ABOUT THE MODELLING OF TEETH MESH FLEXIBILITY IN PLANETARY GEARS

Gear mesh flexibility is a varying and periodic quantity, which depends on several geometric, motion and material parameters; in NVH and structural analyses of systems with transmission problems this stiffness variability can play an important role on the design targets, such as sound quality and fatigue life estimation. Many times the tooth mesh flexibility in gears is modelled by means of lumped parameters formulas obtained from literature or by means of complex finite element models of the contact. In this work the roots of lumped parameters formulas were investigated, as a preliminary and feasibility study for a potential research path in gear condition monitoring, noise source & structural dynamics excitation modelling and transmission errors. Starting from the kinematics of mating rigid teeth in planetary gears with a single stage, the time-varying flexibility contribution of each deflected pair is added with simple assumptions, resulting in the parametric modelling of the torsional stiffness as a kinematics based periodic quantity. Parameters were extracted from this approach, to explore a viable and computationally cost effective geometry based method to model the torsional vibrations and transmission error in planetary gears.