A method for optimizing the efficiency of spiral bevel gears

Abstract

This invention discloses a method for optimizing the efficiency of spiral bevel gears, belonging to the field of gear technology. The method includes the following steps: S101: Performing geometric design of the spiral bevel gear based on basic parameters; performing machining parameter design of the spiral bevel gear based on machining parameters; S102: Conducting geometric contact analysis to obtain geometric contact characteristic parameters; conducting load-bearing contact analysis to obtain load-bearing contact characteristic parameters; S103: Using a fine mesh method, performing elastohydrodynamic lubrication calculations of the spiral bevel gear to obtain oil film parameters; calculating instantaneous transmission efficiency and average transmission efficiency based on the oil film parameters; S104: Establishing a particle swarm optimization-gravity search algorithm model, repeating steps S101 to S103 until the optimal machining parameters for the spiral bevel gear are obtained. Through the above methods, the method proposed in this invention helps to form an efficient system for optimizing the efficiency of spiral bevel gears, thereby improving the design level and quality of spiral bevel gears.

Description

Technical Field

[0001] This invention relates to the field of gear technology, and specifically to a method for optimizing the efficiency of spiral bevel gears. Background Technology

[0002] Spiral bevel gears are widely used in engineering fields such as aerospace and vehicles due to their high load-bearing capacity and smooth transmission, and their operating conditions are increasingly moving towards high speed and heavy load. In high-speed and heavy-load conditions, reducing tooth surface friction helps improve gear durability, lifespan, and efficiency, and power loss in the transmission system is becoming an increasingly important indicator. However, the tooth surface of spiral bevel gears is a high-order curved surface, with numerous design parameters, complex machining, and cumbersome calculations. Whether it is geometric design, machining parameter design, contact analysis, or lubrication calculation, the calculations are complex and the workload is large. The design calculation technology has high bottlenecks, which brings difficulties to efficiency optimization design. Moreover, traditional optimization design methods are time-consuming and computationally intensive, making them difficult to be effective.

[0003] Based on the above analysis, the existing technologies have the following problems and shortcomings: traditional optimization algorithms are time-consuming and computationally intensive; gear design, processing, simulation and other processes involve multiple disciplines, categories and professional knowledge, and no comprehensive professionals have yet conducted systematic research.

[0004] The difficulty in solving the above problems and defects lies in the need to coordinate knowledge from multiple disciplines to form a complete efficiency optimization design system solution, and to ensure the validity of the calculation results and the efficiency of the calculation.

[0005] Based on this, the present invention designs an efficiency optimization design method for spiral bevel gears to solve the above problems. Summary of the Invention

[0006] In view of the above-mentioned shortcomings of the existing technology, the present invention provides a method for optimizing the efficiency of spiral bevel gears.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for optimizing the efficiency of spiral bevel gears includes the following steps:

[0009] S101: Based on the basic principles and design parameters of spiral bevel gear meshing, perform basic calculations for the geometric parameters of spiral bevel gears; then perform initial design and calculation of the machining parameters of spiral bevel gears to obtain the initial machining parameters and their value ranges.

[0010] S102: Geometric contact analysis based on gear meshing principle; and load-bearing contact analysis based on mathematical programming method and finite element method;

[0011] S103: Using the fine mesh method, based on the geometric parameters and load-bearing contact parameters obtained from geometric contact analysis and load-bearing contact analysis, an elastohydrodynamic lubrication model for spiral bevel gears is established and calculations are performed; based on this, the friction coefficient and transmission efficiency of spiral bevel gears are calculated, and the instantaneous transmission efficiency and average transmission efficiency models of spiral bevel gears are obtained.

[0012] S104: Establish a particle swarm optimization algorithm model to form an optimization design process for the machining parameters of spiral bevel gears; based on the above optimization process, repeat steps S101 to S103 until the machining parameters of the spiral bevel gears with the best efficiency are obtained, thereby achieving the optimal parameter design.

