Load Effects on the Dynamics of Spur Gear Transmissions

Gear transmissions in general and spur gears in particular exhibit a different dynamic behavior depending on the level of the transmitted load. This fact justifies the interest in the study of the role of the load in gear dynamics not only in the context of design, vibration and noise control but also for condition monitoring. This task requires the development of advanced models achieving a compromise between accuracy and computation time. In this work, gear and bearing non-linearities associated with the contact among teeth and roller elements have been included, taking into account the flexibility of gears, shafts and bearings. Besides, parametric excitations coming both from gear and bearing supports, as well as clearance, were also considered. Gear contact force calculations are carried out following a hybrid approach which combines both analytical and numerical tools. This lets to achieve accurate results with an acceptable computational effort and thus dynamic analysis becomes feasible. This approach was improved and the calculation speeded up from the point of view of computational time. This was performed by using a pre-calculated value for gear tooth stiffness as a function of load and the angular position when it operates under stationary conditions. On the other hand, bearings were formulated just as deflections of Hertzian type. This means that bending and shearing of races and rolling elements are neglected. However, the variation in the number of loaded rolling elements as a function of the load and the angular position was taken into account. Shaft flexibilities were added to gear and bearing models to define a simple transmission that was used to study the vibratory behavior under different levels of applied torque. In a preliminary study, this model was linearized for several loads, obtaining the corresponding frequencies and mode-shapes in order to assess their variation with this parameter. Finally, dynamic simulations were carried out, showing the modifications undergone by the orbits, meshing contact forces and transmitted bearing forces.