Application of Instantaneous Frequency Analysis(II) -Conditions of Existing Negative Frequency Components-

순간주파수 분석기법의 응용 (2) -주파수의 부호를 결정하는 조건-

An instantaneous frequency analysis is a technique to examine a signature for the rotating machinery if the signal has several transitions within a cycle. This paper discusses the conditions of existing negative frequency components in the instantaneous frequency. By using a signal consisted of two frequency components, the instantaneous frequency analysis is conducted while the amplitude ratio between two frequency components has been changed. The analysis shows that, depending on the amplitude ratio, the instantaneous frequencies have averaged, zero-valued, or negative components. It turns out that the negative-valued instantaneous frequencies, which have been regarded as the noise effect, are the consequence of the calculation process for the multisignal components. The criteria of existing the negative values in instantaneous frequencies is given in terms of the relative amplitude ratio and the frequency difference. Especially when the amplitude ratio approaches to 1, the instantaneous frequency fluctuates ${\pm}\infty$ in theory, which implies that instantaneous frequency has unstable region around the amplitude ratio, 1.Also, as the frequency difference between major signal components is increased, the region of existing negative instantaneous becomes broader. In an instantaneous frequency analysis, therefore, a narrow band analysis is suggested, with extreme care if the amplitude ratio approaches to 1. In this paper, a vibration signal monitored from a rotating machinery is also examined as an application example in order to show the existence of negative instantaneous frequencies components.