On the modelling of excitations in geared systems by transmission errors

This paper introduces an original theoretical approach to the modelling of pinion–gear excitations valid for three-dimensional models of single-stage geared transmissions. Shape deviations and errors on gears are considered and the associated equations of motion account for time-varying mesh stiffness, and also torsional, flexural and axial couplings. Starting from the instantaneous contact conditions between the teeth, the equations of motion are re-formulated in terms of quasi-static transmission errors under load and no-load transmission errors. The range of application of transmission error-based formulations is analysed and some new equations are proposed which make it possible to introduce rigorously meshing excitations via transmission errors. Using an extended finite element model of a spur and helical gear test rig, the dynamic results from the formulations based on transmission errors are compared with the reference solutions. Both sets of results are found to be in close agreement, thus validating the proposed theory. The paper concludes with a critical analysis of the interests and limitations concerning the concept of transmission errors as excitation terms in gear dynamics.