[0013] Furthermore, step S101 specifically includes the following steps:

[0014] S1: Determine and input the basic geometric parameters of the gear according to the design requirements and working conditions of the spiral bevel gear;

[0015] S2: Based on the basic parameters of the spiral bevel gear input in S1, and based on the geometric spatial relationship of the spiral bevel gear, solve its main geometric design parameters through programming;

[0016] S3: Based on the basic geometric parameters of the spiral bevel gear calculated in S2, give the initial control design parameters; carry out the initial design of the spiral bevel gear machining parameters and determine the initial design machining parameters of the spiral bevel gear.

[0017] S4: Initialize the particles for machining or control parameters of the spiral bevel gear;

[0018] S5: Calculation of discrete tooth surfaces of spiral bevel gears.

[0019] Furthermore, in step S1, the basic geometric parameters of the gear are determined and input, mainly including: number of teeth, module, tooth width, pressure angle, shaft intersection angle, helix angle, and direction of rotation.

[0020] Furthermore, in step S2, the main geometric design parameters are solved by programming, including: the cone distance of the large and small gears, the tooth tip angle, the tooth root angle, the pitch cone angle, the crown tip distance, and the arc tooth thickness.

[0021] Furthermore, step S3: Given the initial control design parameters, mainly including: design overlap, major half-shaft, contact path tilt angle, first derivative of transmission ratio and magnitude of geometric transmission error meshing transition point;

[0022] Determining the initial design and machining parameters for spiral bevel gears mainly includes: tool tooth profile angle, tool tip distance, radial tool position, angular tool position, rolling ratio, machine position, vertical gear position, horizontal gear position, and machine tool mounting angle.

[0023] Furthermore, step S102 specifically includes the following steps:

[0024] S6: Based on the basic principle of spiral bevel gear meshing, geometric contact analysis of the large and small gears is carried out to obtain the entrainment velocity vector, the relative sliding velocity vector, the direction vector of the major and minor semi-axis of the contact ellipse, and the curvature radius parameter of the major and minor semi-axis of the contact ellipse.

[0025] S7: By establishing a finite element mesh model, using the finite element method and mathematical programming theory, and taking the working load as the condition, we conduct a bearing contact analysis of the spiral bevel gear to obtain the load distribution at the meshing position of the tooth surface.

[0026] Furthermore, step S7 specifically includes the following steps:

[0027] Step 1: Establish a solid mesh model based on the coordinates of discrete points on the tooth surface and the finite element mesh definition;

[0028] Step 2: Calculate the compliance matrix of the spiral bevel gear mesh model based on the elements;

[0029] Step 3: Calculate the element deformation based on the load conditions to achieve load-bearing contact analysis; the main result parameters obtained are: load and load distribution coefficient.

[0030] Furthermore, step S103 specifically includes the following steps:

[0031] S8: Calculation of oil film pressure and film thickness, and transmission efficiency; specifically including:

[0032] ①Based on the relevant data parameters obtained from S6 and S7, the pressure and thickness parameters of the lubricating oil film of the spiral bevel gear are simulated and calculated using the fine mesh method and the basic theory of elastohydrodynamic lubrication.

[0033] ② Using the oil film parameters and the calculated data in S6 and S7 as input conditions, the sliding friction and rolling friction are calculated, and the instantaneous transmission efficiency of the gear is obtained based on this calculation. Then, the average value of the data within one meshing cycle is taken to obtain the average transmission efficiency.

[0034] Furthermore, step ① specifically includes the following steps:

[0035] Step 1: Calculate the initial mesh, initial pressure, and initial oil film thickness;

[0036] Step 2: Iteratively calculate the pressure and load, and determine whether the convergence condition is met. If convergence is met, proceed to the next step; otherwise, continue the iterative process.

[0037] Step 3: Determine if the grid density is met. If it is, output the calculation results. If not, return to Step 2 for iterative calculation. The main results obtained and output are: oil film pressure and oil film thickness distribution.

[0038] Furthermore, step S104 specifically includes the following steps:

[0039] S9: Based on the particle swarm optimization algorithm, the gravitational coefficient, inertial mass, and global optimal particle optimization parameters are updated according to the optimization variables and the calculated objective function results.

