Estimation and Application of Mean Square Frequency

Abstract

This paper deals with the estimation and application of the mean square frequency and its root, by which the two variables, amplitude and frequency, of almost-periodic signals can be reduced to one variable and consequently the transition of nonstationary vibration signal can be grasped briefly, while the analysis with power spectrum density function is complicated. Firstly it is verified theoretically that a vibration signal can be expressed comprehensively by the mean square frequency and next that it can be expected simply by numerically calculating no more than second order autocorrelation function. As an application the roots of mean square frequencies of sound signal in turning operation which are functions of time are reported. The roots of mean square frequencies in the turning change remarkably at the time chatter begin or thereabouts and consequently it is revealed that the onsets of chatter vibration can be defined by using the mean square frequencies. The mean square frequency are very useful in experimental consideration for nonstationary vibration signal because the signal can be observed as a function of time alone while by nature as a function of amplitude, frequency and time.