Mechanical Stick-Slip Vibrations

Abstract

In this paper we consider the behavior of a two degree-of-freedom mechanical system incorporating static and dynamic friction, assumed to be a decreasing function of the relative sliding velocity. The model consists of two blocks linked by springs, which ride upon a moving belt. The dynamics of the system are described within a four-dimensional phase space. A three-dimensional Poincaré map is discussed together with a simpler one-dimensional map of a scalar variable. Considering the one-dimensional map it is possible to study all the attractors of the system for small belt velocities including the construction of one-dimensional basins of attraction. Thus, albeit in a partial zone of the control-phase space, the global dynamics of the system can be characterized displaying periodic, quasi-periodic and chaotic oscillations.

Analysis of Disc Brake Noise Using a Two-Degree-of-Freedom Model

“…It should be noted that in these simulations the value of 2N is 0) 24 However, if the damping is increased in the system only on one side of the interface, for example in the pad, the size of limit cycle corresponding to the pad decreases, whereas the limit cycle of the disc increases. This is demonstrated in Figure 7, where the damping of the disc is "xed, c "0)01, and the damping of pad is gradually increased.…”

Intermittent Phase Transitions in a Slider-block Model as a Mechanism for Earthquakes

“…Qualitatively, its dynamics are little dierent from that of two stick-slip oscillators (HUANG and TURCOTTE, 1990a, b;RYABOV and ITO, 1995;GALVANETTO et al, 1995), although certain dierences exist. As we are mainly interested in modeling seismicity, we shall not consider various oscillatory regimes which occur at large values of driving velocity (ELMER, 1997), and concentrate on the limit jãj 3 0.…”

Boundary lubrication by adsorption film

“…Actually, research on the stickslip phenomenon, characterized by a non-uniform relative motion between rubbing surfaces, is of vital importance in understanding articular cartilage damage [50], vibrations in vehicle suspensions and brake systems [51], erratic motion in industrial machinery and tools [52], and even active geological faults during an earthquake [53,54]. Although stickslip may be welcome as a way of generating elegant sound by musical instrument such as a violin, more often the appearance of stick-slip is detrimental as damage and wear of the materials are often caused by stick-slip motion accompanied by a harsh noise.…”