The Balancing of Rotating Shafts by Quadratic Programming

The application of quadratic programming methods to the computation of balance weights for rotating shafts is demonstrated. The use of the quadratic programming technique makes possible the minimization of the sum of the squares of the deflections of the balanced shaft when upper bounds have been placed on the magnitudes of the components of the correction weights. A simple shift of coordinates is employed to transform the constraint equations to the standard form necessary for the quadratic program.