# Mathematical model of piston/bit interaction in percussive destruction of rocks

The mathematical model of percussive destruction of rocks is represented by a set of two sub-models. The first sub-model simulates piston/bit interaction and allows finding the bit force on rocks as a function of time. The second sub-model describes the temporal variation of stress state and estimates strength of rock mass. Integration of the sub-models enables determining the influence exerted by the rock-breaking tool parameters and by mechanical characteristics of rock mass on the volume of destruction. The tool affects rock mass by concentrated load along the tool axis. The time variation of the loading modulus is obtained from the first sub-model. The input dimension data are set as the depth of shear cut, torque angle and loading step. The stress state of rocks mass is determined from the numerical solution of an initial– boundary value dynamic problem of elasticity by integration of the method of lines (Crank– Nicolson approach) and the method of finite elements. The strength assessment of rocks uses the criteria of Mohr–Coulomb and Morozov–Petrov, which make it possible to find volume of rock destruction. The calculation is exemplified by a case-study of Rammer G100 hydraulic hammer, Finland.

Keywords: rock mass, percussive tool, mathematical model, method of lines, finite element method, Mohr–Coulomb criterion, Morozov–Petrov criterion.
For citation:

Zhabin A. B., Lavit I. M., Polyakov A. V., Kerimov Z. E. Mathematical model of piston/bit interaction in percussive destruction of rocks. MIAB. Mining Inf. Anal. Bull. 2020;(11):140-150. [In Russ]. DOI: 10.25018/0236-1493-2020-11-0-140-150.

Acknowledgements:

The study was supported by the Tula State University, R&D Project No. 2019-18.

Issue number: 11
Year: 2020
Page number: 140-150
ISBN: 0236-1493
UDK: 622.23.05:622.235
DOI: 10.25018/0236-1493-2020-11-0-140-150
Article receipt date: 23.06.2020
Date of review receipt: 13.07.2020
Date of the editorial board′s decision on the article′s publishing: 10.10.2020

A.B. Zhabin1, Dr. Sci. (Eng.), Professor, e-mail: zhabin.tula@mail.ru,
I.M. Lavit1, Dr. Sci. (Phys. Mathem.), Professor, e-mail: igorlavit@yandex.ru,
A.V. Polyakov1, Dr. Sci. (Eng.), Professor, e-mail: Polyakoff-an@mail.ru,
Z.E. Kerimov1, Graduate Student, e-mail: k-zahit94@mail.ru,
1 Tula State University, 300012, Tula, Russia.

For contacts:

A.B. Zhabin, e-mail: zhabin.tula@mail.ru.

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