Modular hybrid models to simulate the static and dynamic behaviour of high-speed thin-rimmed gears

Several modular hybrid gear dynamic models are presented which account for both the local phenomena associated with the instant contact conditions between the tooth flanks and the more global aspects related to shafts, bearings and particularly the contributions of light thin-rimmed/-webbed gear bodies. The proposed models combine sub-structures, lumped parameter and beam elements to simulate components with linear behaviour such as webs, rims, shafts, etc. while local mesh elasticity is simulated by time-varying, possibly non-linear Winkler foundations. A specific interface has been developed to connect discretised tooth contact lines with continuous finite element models and avoid singularities in tooth load distributions. A number of comparisons with numerical and experimental results show that the proposed modelling is sound and can capture most of the quasi-static and dynamic behaviour of single stage reduction units with thin-webbed gears and/or pinions. Finally, the modelling strategy is applied to the analysis of high–speed industrial gears and results are presented which illustrate the interest of the proposed methodology compared with the classic gear dynamic models.