[0040] S10: Based on S9, further update the calculation parameters for particle gravity magnitude, acceleration, and velocity iteration to determine the direction of subsequent optimization;

[0041] S11: Determine whether the optimal value and the number of iterations meet the convergence condition. If the convergence condition is met, execute S13 and output the optimal solution and optimal design parameters; otherwise, execute S12.

[0042] S12: Based on S9 and S10, update and iterate the optimized design parameters, and then return to S5 to continue iterative optimization;

[0043] S13: When the optimization calculation meets the iterative convergence condition, output the optimal solution and the optimal design parameters for efficiency.

[0044] Beneficial effects

[0045] This invention, under the premise of fixed geometric design parameters, improves tooth surface meshing efficiency by adjusting machining or control parameters to modify contact characteristic parameters and reduce tooth surface friction. The method proposed in this invention helps to form an efficient system for optimizing the calculation model of spiral bevel gear efficiency, thereby improving the design level and quality of spiral bevel gears.

[0046] This invention is based on the modern optimization algorithm model of particle swarm optimization and gravity search. It focuses on the meshing principle of spiral bevel gears, machining parameter design, geometric contact analysis, load contact analysis, elastohydrodynamic lubrication analysis and efficiency calculation. It forms a systematic method for calculating and optimizing the efficiency of spiral bevel gears, which is of great significance for improving the design level of spiral bevel gear tooth surfaces and improving the transmission efficiency of spiral bevel gears. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0048] Figure 1 This is a schematic diagram of the spiral bevel gear efficiency optimization design method provided in an embodiment of the present invention.

[0049] Figure 2This is a flowchart of the spiral bevel gear efficiency optimization design method provided in the embodiment of the present invention.

[0050] Figure 3 This is a relative sliding velocity diagram under a certain set of optimal design parameters provided in an embodiment of the present invention.

[0051] Figure 4 This is a diagram showing the suction speed under a certain set of optimal design parameters provided in an embodiment of the present invention.

[0052] Figure 5 This is a load distribution diagram under a certain set of optimal design parameters provided in an embodiment of the present invention.

[0053] Figure 6 This is the minimum oil film thickness curve under a certain set of optimal design parameters provided in the embodiments of the present invention.

[0054] Figure 7 This is the maximum oil film pressure curve under a certain set of optimal design parameters provided in the embodiments of the present invention.

[0055] Figure 8 This is the instantaneous friction coefficient variation curve under a certain set of optimal design parameters provided in the embodiments of the present invention.

[0056] Figure 9 This is the instantaneous transmission efficiency variation curve under a certain set of optimal design parameters provided in the embodiments of the present invention.

[0057] Figure 10 This is the particle swarm-gravity search optimization fitness curve provided in the embodiments of the present invention. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0059] The present invention will be further described below with reference to embodiments.

[0060] Example 1

[0061] Please refer to the instruction manual appendix. Figure 1 A method for optimizing the efficiency of spiral bevel gears includes the following steps:

[0062] S101: Geometric design of spiral bevel gears based on basic parameters; Machining parameter design of spiral bevel gears based on machining parameters;

[0063] Specifically, based on the basic principles and design parameters of spiral bevel gear meshing (including the number of teeth, module, pressure angle, helix angle, tooth width, etc.), basic calculations for the geometric parameters of spiral bevel gears are carried out; then, the initial design and calculation of the machining parameters of spiral bevel gears are performed to obtain the initial machining parameters and their value ranges.

[0064] S102: Conduct geometric contact analysis to obtain geometric contact characteristic parameters; conduct load-bearing contact analysis to obtain load-bearing contact characteristic parameters;

[0065] Specifically, geometric contact analysis (TCA) is performed based on the gear meshing principle to calculate basic parameters such as the contact ellipse, principal curvature direction, and contact path; and load-bearing contact analysis (LTCA) is performed based on mathematical programming and finite element method to calculate gear contact load distribution curves under specific loads.

[0066] S103: Using the fine mesh method, elastohydrodynamic lubrication calculations are performed on spiral bevel gears to obtain oil film parameters; based on the oil film parameters, instantaneous transmission efficiency and average transmission efficiency are calculated.

