Investigations on bending-torsional vibrations of rotor during rotor-stator rub using Lagrange multiplier method

The ever-increasing need of highly efficient rotating machinery causes reduction in the clearance between rotating and non-rotating parts and increase in the chances of interaction between these parts. The rotor-stator contact, known as rub, has always been recognized as one of the potential causes of rotor system malfunctions and a source of secondary failures. It is one of few causes that influence both lateral and torsional vibrations. In this paper, the rotor stator interaction phenomenon is investigated in the finite element framework using Lagrange multiplier based contact mechanics approach. The stator is modelled as a beam that can respond to axial penetration and lateral friction force during the contact with the rotor. It ensures dynamic stator contact boundary and more realistic contact conditions in contrast to most of the earlier approaches. The rotor bending-torsional mode coupling during contact is considered and the vibration response in bending and torsion are analysed. The effect of parameters such as clearance, friction coefficient and stator stiffness are studied at various operating speeds and it has been found that certain parameter values generate peculiar rub related features. Presence of sub-harmonics in the lateral vibration frequency spectra are prominently observed when the rotor operates near the integer multiple of its lateral critical speed. The spectrum cascade of torsional vibration shows the presence of bending critical speed along with the larger amplitudes of frequencies close to torsional natural frequency of the rotor. When m×1nX frequency component of rotational frequency comes closer to the torsional natural frequency, stronger torsional vibration amplitude is noticed in the spectrum cascade. The combined information from the stator vibration and rotor lateral-torsional vibration spectral features is proposed for robust rub identification.