Balancing of flexible shafts: minimizing the maximum residual vibrations in the sense of D-metric

Based on introducing the concept of the metric induced by a set of vectors, as well as minimizing the maximum amplitude of residual vibrations in the sense of this metric, an approach for determining the balance correction for flexible shafts is presented. The advantages of the proposed method are two-fold. Firstly, the approach is available when upper bound constraints on balance corrections exist, and the resulted balance correction is approximately optimal. Secondly, the balance correction can be easily calculated by solving a linear programming problem.