A Linear Programming Approach for Balancing Flexible Rotors

The feasibility of a new flexible rotor balancing method is demonstrated. Discrete “effective” unbalance components which produce the same observed response as the actual rotor unbalance are identified, and subsequently removed, using linear programming. In addition to satisfying rotor runout observations, the unbalance may be identified such that it is potentially harmful to response at a speed above the level at which the shaft can safely run without balancing. The potentially harmful response corresponds to the linear programming objective function, while the observations become constraints. In addition, further constraints can be included to assure that the size of the calculated balance weights are within practical limits. The versatility of the new approach is demonstrated with example problems using a rotor model for which the response is obtained with a computer code.