[0067] Specifically, the following steps are taken: using the fine mesh method, based on the geometric parameters and load-bearing contact parameters obtained from geometric contact analysis (TCA) and load-bearing contact analysis (LTCA), an elastohydrodynamic lubrication model for spiral bevel gears is established and calculations are performed to obtain parameters such as oil film thickness distribution and pressure distribution; based on this, the friction coefficient and transmission efficiency of the spiral bevel gears are calculated to obtain the instantaneous transmission efficiency and average transmission efficiency model of the spiral bevel gears.

[0068] S104: Establish a particle swarm optimization algorithm model that balances convergence efficiency and the globality of the optimal solution to form an optimization design process for spiral bevel gear machining parameters; based on the above optimization process, repeat steps S101 to S103 until the spiral bevel gear machining parameters with the best efficiency are obtained, thereby achieving the optimal parameter design.

[0069] This invention, under the premise of fixed geometric design parameters, improves tooth surface meshing efficiency by adjusting machining or control parameters to modify contact characteristic parameters and reduce tooth surface friction. The method proposed in this invention helps to form an efficient system for optimizing the calculation model of spiral bevel gear efficiency, thereby improving the design level and quality of spiral bevel gears.

[0070] Example 2

[0071] Please refer to the instruction manual appendix. Figure 2 A method for optimizing the efficiency of spiral bevel gears, specifically including the following steps:

[0072] S1: Input of basic design parameters for spiral bevel gears;

[0073] Specifically, based on the design requirements and operating conditions of the spiral bevel gear, determine and input the basic geometric parameters of the gear, which mainly include: number of teeth, module, tooth width, pressure angle, shaft intersection angle, helix angle, and direction of rotation.

[0074] S2: Calculation of basic geometric parameters of spiral bevel gears;

[0075] Specifically, based on the basic parameters of the spiral bevel gear input in S1, and based on the geometric spatial relationship of the spiral bevel gear, the main geometric design parameters are solved by programming, including: the cone distance of the large and small gears, the tooth tip angle, the tooth root angle, the pitch cone angle, the crown tip distance, the arc tooth thickness, etc.

[0076] S3: Initial design of machining parameters for spiral bevel gears;

[0077] Specifically, based on the basic geometric parameters of the spiral bevel gear calculated by S2, and given initial control design parameters such as design overlap ratio, long half shaft, contact path inclination angle, first derivative of transmission ratio, and amplitude of geometric transmission error meshing conversion point, the initial design of the spiral bevel gear machining parameters is carried out, and the initial design machining parameters of the spiral bevel gear are determined. These parameters mainly include: tool tooth profile angle, tool tip distance, radial tool position, angular tool position, rolling ratio, machine position, vertical gear position, horizontal gear position, and machine tool mounting angle.

[0078] S4: Initialize the particles for machining or control parameters of the spiral bevel gear;

[0079] Specifically, based on the basic principles of modern optimization design, and based on the initial design parameters and their value ranges of the spiral bevel gear determined by S3, optimization variables and their value constraints are determined among the machining parameters and control parameters to form the initial particles of the particle swarm-gravity search algorithm, and parameters such as learning factor, weight coefficient, initial velocity, and number of iterations are determined.

[0080] S5: Calculation of discrete tooth surfaces of spiral bevel gears;

[0081] Specifically, based on the particles initialized in S4 (processing parameters and control parameters, etc.), and based on the spatial differential geometry principle of spiral bevel gears, the equation expression of the spiral bevel gear tooth surface is solved, and the discrete points of the spiral bevel gear tooth surface are solved based on numerical calculation.

[0082] S6: Geometric Contact Analysis (TCA) of Spiral Bevel Gears;

[0083] Specifically, based on the basic principle of spiral bevel gear meshing, geometric contact analysis of the large and small gears is carried out to obtain parameters such as the entrainment velocity vector (related to rotational speed), the relative sliding velocity vector (related to rotational speed), the direction vectors of the major and minor semi-axes of the contact ellipse, and the radius of curvature of the major and minor semi-axes of the contact ellipse.

