Optimization of gear three dimensional modification based on genetic algorithm

The determination method of gear modification parameters is usually based on theoretical calculation or experimental induction, this method is generally difficult to obtain the ideal optimal solution, using genetic algorithm can be more simple to obtain the optimal solution required by the problem. Genetic algorithm is an adaptive global optimization algorithm which imitates the principle of genetic evolution in nature. Firstly, it encodes the object to be studied and generates the initial population. Each individual in the population is a solution of the problem, and carries on the iterative process repeatedly. In each generation, the fitness is used to determine the quality of each individual in the population, and then through the selection and interaction, it can determine the quality of each individual in the population Crossover and mutation operations generate the next generation of individuals.

Among them, selection means that according to the fitness value of each individual, the higher the fitness value, the higher the probability of being selected, and then carry out cross mutation operation to generate new individuals to ensure the diversity of the population. In this way, the population will evolve in the direction of increasing fitness. After several generations of genetic evolution, it will reach or approach the optimal solution of the problem. The working principle of genetic algorithm is shown in Figure 1.

Genetic algorithm mainly includes decoding and coding of parameters, definition of initial population, fitness analysis and selection, crossover, mutation and other steps. The optimization process of genetic algorithm is shown in Figure 2. The four modification parameters of gear are taken as the optimization object. Firstly, each modification parameter is coded and binary coding is used to facilitate the subsequent calculation. Then initialize the population, randomly generate a certain number of population within the variable range of gear modification parameters, and set the number of population n = 100. Then, the fitness of each individual in the population is analyzed, and the fitness function is set as the reciprocal of the gear transfer error. In this way, the larger the fitness value of the defined individual, the better the quality of the individual. According to this method, the fitness value of each individual in the population is analyzed and sorted according to the size. Then the selection, crossover and mutation were carried out. Among them, roulette is used in the selection operation, that is, the probability of each individual being selected is determined according to the percentage of each individual’s fitness value in the total fitness value of the whole population. Crossover and mutation can produce new individuals in the population. Here, the crossover probability is 0.5 and the mutation probability is 0.5. Through the above steps, a new generation of individuals is generated. After iteration to the k-th generation, if the population converges, the calculation will stop, otherwise the iterative calculation will continue until the termination condition is met.

It is very important to optimize the modification parameters of gear by genetic algorithm. As shown in Fig. 3, the optimization result of genetic algorithm for the drum shape in tooth direction is given. It can be seen from Fig. 3 that the optimal tooth drum shape obtained by genetic algorithm is 5.67 μ M. according to this method, the optimal tooth inclination is – 11 μ m, the optimal involute drum shape is 12.31 μ m, and the optimal involute inclination is – 4.8 μ M.