: Here, w is the value of the mapping function and represents a point on the complex plane after the mapping, z is the point on the complex plane to be mapped, ω(η(t)) represents the value of the mapping function ω on the parameter curve η(t), η(t) is the parameter curve and describes a path on a bounded region J, η'(t) represents the derivative of the parameter curve η(t) with respect to t, and i is the imaginary unit. The value of the inverse circular mapping is calculated using Cauchy's integral formula, and the formula is as follows: Here, z １ is the value of the inverse mapping function, representing a point mapped onto the complex plane, and w １ ω is a point on the complex plane that should be inversely mapped, (-１) (ξ(t)) is the inverse mapping function ω on the parameter curve ξ(t). (-１) The value of ξ(t) is represented, ξ(t) is a parameter curve that describes a path on a bounded region J, and ξ'(t) represents the derivative of the parameter curve ξ(t) with respect to t. The method for modifying the shape of a three-dimensional cycloidal gear according to feature 1.

5. Analyzing the fatigue characteristics of the tooth surface as described above and evaluating the fatigue strength of the tooth surface specifically means: Step 1 involves inputting the initial operating status, tooth profile geometric information, and lubrication parameters, and selecting an appropriate mesh size. Step 2 involves selecting relaxation parameters, Step 3 involves solving the discrete Reynolds equation, and in the process of solving it, performing pressure iterations using the Gauss-Seidel method for the low-pressure region and the Jacobi method for the high-pressure region, depending on the pressure differences in the region. Step 4 involves updating pressure, viscosity, density, and elastic deformation, Step 5 checks whether the pressure error conditions are simultaneously met. If they are met, it stores the updated parameters; otherwise, it executes step 2. Step 6 includes calculating the tangential and normal pressures of the contact surface based on the updated parameters, and evaluating the fatigue strength of the tooth surface in combination with the Findley model, i.e., calculating the fatigue index and fatigue probability distribution of the contact surface. The method for modifying the shape of a three-dimensional cycloidal gear according to feature 1.

6. Analyzing the fatigue characteristics of tooth surfaces specifically involves, By combining the Findley index and the Weibull distribution, the fatigue characteristics of the tooth surface were analyzed, and the probability of tooth surface fatigue failure P was determined. f This includes obtaining the following:

7. The aforementioned optimization objective is, Maximum f(b, f, d) = F c (b, f, d) + O s (b, f, d) Here, f(b, f, d) is the target function for optimization, F c (b, f, d) represent the contact force caused by the error term, O s (b, f, d) represent the offset amount caused by the error term, and b, f, and d represent the influence on contact characteristics due to bending deformation of the input crankshaft, the influence on contact characteristics due to the rebound of the pin tooth ends, and the influence on contact characteristics due to the meshing hysteresis angle, respectively. The method for modifying the shape of a three-dimensional cycloidal gear according to feature 1.

8. A three-dimensional cycloidal gear shape modification system, wherein the system is for realizing the three-dimensional cycloidal gear shape modification method described in any one of claims 1 to 7, and specifically, A tooth end face stress optimization design module that uses conformal mapping and a global scaling factor to convert geometric information and stress information between a unit circle and the tooth profile polygon of a cycloidal gear, thereby optimizing the stress distribution at the tooth end face, This module optimizes tooth surface stress distribution for designing an elastohydrodynamic lubrication model under high-pressure operating conditions, analyzing tooth surface fatigue characteristics, and evaluating tooth surface fatigue strength. This system constructs a tooth profile model that includes an error term, and performs synchronized optimization of the tooth end face and tooth surface with the goal of minimizing the sum of the contact force and offset amount. It includes a tooth end face and tooth surface synchronized optimization module to achieve an integrated representation of tooth shape and error. A three-dimensional cycloidal gear shape modification system characterized by the following:

9. An electronic device comprising a processor, memory, and a bus system, wherein the processor and the memory are connected via the bus system, the memory is for storing instructions, and the processor is for executing the instructions stored in the memory so that the three-dimensional cycloid gear shape modification method described in any one of claims 1 to 7 is realized. An electronic device characterized by the following features.

10. A computer storage medium, wherein a computer software product is stored in the computer storage medium, and several instructions included in the computer software product are for causing a computer device to execute the three-dimensional cycloid gear shape modification method described in any one of claims 1 to 7. Computer storage medium.

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