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Mathematical model of oscillations of a drill tool with a drill bit of cutting-scraping type

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Category: Content №1 2020

Last Updated on 17 March 2020

Published on 10 March 2020

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Authors:

I. Chudyk, Dr. Sc. (Tech.), Prof., orcid.org/0000-0002-7402-6962, Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.

P. Raiter, Dr. Sc. (Tech.), Prof., orcid.org/0000-0002-3437-2844, Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.

Ya.Grydzhuk, Cand. Sc. (Tech.), Assoc. Prof., orcid.org/0000-0002-1429-8640, Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.

L.Yurych, orcid.org/0000-0002-2435-9785, Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.

Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2020, (1):52-57
https://doi.org/10.33271/nvngu/2020-1/052

 повний текст / full article

Abstract:

Purpose. Finding the cause and effect relationships between the parameters of non-stationary longitudinal and torsional vibrations of a drilling tool and developing a mathematical model to study their properties.

Methodology. The solution to this problem is based on one of the basic principles of analytical mechanics ‒ the Lagrange principle. The equation of motion of the studied rod mechanical system with four degrees of freedom is made using the Lagrange equation of the second kind, which is one of the next stages of its dynamic analysis.

Findings. In the process of solving this problem on the basis of industrial data, the analysis of axial load functions, angular rotation speed and torque of the drilling tool for their non-stationarity was carried out. The frequency of change in these non-stationary drilling mode functions is set by rapid Fourier transform.

Originality. For the first time, analytical dependences were obtained to determine the forces of cutting and friction on the bit from the second derivatives of the independent generalized coordinates of the mechanical system over time, as well as the relationship between the generalized accelerations of the translational and rotational motions of the bodies of the mechanical system.

Practical value.The practical value of the work is the obtained equations of motion of the system, taking into account the received frequency compositions of the mode parameters of drilling until their subsequent numerical solution. The results of this task will further facilitate the choice of optimal modes of dynamic loading of the drilling tool in order to improve its energy efficiency and reliability. Analysis of the frequency dependences of the change in non-stationary functions of the drilling mode parameters will allow evaluating the level of wear of the rock destruction tool, as well as to predict the durability of the drill string elements.

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