Dynamics of two coupled 4-DOF mechanical linear sliding systems with dry friction.
Data
2015
Tytuł czasopisma
ISSN czasopisma
Tytuł tomu
Wydawca
Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki.
Abstrakt
The paper introduces a model of two identical coupled 4-DOF mechanical
linear sliding systems with dry friction coupled with each other by a linear torsional
spring. The appropriate components (bodies) of the coupled systems are riding on two
separated driving belts, which are driven at constant velocities, and stick-slip
vibrations can be observed. In this case the physical interpretation of the considered
model could be two rows of carriages laying on the guideways and coupled by an
elastic shaft, which are moving at constant velocity with respect to the guideways as a
foundation. From a mathematical point of view the analyzed problem is governed by
eight nonlinear ordinary second order differential equations of motion yielded by the
second kind Lagrange equations. Numerical analysis is performed in Mathematica
software using the qualitative and quantitative theories of differential equations. Some
interesting non-linear system dynamics are detected and reported using the phase
portraits and the Poincaré maps. Next, power spectra obtained by the FFT technique
are reported. The presented results show periodic, quasi-periodic, chaotic and hyperchaotic orbits. Moreover, synchronization effects between the coupled systems are
also detected and studied.
Opis
Słowa kluczowe
systems theory - conference, dynamical systems - conference, teoria systemów, systemy dynamiczne, system przesuwny, suche tarcie, mechaniczne systemy, analiza numeryczna
Cytowanie
Dynamical systems : control and stability ; s. 327-340