Non-linear dynamical simulation of spur gears with indexing errors and profile modifications

Indexing errors can be a cause of significant vibration and overloads in gear systems and already command much designer attention, especially in high speed gearing applications. Furthermore, the instantaneous tooth elastic deflections also contribute to vibration excitation and tooth profile modifications, usually employed to alleviate the ill effects of these errors, further perplex the modelling procedure. Current gear dynamical simulation models either do not consider indexing errors or do so in a simplified context. To address this problem, in this paper the exact geometry of tooth meshing is used as a starting point for a comprehensive dynamical modelling of gear systems, seamlessly incorporating the effect of pitch errors, tooth separation, DOF coupling, and profile modifications. The resulting model is fundamentally non-linear. A single stage spur gear reducer is then simulated dynamically using various scenarios of error distributions and profile modifications and the dynamical response is extracted. Analysis of the results suggests that there are optimal combinations profile modifications for a given maximum index error, which can reduce lateral force amplitude by 50% and load factor by almost 35%, however with larger modifications the benefit diminishes. It is shown that, when excessive modifications are applied, the dynamical responses of gears with different index error magnitudes converge.