Sum and Difference Frequencies in Vibration of High Speed Rotating Machinery

Abstract

A vibration incident on a gas turbine engine was noted where two major excitation frequencies were involved—an excitation synchronous with rotor rotation, associated with rotor unbalance, and an asynchronous excitation associated with fluid inadvertently trapped in the rotor. Spectral analysis of the vibration wave form revealed not only the two base excitation frequencies, but also a component at the difference frequency. A mechanism for generating such a difference frequency is hypothesized—the truncation of the basic “beat frequency” wave form by virtue of clearance in the rotor bearing system. Fourier analysis of the hypothesized excitation wave form indicates that components at difference frequency are indeed generated, and also at the sum frequency and a spectrum of higher harmonics and side band frequencies. The hypothesized wave form’s spectral analysis bears a remarkable resemblance to the measured spectrum, except that low frequencies appear to have been greatly amplified in the experimental case, and high frequencies attenuated. This latter fact is attributed to the transmission characteristics of the gas turbine stator system, and is probably responsible for the lack of precise correspondence between the measured and hypothesized wave forms.