Imbalance Vibration Suppression of Supercritical Shafts With Automatic Balancing Devices

This research explores the use of automatic balancing devices (autobalancers) for imbalance suppression of flexible shafts operating at supercritical speeds. Essentially, autobalancers are passive devices consisting of several balls free to roll within an oil-filled circular track mounted on a rotor or shaft to be balanced. At certain speeds, the stable equilibrium positions of the balls is such that they reduce or cancel the rotor imbalance. This “automatic balancing” phenomena occurs as a result of the non-linear dynamic interaction between the balancer balls and the rotor transverse vibrations. Thus, autobalancer devices can passively compensate for unknown imbalance without the need for a control system and naturally adjust for gradually changing imbalance conditions. Single-plane autobalancers are widely utilized for imbalance correction of computer hard-disk drives and CD-ROM drives as well as for balancing machine tools. While autobalancers can effectively compensate for imbalance of planar disk-type systems and rigid rotors, the use of autobalancing devices on flexible shafts has not been fully considered. This study explores the dynamics and stability of an imbalanced flexible shaft-disk system equipped with a dual ball autobalancer by solving a coupled set of nonlinear equations to determine the fixed-point equilibrium conditions in rotating coordinates. Stability is assessed via eigenvalue analysis of a perturbed system about each equilibrium configuration. It is determined that regions of stable automatic balancing occur at supercritical shaft speeds between each flexible mode. Additionally, the effects of bearing stiffness, autobalancer/imbalance-plane axial offset distance, and relative ball-track viscous damping are each explored. This investigation yields valuable analysis methods and insights for the application of automatic balancing devices to flexible shaft and rotor systems operating at supercritical speeds.