# The analysis of belt conveyor models at different number of approximating masses

For the belt conveyor modeling, this study uses the method of systems composed of elements continuously distributed in finite spatial domains. The motion is transmitted from an element to an element, and the dynamic processes are described using equations with partial derivatives (wave equations). The analytical solution of the systems of such equations is a complex and labor-intensive process. It is possible to simplify calculations by splitting the system into the simplest elements and using the piece-wise linear approximation. This method allows an approximate description of the system with distributed parameters by a system of ordinary differential equations. In this case, the line of a belt conveyor is divided into a number of sections, and the law of variation of strain rate along the length is assumed to be linear within the limits of each section. Then, after certain assumptions for simplifying the model, the Lagrangian equations of the second kind are used. The authors compare the belt conveyor models with different numbers of concentrated masses and assess advantages of each models. The engineering problems solvable using these models are listed.

Keywords: belt conveyor, mathematical model, system with distributed parameters, system with concentrated parameters, Lagrangian equation of the second kind, Simulink, optimal number of approximating masses.
For citation:

Dmitrieva V. V., Sizin P. E. The analysis of belt conveyor models at different number of approximating masses. MIAB. Mining Inf. Anal. Bull. 2022;(1):34-46. [In Russ]. DOI: 10.25018/0236_1493_2022_1_0_34.

Acknowledgements:
Issue number: 1
Year: 2022
Page number: 34-46
ISBN: 0236-1493
UDK: 622.647.2:004.942
DOI: 10.25018/0236_1493_2022_1_0_34
Article receipt date: 09.09.2021
Date of review receipt: 08.10.2021
Date of the editorial board′s decision on the article′s publishing: 10.12.2021
About authors:

V.V. Dmitrieva, Cand. Sci. (Eng.), Assistant Professor, e-mail: dm-valeriya@yandex.ru, Gubkin Russian State University of Oil and Gas (National Research University), 119991, Moscow, Russia,
P.E. Sizin, Cand. Sci. (Phys. Mathem.), Assistant Professor, e-mail: mstranger@list.ru, Institute of Basic Education, National University of Science and Technology «MISiS», 119049, Moscow, Russia.

For contacts:

V.V. Dmitrieva, e-mail: dm-valeriya@yandex.ru.

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