The application of robust design in the machinery industry started relatively late. At the beginning, Li Wei introduced robust design into the machinery industry. After Chen Lizhou and others carried out systematic research on this, the robust design method was really known in the machinery industry. Robust optimization design should consider the uncertainty of design variables, objective functions and constraints at the same time, and use statistical methods to obtain the best set of design parameters in the sense of probability. As one of the traditional mechanical parts, spiral bevel gears are widely used. Zhang Lei and others first began to study the application of robust design in spiral bevel gears. By selecting design variables, setting up objective functions and constraints to establish the model, and obtaining satisfactory results based on orthogonal experimental method, the reliability of spiral bevel gear transmission was guaranteed.
However, in general, the optimal solution obtained by robust design mostly appears at the boundary of the feasible region. When the design variable has some disturbance, its corresponding optimal solution will jump out of the feasible region, resulting in the failure of product optimization design. Therefore, it is necessary to combine robust design with modern design methods to improve the robustness and feasibility of design results. Dong Enguo et al. established the double response surface method planetary gear model. Compared with the traditional robust design method, the influence of uncontrollable factors was added to the design variables, and the interference of uncontrollable factors on the calculated results was taken into account, reducing the influence of uncontrollable factors on the design results. Lu Xinchun and others adopted the method of deviation coefficient transformation to control the influence of uncontrollable factors on the objective function, and improved the anti-interference ability of uncontrollable factors; Compared with the traditional robust design results, the optimal parameter design obtained makes the spiral bevel gear transmission more reliable. In addition, Yang Dechun et al. considered the impact of sensitivity and combined robust design with sensitivity to minimize the sensitivity of the obtained optimal solution to changes in design variables. Lin Yanhong will σ The combination of robust design method and sequential quadratic programming method reduces the sensitivity of design results to design variables. On the premise of satisfying the stability of spiral bevel gears, Sun W and others also combined the optimization design method with the sequential quadratic programming method (SQP) to reduce the sensitivity of design results to design variables.
In addition, in the process of spiral bevel gear optimization, the calculation amount of model optimization and nonlinear constraint problem solving is very large, and the solving process is very complex. Therefore, some scholars combine the optimization algorithm with the gear robust optimization design problem to achieve the purpose of efficient solution. Li QC and others used Matlab to optimize the spiral bevel gear model, making the solution process more efficient. In order to solve the computational complexity caused by the nonlinear problem in the optimization design of spiral bevel gears, Artoni A and others used genetic algorithms to carry out the global optimization design of spiral bevel gears, and obtained the global Pareto optimal solution. Li YG and others used BP neural network to approximate the relevant parameters of the optimal design of spiral bevel gears, and used genetic algorithm to search the optimal solution. The combination of the two methods overcame the problem of low computational efficiency of genetic algorithm. Samban ⁃ dam P et al. proposed a new population-based algorithm – selection breeding algorithm, and proposed fitness conditions on this basis, and obtained the optimal design results. Based on the elite non-dominated genetic sorting algorithm NSGA – Ⅱ, Yao Q solved the optimization design problem of the multi-objective model of spiral bevel gears, and overcame the competition between objectives in the single-objective optimization.
Atila U et al. analyzed and studied the application of artificial algae algorithm, artificial bee colony algorithm, whale optimization algorithm, gray wolf optimization algorithm and particle swarm optimization algorithm in the robust optimization design of spiral bevel gears, and compared with traditional genetic algorithm. The results show that the new algorithm has higher efficiency and better performance in solving the robust optimization problem of spiral bevel gears. Wang Chun and others carried out robust optimization design for spiral bevel gears based on improved particle swarm optimization algorithm, and obtained the optimal solution of parameters by taking advantage of the fast convergence speed and strong search ability of the algorithm.
In view of the uncertainty of variables, some scholars combine the fuzzy optimization design theory with the spiral bevel gear optimization to solve the optimal solution in line with the practical application. Zhao Xiaosong and others carried out fuzzy optimization design for spiral bevel gears based on Matlab genetic algorithm toolbox and fuzzy design theory, and not only obtained the optimal solution, but also obtained the impact of various factors on the objective function, providing guidance for selecting the best design scheme.
Wang C uses the fuzzy optimization design theory, takes the minimum volume and maximum efficiency as the objective function, and obtains the optimal solution close to the practical application based on the genetic algorithm of the predator search strategy. Wang J et al. established the mathematical model of fuzzy reliability optimization, solved the model with genetic algorithm, and obtained the optimized results, which made it more in line with engineering practice.
The research has played a very important role in the development of gear design technology. Not only that, the research of robust optimization of gears provides a certain reference for the robust optimization design of spiral bevel gears, but also points out the direction for the research of robust optimization design of spiral bevel gears with installation errors.