AN EXTENDED MODEL FOR THE ANALYSIS OF THE DYNAMIC BEHAVIOR OF PLANETARY TRAINS

An extended model for determining critical frequencies for tooth loadi ng on spur and helical gear planetary trains is proposed. Torsional, f lexural and axial generalized displacements of all the components are considered and a finite element procedure is used for generality. In o rder to avoid modulations between meshing pulsations and the carrier a ngular velocity, equations are written relative to rotating frames fix ed to planet centers. Depending on their architectures, complex drives are broken down in basic 12 degree of freedom elements, namely: -exte rnal gear element (sun gear-planet element) -internal gear element (ri ng gear-planet element) -pin-carrier element -classical elements for s hafts, beatings, couplings, etc. Details are given for elementary stif fness matrices. Due to contact conditions between mating teeth, these matrices are full and torsional, bending and traction effects are coup led. State equations point to parametrically excited differential syst ems with gyroscopic contributions. A first application of the model is conducted on a 3 planet epicyclic drive whose gyroscopic terms are ne glected. Potentially dangerous frequencies for sun gear-planet and pla net-ring gear contacts are determined and contributions of some compon ents of the planetary train are discussed.