Objective Function of Parametric Optimization of the Speed of a Closed Planetary Mechanism Formed by Two Simple James Planetary Mechanisms

Abstract

The results of building а mathematical model of estimation the speed of the designed construction of the closed planetary mechanism formed from two simple planetary mechanisms of James are presented. The speed of the designed construction of the mechanism is estimated by the value of the equivalent moment of inertia of the mechanism links reduced to its input shaft. A model is a dimensionless function (analogue the equivalent moment of inertia) of two variables - transmission relations of simple planetary mechanisms, and set of numerical parameters. The parameters take into account the values of the coefficients that characterize the mass inertia models of gears and planet carriers, the design and strength limitations of external gears of simple planetary mechanisms of James, as well as the structure of these mechanisms. Set of values of parameters and range of varying of possible values of transmission relations of simple planetary mechanisms influence on position of a minimum of the analogue the equivalent moment of inertia. The influence of the number of planetary gears of simple planetary mechanisms and the moment of inertia of the planet carrier of the differential mechanism on the positions of the minima of the analogues of the reduced moment of inertia of a closed planetary gear was analyzed in calculations for contact strength and bending strength. Based on the function of the analogue of the equivalent moment of inertia, the objective function of parametric optimization of the project fast-acting of the design of a closed planetary mechanism is built. Keywords: simple James planetary mechanism (mechanisms type ); closed planetary mechanism; moment of inertia of gear-wheel; moment of inertia of the planet carrier; moment of inertia of the planetary mechanism; contact strength of the gearing; bending strength of the gearing; parametric optimization; parametric optimization of the equivalent moment of inertia of the planetary mechanism