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Regular and chaotic dynamics of a 4-DOF mechanical system with dry friction

Kosińska A., Awrejcewicz J., Grzelczyk D.

Vibrations in Physical Systems

2016

Vol. 27

195--202

In this paper the model of four degree-of-freedom mechanical sliding system with dry friction is considered. One of the components of the mentioned system rides on driving belt, which is driven at constant velocity. This model corresponds to a row of carriage laying on a guideway, which moves at constant velocity with respect to the guideway as a foundation. From a mathematical point of view the analyzed problem is governed by four second order differential equations of motion, and numerical analysis is performed in Mathematica software. Some interesting behaviors are detected and reported using Phase Portraits, Poincaré Maps and Lyapunov Exponents. Moreover, Power Spectral Densities obtained by the Fast Fourier Transform technique are reported. The presented results show different behaviors of the system, including periodic, quasi-periodic and chaotic orbits.

Dynamics of Mechanical Sliding System with Dry Friction

Grzelczyk D., Awrejcewicz J., Kudra G.

Machine Dynamics Research

2014

Vol. 38, No. 3

61-70

In the paper we consider a four degree of freedom model of a mechanical system with dry friction, which can explain non-regular vibrations of mechanical sliding system. Stick-slip vibrations are studied for the case, where body is riding on a driving belt as a foundation that moves at a constant velocity. From a mathematical point of view, the analyzed problem is governed by a set of nonlinear ordinary second order differential equations of motion, obtained using the Lagrangian method. Numerical analysis is carried out with the qualitative and quantitative theories of nonlinear differential equations reduced to the non-dimensional form. The behavior of the mentioned system is monitored via standard phase portraits, bifurcation diagram as well as Lyapunov exponents. Some interesting numerical results (periodic, quasi-periodic, chaotic and hyper-chaotic orbits) are obtained and reported in the paper.