Calculation of overloads induced by indexing errors in spur gearboxes using multi-degree-of-freedom dynamical simulation

Indexing errors are a cause of significant vibration and overloading in gearboxes and require much designer attention, especially in high-speed applications. Furthermore, the continuously varying elastic deflections of the meshing teeth contribute to vibration excitation and tooth profile corrections, which are usually employed to alleviate the ill effects of these errors and further complicate the modelling of the phenomenon. Current gear dynamical simulation models either do not consider indexing errors or do so in a simplified manner. To address this problem, in this article, 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, degree-of-freedom coupling, and profile corrections. 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 corrections, and the overload factor is calculated. The results show that there are optimal corrections, which can reduce overload by a factor of nearly 35 per cent; however, with bigger corrections, the benefit diminishes. The sensitivity of different design solutions to manufacturing tolerances is investigated and definitive trends are recognized. Finally, a new design recommendation for profile correction is made on the basis of these findings.