On the Robustness of Instabilities in Friction–Induced Vibration

Friction-induced vibration and the noise or wear it causes are everlasting problems in the design of dynamical mechanical systems. The most common way to analyze friction-induced vibration is to determine the borders of linear stability. In that framework, the present study focuses on robustness concepts of systems prone to friction-induced vibration. Here, robustness is defined on two different levels. First, robustness will be considered in a global design perspective, giving an answer to the question of how many realizations within an overall ensemble of possible designs will show instability and if a given stability characteristic remains robust under parameter variations. Second, robustness will be understood with respect to the sensitivity of the system’s eigenvalues against parameter variations in general, focusing on the questions of how single eigenvalues react to parameter variation and if the real parts of the system’s eigenvalues give a measure for changes of stability characteristics under parameter variation. To answer the posed questions, dynamical model systems subject to friction-induced vibration are generated on the basis of specified random processes and evaluated in statistical terms. It shows that the size of the real parts of the eigenvalues, i.e., the growth or decay rates of the linear modes, which are in practice often used as decisive values in the interpretation of stability calculations, cannot be used as a well defined indicator for any kind of the considered robustness concepts. We, thus, suggest a novel measure taking into account variance properties to rate the robustness of systems subject to friction-induced vibration.