Three-dimensional cycloidal gear modification method and system

Abstract

The present invention relates to the technical field of mechanical engineering and provides a three-dimensional cycloidal gear modification method and system. The method comprises: implementing geometric and stress information conversion between a unit circle and a cycloidal gear tooth profile polygon by means of conformal mapping and a global scaling factor, so as to optimize the stress distribution on a tooth end surface; constructing an elastic flow force lubrication model under a high-pressure working condition, analyzing tooth surface fatigue characteristics, and evaluating tooth surface fatigue strength; and constructing a tooth profile model containing an error term, and, using the minimization of the sum of a contact force and an offset as an optimization objective, performing synchronous optimization of the tooth end surface and the tooth surface, so as to achieve an integrated representation of a tooth form and error. The present invention achieves integrated accurate optimization of the tooth form and error, and further improves the meshing smoothness, durability, and operation stability of the gear. The present invention brings higher efficiency, better quality, and lower energy consumption to industrial production, and exhibits broad application prospects and market value.

Description

Three-dimensional cycloid gear tooth modification method and system TECHNICAL FIELD

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

[0002] In mechanical transmission systems, cycloid tooth profile design is one of the key technologies for improving transmission efficiency, reducing noise, and enhancing durability. In recent years, it has received extensive attention and research. With the continuous progress of industrial technology, especially the rapid development of high-precision manufacturing and automation control technology, higher requirements are put forward for the design of cycloid tooth profile. In this context, advanced modification techniques such as equidistant modification, displacement modification, and angle modification have emerged as important means to optimize gear contact characteristics, reduce stress concentration, and improve transmission accuracy and durability.

[0003] Equidistant modification technology adjusts the pin tooth diameter accurately to ensure equal distance contact of the cycloid gear during transmission, effectively improving the stability and accuracy of the transmission system, and is particularly suitable for precision mechanical systems with strict requirements on transmission accuracy. Displacement modification technology focuses on changing the diameter of the pin tooth distribution circle to optimize the relative position relationship between gears to adapt to complex and variable load conditions in heavy machinery, significantly improving the carrying capacity and service life of the gear. In addition, the angle modification technology adjusts the initial machining angle to accurately control the tooth profile shape and meshing characteristics, providing more stable dynamic performance for high-speed gear systems.

[0004] Traditional tooth profile construction methods, such as those based on homogeneous coordinate transformation, are widely used, but they are not suitable for complex tooth profile shapes, have low computational efficiency, and are difficult to express intuitively. At the same time, the selection and optimization of modification variables often rely on the experience of engineers, lack of systematic theoretical guidance and accurate calculation models, resulting in performance fluctuations and instability in actual application.

[0005] To overcome these limitations, numerical calculation methods and simulation techniques have been widely applied in the field of cycloid tooth profile design in recent years. 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, in the face of high-precision and complex shape design requirements, existing technologies still have limitations, especially in high-precision calculation and error correction, which still need further research and development.

[0006] To achieve precise, efficient, and intelligent design of cycloidal gear tooth profiles, it is necessary to conduct in-depth exploration and innovation in areas such as high-precision calculations, error correction techniques, and multi-variable, multi-objective optimization algorithms. This will provide strong technical support for the design and manufacturing of key mechanical components such as RV reducers, and drive the development of mechanical transmission systems towards higher performance, longer lifespan, and lower noise. Summary of the Invention

[0007] To address this, embodiments of the present invention provide a three-dimensional cycloidal gear modification method and system, which solves the problems of deformation and wear caused by stress concentration in the design of cycloidal gears in the prior art, as well as the problem of contact fatigue caused by uneven contact stress under elastohydrodynamic lubrication conditions.

[0008] To address the aforementioned problems, embodiments of the present invention provide a three-dimensional cycloidal gear modification method, the method comprising:

[0009] By using conformal mapping and a global scaling factor, geometric and stress information conversion between the unit circle and the cycloidal gear tooth profile polygon is achieved to optimize the stress distribution on the tooth end face.

[0010] A elastohydrodynamic lubrication model under high pressure conditions was constructed to analyze tooth surface fatigue characteristics and evaluate tooth surface fatigue strength.

