Fourier Series Analysis of Epicyclic Gearbox Vibration

Epicyclic gears are used in many applications because they can achieve a large torque/speed ratio in a compact package. In most gearboxes, the estimated spectrum of the vibration signal is symmetric and centered at the meshing frequency. For epicyclic gears, the estimated spectrum is typically asymmetric and the dominant frequency component does not occur at the meshing frequency. This is an important observation because some of the popular methods of fault detection use the meshing frequency and sideband signal power as an indication of the gearbox health @1,2#. McFadden and Smith @3# were the first to recognize that this effect was due to the varying phase angles of the vibration produced by each of the planet gears. They used phasor sums to identify the dominant spectral components, but were unable to predict the relative amplitudes of the dominant components. This study generalizes their work using continuous-time Fourier series ~CTFS! analysis. This provides a more thorough and intuitive explanation of the observed spectrum and leads to a number of insights that could not be gained with phasor sums alone.