Stationary transducer response to planetary-gear vibration excitation with non-uniform planet loading

A relatively simple first-principles mathematical model of a generic planetary gear system is developed. System imperfections included are planet-to-planet variability in planet/ring-gear loading and generic ring-gear imperfections. General formulas for Fourier-series spectrum contributions of fixed-transducer responses to transmission-error vibratory excitations caused by planet/ring-gear tooth-meshing harmonics and ring-gear imperfections are derived, which include predicted effects caused by planet-to-planet variability in planet/ring-gear loading. Good approximations to the coefficient of variation of planet loading (CVPL) are shown to be readily obtainable from measured planet-carrier rotational-harmonic spectra obtained by fixed transducers. The predicted spectrum behavior is compared with fixed-accelerometer response spectra measured from UH-60A planetary systems without and with planet-loading variability caused by a cracked planet-carrier plate. The main features of predicted and measured spectra are in good agreement.