Dynamic of a statically unbalanced rotor with eccentric ball autobalancer

Abstract

A statically unbalanced rotor equipped with an automatic ball balancer, the axis of symmetry of which does not coincide with the symmetry axis of the rotor, is considered. Based on a simple model of the Jeffcott’s rotor, the equations of motion of the system are derived in the fixed and rotating coordinate systems, as well as the equations describing the steady-state modes of motion. Fundamentally unenforceability of the conditions of existence of balanced steady-state mode for a rotor with variable imbalance is established. For autobalancer with two balls the possibility of the existence of two different types of unbalanced steady-state modes is shown. The steady-state mode with a constant residual vibration, whose amplitude is independent of the angular velocity and is equal to eccentricity of the balancer, is proposed to be called half-balanced. A solution that corresponds to half-balanced mode is constructed explicitly; the conditions of its existence and sustainability are found. Two-parameter stability diagrams for half-balanced steadystate mode are constructed using numerical methods. Numerical study of nonstationary motion modes of the rotor when it rotates at a constant angular velocity is performed. Refs 6. Figs 5.

Keywords:

the ball autobalancing device, statically unbalanced rotor