[0084] S7: By establishing a finite element mesh model, using theories such as the finite element method and mathematical programming, and taking the working load as the condition, we carry out the load contact analysis (LTCA) of the spiral bevel gear to obtain the load distribution at the meshing position of the tooth surface.

[0085] Conducting load-bearing contact analysis under applied load conditions includes the following steps:

[0086] Step 1: Establish a solid mesh model based on the coordinates of discrete points on the tooth surface and the finite element mesh definition;

[0087] Step 2: Calculate the compliance matrix of the spiral bevel gear mesh model based on the elements;

[0088] Step 3: Calculate the element deformation based on the load conditions to achieve load-bearing contact analysis;

[0089] The main parameters obtained by load contact analysis (LTCA) of spiral bevel gears include load and load distribution coefficient.

[0090] S8: Calculation of oil film pressure and film thickness, and calculation of transmission efficiency;

[0091] Specifically, it includes:

[0092] ① Based on the relevant data parameters obtained from S6 and S7 calculations, the simulation calculations of parameters such as lubricating oil film pressure and thickness of spiral bevel gears are carried out using the refined mesh method and the basic theory of elastohydrodynamic lubrication; including the following steps:

[0093] Step 1: Calculate the initial mesh, initial pressure, and initial oil film thickness;

[0094] Step 2: Iteratively calculate the pressure and load, and determine whether the convergence condition is met. If convergence is met, proceed to the next step; otherwise, continue the iterative process.

[0095] Step 3: Determine if the grid density has been reached. If it is, output the calculation result; otherwise, return to Step 2 for iterative calculation.

[0096] The main results calculated and output include: oil film pressure and oil film thickness distribution, etc.

[0097] ② Using the oil film parameters and the calculated data in S6 and S7 as input conditions, the sliding friction and rolling friction are calculated, and the instantaneous transmission efficiency of the gear (objective function) is obtained based on this calculation. Then, the average value of the data within one meshing cycle is taken to obtain the average transmission efficiency.

[0098] S9: Updates gravitational coefficient, inertial mass, global optimal particle, etc.

[0099] Specifically, the process involves: calculating particle fitness and updating parameters based on particle fitness; and updating optimization parameters such as gravitational coefficient, inertial mass, and globally optimal particle based on the particle swarm optimization algorithm and the calculated objective function results.

[0100] S10: Calculate particle gravitational force, acceleration, velocity, etc.;

[0101] Specifically, based on S9, the iterative parameters for calculating particle gravity, acceleration, velocity, etc., are further updated to determine the direction of subsequent optimization.

[0102] S11: Determine whether the optimal value and the number of iterations meet the convergence conditions. If the convergence conditions are met, execute S13 and output the optimal solution and optimal design parameters; otherwise, execute S12.

[0103] S12: Optimize design, optimize parameters, and update particles;

[0104] Specifically, the design parameters are updated and iterated based on S9 and S10, and then returned to S5 to continue iterative optimization.

[0105] S13: When the optimization calculation meets the iterative convergence condition, output the optimal solution and the optimal design parameters for efficiency.

[0106] This application uses a particle swarm optimization algorithm to iteratively solve geometric contact analysis, load-bearing contact analysis, elastohydrodynamic lubrication calculation, and efficiency optimization of spiral bevel gears. It can calculate the optimal design parameters and optimal solution that satisfy the constraints.

[0107] in, Figure 3 , Figure 4 These are the relative sliding velocity diagram and the entrainment velocity diagram under the optimal design parameters of a certain example provided in the embodiments of the present invention;

[0108] Figure 5 , Figure 6 , Figure 7 These are, respectively, the load distribution diagram, minimum oil film thickness curve, and maximum oil film pressure curve under the optimal design parameters of a certain example provided in the embodiments of the present invention;

[0109] Figure 8 , Figure 9 The figures show the instantaneous friction coefficient curve and the instantaneous transmission efficiency change curve under the optimal design parameters of a certain example provided in the embodiment of the present invention, wherein the average transmission efficiency is the optimization target of the present invention, and the average transmission efficiency obtained after optimization is 99.58%.

