Robust Optimal Balancing of High-Speed Machinery Using Convex Optimization

For high-speed rotating machinery, such as turbomachinery, the vibration caused by the rotor mass imbalance is a major source of maintenance problems. Vibration reduction by balancing under practical constraints and data uncertainty is often a challenging problem. In this paper, we formulate the problem of high-speed flexible rotor balancing as a convex optimization problem. This formulation not only solves the minmax balancing problem efficiently, but also allows the inclusion of various practical constraints. This formulation can be extended in a generalized unified balancing approach, which combines the advantages of both the influence coefficient approach and the modal balancing. Furthermore, a robust balancing approach is also developed to handle uncertainties in the influence coefficient and in the vibration response. This robust balancing approach provides the safeguard for the worse case scenario under the unknown but bounded uncertainty. All the resulting optimization problems are solved by second order cone programming. A large turbine generator balancing case is used to demonstrate that the proposed balancing technique provides the flexibility and efficiency beyond those of the existing balancing methods.