抄録
It is widely accepted that transmission error fluctuations correlate well with the dynamic behavior of gears and most models in the literature are, to a lesser or greater extent, based on this concept. The objective of this paper is to present some recent advances in the modeling of tooth mesh excitations and dynamic tooth loads in relation with transmission errors. Based on a multi-degree of freedom finite element model of single stage gear system, the excitation functions are derived from the contact conditions between the teeth and the equations of motion are presented in terms of quasi-static transmission errors under load and no-load transmission errors. The range of application of the transmission error-based formulations is then analyzed and the link between transmission errors and dynamic tooth loads is examined. It is demonstrated that, as long as the linear behavior of helical gears is considered, a perturbation technique leads to an approximate formula which makes it possible to compute effectively dynamic tooth loads. Comparisons with the results obtained by a time-step integration method are favorable with considerable gains in computational time when multi-degree of freedom models are employed. From the same theoretical foundation, it is finally demonstrated that, in certain conditions, a linear relationship can be found between dynamic transmission error variations and dynamic tooth loads, thus confirming some recent experimental evidence obtained on a spur gear test rig.
