Mode coupling instability in friction-induced vibrations and its dependency on system parameters including damping

Abstract

Friction-induced vibrations due to coupling modes can cause severe damage and are recognized as one of the most serious problems in industry. In order to avoid these problems, engineers must find a design to reduce or to eliminate mode coupling instabilities in braking systems. Though many researchers have studied the problem of friction-induced vibrations with experimental, analytical and numerical approaches, the effects of system parameters, and more particularly damping, on changes in stableunstable regions and limit cycle amplitudes are not yet fully understood. The goal of this study is to propose a simple non-linear two-degree-of-freedom system with friction in order to examine the effects of damping on mode coupling instability. By determining eigenvalues of the linearized system and by obtaining the analytical expressions of the Routh-Hurwitz criterion, we will study the stability of the mechanical system's static solution and the evolution of the Hopf bifurcation point as functions of the structural damping and system parameters. It will be demonstrated that the effects of damping on mode coupling instability must be taken into account to avoid design errors. The results indicate that there exists, in some cases, an optimal structural damping ratio between the stable and unstable modes which decreases the unstable region. We also compare the evolution of the limit cycle amplitudes with structural damping and demonstrate that the stable or unstable dynamic behaviour of the coupled modes are completely dependent on structural damping.

Paradoxes of dissipation‐induced destabilization or who opened Whitney's umbrella?

“…Here the relative damping coefficients are denoted by Fig. 9(b) shows the numerically calculated domain of asymptotic stability of the drum brake in the space of the friction coefficient μ and two damping coefficients η 1 and η 2 with the Whitney umbrella singularity [99].…”

“…In order to study squeal vibration in drum brakes Hultén [40,99] introduced a model shown in Fig. 9(a).…”

Nonlinear transient vibrations and coexistences of multi-instabilities induced by friction in an aircraft braking system

“…4(a) and (b). No structural damping is added for this calculation (for more details about the effects of damping on stability see [14,25,26,27,28,29]). Five instabilities are calculated between 0 and 800 Hz, corresponding to the frequency range in which the analytical model is assumed to be efficient.…”

Effect of Control Measures on Wheel/Rail Noise When the Vehicle Curves

“…Huang [23] reviewed the curve squeal models, and developed a curve squeal model including a self-excited loop and relationship between wheel/rail motions and contact forces. A number of authors have proposed an alternative mechanism based on 'mode coupling', which has been explained in a simplified form by Hoffmann et al [24,25], see also [26]. More recently Thompson comprehensively reviewed two mechanisms ('falling friction' and 'mode coupling'), experimental and theoretical work in the field of curve squeal and discussed mitigation measures in terms of these two mechanisms [27].…”