Numerical bifurcation analysis of a friction-driven vibro-impact system

Abstract

The dynamic response of a friction-driven vibro-impact system is presented. The system has two degrees-of-freedom with discontinuous nonlinear forces applied (dry friction and impact). This new self-exciting system tends to self-synchronisation with a potential industrial application in the field of percussive-rotary drilling. Friction-induced vibration is used as the source of excitation of impacts, which in turn influences the parameters of stick–slip motion. The friction force is defined as a nonlinear function of the drive velocity and allows for self-excitation. The dynamic coupling of vibro-impact action with the stick–slip process provides entirely new adaptive features important for practical application. The self-exciting process (stick–slip) depends on the mechanical properties of the medium interacting with the device. In this paper, which is the initial stage of a series of investigations into the full dynamic response of the system for scientific and engineering interests, the dynamic behaviour of the system motion without impact is presented. The equations of motion are solved numerically and the analysis is focused on the effects that discontinuity induced bifurcations have on the system. Within the scope of the assumptions made, a bifurcation diagram provides a further understanding of the system dynamic behaviour. Self-excitation and self-synchronisation using a single drive has some advantages that can be exploited in oil drilling applications.