Research dynamic modes of stick-slip effect with the account of hereditarity

Roman Parovik,W.J Miloch,G.M Vodinchar,B.M Shevtsov

doi:10.1051/e3sconf/20186202015

Abstract

In study with the help of the spectrum of maximal Lyapunov exponents, dynamic regimes of the stick-slip effect were studied with allowance effect of hereditarity. Spectrum of the Lyapunov exponents were constructed using the Wolff algorithm with Gram-Schmidt orthogonalization depending on the values of the control parametersfriction and adhesion coefficients, as well as fractional index values, which determine the heredity of the dynamical system under consideration. The existence of an area of positive values of the maximum Lyapunov exponents is shown, which indicates the presence of chaotic regimes. Oscillograms and phase trajectories are constructed.

Highlights

IntroductionThe stick-slip effect is investigated in tribology when the load moves on a spring along some surface of a solid body that has adhesion and dynamic friction [1]
The stick-slip effect is investigated in tribology when the load moves on a spring along some surface of a solid body that has adhesion and dynamic friction [1]. With this movement of the load, quasiperiodic glide, its adhesion and detachment from the surface can occur, depending on the strength of the adhesion energy of the solid surface and the rigidity of the spring [2], [3]. Such motion regimes are encountered, for example, when describing the motion of a probe along the surface of a solid in an atomic force microscope in micro and nano scales [2], while studying the effect of deformation localization on the stability of friction sliding in dense amorphous materials [4], but on a macro scale the stick-slip effect is investigated, for example, in a distributed model of a drill string with Coulomb friction along a well [5], in a mechanical earthquake model [6] based on the motion of lithospheric plates and can manifest itself in electromagnetic signals lach of lithospheric origin [7]
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Summary

Introduction

The stick-slip effect is investigated in tribology when the load moves on a spring along some surface of a solid body that has adhesion and dynamic friction [1] With this movement of the load, quasiperiodic glide, its adhesion and detachment from the surface can occur, depending on the strength of the adhesion energy of the solid surface and the rigidity of the spring [2], [3]. Such motion regimes are encountered, for example, when describing the motion of a probe along the surface of a solid in an atomic force microscope in micro and nano scales [2], while studying the effect of deformation localization on the stability of friction sliding in dense amorphous materials [4], but on a macro scale the stick-slip effect is investigated, for example, in a distributed model of a drill string with Coulomb friction along a well [5], in a mechanical earthquake model [6] based on the motion of lithospheric plates and can manifest itself in electromagnetic signals lach of lithospheric origin [7]

Statement of the problem

Results of the study

Conclusion