One realisation of an automatic balancer uses two or more balls that are free to travel in a race, filled with a viscous fluid, at a fixed distance from the shaft centre. The objective is for the balls to position themselves so that they counteract any residual unbalance. The fact that no external force is required to achieve balance, that is the system is passively controlled, means that the balancer is potentially able to cope with a time-varying unbalance. Typical applications include optical disc drives and machine tools. However, the usefulness of this device depends on the balanced steady state solution being achievable and stable. This paper describes a dynamic model of a Jeffcott rotor with an automatic balancer and provides a non-linear analysis of its dynamics to determine steady states and their bifurcations as parameters are varied. The pseudospectra of the linearization of the system about a balanced steady state solution are computed. This approach allows the eigenvalues that are most sensitive to perturbation to be quantified. Furthermore, how the sensitivity of the eigenvalues influences the transient response may be determined. These tools will help to design reliable and robust automatic balancers.
|Publication status||Published - 2005|