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Autonomous quasi-harmonic and forced vibration of frictional systems Ko, Pak Lim


The behaviour of a system subject to quasi-harmonic type frictional oscillation was investigated. The same frictional system with external excitation was also investigated both experimentally and theoretically. Various frictional material combinations including steel, polymer, rubber and fibre materials and lubricants were used to provide different forms of friction characteristics. The dynamic friction-velocity curves were obtained by recording simultaneously the acceleration force, damping force, spring force and friction force during one cycle of the quasi-harmonic oscillation. The curves were expressed as a function of sliding velocity and were represented by nth order polynomials as well as by exponential expressions. The first approximation methods by Krylov and Bogoliuboff were used to solve the nonlinear, differential equations of motion in both the autonomous and non-autonomous cases. In addition, the method of harmonic balance was also used in the non-autonomous case. In both cases, the Runge-Kutta numerical method was used to investigate the transient state of the oscillations. Theoretical results for the autonomous system indicated that the humped form friction-velocity curve was a necessary condition for the existence of quasi-harmonic oscillation. Subharmonic entrainment at the frequency of the autoperiodic oscillation or harmonic entrainment at the external excitation frequencies, depending on the magnitude of the external excitation, were also predicted from the analysis. Experimental results were obtained from a pin on disc type frictional system having a track velocity range of 0.04 in/sec to 13.5 in/sec. External excitation forces were obtained by applying the principle of out-of-balance mass. The frequency range of the external excitation is 0-90 cps. The growth and decay of the quasi-harmonic oscillation was observed. In the non-autonomous case, 'quenching' of the autoperiodic oscillation by the external excitation was recorded. In general, the experimental results substantiate the predictions of the theoretical analyses. The experimental results also showed that the vertical external excitation has the effect of reducing the maximum static friction and subsequently extinguishing stick-slip oscillation.

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