An Electromechanical System with Uncertain Stick-Slip Oscillations

Abstract

This work analyzes the stochastic response of an electromechanical system with stick-slip oscillations. The system is composed of two interacting subsystems, a mechanical with Coulomb friction and an electromagnetic (a DC motor). An imposed source voltage in the DC motor stochastically excites the system. This excitation, combined with the dry-friction, induces in the mechanical subsystem stochastic stick-slip oscillations. The resulting motion of the mechanical subsystem can be characterized by a random sequence of two qualitatively different and alternate modes, the stick- and slip-modes, with a non-smooth transition between them. The duration of each stick-mode is uncertain and depends on electromagnetic and mechanical parameters and variables, specially the position of the mechanical subsystem during the stick-mode. Duration and position are dependent random variables and must be jointly analyzed. The objective of this paper is to characterize and quantify this stochastic dependence, a novelty in the literature. The high amount of data required to perform the analysis and to construct joint histograms puts the problem into the class of big data problems.