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UBC Theses and Dissertations

Quasi-harmonic friction induced vibration Ko, Pak Lim


The behaviour of the quasi-harmonic type frictional oscillation for steel sliding surfaces was investigated both experimentally and theoretically. The kinetic coefficient of friction, which was expressed as a function of sliding velocity, was represented by a polynomial. The slowly varying amplitude and phase method of Kryloff and Bogoliuboff was used to solve the non-linear differential equation of motion. The calculations were carried out on the computer. The theoretical analysis suggests that the amplitude of the quasi-harmonic oscillation increases almost linearly as the driven surface velocity increases until a critical velocity is reached where the friction-velocity curve begins to flatten out. Beyond this point the oscillation diminishes to zero. Experiments were carried out mainly on unlubricated surfaces at driven surface velocities ranging from 0.5 in/sec to 25 in/sec. The results revealed that for short running distances frictional oscillation of the stick-slip type could occur. Frictional oscillation of the quasi-harmonic type existed in the system when negative slope appeared in the low velocity region of the friction-velocity curve after a run-in period. The growth and decay of the vibration amplitude with variation in driven surface velocity has been observed and this substantiates the findings of the theoretical analysis.

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