A multi-objective parameter optimization method for wind turbine gear systems

Abstract

The present invention discloses a multi-objective parameter optimization method for a wind turbine gear system, which relates to the field of gear vibration optimization. First, a three-dimensional model is established based on the design parameters of a 1.5MW wind turbine gear system, and a rigid-flexible coupling dynamic model is used to perform simulation experiments to increase the real impact during the gear meshing process. Secondly, in order to reduce the vibration impact problem during the meshing process of the wind turbine gear system, and at the same time under the requirement of high-precision volume, an optimization mathematical model is established based on the total overlap of the gear pairs and an improved volume calculation method. Thirdly, in terms of algorithm improvement, the local sparsity of individuals is introduced into the crowding calculation formula with variance to enhance the discrimination of the crowding calculation. In addition, the elite retention strategy is improved by expanding the number of sorting sequences and leaving individuals with high diversity in the front sequence to solve the convergence and extensiveness of individuals in the algorithm optimization. Finally, the performance indicators and experimental results before and after the algorithm improvement are compared to verify the effectiveness of the multi-objective optimization design.

Description

Technical Field

[0001] The invention belongs to the technical field of wind turbine gear system vibration optimization, and relates to a method of parameter optimization modeling and multi-objective optimization algorithm strategy. Background Art

[0002] Gearbox transmission systems are characterized by diverse operating environments, complex operating conditions, and high failure rates. Their proper operation is essential for ensuring the operation of the entire wind turbine. Gear systems are a crucial component of wind turbine power transmission, but due to uncertain external excitations under heavy loads and variable wind speeds, they can generate significant vibration and noise. Therefore, optimizing the design and simulation analysis of wind turbine transmission systems is crucial.

[0003] The design parameters for gear system vibration optimization are mostly complex nonlinear relationships, so their optimization is more difficult than general design optimization. In recent years, with the increasing requirements for lightweight, reliable, and low-noise gears, the requirements for gear vibration optimization have also become higher and higher. Multi-objective optimization problems have become one of the most popular research topics in recent years. Many researchers use multi-objective genetic algorithms to optimize gear system parameter models because it overcomes the problem of falling into local solutions when solving complex nonlinear systems. In the study of multi-objective genetic algorithms, the literature [ZHANG P, QIAN YY, QIAN Q. Multi-objective optimization for materials design with improved NSGA-II [J]. Materials Today Communications, 2021, 28: 102709.] introduced cosine similarity when calculating crowding, so that the population of offspring gathers in the preferred direction, which reflects the superiority of the algorithm in terms of convergence and diversity. Reference [Yang Yuanqing, Zhang Jianlong, Wang Dayong, Zheng Decong. Optimization of 404P tractor gear train based on multi-objective genetic algorithm [J]. Agricultural Engineering, 2022, 12(01): 91-96.] The non-dominated sorting genetic algorithm with elite strategy built into Matlab was used to optimize the mathematical model of the gear train with minimum mass, high fatigue strength and highest shifting smoothness, thereby improving the transmission performance of the gearbox. Reference [JIANG X. Improved NSGA-II for the Job-shop Multi-objective Scheduling Problem [J]. International Journal of Performability Engineering, 2018, 14(5): 891-898.] The non-dominated sorting algorithm was optimized, and an improved elite strategy was used to dynamically adjust the elite solution set of NSGA-II. The global search capability and solution efficiency of the improved algorithm were then verified through a multi-objective JSP example. Reference [Jiang Yixiao, Ji Weixi, He Xin, Su Xuan. Multi-objective flexible job shop low-carbon scheduling based on improved non-dominated sorting genetic algorithm [J]. China Mechanical Engineering, 2022, 33(21): 2564-2577.] Considering the population evolution stage and individual quality, a probability distribution function is designed to replace the traditional non-dominated sorting and crowding size determination retention strategy, and add corresponding retention probabilities for individuals of different non-dominated levels.Reference [Zhang Chaoyong, Dong Xing, Wang Xiaojuan, Li Xinyu, Liu Qiong. Multi-objective flexible job shop scheduling based on improved non-dominated sorting genetic algorithm [J]. Journal of Mechanical Engineering, 2010, 46(11): 156-164.] introduced a distribution function in the improvement of the elite retention strategy to limit the number of parent elite solutions, thereby improving the NSGA-II algorithm and avoiding the phenomenon that most non-dominated solutions are on the non-dominated surface of order 1 during the evolution process. Reference [Wang Rongbing, Xu Hongyan, Guo Jun. Adaptive non-dominated sorting genetic algorithm [J]. Control and Decision, 2018, 33(12): 2191-2196.] proposed an adaptive non-dominated sorting elite retention method, whose adaptive parameters are adjusted according to the algorithm running stage, running generation and population non-dominated individuals, thereby improving the convergence and diversity of the original algorithm. Reference [Liu Caijie, Xu Zhitao, Zhang Qin, Zhang Libo, Yao Kun. Green Scheduling of Flexible Job Shops Based on NSGA-Ⅱ under Time-of-Use Electricity Prices [J]. China Mechanical Engineering, 2020, 31(05): 576-585.] For the problem of multiple individuals with the same target value when solving the algorithm, the new individuals are excluded in the subsequent process, and the elite retention strategy is used to obtain a new population by grouping, statistics, and screening. Reference [Yuan Shuaipeng, Li Tieke, Wang Bailin. Improved Fast Non-dominated Sorting Genetic Algorithm with Elite Strategy for Multi-objective Steelmaking-Continuous Casting Production Scheduling [J]. Computer Integrated Manufacturing Systems, 2019, 25(01): 115-124.] An adaptive grid method selection strategy is proposed to improve the fast non-dominated sorting genetic algorithm with elite retention strategy, which overcomes the deficiency of the traditional Pareto dominance method in losing useful information when selecting discrete individuals.

