ABSTRACT
A hybrid lumped parameter-finite element dynamic model is considered in which the housing and bearings are simulated by lumped stiffness elements and the shafts are discretized in beam elements. A specific gear element is introduced which is derived from the formulation of Velex & Maatar (1996) for solid pinions and gears. In order to incorporate deformable gear bodies, the initial 6 rigid-body Degrees-of-Freedom (DOF) are replaced by the master node DOFs of a substructure (Herting 1985) which is constructed from a 3D finite element model of the flexible wheel (3 translational DOFs per node). The modified gear element therefore connects the 6 DOFs at the pinion center (still considered as solid) to the DOFs of the sub-structured deformable gear body via
1 INTRODUCTION
Profile modifications are usually needed in spur and helical gears transmitting significant power in order to avoid corner contacts and reduce mesh excitations. Numerical models and analytical developments (Maatar & Velex 1996, Baud & Velex 2002, Ajmi & Velex 2005, Abousleiman & Velex 2006, 2007, Bettaieb & Velex 2006, Bettaieb et al. 2007) have been proposed for solid gears which include closed-form formulae defining the set of optimum symmetric profile reliefs minimizing transmission error time-variations (Master Curves, according to Bruyère et al. 2015, Velex et al. 2011).
