A Novel Loaded Tooth Contact Analysis Procedure with Application to Internal-External Straight Bevel Gear Mesh in a Pericyclic Drive

A comprehensive numerical loaded tooth contact analysis (LTCA) model is proposed for straight bevel gears that exhibit large number of teeth in contact, well beyond the involute line of action limits. This kind of contact is observed when the meshing gears have conformal surfaces, as in a pericyclic mechanical transmission, and is traditionally analyzed using finite element simulations. The pericyclic drive is kinematically similar to an epicyclic bevel gear train and is characterized by load sharing over large number of teeth in an internal-external bevel gear mesh, large shaft angles (175-178 deg), nutational gear motion, and high reduction ratio. The contact region spreads over a large area on the gear tooth flank due to high contacting surface conformity. Thus, a thick plate finite strip method (FSM) was utilized to accurately calculate the gear tooth bending deflection. Based on the tooth deformation calculation model and accounting for initial surface separation, a variational framework is developed to simultaneously solve for load distribution and gear tooth deformation. This is followed by calculation of contact stress, bending stress, mesh stiffness, and transmission error. The results demonstrate the high-power density capabilities of the pericyclic drive and potential for gear noise reduction. The model developed herein is applied with real gear tooth surfaces, as well.