A decomposition method for the fast computation of the transmission error of with holes

The prediction of noise and vibrations generated by geared systems remains a challenging field of study. The analysis of such systems is computationally demanding mainly due to the large size of the finite element model used to describe the system and the nonlinear behaviour arising from the contact between the gear teeth. As a consequence, very few models have been proposed to handle lightweight gears which are widespread in current industrial designs. Lightweight gears lead to a strong modification of the gear compliance, and therefore the contact force distribution. The static transmission error and the mesh stiffness fluctuations are thus influenced by these changes. In this paper, a 2D decomposition method is proposed to compute the static transmission error of gears with holes in the gear blanks without heavy computational effort. The original methodology relies on the substructuring of the holed gear blank from the gear teeth. It is applied on several spur gear systems with holed gear blanks and compared with a fully flexible multibody method. The validity of the approach is assessed in terms of static transmission error and mesh stiffness fluctuations. Moreover a parametric study is carried out using the 2D decomposition method in order to analyse the influence of holes regarding their position and number.