stability analysis of a ball–rod–spring automatic balancer

the traditional ball-type automatic balancer, which consists of several balls moving along a fixed circular orbit, has been applied to different fields for rotational vibration reduction. under proper working conditions, the balls will counter-balance the rotor by positing to appropriate locations. this particular equilibrium configuration is referred to as the perfect balancing configuration. the unbalance vibrations at steady state can be totally suppressed only if the perfect balancing configuration is stable. the stability of the perfect balancing configuration depends on the parameters of the system. to achieve perfect balancing, the system parameters must lie in the stable region of the perfect balancing configuration in the parameter space. an automatic balancer with a larger stable region of the perfect balancing configuration will be more robust. this paper provides a detailed analysis of a new design of auto-balancer, the ball–rod–spring balancer, which is aimed to increase the stable region of the perfect balancing configuration. a theoretical model of a rotor packed with a two-unit ball–rod–spring balancer is constructed. closed form formulae of the equilibrium configurations are presented. the stability of each equilibrium configuration is investigated both analytically and numerically. results of numerical analysis confirm that the stable region of the perfect balancing configuration of the new design is larger than that of the traditional fixed orbit balancer.