An extended model for determining dynamic tooth loads 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 satellite centers. Depending on their architectures, complex drives are broken down in basic 12 degree of freedom elements, namely:
- external gear element (sun-satellite element)
- internal gear element (ring-satellite element)
- pin-carrier element
- classical elements for shafts, bearings, couplings, ...
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 satellite epicyclic drive whose gyroscopic terms are neglected. Potentially dangerous frequencies for sun-satellite and satellite-ring contacts are determined and contributions of the environment of the planetary train are discussed. Numerical results underline the influence of satellite-carrier links on critical frequencies for tooth loading.