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 prove that our heuristics provide the same worst-case guarantee in terms of residual unbalance as does total enumeration. Furthermore, computational tests show that our heuristics are orders of magnitude faster and not far from optimum on average. The balancing of rotating elements in modern machinery is critical, and is done in some cases by sophisticated balancing machines. The presence of unbalance in a rotating machine results in vibrations and excess stresses on the bearings, both of which shorten its useful life. Static unbalance, the primary source of unbalance in narrow, disc-shaped rotors such as turbine fans, occurs when the center of gravity of the fan does not coincide with the axis of rotation. Static balancing is the process of reducing unbalance primarily by adding or removing The rst author is at the Department of Mechanical Engineering of Concordia University, Montreal, CANADA. The others are at the School of Industrial and Systems Engineering of the Georgia Institute of Technology, Atlanta, GA USA.