Effect of waveform on the effectiveness of tangential dither forces to cancel friction-induced oscillations

High-frequency dither forces are often used to reduce unwanted vibration in frictional systems. This paper examines how the effectiveness of these dither-cancellation techniques is influenced by the nature of periodic signal employed. The paper investigates a single-degree-of-freedom (sdof) system consisting of a mass in frictional contact with a translating belt using two different models of friction. Prior work by the authors focused on sinusoidal dither waveforms. This paper extends this analysis to general, periodic dither forces. Using an averaging technique, the optimal waveforms are determined among periodic signals having either unit-amplitude or unit-rms value. For unit-amplitude dither signals, it is found that square waveforms are able to quench self-excited oscillations with the smallest amplitude of all waveforms of equal strength at every belt speed. Among unit-rms dither waveforms, square waves are best for low belt speeds, but sinusoidal dither is revealed to be best in higher ranges of belt speed. After studying generic waveforms, the results are specialized for three specific examples: sinusoidal, triangular, and square. In particular, the relative performance of the three waveforms is studied using an averaging technique as well as direct time integration.