Equilibrium Configurations of a Long Rigid Rotor and Auto-Balancer System

Due to the demand of higher and higher efficiency, the rotational speed of rotary machinery has been increased continually. At high rotational speeds, even a small amount of unbalance may induce significant vibrations. Therefore, precise balancing of high-speed rotors has become more and more important. The ball-type automatic balancer, under proper conditions, can suppress arbitrary amount of unbalance and has been successfully applied to two dimensional planar rotor systems. However, relatively few studies have been conducted on its application to three dimensional long rotor systems. This paper investigated equilibrium configurations of a long rigid rotor equipped with an automatic balancer on each end. The rotor was supported at each end by isotropic linear springs and viscous dampers. First, the mathematical model of the system consisting of the long rigid rotor, auto-balancers and the suspension was constructed. Second, the governing equations were derived by Lagrange''s equations and the equilibrium equations were presented. There are totally sixteen different types of equilibrium configurations. Under specific conditions, some equilibrium configurations can be determined analytically. However, in general, equilibrium configurations can only be determined numerically. We investigated the dependence of equilibrium configurations on system parameters comprehensively. For each equilibrium configuration, the variation of the vibration amplitude of the system with the rotational speed was studied in detail. The existence and stable rotational speed regions of the equilibrium configurations were identified. Finally experiments were conducted to verify the numerical results.