Modal Properties of Contra-rotating Encased Differential Gear Train Used in Coaxial Helicopter

Abstract

Planetary gear train is widely used in the aerospace and automotive industries, but the vibration problems caused by the dynamic meshing forces and bearing forces of the system affect its reliability and longevity. Modal analysis is the basis for optimal design of structural dynamic characteristics. In this paper, the characteristics of natural frequencies and mode shapes of an encased differential gear train for the main reducer of a coaxial helicopter are analyzed. Considered with the coupling between stages and gyroscopic effect, a translational–rotational dynamic model for the planetary gear train which can transmit a single input to two contra-rotating outputs with equal speeds is established by the lumped-parameter method. Based on this model, the modal properties of the system are studied by numerical simulation and mathematically proved. The results indicate that all vibration modes of the planetary gear train can be categorized as four classes: rotational mode, translational mode, stepped planet mode and planet mode, and the typical mode shapes are graphically displayed. The magnitude of the natural frequencies corresponding to the planet mode and the stepped planet mode is not affected by the number of planets.