[0004] Considering volume as one of the optimization target models, the literature [Marcelin J L. Genetic Optimisation of Gears [J]. The International Journal of Advanced Manufacturing Technology, 2001, 17 (12): 910-915.] uses a genetic algorithm to perform multi-objective optimization of gear pairs, and uses weighted factors combined with the average method to calculate the objective functions such as the volume of the gear pair, the balance of sliding velocity, and the balance of contact pressure for optimization design. The literature [Zong Changfu, Ren Minghui, Wan Ying, et al. Macro-parameter Vibration Reduction Optimization Design of Transmission Helical Gears [J]. Journal of Jilin University: Engineering Edition, 2016, 46 (6): 1772-1779.] uses a weighted genetic algorithm to optimize the improved Ishikawa method, taking the obtained transmission error and volume as the optimization objects, and achieves a vibration reduction effect. References [Yan Fuwu, Wang Hongjian, Tian Shaopeng, et al. Multi-objective reliability optimization of transmission gear train based on the second generation non-dominated sorting genetic algorithm [J]. Automotive Engineering, 2010 (3): 234-237.] Multi-objective genetic algorithm is used to optimize the three objective functions of volume, center distance and overlap, and the Pareto optimal solution set is obtained. References [SedakM, B.Multi-objective Optimization of Planetary Gearbox with AdaptiveHybrid Particle Swarm Differential Evolution Algorithm[J].Applied Sciences,2021,11(3):1107.] Taking into account factors such as the volume, center distance, contact ratio, and power loss of the planetary gearbox, the weight of the gear is reduced, the transmission efficiency is improved, and the premature failure of the gear is prevented. References [Jiang Chunming, Ruan Miqing. Multi-objective reliability optimization design of automotive mechanical transmission[J].Automotive Engineering,2007,29(12):1090-1093.] Taking the gear transmission as the research object, the optimization objective function of minimizing the volume of the gear system and maximizing the gear overlap is established, and the optimization tool Matlab is used for optimization. Reference [Zhao Ning, Yang Jie. Multi-objective optimization design of high-contact cylindrical gear transmission [J]. Mechanical Transmission, 2012, 36(7):4.] Taking the maximum contact of gear pairs, the minimum pitch circle volume and equal bending strength as the optimization objectives, a mathematical model for the multi-objective optimization design of cylindrical gear pairs was established, and the optimization was carried out using the NSGA-II algorithm.