[0110] Figure 10 The particle swarm optimization fitness curve provided in this embodiment of the invention reflects the optimization iteration process of this optimization example.

[0111] This application uses the basic parameters of spiral bevel gears as input conditions to carry out basic geometric design; uses the basic machining parameters or control parameters of spiral bevel gears as adjustable variables to carry out machining parameter design; solves and performs geometric contact analysis (TCA) on the tooth surface model of spiral bevel gears under specific machining parameters to obtain parameters such as tooth surface contact ellipse, contact path, principal curvature principal direction; performs load contact analysis (LTCA) to obtain tooth surface load distribution curve; based on the parameters obtained from geometric contact analysis (TCA) and load contact analysis (LTCA), uses the mesh refinement method to carry out elastohydrodynamic lubrication calculation of spiral bevel gears to obtain oil film thickness and oil film pressure, and calculates the instantaneous transmission efficiency and average transmission efficiency of spiral bevel gears based on this; and uses the particle swarm-gravity search coupled intelligent optimization algorithm as a basis, with machining parameters or control parameters as design variables, carries out optimization with the goal of optimal transmission efficiency, thereby obtaining the machining parameter design with optimal transmission efficiency within a certain range.

[0112] The embodiments of the present invention can be implemented using different optimization algorithms, different programming languages, and different computing platforms. The methods for conducting load contact analysis, elastohydrodynamic lubrication calculation, and efficiency calculation are not unique.

[0113] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing the efficiency of spiral bevel gears, characterized in that: Includes the following steps: S101: Based on the basic principles and design parameters of spiral bevel gear meshing, perform basic calculations for the geometric parameters of spiral bevel gears; then, perform initial design and calculation of the machining parameters of spiral bevel gears to obtain the initial machining parameters and their value ranges; calculate the discrete tooth surfaces of spiral bevel gears according to the initial machining parameters and their value ranges to obtain the coordinates of discrete points on the tooth surfaces. S102: Geometric contact analysis based on gear meshing principle; construct solid mesh model by using discrete point coordinates on tooth surface and finite element mesh definition, and conduct load-bearing contact analysis based on mathematical programming method and finite element method; S103: Using the fine mesh method, based on the geometric parameters and load-bearing contact parameters obtained from geometric contact analysis and load-bearing contact analysis, an elastohydrodynamic lubrication model for spiral bevel gears is established and calculations are performed; based on this, the friction coefficient and transmission efficiency of spiral bevel gears are calculated, and the instantaneous transmission efficiency and average transmission efficiency models of spiral bevel gears are obtained. S104: Establish a particle swarm optimization algorithm model to form an optimized design process for spiral bevel gear machining parameters; repeat steps S101 to S103 until the optimal spiral bevel gear machining parameters are obtained.

2. The method for optimizing the efficiency of spiral bevel gears according to claim 1, characterized in that, Step S101 specifically includes the following steps: S1: Determine and input the basic geometric parameters of the gear according to the design requirements and working conditions of the spiral bevel gear; S2: Based on the basic parameters of the spiral bevel gear input in S1, and based on the geometric spatial relationship of the spiral bevel gear, solve its main geometric design parameters through programming; S3: Based on the basic geometric parameters of the spiral bevel gear calculated in S2, give the initial control design parameters; carry out the initial design of the spiral bevel gear machining parameters, and determine the initial design machining parameters of the spiral bevel gear. S4: Initialize the particles for machining or control parameters of the spiral bevel gear; S5: Based on the particles initialized in S4, calculate the discrete tooth surface of the spiral bevel gear according to the spatial differential geometry principle of spiral bevel gears.

3. The method for optimizing the efficiency of spiral bevel gears according to claim 2, characterized in that, In step S1, the basic geometric parameters of the gear are determined and input, which mainly include: number of teeth, module, tooth width, pressure angle, shaft intersection angle, helix angle and direction of rotation.

