Abstract
A modular model for the simulation of the dynamic behavior of multi-stage spur and helical gears is presented. It is mostly based on shaft finite elements combined with some specific gear elements which account for torsional-flexural-axial couplings, parametric and external excitations. Each tooth contact on theoretical base planes is assimilated to a line contact and discretized in accordance with the contact line evolutions when pinions and gears are rotating. A local stiffness and a normal deviation which represent gear tooth elasticity and tooth shape modifications or/and errors are associated with each cell of the time-dependent grid.
Seeking particular stable solutions only, the equations of motion are linearized and solved by using a specific spectral method which has been adapted to parametrically excited systems submitted to broad band parametric and external excitations.
Numerical simulations (dynamic transmission errors and displacements) have been performed for two different two-stage geared trains, i. e., a dual speed reducer (two pinion-gear pairs) and a dual mesh reverse idler (3 gears). The role and the definition of profile modifications (short/long reliefs), the contributions of pitch errors and the influence of the mesh relative orientation on the system dynamic behavior are examined. Finally, the nature and the intensity of the inter-mesh couplings in a double stage geared unit are discussed.