[0005] In summary, in view of the defects of the existing multi-objective parameter optimization method of gear system, corresponding solutions are proposed:

[0006] (1) Existing gear system parameter optimization methods often use approximate solution formulas when using gear volume as a multi-objective optimization mathematical model, resulting in low gear accuracy. To meet the high-precision requirements for helical gear system volume calculations, this paper proposes a formula for solving the arc length at any cross section of the gear teeth, which is then converted into a calculation method of arc integral. Finally, a calculation method for solving the gear volume with high accuracy is derived.

[0007] (2) The existing NSGA-II algorithm cannot obtain better individuals. Existing studies mostly adopt conventional elite retention strategies to retain excellent population individuals; and use crowding calculation formulas with less discrimination effect to retain population individuals with better diversity. These strategies have the defects of a fixed number of excellent individuals and low discrimination of diverse individuals in the population. The improved algorithm of the present invention realizes the discrimination strength of population individual crowding calculation and retains more population individuals with higher diversity, finally solving the existing shortcomings of the algorithm. Summary of the Invention

[0008] Building on the research of numerous scholars on multi-objective gear optimization, a mathematical model for increasing the contact ratio and reducing the volume of high-speed helical gears in wind turbine gear systems was established to mitigate meshing impact vibration. The calculation of the gear clearance volume is often overlooked, but it affects the accuracy of helical gear volume calculations, so the clearance volume of the gear should be considered. Based on these limitations, a formula for calculating the arc length on any cross-section of a helical gear tooth was derived, which was then used to calculate the clearance volume. Finally, an improved multi-objective genetic algorithm was employed for optimization, and the performance of the improved algorithm was evaluated using inversion generation distance and diversity metrics.

[0009] In view of this, the technical solution adopted by the present invention is: a method for optimizing parameters of a wind turbine gear system, comprising the following steps:

[0010] Step 1: Establish a three-dimensional model of the rigid-flexible coupling of the wind turbine gear system. The vibration effects caused by meshing impact during gear engagement are analyzed. The high-speed stage of the wind turbine gear system is selected as the optimization target. The parallel-axis helical gear system of the wind turbine gear system is then made flexible to establish a rigid-flexible coupling dynamic model. When establishing the wind turbine gear system model, the present invention utilizes flexible processing of the optimized helical gear stage to ensure realistic deformation during gear meshing.

[0011] Step 2: To address the impact vibration generated during meshing of wind turbine gear systems, we improved gear meshing smoothness and reduced gear volume as a means of reducing meshing impact. A mathematical model for wind turbine gear system optimization was established, with the objective functions being the total gear pair contact and volume.

[0012] Step 3: Based on the range of the upper and lower limits of the variables in the optimized mathematical model and in combination with the gear-related constraints, a generation of initial populations is randomly generated. The objective function value is calculated by optimizing the mathematical model and then substituted into the improved multi-objective genetic algorithm for solution. The present invention uses an improved multi-objective genetic algorithm to optimize the dual-objective mathematical model. The algorithm introduces a sparse factor of individuals in the local range and combines it with the variance solution formula in the global space and improves the idea of ​​the elite retention strategy.

[0013] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the above-mentioned method for multi-objective parameter optimization of a wind turbine gear system when executed by a processor.

[0014] Compared with the existing technology, the present invention has the following beneficial technical effects:

[0015] (1) In terms of dynamic simulation model, in order to highlight the characteristics of the meshing process of the optimized object of the wind turbine gear system, flexible processing is used to optimize the gear stage system. The other gear stages maintain rigid characteristics. At the same time, the influence of gear bearing deformation can be ignored. Finally, the simulation results before and after optimization can be truly reflected.

[0016] (2) A method for calculating the gap volume is proposed, which can solve for the arc length of any gear tooth cross section. The parametric equation of the elliptical mapping can be used to solve for the cross-section arc length, and then the gap volume can be calculated. The calculation accuracy of the helical gear volume is significantly improved.

