Stationary transducer response to planetary-gear vibration excitation II: Effects of torque modulations

The frequency spectra of the outputs of transducers fixed to the ring gears of planetary-gear systems contain useful information pertaining to the health of such systems. The effects on such frequency spectra arising from non-uniform loading carried by the M planets in such systems was derived and illustrated in “Stationary transducer response to planetary-gear vibration excitation with non-uniform planet loading,” by Mark and Hines [W.D. Mark, J.A. Hines, Stationary transducer response to planetary-gear vibration excitation with non-uniform planet loading, Mechanical Systems and Signal Processing 23 (2009) 1366–1381]. The present paper extends this earlier analysis by predicting the added effects on such frequency spectra caused by planet-carrier torque modulations. It is shown that such torque modulations produce “sideband” harmonics on the harmonic contributions arising from uniform loading carried by the planets, and additional “sideband” harmonics on the harmonic contributions arising from the lack of uniformity of loading carried by the planets. An example is discussed for torque modulations with a period of 1/B times the planet-carrier rotation period. This example illustrates the effects of torque modulations on the transducer output spectra of a UH-60A rotorcraft with a B=4 blade rotor and M=5 planets.