Based on the above basic ideas, the optimal design of the double arc gear transmission is divided into two stages. First establish the objective function and determine the constraints. The objective function is an analytical expression that represents a certain performance metric that the design is pursuing. Generally, there are many indicators to be pursued in the design. Obviously, the most important indicators should be used as the goal of design pursuit to establish the objective function. There are two main indicators for the design of arc gear reducer: one is the performance index, that is, the designed reducer has sufficient strength, stiffness and life when transmitting a certain power and speed ratio, and has good craftability and good performance. Dynamic properties. The second is the economic indicator, that is, under the premise of satisfying the performance index, the reducer is expected to have the smallest volume, light weight and low cost, and is competitive in the market.
Through analysis, we take the economic indicators of the reducer as the goal of optimization design, and the performance index is guaranteed by the constraint function of the design variables. That is to say, the total volume of the gear is the minimum goal. After the objective function is determined, according to the known gear ratio, the power gives the parameter range for the solution selection. Using the relationship between continuous variables and discrete variables, the continuous variables are transformed into discrete variables, and the discreteness of the variables is fully used to enumerate all the design points in the range. For each scheme, the infeasible schemes are excluded by using various constraints. Thereby, a plurality of feasible solutions corresponding to each group of discrete variable combinations are obtained. In the second stage, the comprehensive evaluation method of fuzzy mathematics is used. According to the weight coefficient of each evaluation index, each item is judged on each index, and finally the optimal plan is determined.