[0017] (3) In terms of crowding calculation, the characteristics of local and global uniformity are taken into account, and an improved operator is used for calculation to avoid mistakenly retaining individuals with poor diversity. In order to solve the problem of mistakenly retaining poor individuals in the same front sequence in the traditional elite retention strategy, which leads to poor diversity between individuals, an attenuation factor is introduced to expand the scale of the elite retention sequence to retain individuals with higher diversity in different front sequences to a greater extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is the structural principle diagram of the wind turbine transmission system;

[0019] Figure 2 Flowchart for multi-objective optimization algorithm;

[0020] Figure 3 Keep the strategy map for the elite;

[0021] Figure 4 is the Pareto optimal solution set before and after the improvement of the multi-objective genetic algorithm;

[0022] Figure 5 Graph of non-dominated sequence values ​​in the elite retention strategy before and after optimization algorithm improvement;

[0023] Figure 1 Among them, ① wind wheel, ② first-stage planetary gear system, ③ second-stage parallel shaft helical gear, ④ third-stage parallel shaft helical gear, ⑤ generator. DETAILED DESCRIPTION

[0024] (1) Establishing a rigid-flexible coupling model of wind turbine gear system

[0025] The wind turbine gear system transfers the wind energy absorbed by the wind turbine blades to the generator and obtains the corresponding motion state. It is the core part of power transmission. The gearbox transmission system combines the first-stage planetary gear with the second-stage parallel-axis helical gear system by taking advantage of the compact structure, small size, smooth transmission and large transmission ratio of the planetary gear system and the parallel-axis gear system. Its design parameters are: rated power of 1.5MW, transmission ratio set to 97.4; input speed of 17r / min. Material parameters, 20CrMnMo alloy structural steel is used, Young's modulus E = 200Gpa, Poisson's ratio μ = 0.3, mass density ρ = 7850kg / m 3 .

[0026] like Figure 1 As shown in the figure, the rigid-flexible coupling dynamic model includes a wind wheel ①, a first-stage planetary gear train ②, a second-stage parallel-axis helical gear ③, a third-stage parallel-axis helical gear ④, and a generator ⑤. First, the wind wheel ① acts as the input stage to drive the planetary gears of the first-stage planetary gear train ② to rotate. After acceleration, the output speed of the sun gear of the first-stage planetary gear train ② drives the second-stage parallel-axis helical gear ③ to rotate. Then, the output-stage gear of the second-stage parallel-axis helical gear ③ drives the transmission shaft to drive the third-stage parallel-axis helical gear ④ to rotate. Finally, the third-stage parallel-axis helical gear ④ drives the connecting shaft of the generator and the high-speed gear to rotate together.

[0027] According to the structural principle Figure 1 , impose constraints on the simulation process. The gear model established in the SolidWorks environment and the gear modal neutral file in ANSYS are imported into ADAMS and replaced with a rigid-flexible coupling model. Constraints are added to each part of the wind turbine gear system. For planetary stage transmission, a rotating pair of the planetary carrier and the sun gear relative to the ground, a rotating pair between the planetary gear and the planetary carrier, and a fixed pair of the inner ring gear relative to the ground are imposed. For medium and high speed transmission, a fixed pair of the gear relative to the rotating shaft, and a rotating pair of the rotating shaft relative to the ground are imposed. Contact forces are added between gears, and the contact types are between entities and between flexible bodies. In order to simulate the working principle between the gear system and the generator, the speed absorbed by the wind turbine is applied to the planetary carrier, and a counter-torque relative to the speed is applied to the high-speed stage shaft. The design parameters of the wind turbine gear system are shown in Table 1.

[0028] Table 1 Basic parameters of wind turbine gear transmission system

[0029]

[0030]

[0031] In the simulation, the gear meshing relationship is defined as the contact collision force based on the impact function, that is, the gears interact with each other through the contact collision force and friction force. The specific function expression is:

[0032]

[0033] Where k is the contact stiffness coefficient, e is the nonlinear index, and F s is a step function, C max is the maximum damping coefficient when the maximum penetration depth is reached, d c is the penetration depth at maximum damping. x is the contact penetration between gears.