[0011] A tooth profile model incorporating error terms is constructed, with the optimization objective of minimizing the sum of contact force and offset. The tooth end face and tooth surface are simultaneously optimized to achieve an integrated representation of tooth profile and error.

[0012] The mathematical expression for the tooth profile model including the error term is:

[0013] in, Δ b ,Δ f For error term; e is eccentricity, R b z is the radius of the center circle of the needle teeth; b δ represents the number of needle teeth. d Let r be the hysteresis angle, b, f, and d represent the effects of the input crankshaft bending deformation on the contact characteristics, the effect of pin tooth end runout on the contact characteristics, and the effect of the meshing hysteresis angle on the contact characteristics, respectively; u The radius of the needle tooth circle; For the cycloidal wheel, a rotating arm of length e rotates around center O during its rotation. a Angle of rotation; The end angle; Add a hysteresis angle δ to the rotation angle of the rotating crank respectively. d Later and The correction; x, y represent the coordinate positions.

[0014] Preferably, the The hysteresis angle δ is added to the rotation angle of the crank respectively d The correction of the rear pair And The correction is specifically expressed as:

[0015] Wherein, a is a coefficient, r b is the radius of the pitch circle of the pin tooth, z a represents the number of cycloid teeth.

[0016] Preferably, for single-connected polygon domain mapping, the calculation formula of the conformal mapping is:

[0017] Wherein, the original vertex ω k of the polygon corresponds to the vertex z k mapped on the circle; at the point ω k , the tangent angle of the polygon is (1-a k )π, a k is a complex parameter related to the vertex z k of the polygon; C and C1 are constants, which are set according to physical boundary conditions; n is the number of edges of the polygon; z represents a point on the complex plane to be mapped; ω represents a mapping function.

[0018] Preferably, for bounded multi-channel polygon domain mapping, the calculation formula of the conformal mapping is:

[0019] According to the boundary value of the Koebe iteration method of the bounded multiply connected region, the mapping value of the point inside the multiply connected region is calculated by the Cauchy integral formula, and the calculation formula is:

[0020] Wherein, w is the value of the mapping function, representing a point on the complex plane after mapping; z is a 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 a parameter curve, which describes the path on the bounded region J; η'(t) represents the derivative of the parameter curve η(t) with respect to t; i is the imaginary unit;

[0021] The value of the circular inverse mapping is calculated by the Cauchy integral formula, and the calculation formula is:

[0022] Wherein, z1 is the value of the inverse mapping function, representing a point on the complex plane; w1 is a point on the complex plane to be inversely mapped; ω -1 (ξ(t)) represents the inverse mapping function ω -1a value on a parametric curve ξ(t); ξ(t) is a parametric curve, describing a path on a bounded region J; ξ'(t) represents the derivative of the parametric curve ξ(t) with respect to t.

[0023] Preferably, the analysis of the tooth surface fatigue characteristics and the evaluation of the tooth surface fatigue strength specifically include:

[0024] Step 1: input initial working conditions, tooth profile geometric information and lubrication parameters, and select appropriate grid size;

[0025] Step 2: select relaxation parameters;

[0026] Step 3: solve the discrete Reynolds equation, in the solving process, according to different region pressures, the Gauss-Seidel method is used in low pressure areas, and the Jacobi method is used in high pressure areas to perform pressure iteration;

[0027] Step 4: update pressure, viscosity, density and elastic deformation;

[0028] Step 5: check whether the pressure error condition is met at the same time, if met, store the updated parameters; if not met, execute step 2;

[0029] Step 6: based on the updated parameters, calculate the tangential pressure and normal pressure of the contact surface, and evaluate the fatigue strength of the tooth surface by combining the Findley model, that is, calculate the contact surface fatigue index and fatigue occurrence probability distribution.

[0030] Preferably, the analysis of the tooth surface fatigue characteristics specifically includes:

[0031] The tooth surface fatigue characteristics are analyzed by combining the Findley index and the Weibull distribution, and the tooth surface fatigue failure probability P is obtained f :

[0032] In the formula, F i is the Findley fatigue index, is the threshold value, is the scaling parameter, A ref is the reference area, and m is the Weibull index.

