Open Access

Matthias Graf, Tobias Lankenau

• When engineers add damping to a vibrating system, they typically expect that this will result in a more stable system. However, a few rather complex examples are known that show the opposite trend: situations in which damping generates friction-induced vibration (damping paradox). In this study, we demonstrate that a simple but new surrogate model suffices to explain this effect, by analyzing a model with only one degree of freedom and a constant coefficient of friction. The instability of this model increases with an increase in the viscous damping coefficient perpendicular to the sliding direction. This shows that an unfavorable combination of geometric mounting of a friction-exposed mass together with ill-positioned damping can generate friction-induced vibration that would not appear without damping. The results are confirmed by finite element analysis and the corresponding complex eigenvalues. The excited mode shapes and frequencies correspond well with laboratory tests. This has consequences for applications such as the development of vehicle brake shims, which provide damping properties perpendicular to the sliding direction.