Rotor Vibration under the Coupled Effects of Mass Unbalance and Asymmetric Bearings

Abstract

Large unbalance in rotor-dynamic systems is typically responsible for high energy vibrations and the consequent decrease in machine life. This paper presents an analytical model developed using Lagrangian mechanics and partial differential equations (PDEs) for the purpose of early fault-detection in rotor-bearing systems. The model was validated through a Fortran based program, RDA99 developed by Adams (2010), by successfully quantifying the single-peak unbalance response of the simple 8 DOF and 12 DOF rotor-bearing mass stations over two cases. Case I uses bearings with symmetric stiffness and damping matrix. The critical speed for Case I occurred at 1690 rpm and orbital shapes of each mass station was found to be circular with forward-whirl orbits. In Case II asymmetrical bearing stiffness and damping coefficient matrices demonstrate an anisotropic system. Critical speed occurred at 1655 rpm and rotor, bearing and pedestal orbits were seen to be elliptical and changing with shaft speed. Both cases demonstrated a significant shaft bending contribution to the disk displacement.