[0033] Preferably, the optimization target is: minimizef(b,f,d)=F c (b,f,d)+O s (b,f,d);

[0034] Wherein, f(b,f,d) is the objective function of optimization; F c (b,f,d) represents the contact force generated due to the error term; O s(b, f, d) represent the offset amount due to the error term; b, f, d represent the influence of the input crankshaft bending deformation on the contact feature, the influence of the needle tooth end bounce on the contact feature, and the influence of the meshing lag angle on the contact feature, respectively.

[0035] The embodiment of the present application further provides a three-dimensional cycloid gear modification system, which is used for realizing the three-dimensional cycloid gear modification method.

[0036] The tooth end face stress optimization design module is used for realizing the conversion of the geometric and stress information between the unit circle and the cycloid tooth profile polygon through the conformal mapping and the global scaling factor, so that the tooth end face stress distribution is optimized.

[0037] The tooth face stress distribution optimization design module is used for constructing the elastohydrodynamic lubrication model under the high-pressure working condition, analyzing the tooth face fatigue characteristics, and evaluating the tooth face fatigue strength.

[0038] The tooth end face and tooth face synchronous optimization module is used for constructing the tooth profile model containing the error term, taking the sum of the contact force and the offset amount as the optimization target, and performing the synchronous optimization of the tooth end face and the tooth face, so that the integrated representation of the tooth profile and the error is realized.

[0039] The embodiment of the present application further provides an electronic device, which comprises a processor, a memory and a bus system, the processor and the memory are connected through the bus system, the memory is used for storing instructions, and the processor is used for executing the instructions stored in the memory to realize the three-dimensional cycloid gear modification method.

[0040] The embodiment of the present application further provides a computer storage medium, which stores a computer software product, the computer software product comprises a plurality of instructions, and the plurality of instructions are used to make a computer device execute the three-dimensional cycloid gear modification method.

[0041] From the above technical solutions, the present application has the following beneficial effects:

[0042] The embodiment of the present application provides a three-dimensional cycloid gear tooth modification method and system, realizes efficient collaborative optimization of the tooth end face and the tooth face by integrating the conformal mapping, the global scaling factor and the elastohydrodynamic lubrication model under high pressure working conditions. The method not only significantly improves the calculation efficiency (up to 4.75%), but also accurately controls the stress distribution of the tooth end face, ensures the uniformization of the contact force, and effectively slows down the wear speed. At the same time, the elastohydrodynamic lubrication model constructed deeply analyzes the tooth face fatigue characteristics, and significantly enhances the tooth face durability. In addition, by constructing a tooth profile model containing error terms, the integrated and accurate optimization of the tooth shape and the error is realized by taking the sum of the contact force and the offset as the target, further improving the meshing smoothness, durability and running stability of the gear. In summary, the present application takes technical innovation as the core, significantly improves the comprehensive performance of the cycloid gear, brings higher efficiency, better quality and lower energy consumption to industrial production, and shows broad application prospect and market value. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly described below. The features and advantages of the present application can be more clearly understood by referring to the drawings. The drawings are schematic and should not be understood as any limitation on the present application. Those skilled in the art can obtain other drawings according to these drawings without creative labor. Among them:

[0044] Fig. 1 is a flow chart of a three-dimensional cycloid gear modification method provided in the embodiment;

[0045] Fig. 2 is a schematic diagram of the cycloid gear tooth profile forming process in the embodiment;

[0046] Fig. 3 is a block diagram of a three-dimensional cycloid gear modification system provided in the embodiment. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical scheme and advantages of the embodiments of the present application more clear, the technical scheme in the embodiments of the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0048] Embodiment one

[0049] In order to solve the deformation and wear problems caused by stress concentration in the design of the cycloid gear in the prior art, and the uneven contact stress under the elastohydrodynamic lubrication condition to cause contact fatigue, as shown in Figure 1, an embodiment of the present application proposes a three-dimensional cycloid gear modification method, which comprises:

[0050] S1: Through conformal mapping and global scaling factor, the geometric and stress information conversion between the unit circle and the cycloid gear profile polygon is realized to optimize the stress distribution of the tooth end face;

[0051] S2: The elastohydrodynamic lubrication model under high pressure working condition is constructed, the tooth surface fatigue characteristics are analyzed, and the tooth surface fatigue strength is evaluated;

[0052] S3: The tooth profile model containing error items is constructed, the sum of the contact force and the offset is minimized as the optimization target, the synchronous optimization of the tooth end face and the tooth surface is carried out, and the integrated representation of the tooth profile and the error is realized.

