Active Vibration Control of Rotor-Bearing Systems

Abstract

Rotating machinery is commonly used in many mechanical systems, including electrical motors, machine tools, compressors, turbo machinery and aircraft gas turbine engines. Typically these systems are affected by exogenous or endogenous vibrations produced by unbalance, misalignment, resonances, material imperfections and cracks. Vibration caused by mass unbalance is a common problem in rotating machinery. Rotor unbalance occurs when the principal inertia axis of the rotor does not coincide with its geometrical axis and leads to synchronous vibrations and significant undesirable forces transmitted to the mechanical elements and supports. Many methods have been proposed to reduce the unbalance-induced vibration, where different devices such as electromagnetic bearings, active squeeze film dampers, lateral force actuators, active balancers and pressurized bearings have been developed (Blanco et al., 2008) (Guozhi et al., 2000) (Jinhao & Kwon, 2003) (Palazzolo et al., 1993) (Sheu et al., 1997) (Zhou & Shi, 2001). Passive and active balancing techniques are based on the unbalance estimation to attenuate the unbalance response in the rotating machinery. The Influence Coefficient Method has been used to estimate the unbalance while the rotating speed of the rotor is constant (Lee et al., 2005) (Yu, 2004). This method has been used to estimate the unknown dynamics and rotorbearing system unbalance during the speed-varying period (Zhou et al., 2004). On the other hand, there is a vast literature on identification methods (Ljung, 1987) (Sagara & Zhao, 1989) (Sagara & Zhao, 1990), which are essentially asymptotic, recursive or complex, which generally suffer of poor speed performance. This chapter presents an active vibration control scheme to reduce unbalance-induced synchronous vibration in rotor-bearing systems supported on two ball bearings, one of which can be automatically moved along the shaft to control the effective rotor length and, as an immediate consequence, the rotor stiffness. This dynamic stiffness control scheme, based on frequency analysis, speed control and acceleration scheduling, is used to avoid resonant vibration of a rotor system when it passes (run-up or coast down) through its first critical speed. Algebraic identification is used for on-line unbalance estimation at the same time that the rotor is taken to the desired operating speed. The proposed results are strongly based on the algebraic approach to parameter identification in linear systems reported (Fliess & Sira, 2003), which requires a priori knowledge of the mathematical model of the