Adaptive grid-size finite element modeling of helical gear pairs

A method for solving the contact problem for generic helical gear pairs (either external or inter- nal) is described. Gear profiles are obtained by means of numerical simulation of the cutting pro- cess and an accurate description is provided in terms of NURBS curves or surfaces. A new method for finding the enveloping profiles for a generic tool (e.g. from a measured topography) is pro- posed. The minimum number of parameters needed to describe the profile in the presence of tip and root reliefs, helix modification and crowning is discussed. A reference structured grid is de- fined on the tooth, then refinement criteria are applied in order to obtain accurate solutions in terms of tooth deflection, contact pressure and fillet stress. The method allows to automatically perform a Loaded Tooth Contact Analysis (LTCA) starting from the design data of a gear pair. Re- sults from the LTCA include contact pressure and contact pattern maps, as well as maximum fillet stress and fatigue strength. Combining several analyses within a mesh cycle, information about the Static Transmission Error (STE) and mesh stiffness is provided. The whole procedure has been implemented in a software called helical pair. A comparison with other approaches is given.