[0053] From the above technical solution, it can be known that the present application proposes a three-dimensional cycloid gear modification method, first, through the stress analysis of the tooth end face by using the conformal mapping and global scaling factor technology, the efficient geometric and stress information conversion between the unit circle and the tooth profile polygon is realized. Then, the machining and running error items are introduced, the neural network proxy model, genetic algorithm and least square boosting proxy model based on Bayesian optimization are combined to optimize the tooth end face stress, so as to ensure the uniform distribution of stress and slow down the wear. Then, aiming at the uneven tooth surface contact stress problem, the elastohydrodynamic lubrication model under high pressure working condition is constructed, the mode search optimization method is used to regulate the system running parameters, the tooth surface fatigue characteristics are quickly analyzed and optimized. Finally, the synchronous optimization of the tooth end face and the tooth surface is carried out, the sum of the contact force and the offset is minimized as the optimization target, the response surface optimization method is used, the integrated representation of the tooth profile and the error is verified and optimized by combining the finite element analysis, the uniformization of the tooth end face and the tooth surface contact force distribution is realized, and the overall performance and service life of the cycloid gear are further improved.

[0054] In the embodiment, in step S1, through conformal mapping and global scaling factor, the geometric and stress information conversion between the unit circle and the cycloid gear profile polygon is realized to optimize the stress distribution of the tooth end face.

[0055] Wherein, for single-connected polygon domain mapping, the calculation formula of conformal mapping is:

[0056] Wherein, the original vertex ω of the polygon k Corresponding to the vertex z k after mapping to the circle; at the point ω k , the tangent angle of the polygon is (1-a k )π, and a k is a parameter related to the vertex zk Related complex parameters; C and C1 are constants, which are set according to physical boundary conditions; n is the number of edges of the polygon; z represents a point on the complex plane to be mapped; ω represents a mapping function.

[0057] For bounded multi-channel polygon domain mapping, the calculation formula of the conformal mapping is:

[0058] According to the boundary value obtained by the Koebe iteration method of the bounded multiply connected region, the mapping value of the internal point of the multiply connected region is calculated by the Cauchy integral formula, and the calculation formula is:

[0059] Where w is the value of the mapping function, representing a point on the complex plane after mapping; z is a 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 a parameter curve, describing the path on the bounded region J; η'(t) represents the derivative of the parameter curve η(t) with respect to t; i is the imaginary unit;

[0060] The value of the circular inverse mapping is calculated by the Cauchy integral formula, and the calculation formula is:

[0061] Where z1 is the value of the inverse mapping function, representing a point on the complex plane; w1 is a point on the complex plane to be inversely mapped; ω -1 (ξ(t)) represents the value of the inverse mapping function ω -1 on the parameter curve ξ(t); ξ(t) is a parameter curve, describing the path on the bounded region J; ξ'(t) represents the derivative of the parameter curve ξ(t) with respect to t.

[0062] Global scaling factor: in geometric calculation, in order to determine the average radius of a two-dimensional polygon P based on its geometric center, the present application adopts a structured method. The polygon P is composed of n vertices, and the coordinates of each vertex are represented as (x i ,y i ), where i is from 1 to n. The formal steps to calculate the average radius r avg of the polygon are as follows:

[0063] First, organize all the vertices of the polygon into a two-dimensional matrix, although this matrix is not directly needed in direct calculation, but this step embodies the concept of data integration;

[0064] Next, calculate the geometric center (C x ,C y ) of the polygon according to the coordinates of the vertices. The coordinates of the geometric center are given by the arithmetic mean of the vertex coordinates, i.e.:

[0065] Then, for each vertex (x i ,y i ) of the polygon, calculate its Euclidean distance d x to the geometric center (C y ,C i ), using the formula

[0066] Finally, average all the Euclidean distances of the vertices to the geometric center to obtain the average radius r avg of the polygon, i.e.