[0034] According to Hertz contact theory, the gear contact parameters in ADAMS are obtained, and the contact stiffness coefficient between gears is:

[0035]

[0036] Where, E1 and E2 are the elastic moduli of the two gear materials, μ1 and μ2 are the Poisson's ratios of the two gear materials, and R1 and R2 are the pitch circle radii of the two gears.

[0037] (2) Establish a dual-objective model that increases overlap and considers gap volume

[0038] While ensuring reasonable mechanical properties and reliability, the gear system requires a compact and lightweight gear transmission structure to save materials and reduce costs. Therefore, volume is used as one of the optimization objective functions. The volume of helical gears is generally solved by an approximate method, and the accuracy of the solution is not high. The volume of the helical gear is approximately represented by a cylinder with the same diameter as the pitch circle of the gear. In solving the volume of helical gears, the volume of the gear clearance should be considered to improve the accuracy of the volume solution. The tooth profile of the helical gear tooth surface is an involute, so a mapping ellipse method of the cross section at the tooth profile point is used to solve the arc length at the gear clearance along the spiral angle direction.

[0039] The helix angle of the helical gear is β, and the cross-sectional circle with a radius of r is projected into an ellipse in the helical direction. Its equation is:

[0040]

[0041] Where x is the horizontal coordinate of the cross-section circle, and y is the vertical coordinate of the cross-section circle.

[0042] The cut cylinder S i The arc length is:

[0043]

[0044] Where θ is the differential symbol of the arc length integral, It is the included angle of arc length of any cross section of the gear tooth.

[0045] It can be obtained from the characteristics of the pitch circle. Taking the pitch circle section as the boundary, the arc length angle at any cross section of the gear tooth The expression is:

[0046]

[0047] Where r is the radius of any section circle, r0 is the radius of the pitch circle, is the arc of a single tooth at the pitch circle.

[0048] The cross section of the tooth point at the gap of the helical gear is an inclined curve, so the gap volume is regarded as a cuboid along the tooth cross section, and its expression is:

[0049] V j =S i hlz (6)

[0050] Where S i is the arc length of any section, h is the gap height, l is the length of the gear tooth, z is the number of gear teeth, V j is the clearance volume of the helical gear.

[0051] in,

[0052] h=h f -h a

[0053] Where h f is the tooth root height, h a It is the tooth top height.

[0054] Considering the gear clearance, the total volume V of the high-speed gear pair is:

[0055]

[0056] Where i is the transmission ratio of the high-speed stage.

[0057] The objective function of the optimized design is designed by formula (7):

[0058]

[0059] For the vibration analysis purposes proposed in this study, gear pair contact was selected as one of the optimization targets. This can reduce vibration response, improve gear transmission smoothness, and enhance mechanical performance. Contact is defined as the ratio of the length of the meshing line of a pair of gears to the base circle pitch. The total contact of helical gears is composed of two parts: the end face contact and the axial face contact:

[0060] ε=ε α +ε β (9)

[0061] where ε α is the gear pair end face contact ratio, ε β is the axial contact ratio of the gear pair, which is calculated as:

[0062]

[0063]

[0064] Where z1 and z2 are the number of teeth of the small gear and the large gear, and α is t1 , α t2 is the tooth tip circle end surface of the pinion and gear, α' t is the gear end face engagement angle, b is the tooth width, m n is the normal modulus, and β is the helix angle.

[0065] in:

[0066] α t =arctan(tanα n / cosβ) (12)

[0067]

[0068]

[0069] Where, α n represents the normal pressure angle, Indicates the gear modification coefficient.

