A non-linear friction work formulation for the analysis of self-excited vibrations

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Journal Article
Journal of Sound and Vibration, 2019, 443 pp. 328 - 340
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© 2018 Elsevier Ltd Even though much research has been devoted to understand friction-induced vibrations, its root cause is not yet fully understood. Reliable prediction of friction-induced unstable vibrations such as in brake squeal or hip squeak remains a challenge because of nonlinearities involved and because the complex eigenvalue analysis (CEA) widely used in industry is linear. The energy fed back into the system by friction has been shown to be useful for analysis of measurements and numerical simulations. In numerical simulations, the linearised method of feed-in energy, calculated purely based on friction work has provided some insights into the physical mechanism for instabilities. However, the dynamics due to friction-induced instabilities is highly nonlinear and damping may offset some or all of the excess friction energy provided to the system. By using a nonlinear 2-DOF dry friction oscillator, a nonlinear friction work formulation is proposed to demonstrate that in combination with viscous damping the energy budget provides an improved analysis capability over linearised friction work. The results highlight the potential of nonlinear friction work as a reliable tool to study friction-induced instabilities to gain deeper physical insights into squeal triggering mechanisms and to better understand the over- and under-predictive character inherent to linear methods.
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