Self-excited vibration caused by time delay

（Estimation of generated frequency using time-varying phase difference）

Abstract

Pattern formation phenomena in contact rotating systems are caused by self-excited vibrations due to time-delay characteristics of the system. Since the ranges of rotational speed where the self-excited vibration occurs are close to those where resonance occurs due to unevenness of the roll surface or nonlinearity, it is difficult to determine in practical situations whether the self-excited vibration occurs or not, especially when its amplitude is small and the frequency resolution is low. One possible approach is to use the time-varying phase difference between the self-excited vibration and the roll rotation that is observed when frequency analyses are conducted with a low frequency resolution. This paper derives an analytical expression describing the relationship between the temporal variation of the phase difference and the actual frequency difference for two signals with close frequencies, verifying its effectiveness both theoretically and experimentally.