[0067] This method provides an important reference basis for the polygon scaling geometric transformation, i.e., the average radius r avg , which reflects the average expansion degree of the polygon around its geometric center.

[0068] Specifically, the optimization of the tooth end face includes: using the conformal mapping and the global scaling factor to realize the mutual conversion of the geometric and stress information of the unit circle and the polygon of the cycloid gear profile, and improving the calculation efficiency. The machining and running error items (such as the bending deformation of the input crank shaft, the needle tooth end bounce and the meshing lag angle) are introduced into the tooth end face model to construct the tooth profile model containing the error items. The optimal error parameter combination before and after the contact force fluctuation is obtained by using the neural network proxy model and the pattern search method, combining the genetic algorithm and the least square promotion proxy model of the Bayesian optimization, so that the uniform distribution of the tooth end face stress is realized. The maximum allowable error value is determined by combining the response surface optimization method, and the transition of the contact force after optimization is verified to be smoother by the finite element method.

[0069] In the embodiment, in step S2, an elastohydrodynamic lubrication model under high pressure working condition is constructed, and fatigue characteristics of the tooth surface are analyzed to evaluate fatigue strength of the tooth surface.

[0070] Specifically, in order to solve the problem of uneven tooth surface contact stress under elastohydrodynamic lubrication condition, the elastohydrodynamic lubrication model under high pressure working condition is constructed, the Findley index and Weibull distribution are combined, and the fatigue evolution law of the tooth surface is analyzed. The mode search optimization method is used to adjust the system operating parameters, so that the fatigue characteristics of the contact surface under different working conditions are quickly analyzed and optimized to slow down the wear rate.

[0071] The elastohydrodynamic lubrication model under high pressure working condition adopted by the present application is as follows:

[0072] In the formula, P t is called the breaking pressure, η is the viscosity, η o is the initial viscosity, P a = 0.7P t , and P b = 1.4Pt ; c0, c1, c2, c3, a, a2 are coefficients.

[0073] In this embodiment, the tooth surface is analyzed according to the above model, the data is fitted by using the Gaussian model according to the experimental measurement data, and the conclusion formula is as follows: wherein is the dimensionless viscosity. The model can well explain the relationship between pressure and years, and the model fitting degree R 2 is 0.9998, indicating that the model fitting degree is high.

[0074] Further, the fatigue characteristics of the tooth surface are analyzed, and the fatigue strength of the tooth surface is evaluated, specifically including:

[0075] Step 1: input initial working conditions, tooth profile geometric information and lubrication parameters, and select appropriate grid size;

[0076] Step 2: select relaxation parameters;

[0077] Step 3: solve the discrete Reynolds equation, in the solving process, according to the different regional pressure, the low pressure area adopts Gauss-Seidel method, and the high pressure area adopts Jacobi method to carry out pressure iteration;

[0078] Step 4: update pressure, viscosity, density and elastic deformation;

[0079] Step 5: check whether the pressure error condition is met at the same time, if met, store the updated parameters; if not met, execute step 2;

[0080] Step 6: based on the updated parameters, calculate the tangential pressure and normal pressure of the contact surface, and evaluate the fatigue strength of the tooth surface by combining Findley model, that is, calculate the contact surface fatigue index and fatigue occurrence probability distribution.

[0081] The fatigue characteristics of the tooth surface are analyzed by combining Findley index and Weibull distribution, and the tooth surface fatigue failure probability P f :

[0082] In the formula, F i is the Findley fatigue index; is the threshold value, which is set to 0.86; is the scaling parameter, A ref is the reference area, A ref = 1 μm 2 ; m is the Weibull index, m = 10.

[0083] In the embodiment, in step S3, a tooth profile model containing error terms is constructed to minimize the sum of contact force and offset as the optimization objective, to perform synchronous optimization of the tooth end face and tooth face, and to realize integrated representation of tooth profile and error.

