Dynamic research of elementary differential gear with elastic links

Abstract

Many research works are devoted for study of static and dynamic parameters of planetary gears of various designs. A number of dynamic problems can be solve accurately enough without taking into account the elasticity of loaded elements. In calculations of mining machines transmissions dynamic processes must be considered gear flexibility as is much more than flexibility of large diameter and small length shafts. In this article are considered possibilities and features of research of dynamic phenomena that take a place in planetary mechanisms of mining machine transmissions. For this purpose planetary mechanisms are presented as elastic mechanical systems. For research the dynamic model of elementary differential mechanism with taking into account the link elasticity is used. For this purpose the differential gear presented as equivalent planetary row with inertialess planetary carrier. Main links of such mechanism have inertia moments determined by known formulas. The equivalent dynamic model of elementary differential gear is presented as three-mass branched system. Moments of elasticity, occurring in mechanical constraints of system, are determined. Equations of movement for each of the masses give the linear homogeneous differential equation system or free oscillations equation system of mechanism. This system is representable as linear algebraic equation system. Particular solutions of inhomogeneous differential equation system are of practical interest, as they permit to make the analysis of the effect of external loads, acting on the mechanism. Operator solution method application will give particular solutions of linear inhomogeneous differential equations. Received systems will allow solving many dynamic tasks of elastic mechanical systems: character change and maximum values of mechanism links dynamic loads, periods and frequencies of oscillations, conditions of the resonant state of the mechanical system.