Stick–slip vibration of an oscillator with damping

Abstract

This paper proposes a new criterion for the occurrence of stick-slip vibration in an oscillator excited by a moving belt. Equations of motion were derived for a single-degree-of-freedom oscillator excited by the friction between the oscillator mass and a moving belt, considering two types of velocity-dependent friction models: exponential and polynomial. Based on the derived equations, dynamic responses were analyzed for various damping values, and it was found that the damping value determines the classification of oscillator motion among stick-slip, pure slip, and damped slip motions. Furthermore, a criterion for the occurrence of stick-slip motion, expressed in an integral form, was derived in terms of friction and damping forces. Using the least squares method, closed forms for the damping values to determine the occurrence of stick-slip vibration were obtained as functions of normal force, relative speed between contact surfaces, and friction parameters. In addition, the effects of the belt speed and of friction parameters on the occurrence of stick-slip vibration were also investigated.

Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments

“…Engineers are generally more concerned about subcritical (hard) bifurcations as a small perturbation around the equilibrium position can lead the system to large amplitude vibration states, which the structure may not tolerate [5]. A number of authors have studied the "Mass-on-moving-Belt" model ("MB model" in the following), Tondl [6], Hetzler et al [7], Hetzler [8], Won and Chung [9], Nayfeh and Mook [10], Mitropolskii and Van Dao [11], Popp [12], Popp et al [13], Hinrichs et al [14], Andreaus and Casini [15], Awrejcewicz and Holicke [16], Awrejcewicz et al [17], which present various types of analysis of a mass-on-belt system with various kinds of friction laws, and provide in some cases, analytical expressions for the change between stick-slip and pure-slip oscillations. Many authors have attempted to use fast vibrations which in some respects seems to transform classical Coulomb friction into viscous-like damping ( [5,18]).…”

Beyond Slow-Fast: Relaxation Oscillations in Singularly Perturbed Nonsmooth Systems

“…The similarities are illustrated in Fig. 1.2, which compares closed PWS orbits obtained via (a) singular limit analysis of vdP-type systems [33,73,74], and (b) PWS analysis of a model for mechanical oscillations subject to (discontinuous) friction [3,94,104,110]. In the context of GSPT and slow-fast systems (1.4) resp.…”

Two-stroke relaxation oscillators

“…An appropriate form appears in, e.g. [22,23,9] (see also [24,10]): Remark 2.2. Note that positivity of µ(v r ) and the presence of the sgn(v r ) term in (2.13) leads to a jump discontinuity at v r = 0.…”