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.


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.


1.        Slobodyanik T. M. Intelligent design of mining machine drives. Sbornik nauchnykh trudov po materialam mezhdunarodnoy nauchno-prakticheskoy konferentsii «Nauchnyy potentsial XXI veka», 04—06 July 2017, Yekaterinburg, 2017, pp. 142—145. [In Russ].


2.        Zarubina E. M., Nikitina O. A. and Slobodyanik Т. М. Advances in Economics, Business and Management Research. 2019. V79 («Far East Con»), pp. 132—134.


3.        Nikitina O. A., Slobodyanik T. M., Melikhova Yu. M. Development of an action plan for restructuring the accounts payable of the repair enterprise. Guide to the entrepreneur. 2016. No 31. Pp. 114—120.


4.        Nikitina O. A., Litovskaya Yu. V., Savinkova T. A., Zinoveva E. G., Ponomareva O. S. The use of the budget planning mechanism in construction companies: evidence from LLC «Stroytekhnologiya». Espacios. 2017. Vol. 38. No 33. Pp. 17—26.


5.        Nikitina O. A., Litovskaya Yu.V., Ponomareva O. S. Development of the Cost Management Mechanism for Metal Products Manufacturing Based on Budgeting Method. Academy of Strategic Management Journal. 2018, Vol. 17, Issue 5, Рp. 1—7.


6.        Gorbatyuk S. M., Gerasimova A. A., Belkina N. N. Applying thermal coatings to narrow walls of the continuous-casting molds. Materials Science Forum 2016;870:564—567.


7.        Gerasimova A. A., Radyuk A. G., Titlyanov A. E. Creation of a diffusional aluminum layer on the narrow walls of continuous-casting molds. Steel in Translation 2015;45(3):185—187.


8.        Keropyan A. M., Gerasimova A. A. Connection of the temperature in contact area of the wheel-rail system with the slope of industrial railway transport. Izvestiya Vysshikh Uchebnykh Zavedenij. Chernaya Metallurgiya 2017;60(5):355—363.


9.        Slobodyanik T. M., Nikitina O. A. Designing economical drives of mining machines. Deposited manuscript No 1134/07-18 from 21.05.2018, 6 p. Gornyy informatsionno-analiticheskiy byulleten’. 2018, no 7, pp. 115. [In Russ].


10.     Semencha P. V., Zislin Yu. A. Reduktory gornykh mashin. Konstruktsii, raschet i ispytaniya [Reducing gears of mining machines. Design, calculation and testing], Moscow, Nedra, 1990, 238 p.


11.     Kudryavtsev V. N. Planetarnye peredachi [Planetary gears], Moscow, Mashinostroenie, 1966, 308 p.


12.     Komarov M. S. Dinamika mekhanizmov i mashin [Dynamics of mechanisms and machines], Moscow, Mashinostroenie, 1969, 296 p.


13.     Pivovarov A. O. Designing planetary gears without excessive ganging. Fundamental'nye issledovaniya. 2013, no 6—3, pp. 556—560. [In Russ].


14.     Diachenko P. V. Modeling influence of rolling bearing bush and vibration damping in catching of toothed wheels. Vіsnik dnіpropetrovs'kogo natsіonal'nogo unіversitetu zalіznichnogo transportu іm. akademіka V. Lazaryana. 2011, no 36, pp. 16—24.


15.     Kryukov V. A., Savel'eva L. V. Selection of low of variation in mesh stiffness in modeling gearing dynamics. Izvestiya Tul'skogo gosudarstvennogo universiteta. Tekhnicheskie nauki. 2015, no 11-1, pp. 65—70. [In Russ].


16.     Slobodyanik T. M., Nikitina O. A. Design of planetary gears in mining machinery. Deposited manuscript No 1131/07-18 от 21.05.2018, 7 p. Gornyy informatsionno-analiticheskiy byulleten’. 2018, no 7, pp. 46. [In Russ].


17.     Veyts B. L., Kochura A. E., Martynenko A. M. Dinamicheskie raschety privodov mashin [Dynamic designs of machine drives], Leningrad, Mashinostroenie, 1971, 352 p.


18.     Kozhevnikov S. N. Dinamika mashin s uprugimi zven'yami [Dynamics of machines with elastic elements], Kiev, izd-vo AN SSSR, 1961, 160 p.

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