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The optimization method and the solver are based on the characteristics of the established mathematical model, that is, the constrained nonlinear programming problem. This paper adopts the internal penalty function optimization method. Firstly, the inner point penalty function method is used to transform the constrained optimization problem into an unconstrained optimization problem, and then the POWELL method is used to solve the unconstrained optimization problem. The quadratic interpolation method is used in determining the optimal step size for one-dimensional optimization. According to the above theory and method, the author has compiled a set of calculation procedures, as shown in the program flow chart.
Calculation examples and results analysis A planetary gear transmission system is taken as an example to illustrate the specific implementation process of reliability optimization design. In the design calculation of this paper, the following parameters are used: P=856kW, m=5mm,=7.75×10-6kg/mm3, xi(l)=20mm (i=1,2,...,n), input shaft speed 2150 rpm; tooth shape is involute, =20°, gear material is alloy gear steel 1, both are carburized and quenched, allowable bending fatigue strength is 968 MPa, allowable contact fatigue strength is 2119 MPa, l, k and n They are 8, 4 and 17.
The results of traditional design, optimized design and reliability optimized design are given. It can be seen that the original design f(x)=5.0729×106; the optimal solution can be obtained after 18 iterations, f(x)=4.2746×106, which is 15.45 lower than the traditional design volume; if the penalty function method is used For the reliability optimization design, when the coefficient of variation of the random variable is taken as 0.01, the optimal solution is f(x)=4.4596×106, which is 12.08 lower than the target value by the traditional design method; when the coefficient of variation of the random variable is 0.10 The optimal solution is f(x)=4.7582×106, which is only 6.45 lower than the traditional design method.
General design, optimization design and reliability optimization design results design variables initial design optimization design reliability optimization design (1) reliability optimization design (1) take the coefficient of variation of all random variables is 0.01; (2) take all random variables The coefficient of variation is 0.10.
Conclusion The reliability optimization design method of the gear transmission system proposed in this paper considers the uncertainty affecting the design variables, and the reliability and optimization parameters are closely related to the function form, which avoids the selection of the safety factor in the traditional planetary gear train design method. The unfavorable factors affected by the experience of the designer, and the introduction of performance constraints based on the reliability design criteria, make the optimization model closer to the engineering reality. The numerical analysis results show that the minimum volume ratio of the planetary gearbox obtained by the reliability optimization design method is reduced by 12.08 by the traditional design method, which is 3.37 compared with the general optimization design method, which is mainly due to the consideration of the design variables. Caused by randomness. It can be seen that the parameter optimization design method of planetary gear transmission system based on reliability constraint is much more reasonable than traditional conventional design and general optimization design. It is a comprehensive design method worthy of reference.