[0070] The trend of increasing overlap is defined as the target optimization function by equations (10) and (11):

[0071]

[0072] The design variables are determined based on the selected objective function. The optimization of the helical gear contact ratio and volume is affected by the main parameters such as gear module, gear width, number of teeth, and helix angle. While maintaining a fixed transmission ratio, other variable parameters are optimized. The design variables are:

[0073] X=[x1,x2,x3,x4] T =[m n ,z1,b,β] T

[0074] Constraints C1 and C2 on the number of teeth of the driving gear not less than the minimum number required to produce undercutting:

[0075]

[0076]

[0077] To ensure high efficiency of gear transmission, the constraint condition C3 that the axial overlap is greater than 1 is:

[0078]

[0079] Minimum tooth top thickness constraint C4:

[0080]

[0081] Where, d a is the diameter of the tooth top circle, α is the pitch circle pressure angle, α a is the tooth top circle pressure angle, and x is the displacement coefficient.

[0082] The pinion tooth width meets Constraints C5 and C6:

[0083]

[0084]

[0085] Where, Represent the lower and upper limits of the tooth width conditions, respectively, and then Take 0.9, Take 1.4, d represents the gear pitch circle diameter.

[0086] Tooth surface contact fatigue strength constraint C7:

[0087]

[0088] In the formula, [σ H ] is the allowable contact stress, K represents the gear load coefficient, and T1 is the load torque of the high-speed gear.

[0089] The bending fatigue strength constraint C8 of the high-speed shaft pinion is:

[0090]

[0091] Bending fatigue strength constraint C9 of high-speed shaft gear:

[0092]

[0093] In the formula, [σ F ]1、[σ F ]2 represents the allowable bending stress of the pinion and gear, It represents the tooth width coefficient, and Y1 and Y2 are the tooth shape coefficients of the high-speed pinion and gear.

[0094] The tooth form factor for high-speed stage is calculated as follows:

[0095]

[0096] Y2=0.2824+0.0003539(i1z1)-0.000001576(i1z1) 2 (26)

[0097] (3) Improved multi-objective optimization algorithm

[0098] Improve the elite retention strategy and congestion calculation method of the multi-objective genetic algorithm to increase the convergence and extensiveness of individuals in the algorithm optimization process. According to the multi-objective genetic algorithm strategy, define the optimization variables, optimization objectives, and constraints of the wind turbine gear system. Figure 2 As shown, the improved multi-objective optimization algorithm includes the following steps:

[0099] (3.1) Initialize the population P0 within the range of the upper and lower limits of the optimization model parameters;

[0100] (3.2) Perform fast non-dominated sorting and congestion calculation on the population P0; when the population is the first generation initial population, the population is used as the initialization population for the next generation cycle. Non-dominated level i rank and crowding distance i d , if i rank ≤j rank And i d >j d , it means that individual i is better than j. In order to avoid mistakenly retaining poor individuals and ensure population diversity, the present invention adopts a method of using the individual variance value in the local range as a sparse factor in the global space, and then combines it with the individual variance solution formula in the global space, which not only ensures the uniformity of the individual local distance distribution but also takes into account the uniformity of the individual distance distribution in space. k The size of determines the diversity of individuals. The crowding distance formula is:

[0101]

[0102]

[0103] Where, is the original crowding calculation formula after sorting the targets, N is the population size, is the target mean of individual i, and It is expressed as the target value before and after individual i, and represents the maximum and minimum values ​​of an individual, The summation base expression representing the target value of individual i.

[0104] (3.3) Use the evolutionary method of selection, crossover, and mutation to obtain subpopulations and construct a new population with twice the size of the original population;

[0105] (3.4) Perform fast non-dominated sorting and crowding calculation on the reconstructed population; each individual in the population has two characteristics that use the calculated crowding distance and sequence value to prepare for population pruning;

[0106] (3.5) The population doubles due to the merger of the parent and child populations. The elite retention strategy calculates the crowding degree after non-dominated sorting and retains the initial population size until it reaches a certain size, with a greater probability of retaining the best individuals in the evolution process. Since the traditional elite retention strategy is fixed, it will lead to poor diversity among individuals, which in turn affects the convergence of the solution set. Figure 3 As shown, the present invention introduces an attenuation factor of the elite retention strategy, which is used to expand the scale of the sorted sequence and retain the individuals with the highest diversity in the front sequence to the greatest extent. Its calculation formula is:

[0107]

[0108] Where p is the rate of individuals retained in the front sequence, α is the attenuation factor, which ranges from 0.1 to 0.01, and k is the total ranking value.

