BALANCING HYDRAULIC-TURBINE RUNNERS - A DISCRETE COMBINATORIAL OPTIMIZATION PROBLEM

Hydraulic turbine runners are massive objects which require balancing during manufacturing. This paper presents the formulation of the balancing problem as a discrete combinatorial optimization problem and describes its approximation solution by a Monte Carlo method. Despite the uncertainties in blade masses and centers of gravity the computation of counter-weight mass location using the Monte Carlo approach certainly paid off in terms of speed of computational and general reduction in counter-weight sizes. Also, generalizing to three dimensions is of little interest due to the complicated blade shapes and because counter weights can go only on the crown.