Friction-induced vibration in linear elastic media with distributed contacts.

摘要

When there is friction between two parts in contact relative motions may generate vibrations and noise which can cause serious problems in applications. In this study friction-induced vibrations in elastic media subjected to distributed contacts are investigated in order to understand mechanisms responsible for generations of noise and vibrations. We investigated system stability and stick-slip oscillations to explain friction-induced vibration in linear elastic media with distributed contacts.; A one-dimensional elastic media with fixed-end boundary conditions are investigated. The system is marginally stable when the coefficient of friction is a constant. Under fixed-end boundary conditions distributed friction leads to a non-self-adjoint system. A non-self-adjoint eigenvalue problem and an eigenvalue problem based on a proper inner product are reviewed as alternative methods in handling non-self-adjoint systems. A contradictory result between the exact and an assumed mode projection based on the non-self-adjoint formulation is presented as a cautionary example.; Under periodic boundary conditions the one-dimensional system is destabilized with a constant coefficient of friction. The destabilizing phenomena occur in the form of unstable traveling waves propagating in the direction of the slider velocity. External and internal damping play stabilizing roles in system stability. By constructing a discretized lumped-parameter model, the non-symmetric eigenvalue problem is studied. A negative-slope in friction-velocity curve destabilizes the system.; Stick-slip oscillations are analyzed with the lumped-parameter discretized model. An algorithm for handling nonlinear stick-slip oscillations is presented. Series of detachments over whole domains and localized small-grouped stick-slip oscillations are observed. Effects of system parameters on stick-slip oscillations are considered as well. Under high normal loads, the frequency of the series of detachments is lowered and frequency of small-grouped motions is increased. Sustained stick-slip oscillations are observed when the friction-velocity curve is discontinuous (μ_s > μ _k) and the system is linearly unstable. With the help of finite element analysis dynamic behaviors of one- and two-dimensional linear elastic systems are investigated.