Parametrically induced Jeffcott rotor due to varying stiffness of the supporting rolling bearing elements

In this paper a Jeffcott rotor system mounted on rolling bearings is considered. The most common source of unwanted vibration is resonant vibrations encountered at critical speeds. A widely adopted method to estimate the response of the spinning rotors at critical speeds is the Harmonic Balance Method. In addition, because of the time - varying stiffness introduced by the bearings during the rotation, an internal excitation which is known as Parametric Excitation is generated. Due to this phenomenon, there may be speed intervals which may trigger unstable responses in the system. These regions can be identified by sets of lines which are called Transition Curves (TCs) on the Mass - varying compliance frequency plane, i.e. the so called “stability plot”. However, obtaining such transition curves may be too computationally expensive for a complex system. The paper explores the possibility of using Harmonic Balance Method to track the presence of such unstable regions in the Frequency Response of the system in presence of unbalance.