Моделирование и анализ параметрической оптимизации массы замкнутого планетарного механизма, образованного двумя простыми планетарными механизмами Джеймса

Abstract

The mathematical model of estimation of a design mass of the closed planetary mechanism formed from two simple planetary mechanisms of James (mechanism of type A͞I ), taking into account their structural diagrams and design constraints, determined by the conditions of contact and bending strengths of external gearing of sun gears and satellites, is offered. A model is a dimensionless function (analogue of mass) of two variables – transmission relations of simple planetary mechanisms, and set of numerical parameters. As parameters of analogue of mass coefficients are chosen, characterizing the models of mass of gear wheels and carriers, structural and strength limitations of the external gearing of simple planetary mechanisms of the type A͞I, and also structure of these mechanisms. In the program Mathcad differential properties of the offered model and influence on position of minimum of analogue of mass are investigational depending on the numerical values of his parameters. Documents of the Mathcad program are presented that implement computer modeling of algorithms for parametric optimization of mass closed planetary mechanism, where the function of the analogue of the mass of the given mechanism is used as the objective function. A comparative analysis of minimizing the design mass of two kinematic schemes of planetary mechanisms is considered – closed planetary mechanism and in-line planetary of the type 2 × A͞I.