[0109] (3.6) Determine whether the number of iterations a has been reached. If not, go to step (3.3) and continue until the set number of loops a is reached, and then output the optimal solution.

[0110] Multi-objective optimization algorithms are evaluated based on the convergence and diversity of their solution sets. The widely used IGD (Inverted Generational Distance) and Spread diversity metrics are used. The IGD performance metric represents the minimum sum of distances between individuals on the true Pareto front and the set of individuals obtained by the algorithm. Smaller IGD performance metrics indicate better convergence and distribution of the algorithm. It is calculated as:

[0111]

[0112] Where N * is the size of the solution set, d i is the Euclidean distance from the i-th true frontier point to the solution set. The smaller the evaluation index is, the better the convergence of the algorithm.

[0113] Spread diversity index measures the breadth of the solution set. The smaller the value of Spread, the better the diversity of the solution set. It is calculated as:

[0114]

[0115] Where, is the average distance, d l is the minimum Euclidean distance of non-dominated sorting, d f is the maximum Euclidean distance of the non-dominated sort.

[0116] The structural principle diagram of the multi-objective parameter optimization of the wind turbine gear system is as follows Figure 1 . Figure 2 This is the flow chart of the multi-objective optimization algorithm. Figure 3 Schematic diagram of the improved elite retention strategy. Figure 4 The results of the optimization algorithm before and after improvement show that the solution set obtained by the improved NSGA-II algorithm is better than that of the standard NSGA-II algorithm, closer to the Pareto front ideal curve, and has a better distribution. From the distribution of non-dominated sequence values ​​in the elite retention strategy before and after improvement Figure 5 It can be seen that the improved NSGA-II algorithm has more sequence value distributions, achieving the purpose of expanding the retention of excellent individuals in non-dominated sorting.

Claims

1. A multi-objective parameter optimization method for a wind turbine gear system, characterized in that: The following steps are involved: Step 1: Select the high-speed stage of the wind turbine gear system as the optimization object, and make the parallel-axis helical gear system of the wind turbine gear system flexible to establish a rigid-flexible coupling dynamic model; Step 2: Establish a mathematical model for optimizing the wind turbine gear system. The objective function of the model is the total contact ratio of the gear pairs and the improved volume formula. The mathematical model with the total contact ratio and volume of the gear pair as the optimization target is as follows: Where m n is the normal module, z1 and z2 are the number of teeth of the pinion and gear, b is the tooth width, i is the transmission ratio, β is the helix angle, V j Considering the clearance volume for the helical gear stage, α t1 , α t2 is the tooth tip circle end surface of the pinion and gear, α′ t is the gear end face engagement angle; When calculating the volume of helical gears with volume as the optimization objective, the volume of the gear clearance is taken into account as follows: The helix angle of the helical gear is β, and the cross-sectional circle with a radius of r is projected into an ellipse in the helical direction. Its equation is: Where x is the abscissa of the cross-section circle, and y is the ordinate of the cross-section circle; The arc length of the intercepted single tooth width is: Where θ is the differential symbol of the arc length integral, Consider the included angle of arc length of any cross section of the gear tooth; It can be obtained from the characteristics of the pitch circle. Taking the section at the pitch circle as the boundary, the arc length angle at any section of the gear tooth is The construction formula is: Where r is the radius of any section circle, r0 is the radius of the pitch circle, is the arc of a single tooth at the pitch circle; Then the clearance volume of the helical gear is: V j =S i hlz (8) Where h is the gap height, S i is the arc length of any section, l is the length of the gear tooth, and z is the number of gear teeth; in, h=h f -h a Where h f is the tooth root height, h a is the tooth top height; Step 3: Based on the range of upper and lower limits of the variables in the optimized mathematical model and combined with the gear-related constraints, a generation of initial population is randomly generated, and the objective function value is calculated by optimizing the mathematical model and substituted into the improved multi-objective genetic algorithm for solution; specifically, the following steps are included: (1) Initialize the population P0 within the value range of the optimization variable; (2) Perform fast non-dominated sorting and congestion calculation on the population P0; when the population is the first generation initial population, the population is used as the initialization population for the offspring cycle, and the non-dominated level i rank and crowding distance i d , if i rank ≤j rank And i d >j d , it means that individual i is better than j; through dis k The size of determines the diversity of individuals, and the crowding distance formula is: Where, is the original crowding calculation formula after sorting the targets, N is the population size, is the target mean of individual i, and It is expressed as the target value before and after individual i, and represents the maximum and minimum values ​​of an individual, The summation base expression representing the target value of individual i; (3) Using the evolutionary method of selection, crossover, and mutation to obtain subpopulations, and construct a new population with twice the number of the original population; (4) Perform fast non-dominated sorting and crowding calculation on the reconstructed population, and use the calculated crowding distance and sequence value to prepare for population pruning; (5) The elite retention strategy is used to prune the population to its original size. By introducing the α decay factor, the diversity of the population is increased and the size of the sequence values ​​in the pruned population is expanded. The elite retention strategy is: Where p is the individual retention rate of the front-end sequence, and α is the attenuation factor; (6) Determine whether the number of cycles a has been reached. If not, go to step (3) and continue until the set number of cycles a is reached, and then output the optimal solution.

