Theoretical frequency analysis of vibrations from planetary gearboxes

A phenomenological model descriptive of the vibrations generated on a single-stage planetary gearbox when measured with a sensor mounted on the outer part of the ring gear is developed in time domain. First, only the internal meshing processes are considered. The model is analyzed relying on the Fourier theory to provide a detailed theoretical background which explains the different spectral structures observed on planetary gearbox vibrations. It is proposed that planetary gearboxes can be classified in four groups each presenting specific features on the structure of the vibration spectrum. Each group is carefully analyzed and illustrated with examples. Afterwards, the influences on the vibrations of the external gear meshing processes and the transmission path of vibrations from their source to the sensor through the sun gear and carrier plate are studied. It is concluded that the external meshing processes can affect all spectral components of the total vibrations differently, depending on if the number of the teeth of the planet gears is even or odd. Differently, the transmission path through the sun gear and carrier plate affects only the spectral components at the gear mesh frequency and its harmonics. Considering the factors presented in this work, the expected spectral components of the vibrations measured on any non-faulty planetary gearbox can be estimated a-priori, thus representing a valuable aid in view of failure diagnosis on these mechanical systems.