## DYNAMICS OF ELEMENTARY DIFFERENTIAL COMPOSED OF ELASTIC BODIES

Static and dynamic parameters of planetary gearing of different design are widely addressed in literature. Some of dynamic problems can be solved at sufficient exactness without regard to elasticity of of loaded elements. In the dynamic analysis of transmission gears of mining machines, it is necessary to account for the gear yielding as it largely exceeds the yielding of shafts of large diameters and small length. This article discusses capacities and features of studies into dynamic events in the planetary mechanisms of transmission gears of mine dump trucks, shearers and roadheaders as well as loaders when the planetary mechanisms are presented as elastic mechanical systems. The study uses a dynamic model of an elementary differential with regard to elasticity of components. To this effect, the differential is presented as an equivalent series with an inertialess carrier and with basic elements having moments of inertia found from the known formulas. The equivalent dynamic model of the elementary differential is presented as a branched three-mass system. Moments of elasticity are determined in ganging of the system. The equations of motion of each mass make the system of linear uniform differential equations or the system of equations of free vibrations of the mechanism; this system can be presented by a set of linear algebraic equations. The practical interest lies in the partial solutions of the systems of nonuniform differential equations as the make it possible to analyze influence of external loads on the mechanism. The operator method allows finding partial solutions of the linear nonuniform differential equations. The obtained systems of equations can be used to solve such problems in the dynamic theory of elasticity as determination of the behavior and maximums of dynamic loads on the elements of the mechanism, periods and frequencies of vibrations, and resonant behavior conditions.

For citation: Slobodyanik T. M., Balakhnina E. E. Dynamics of elementary differential composed of elastic bodies. MIAB. Mining Inf. Anal. Bull. 2019;(9):204-210. [In Russ]. DOI: 10.25018/0236-14932019-09-0-204-210.

Keywords

Dynamic analysis, elementary differential, inertialess carrier, elasticity, differential equation.

Issue number: 9
Year: 2019
ISBN: 0236-1493
UDK: 621.01 (075.8)
DOI: 10.25018/0236-1493-2019-09-0-204-210
Authors: Slobodyanik T. M., Balakhnina E. E.

About authors: T.M. Slobodyanik, Cand. Sci. (Eng.), Assistant Professor, e-mail: tslobodyanik@gmail.com, E.E. Balakhnina, Cand. Sci. (Eng.), Assistant Professor, e-mail: autobusred@yandex.ru, National University of Science and Technology «MISiS», 119049, Moscow, Russia. Corresponding author: T.M. Slobodyanik, e-mail: tslobodyanik@gmail.com.

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