Analisi del comportamento dinamico di riduttori epicicloidali mediante modellazione a parametri concentrati ed analisi sperimentale

The topic addressed in this PhD thesis is the development of a rotational Lumped Parameter model to analyze the dynamic behavior of planetary gearbox. This model allows the study of the gearbox torsional vibrations. In particular, the study carried out in this thesis has focused on simple planetary trains, with three planets and an the outer fix ring. Therefore the following five rotational degree of freedom have been taken into account: the sun rotation, the rotation of the three planets and the carrier rotation. In the first part of the work, the attention has been focused on a correct description of the gearbox geometry ( especially on the toothed wheels geometry) and on the operating characteristics, such as pressure angles and center to center distance. The definition of the geometry was then used for the development of a complex finite element model that, combined with an analytical formulation, allows to obtain the meshing stiffness, depending on the operating conditions of the gearbox. This meshing stiffness was used in the lumped parameter model to define the meshing forces, formed from an elastic component and from a viscous damping component. In addition to the meshing forces, the lumped parameter model considers the inertial actions and the external actions given by the driving torque and the resistant torque. From the simulation results it is possible to analyze the instantaneous angular velocity, the instantaneous angular acceleration of all wheels in different operating conditions, the variation of the meshing stiffness and the forces variations during the gearbox operations. The model is ready for an extension to the translational degrees of freedom, for which the formulation has already been developed. After having developed the entire model, some experimental tests were carried out in order to acquire the torsional vibratory signals of the gearbox unit studied. The tests were performed at different rotational speeds and with different torques applied. The experimental signals obtained have been used to validate the theoretical model. Overall, the research activity is scientifically relevant because it allows, through the development of a lumped parameter model, the study of torsional vibrations of planetary gear units. The model includes the most relevant dynamic phenomena involved in the gearbox, thus allowing the evaluation of the forces that mainly determine the vibrational signature of the studied gearbox. For this reason, the model can be considered a useful tool to support the design and prototyping, as it allows to identify the causes of undesirable dynamic effects and allows to evaluate the effect of any design changes on the dynamic behavior of the gearbox.