An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains

[+] Author and Article Information
A. Saada, P. Velex

Laboratoire de Mécanique des Contacts, URA CNRS 856, INSA, Bât. 113, 20, Av. Albert Einstein, 69621 Villeurbanne Cédex, France

J. Mech. Des 117(2A), 241-247 (Jun 01, 1995) (7 pages) doi:10.1115/1.2826129 History: Received December 01, 1992; Revised November 01, 1994; Online December 11, 2007


An extended model for determining critical frequencies for tooth loading on spur and helical gear planetary trains is proposed. Torsional, flexural and axial generalized displacements of all the components are considered and a finite element procedure is used for generality. In order to avoid modulations between meshing pulsations and the carrier angular velocity, equations are written relative to rotating frames fixed to planet centers. Depending on their architectures, complex drives are broken down in basic 12 degree of freedom elements, namely: external gear element (sun gear-planet element); internal gear element (ring gear-planet element); pin-carrier element; classical elements for shafts, bearings, couplings, etc. Details are given for elementary stiffness matrices. Due to contact conditions between mating teeth, these matrices are full and torsional, bending and traction effects are coupled. State equations point to parametrically excited differential systems with gyroscopic contributions. A first application of the model is conducted on a 3 planet epicyclic drive whose gyroscopic terms are neglected. Potentially dangerous frequencies for sun gear-planet and planet-ring gear contacts are determined and contributions of some components of the planetary train are discussed.

Copyright © 1995 by The American Society of Mechanical Engineers
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