[0084] Specifically, the application considers operating error terms, and constructs a tooth profile model containing error terms. A single tooth profile contact force distribution is optimized using a response surface optimization method, to ensure synchronous optimization of the tooth end face and tooth face. The sum of contact force and offset is minimized as the optimization objective, to realize integrated representation of tooth profile and error. Through synchronous optimization, the contact force distribution of the tooth end face and tooth face is more uniform, and the wear rate is slowed down. In combination with finite element analysis, the performance of the tooth end face and tooth face structure after synchronous optimization in actual operation is verified, to ensure realization of the optimization objective.

[0085] The mathematical expression of the tooth profile model containing error terms (considering input crank shaft bending deformation error, needle tooth end jump error and hysteresis angle error) is as follows:

[0086] Wherein, Δ b ,Δ f is an error term; e is an eccentricity, R b is a needle tooth center circle radius; z b is a needle tooth number; δ d is a hysteresis angle, b, f, d respectively represent the influence of input crank shaft bending deformation on contact characteristics, the influence of needle tooth end jump on contact characteristics, and the influence of meshing hysteresis angle on contact characteristics; r u is a needle tooth circle radius; is the angle of rotation of the length e of the rotating arm around Oa during the rolling process of the cycloidal gear; is the end angle; respectively add the hysteresis angle δ d to the correction of and ; x, y represent coordinate positions.

[0087] Further, r b is the radius of the needle tooth distribution pitch circle, z a represents the number of cycloidal gear teeth; ∠O b O u K is defined as the end angle, and is represented by ​Figure 2 shows a cycloid tooth profile forming process, specifically, a short amplitude cycloid (cycloid tooth profile) refers to a locus of a point in a rolling circle when a moving circle makes pure rolling motion around a fixed circle. The specific process is as follows: in a fixed rectangular coordinate system XO a Y, the cycloid wheel pitch circle (radius r a ) is fixed, hereinafter referred to as circle r a , the pin tooth distribution pitch circle (radius r b ), hereinafter referred to as circle r b , is centered at O a , and makes pure rolling motion around circle r a , and the distance between the two circle centers is e. When the length of the rotating arm e rotates around the center O a φ Ha , the rotating angle of the line connecting the centers O u and O b is φ ba degrees. Point P is the instantaneous velocity center when circle r a makes pure rolling motion. After connecting O u and P, the intersection K of the line and the pin tooth circle (i.e. circle r u ) is the point corresponding to the angle on the cycloid wheel.

[0088] Further, the optimization target of the present application is to minimize f(b,f,d) = F c (b,f,d) + O s (b,f,d);

[0089] Wherein, f(b,f,d) is the objective function of optimization; F c (b,f,d) represents the contact force generated due to the error term; O s (b,f,d) represents the offset generated due to the error term; b, f, d represent the influence of input crank shaft bending deformation on contact characteristics, the influence of pin tooth end runout on contact characteristics, and the influence of meshing lag angle on contact characteristics, respectively.

[0090] Example two

[0091] As shown in Figure 3, the present application provides a three-dimensional cycloid tooth gear modification system, which is used to realize the three-dimensional cycloid tooth gear modification method of the above-mentioned embodiment one, and specifically comprises:

[0092] A tooth end face stress optimization design module 100 is used to realize the conversion of geometric and stress information between the unit circle and the cycloid tooth profile polygon through conformal mapping and global scaling factor, so as to optimize the tooth end face stress distribution;

[0093] A tooth surface stress distribution optimization design module 200 is used to construct an elastohydrodynamic lubrication model under high pressure working condition, analyze tooth surface fatigue characteristics, and evaluate tooth surface fatigue strength.

[0094] The tooth end face and tooth face synchronous optimization module 300 is used for constructing a tooth profile model containing error terms, taking the sum of the contact force and the offset as the optimization target, performing synchronous optimization of the tooth end face and the tooth face, and realizing integrated representation of the tooth profile and the error.

