Dynamic tooth loads and quasi-static transmission errors in helical gears – Approximate dynamic factor formulae

Based on both single and multi degree of freedom models, some original results are presented which establish a formal link between dynamic tooth loads and quasi-static transmission errors in helical gear sets. It is demonstrated that, as long as linear behaviour is considered, a perturbation technique leads to approximate formulae which make it possible to compute effectively dynamic tooth loads. Comparisons with the results obtained by a time-step integration method are favourable with considerable gains in computational time when multi degree of freedom models are employed. The proposed methodology looks promising in the context of statistical approaches to dynamic tooth loads when parameter variability/uncertainties cannot be ignored.