4. The method for optimizing the efficiency of spiral bevel gears according to claim 2, characterized in that, In step S2, the main geometric design parameters are solved by programming, including: the cone distance between the large and small gears, the tooth tip angle, the tooth root angle, the pitch cone angle, the crown tip distance, and the arc tooth thickness.

5. The method for optimizing the efficiency of spiral bevel gears according to claim 2, characterized in that, Step S3: Given the initial control design parameters, which mainly include: design overlap ratio, major half-shaft, contact path tilt angle, first derivative of transmission ratio, and magnitude of geometric transmission error meshing transition point; Determining the initial design and machining parameters for spiral bevel gears mainly includes: tool tooth profile angle, tool tip distance, radial tool position, angular tool position, rolling ratio, machine position, vertical gear position, horizontal gear position, and machine tool mounting angle.

6. The method for optimizing the efficiency of spiral bevel gears according to claim 2, characterized in that, Step S102 specifically includes the following steps: S6: Based on the basic principle of spiral bevel gear meshing, geometric contact analysis of the large and small gears is carried out to obtain the entrainment velocity vector, the relative sliding velocity vector, the direction vector of the major and minor semi-axis of the contact ellipse, and the curvature radius parameter of the major and minor semi-axis of the contact ellipse. S7: By establishing a finite element mesh model, using the finite element method and mathematical programming theory, and taking the working load as the condition, we conduct a bearing contact analysis of the spiral bevel gear to obtain the load distribution at the meshing position of the tooth surface.

7. The method for optimizing the efficiency of spiral bevel gears according to claim 6, characterized in that, Step S7 specifically includes the following steps: Step 1: Establish a solid mesh model based on the coordinates of discrete points on the tooth surface and the finite element mesh definition; Step 2: Calculate the compliance matrix of the spiral bevel gear mesh model based on the elements; Step 3: Calculate the element deformation based on the load conditions to achieve load-bearing contact analysis; the main result parameters obtained are: load and load distribution coefficient.

8. The method for optimizing the efficiency of spiral bevel gears according to claim 6, characterized in that, Step S103 specifically includes the following steps: S8: Calculation of oil film pressure and film thickness, and transmission efficiency; specifically including: ①Based on the relevant data parameters obtained from S6 and S7, the pressure and thickness parameters of the lubricating oil film of the spiral bevel gear are simulated and calculated using the fine mesh method and the basic theory of elastohydrodynamic lubrication. ② Using the oil film parameters and the calculated data in S6 and S7 as input conditions, the sliding friction and rolling friction are calculated, and the instantaneous transmission efficiency of the gear is obtained based on this calculation. Then, the average value of the data within one meshing cycle is taken to obtain the average transmission efficiency.

9. The method for optimizing the efficiency of spiral bevel gears according to claim 8, characterized in that, Step ① specifically includes the following steps: Step 1: Calculate the initial mesh, initial pressure, and initial oil film thickness; Step 2: Iteratively calculate the pressure and load, and determine whether the convergence condition is met. If convergence is met, proceed to the next step; otherwise, continue the iterative process. Step 3: Determine if the grid density is met. If it is, output the calculation results. If not, return to Step 2 for iterative calculation. The main results obtained and output are: oil film pressure and oil film thickness distribution.

10. The method for optimizing the efficiency of spiral bevel gears according to claim 8, characterized in that, Step S104 specifically includes the following steps: S9: Based on the particle swarm optimization algorithm, the gravitational coefficient, inertial mass, and global optimal particle optimization parameters are updated according to the optimization variables and the calculated objective function results. S10: Based on S9, further update the calculation parameters for particle gravity magnitude, acceleration, and velocity iteration to determine the direction of subsequent optimization; S11: Determine whether the optimal value and the number of iterations meet the convergence condition. If the convergence condition is met, execute S13 and output the optimal solution and optimal design parameters; otherwise, execute S12. S12: Based on S9 and S10, update and iterate the optimized design parameters, and then return to S5 to continue iterative optimization; S13: When the optimization calculation meets the iterative convergence condition, output the optimal solution and the optimal design parameters for efficiency.

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