[0095] The three-dimensional cycloidal gear modification system is used for implementing the three-dimensional cycloidal gear modification method, and therefore the specific embodiments of the three-dimensional cycloidal gear modification system can refer to the foregoing embodiments of the three-dimensional cycloidal gear modification method. For example, the tooth end face stress optimization design module 100, the tooth face stress distribution optimization design module 200, and the tooth end face and tooth face synchronous optimization module 300 are respectively used for implementing steps S1, S2, and S3 of the three-dimensional cycloidal gear modification method. Therefore, the specific embodiments can refer to the descriptions of the respective embodiments, and details are not described herein again to avoid redundancy.

[0096] Embodiment three

[0097] The embodiment of the present application provides an electronic device, which comprises a processor, a memory, and a bus system. The processor and the memory are connected through the bus system. The memory is used for storing instructions, and the processor is used for executing the instructions stored in the memory to implement the three-dimensional cycloidal gear modification method.

[0098] Embodiment four

[0099] The embodiment of the present application provides a computer storage medium, which stores a computer software product. The computer software product comprises a plurality of instructions for causing a computer device to execute the three-dimensional cycloidal gear modification method.

[0100] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt a computer program product in the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer usable program codes.

[0101] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart and / or block diagram block or blocks.

[0102] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart and / or block diagram block or blocks. The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart and / or block diagram block or blocks.

[0103] Obviously, the above-described embodiments are only examples for clearly illustrating the present application and are not intended to limit the present application. Based on the above description, one of ordinary skill in the art can further make other different forms of changes or modifications. Here, it is not necessary or possible to enumerate all the embodiments. The obvious changes or modifications derived therefrom are still within the protection scope of the present application.

Claims

1. A method of modifying a three-dimensional cycloidal gear tooth, the method comprising: Comprise: Through conformal mapping and global scaling factor, the geometric and stress information conversion between unit circle and cycloidal tooth profile polygon is realized to optimize the stress distribution of tooth end face; The elastohydrodynamic lubrication model under high pressure working condition is constructed to analyze the fatigue characteristics of tooth surface and evaluate the fatigue strength of tooth surface; The tooth profile model containing error term is constructed to minimize the sum of contact force and offset as the optimization objective, the synchronous optimization of tooth end face and tooth surface is carried out, and the integrated representation of tooth profile and error is realized. The mathematical expression of the tooth profile model including the error term is: wherein Δ b ,Δ f is an error term; e is eccentricity, R b is the radius of the center circle of the needle tooth; z b is the number of needle teeth; δ d is the lag angle, b, f, d respectively represent the influence of the bending deformation of the input crank shaft on the contact feature, the influence of the needle tooth end bounce on the contact feature, and the influence of the meshing lag angle on the contact feature; r u is the radius of the needle tooth circle; for the length e of the rotating arm around the center O a the angle of rotation; for the end angle; addition of a hysteresis angle δ to the rotating crank rotation angle d posterior pair and The correction of the formula is as follows: x, y represent coordinate positions.

2. The method of claim 1, wherein the three-dimensional cycloidal gear tooth modification is performed by a computer numerical control (CNC) machine. the addition of a hysteresis angle δ to the rotating crank rotation angle d posteriori and is modified to: where a is a coefficient, r b is the radius of the pitch circle of the pin teeth, z a denotes the number of cycloidal teeth.

3. The method of claim 1, wherein the three-dimensional cycloidal gear tooth modification is performed by a computer numerical control (CNC) machine. For single connected polygonal domain mapping, the computational formula of the conformal mapping is: where ω is the original vertex of the polygon k corresponding to the vertex z on the circle k ; at the point ω k , the tangent angle of the polygon is (1-a k )π, a k is a complex parameter related to the vertex z k of the polygon; C and C1 are constants, which are set according to physical boundary conditions; n is the number of edges of the polygon; z represents a point on the complex plane to be mapped; ω represents a mapping function.

