Stiffness estimation from random response in multi-mass rotor bearing systems

This paper describes a procedure for extraction of the linear and nonlinear stiffness parameters in rotors with multiple discs, supported in rolling element bearings. The analysis puts forth a technique, which can be employed on-line, for processing the rotor vibrations picked up at the bearing caps, as it does not require an a priori knowledge of the excitation force. The problem is formulated for a multi-degree, nonlinear, balanced rotor system experiencing random excitations from the bearings, caused due to imperfections and deterioration of the rolling surfaces as well as from the other random sources, like inaccuracies in alignment, etc. The governing equations of motion are subjected to coordinate transformation and subsequently modeled into the Fokker-Planck equations through the Markov vector approach. The solution procedure for the Fokker-Planck equation and the assumptions involved are outlined. A curve fitting algorithm is proposed to process the solution to the Fokker-Planck equation for the inverse problem of parameter estimation from the measured response. The technique is illustrated on a laboratory rotor rig and the estimated parameters are compared with those obtained through analytical models available for isolated bearings.