Analytical methods for determining the effect of the dynamic process on the nonlinear flexural vibrations and the strength of compressed shaft
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- Category: Geotechnical and mining mechanical engineering, machine building
- Last Updated on 17 November 2017
- Published on 17 November 2017
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Authors:
P.Ya.Pukach, Dr. Sc. (Tech.), Assoc. Prof., Lviv Polytechnic National University, Professor of the Department of Higher Mathematics, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
I.V.Kuzio, Dr. Sc. (Tech.), Prof., Lviv Polytechnic National University, Head of the Department of Mechanics and Mechanical Engineering Automation, Lviv, Ukraine.
Z.M.Nytrebych, Dr. Sc. (Phys.-Math.), Prof., Lviv Polytechnic National University, Head of the Department of Higher Mathematics, Lviv, Ukraine.
V.S.Ilkiv, Dr. Sc. (Phys.-Math.), Prof., Lviv Polytechnic National University, Professor of the Department of Higher Mathematics, Lviv, Ukraine.
Abstract:
Purpose. Determining the dynamic factor of industrial equipment safety by studying the dynamic processes in a nonlinear compressed shaft type oscillation system, which is widely used in mining industry. Such systems have previously been studied in literature solely based on the numerical modelling approach. In this paper, it is proposed to use asymptotic methods of nonlinear mechanics and the method of special periodic functions for thorough investigation of dynamics of the above systems and the conditions of resonance phenomena occurrence. We also describe the method for determining the dynamic factor of safety for boring equipment.
Methodology. The methods for analysing resonant oscillation regimes and determining the factor of safety for industrial equipment elements are based on asymptotic methods of nonlinear mechanics, wave theory of motion and the use of special Ateb-functions.
Findings. In this paper, the conditions of resonant oscillations for given nonlinear compressed shaft type systems are analytically obtained depending on system parameters and the method for calculating the dynamic factor of safety for industrial equipment elements is described.
Originality. Scientific novelty lies in the fact that, for the first time, the calculation of dynamic processes in compressed shaft type systems is done based on analytical approaches that allow, in contrast to numerical and experimental approaches, investigating the dynamics features of such systems more precisely and avoiding the occurrence of unwanted resonant modes in mining equipment.
Practical value. The presented method allows not only solving the problems of analysis, but also solving important problems of oscillation system synthesis at the design stage as well as choosing the elastic characteristics of dynamic systems and calculating the dynamic factor of safety for drilling equipment, taking into account the possible resonance phenomena. These mining machine features allow performing mining operations efficiently and safely.
References:
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3. Pukach, P. Ya. and Kuzio, I. V., 2015. Resonance phenomena in quasi-zero stiffness vibration isolation systems. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 3, pp. 62‒67.
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5. Shevchenko, F. L. and Pettyk, Yu. V., 2010. Influence of speed of flowing liquid on stability of boring column. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 1, pp. 69‒72.
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7. Ulitin, G. M., 2007. Mathematical model of impact processes in the two-stage drill strings. Vibration in engineering and technology, 3(48), pp. 68‒71.
8. Pukach, P. Ya., 2016. Investigation of bending vibrations in Voigt-Kelvin bars with regard for nonlinear resistance forces. Journal of Mathematical Sciences, 215(1), pp. 71‒78.
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