Automatic Balancing of Twin Co-Planar Rotors

Abstract

This paper explores the dynamics and stability of a twin rotor system fitted with passive automatic balancing devices (ABD). Essentially, autobalancers consist of several freely moving eccentric balancing masses. At certain speeds, the stable equilibrium position of the balancer masses is such that they naturally adjust to cancel the rotor imbalance. This “automatic balancing” phenomena occurs as a result of nonlinear dynamic interactions between the balancer masses and the rotor vibrations. Previous studies have explored automatic balancing of single rotors. In particular, ABDs are widely utilized for imbalance correction in computer optical disk and hard-drive applications. For such systems, automatic balancing occurs at supercritical operating speeds. While automatic balancing of single rotors is generally well understood, there has been only limited work on the topic of multirotor system automatic balancing. Therefore, this investigation considers a twin co-planar rotor system consisting of two symmetrically situated rotors mounted on a common flexible foundation structure. Both rotors are fitted with ABDs and the simultaneous autobalancing behavior of both rotors is investigated. Here, the nonlinear equations-of-motion of the twin-rotor/ABD system are derived and the asymptotic stability about the balanced condition is determined via a perturbation and floquet analysis. It is found that for the case of co-rotating rotors, automatic balancing is only achievable at supercritical speeds relative to the system torsional and lateral modes. However, for counter-rotating rotors, automatic balancing occurs at both subcritical and supercritical speeds relative to the foundation torsional mode. In this investigation, a dimensionless parameter study conducted to explore the effects of rotation speed, torsion and lateral mode placement, twin-rotor imbalance phasing, autobalancer mass, and damping for both the co- and counter-rotating cases. By considering the dynamic interactions between two rotor/ABD sub-systems, it is hoped that this study will provide valuable insight into the use of ABDs in multirotor system applications.