Dynamic Behavior of Very-High Speed Rotors at Non-stationary Conditions

Speed reducers with input shafts spinning at very high speeds (up to 42 000 rpm) are generally associated to electric motors, which are more and more used especially in the automotive field, in order to bring the rotational speed to the most efficient window. Accurate modeling of those rotating machinary behavior is crucial to improve product reliability and to prolong machinery life. Many studies are conducted with an imposed angular speed, which is in most of the cases considered as constant or, in best cases, which follows a given variation law. In this paper, the study is performed with no assumption on the rotational speed. A variable driving torque is induced to the input shaft and the instantaneous angular speed (IAS) is deduced from the dynamic problem coupled to an angular approach. As a result, the IAS takes into account not only the induced torque perturbations but also the periodic geometry of the whole structure (e.g.: bearings and gears). The aim of this work is to extend the existing model based on the Finite Element Method by introducing an enhancement of the gyroscopic effect matrices without any assumption on the spinning speed. This model will lead to the introduction of coupling between the flexural and torsional degrees of freedom as well as to a non-linearity in the modeling of the studied system. The aim is to improve the accuracy of simulations for the rotor dynamics in non-stationary conditions especially when getting through critical speeds.