Analytical approximations for stick-slip vibration amplitudes |
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Authors: | Jon Juel Thomsen Alexander Fidlin |
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Institution: | a Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark Building 404, DK-2800 Lyngby, Denmark b Tennesseealee 35, D-76149 Karlsruhe, Germany |
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Abstract: | The classical “mass-on-moving-belt” model for describing friction-induced vibrations is considered, with a friction law describing friction forces that first decreases and then increases smoothly with relative interface speed. Approximate analytical expressions are derived for the conditions, the amplitudes, and the base frequencies of friction-induced stick-slip and pure-slip oscillations. For stick-slip oscillations, this is accomplished by using perturbation analysis for the finite time interval of the stick phase, which is linked to the subsequent slip phase through conditions of continuity and periodicity. The results are illustrated and tested by time-series, phase plots and amplitude response diagrams, which compare very favorably with results obtained by numerical simulation of the equation of motion, as long as the difference in static and kinetic friction is not too large. |
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Keywords: | Friction Stick-slip Self-excited vibrations |
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