4. The method of claim 1, wherein the three-dimensional cycloidal gear tooth modification is performed by a computer numerical control (CNC) machine. For bounded multi-channel polygon domain mapping, the calculation formula of the conformal mapping is as follows: According to the boundary value obtained by Koebe iteration method of bounded multiply connected region, the mapping value of the interior point of multiply connected region is calculated by Cauchy integral formula, and the calculation formula is: Wherein, w is the value of the mapping function, which represents the point on the complex plane after 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 a parameter curve, which describes the path on the bounded region J; η'(t) represents the derivative of the parameter curve η(t) with respect to t; i is the imaginary unit; The Cauchy integral formula is used to calculate the value of the inverse mapping of a circle, and the calculation formula is: where z1is the value of the inverse mapping function, representing a point on the complex plane; w1is the point on the complex plane to be inversely mapped; ω -1 (ξ(t)) represents the inverse mapping function ω -1 the value on the parametric curve ξ(t); ξ(t) is a parametric curve, describing a path on the bounded region J; ξ'(t) represents the derivative of the parametric curve ξ(t) with respect to t.

5. The method of claim 1, wherein the three-dimensional cycloidal gear tooth modification is performed by a computer numerical control (CNC) machine. The analysis of the fatigue characteristics of the tooth surface and the evaluation of the fatigue strength of the tooth surface specifically include: Step 1: input initial working condition, tooth profile geometric information and lubrication parameters, and select appropriate grid size; Step 2: select relaxation parameters; Step 3: solve the discrete Reynolds equation, in the solving process, according to the different regions of pressure, the Gauss-Seidel method is used in the low pressure area, and the Jacobi method is used in the high pressure area to carry out pressure iteration; Step 4: update the pressure, viscosity, density and elastic deformation; Step 5: check whether the pressure error condition is met at the same time, if met, store the updated parameters; if not met, execute step 2; Step 6: based on the updated parameters, calculate the tangential pressure and normal pressure of the contact surface, and evaluate the fatigue strength of the tooth surface by combining the Findley model, that is, calculate the contact surface fatigue index and fatigue probability distribution.

6. The method of modifying the profile of a three-dimensional cycloidal gear tooth according to claim 1, wherein, The analysis of the fatigue characteristics of the tooth surface specifically includes: The fatigue failure probability P of the tooth surface is obtained by combining the Findley index with the Weibull distribution analysis of the tooth surface fatigue characteristics f : In the formula, F i is the Findley fatigue index, Fi0 is the threshold, Fi0 is the scaling parameter, and A is the scaling parameter. ref The area is for reference, and m is the Weibull index.

7. The method of modifying the profile of a three-dimensional cycloidal gear tooth according to claim 1, wherein, The optimization objective is: minimize f(b,f,d) = F c (b,f,d) + O s (b,f,d); where f(b,f,d) is the optimized objective function; F c (b,f,d) represents the contact force due to the error term; O s (b,f,d) represents the offset due to the error term; b, f, d represent the influence of the input crankshaft bending deformation on the contact feature, the influence of the needle tip runout on the contact feature, and the influence of the meshing lag angle on the contact feature, respectively.

8. A three-dimensional cycloidal gear tooth modification system, characterized by, The system is used to realize the three-dimensional cycloidal gear modification method of any one of claims 1 to 7, and specifically includes: The tooth end face stress optimization design module is used to realize the geometric and stress information conversion between unit circle and cycloidal tooth profile polygon through conformal mapping and global scaling factor to optimize the stress distribution of tooth end face; The tooth surface stress distribution optimization design module is used to construct the elastohydrodynamic lubrication model under high pressure working condition, analyze the fatigue characteristics of tooth surface and evaluate the fatigue strength of tooth surface; The tooth end face and tooth surface synchronous optimization module is used to construct the tooth profile model containing error term, take the sum of contact force and offset as the optimization objective, carry out the synchronous optimization of tooth end face and tooth surface, and realize the integrated representation of tooth profile and error.

9. An electronic device, comprising: The electronic device includes a processor, a memory and a bus system, the processor and the memory are connected through the bus system, the memory is used to store instructions, and the processor is used to execute the instructions stored in the memory to realize the three-dimensional cycloidal gear modification method of any one of claims 1 to 7.

10. A computer storage medium, characterized in that, The computer storage medium stores a computer software product, and the computer software product comprises a plurality of instructions to enable a computer device to execute the three-dimensional cycloid gear tooth modification method in any one of claims 1 to 7.

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