Modelo para el estudio del comportamiento vibratorio de transmisiones planetarias

Abstract

Gear transmissions can be found in the majority of power transformation machinery. Despite the high degree of evolution in this field, the demand for increasingly efficient and reliable designs and the need for condition maintenance tools requires a better knowledge of these systems. In response to this need for knowledge on gear transmissions, the computational modeling has emerged as a major research line. Among the variety of existing transmissions, planetary gears stand out for their compactness and lightness and a number of additional features such as coaxiality, variable gear ratio and symmetry of forces in the central members. Being widely used in all kinds of applications, planetary transmissions have been given special attention in the modeling research line. In this Thesis a dynamic model of spur gear planetary transmissions is developed, with some enhanced capabilities over the existing models. The model can be used with any geometry of involute gear, including corrected wheels or profiles with tip or bottom relief. Moreover, the model manages multiple contacts in both directions, in and out of the line of action. The algorithm used for the calculation of contact forces is based on a hybrid method that combines finite element models and analytical formulations, the latter used for calculation of local deformation. The model takes into account the coupling of the deformation through the flexibility of the wheel bodies, solving all the individual meshes in the planetary transmission jointly. It is also presented a model for the calculation of bearings contact forces, which includes the ability to use ball and roller elements. All modeling elements have been integrated into a complete planetary transmission model of lumped parameters with dynamic capabilities. The introduction of dissipative forces is also considered, friction as well as damping due to the lubricant and body deformation. The usefulness of the developed model is validated through the static and dynamic simulation of a transmission example. Positioning and eccentricity errors in the planets have been also implemented in the model, and different configurations with fixed or floating central bodies has been considered, in order to evaluate their impact in terms of load sharing ratio between the different paths.