Effect of Elasticity of Shafts, Bearings, Casing and Couplings on the Critical Rotational Speeds of a Gearbox

The aim of this study is to analyse the influence of the mechanical characteristics of the set of components on the critical rotational speeds of a gearbox. The case of a gearbox fitted out with a helical gear pair was considered. The shafts and the casing were discretised using the finite element method. The elastic coupling between the toothed wheels was characterised by a 12 x12 stiffness matrix. The bearings were modelled using radial, axial and rotational stiffness elements. The calculation of the vibration response induced by the static transmission error showed that the highest dynamic mesh forces correspond to a resonant excitation of modes which have a high potential energy associated with the mesh stiffness. The numerical simulations performed showed that a realistic prediction of the critical rotational speeds should take account of all the components of the gearbox.