Balancing of high-speed rotating machinery using convex optimization

The vibration caused by rotor mass imbalance is a major source of maintenance problems in high-speed rotating machinery. To minimize the vibration by balancing under practical constraints and data uncertainty is a decision making problem. In this paper, the flexible rotor balancing problem based on the influence coefficient method is formulated as a convex optimization problem. This formulation not only solves the minmax balancing problem, but also allows balancers to handle various kinds of practical balancing constraints and data uncertainty. Furthermore, this formulation is extended to a unified approach in which modal weight distributions are obtained by solving general inequality constraints. Second Order Cone Programming (SOCP) is employed to solve the general weighted minmax and least-squares balancing problems. To deal with data uncertainty, a robust balancing approach is developed. A real world balancing example is presented and solved to demonstrate the effectiveness of this formulation. The convex optimization tool provides this new balancing technique with the flexibility and efficiency which cannot be achieved by the existing balancing methods.