Investigation of Planetary Gear Elastic Vibrations Using a Finite Element/Contact Mechanics Formulation

Abstract

Abstract The characteristics of the elastic vibrations for the individual gears used in planetary arrangements are important for predicting noise emissions, analyzing potential failure modes, and detecting damage. This work uses a finite element/contact mechanics planetary gear model to investigate the time and spectral vibration properties of the sun, planet, and ring in a fixed-ring configuration. Ring gears have periodic material point accelerations over a planet-pass cycle. Their spectrum has low frequency components at multiples of the planet-pass frequency and high frequency components that appear in clusters near each mesh frequency harmonic. Each cluster contains vibrations at the mesh frequency and upper and lower sidebands separated by the planet-pass frequency. Because of the ring’s compliance, the sideband components are meaningfully larger than the mesh frequency component, and noticeable asymmetry occurs in their amplitudes. The vibrations of a material point on the rotating sun is periodic with the planet-pass period relative to the sun. Therefore, the sideband frequencies observed on the sun are completely different with those on the ring. The rotating sun’s spectrum has low frequency components at multiples of the planet-pass frequency relative to the sun. Each of its clusters contains the mesh frequency component with sidebands at multiples of the planet-pass frequency relative to the sun. Material points on rotating planet gears have periodicity and sideband behavior related to the planet frequency relative to the carrier. Their spectral content is thus different from both the stationary ring and rotating sun. The spectral vibration features demonstrated in this work could be used by condition indicators to detect damage on the individual gears used in planetary arrangements.