2. The multi-objective parameter optimization method for a wind turbine gear system according to claim 1, characterized in that: The rigid-flexible coupling dynamic model includes a wind wheel (①), a first-stage planetary gear train (②), a second-stage parallel-axis helical gear (③), a third-stage parallel-axis helical gear (④), and a generator (⑤). First, the wind wheel (①) serves as an input stage to drive the planetary gear of the first-stage planetary gear train (②) to rotate. After acceleration, the output speed of the sun gear of the first-stage planetary gear train (②) drives the second-stage parallel-axis helical gear (③) to rotate. Then, the output-stage gear of the second-stage parallel-axis helical gear (③) drives the transmission shaft to drive the third-stage parallel-axis helical gear (④) to rotate. Finally, the third-stage parallel-axis helical gear (④) drives the connecting shaft of the generator and the high-speed gear to rotate together.

3. The multi-objective parameter optimization method for a wind turbine gear system according to claim 2, characterized in that: Gears interact with each other through contact collision force and friction force. The specific function expression is: Where k is the contact stiffness coefficient, e is the nonlinear index, and F s is a step function, C max is the maximum damping coefficient when the maximum penetration depth is reached, d c is the penetration depth at maximum damping, x is the contact penetration between gears; The contact stiffness coefficient between gears is: Where, E1 and E2 are the elastic moduli of the two gear materials, μ1 and μ2 are the Poisson's ratios of the two gear materials, and R1 and R2 are the pitch circle radii of the two gears.

4. The multi-objective parameter optimization method for a wind turbine gear system according to claim 1, characterized in that: The optimization of the objective function is affected by the following parameters: The driving gear should not have less than the minimum number of teeth required to produce undercutting. Constraints C1 and C2: To ensure high efficiency of gear transmission, the constraint condition C3 that the axial overlap is greater than 1 is: Minimum tooth top thickness constraint C4: Where, d a is the diameter of the tooth top circle, α is the pitch circle pressure angle, α a is the tooth tip circle pressure angle, x is the displacement coefficient; The pinion tooth width meets Constraints C5 and C6; Where, They represent the lower and upper limits of the tooth width conditions, and d represents the pitch circle diameter of the gear; Tooth surface contact fatigue strength constraint C7: In the formula, [σ H ] is the allowable contact stress, K represents the gear load factor, and T1 is the load torque of the high-speed gear; Bending fatigue strength constraint condition C8 of high-speed shaft pinion: Bending fatigue strength constraint condition C9 of high-speed shaft gear: In the formula, [σ F ]1、[σ F ]2 represents the allowable bending stress of the pinion and gear, It represents the tooth width coefficient, and Y1 and Y2 are the tooth shape coefficients of the high-speed pinion and gear.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the wind turbine gear system multi-objective parameter optimization method according to any one of claims 1 to 4 are implemented.

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