A dynamic model for the study of gear transmissions

Abstract

In this work a previous model developed by the authors for the quasi-static analysis of spur gear transmissions supported by ball bearings was modified extending its capabilities to dynamic analysis. The model combines a finite element and an analytical formulation achieving sufficient accuracy and computational efficiency to make dynamic analysis feasible. Non-linearity associated with the contact among teeth was included, taking into account the flexibility of gears, shafts and bearings. Furthermore, parametric excitations originating both from gear and bearing supports, as well as clearance, were also taken into account. An example of a simple transmission is presented providing several results obtained using the proposed model. Nevertheless, in spite of its usefulness, particularly in the case of variable torque loads, and its improved capabilities compared with other procedures, this approach still requires a high computational effort. As a consequence in those cases where the transmission operates under stationary conditions the formulation could be simplified by using a pre-calculated value for each the gear tooth stiffness as a function of the angular position. Once again, the original model is useful, taking advantage of its computational efficiency in the calculation of these stiffness coefficients throughout a meshing period. The improved model is applied to the same transmission and the consequences of a misleading calculation of the stiffness coefficients are shown. Then, it was used to study the vibratory behaviour under different levels of applied torque, showing the modifications suffered by the orbits, meshing contact forces and particularly the spectra obtained for bearing forces.