Heuristics for balancing turbine fans

We develop heuristics for a problem that models the static balancing of turbine fans: load point masses at regularly spaced positions on the periphery of a circle so that the residual unbalance about the center – which corresponds to the axis of rotation of the fan – is as small as possible. We give worst-case guarantees for our heuristics in terms of residual unbalance. For the case of an even number of blades, we show that one of our heuristics provides the same worst-case guarantee (with respect to the ideal of perfect balance) as does total enumeration. Furthermore, computational tests show that our heuristics are orders of magnitude faster and not far from optimum on average.