Three Dimensional Model for A Helical Planetary Gear Train Vibration Analysis
Riadh Hbaieb, Fakher Chaari, Tahar Fakhfakh, Mohamed Haddar
Mechanics Modeling and Production Research Unit National School of Engineers of Sfax - BP. W - 3038 Sfax - TUNISIA
ABSTRACT: In this paper, a three dimensional model of a helical planetary gear train for determining critical frequencies is
proposed. Transverse, torsional, axial and rotational motions of the mounted gears are considered. The governing
equation of motion is derived. An analytical expression of the time varying gearmesh stiffness is presented and
its mean value was used to solve the eigenvalue problem whose gyroscopic terms are neglected.
One application of the model is conducted on a planetary gear train with four planets, critical frequencies for the system are determined and their sensitivity to the helix angle has been examined. It was found that the natural modes can be classified into three classes depending on their modal displacements and that the helix angle affects significantly the natural frequencies.