Acceleration through critical speeds of an anisotropic, non-linear, torsionally stiff rotor with many degrees of freedom

Abstract

It is well known that the amplitude of the unbalance response of a rotor which runs through a critical speed can be reduced by increasing the value of the acceleration. However, the models which are used for the computation of the unbalance response can be used only for constant speed running, and the solutions dealing with accelerating rotors which can be found in the literature refer to very simple geometrical layouts. The aim of the work reported here is to extend the usual mathematical models based on the finite element method to the study of the dynamic behaviour of rotors with non-constant angular speed. Both the non-linear behaviour of the rotor and its geometrical or inertial anisotropy have been taken into account. The case of a torsionally stiff rotor running with a given law ω( t) is studied in detail. Several examples, including a practical one dealing with a complex rotor running on non-linear bearings, conclude the work.