Development and application of a unified balancing approach with multiple constraints

The development of a general analytic approach to constrained balancing that is consistent with past influence coefficient methods is described. The approach uses Lagrange multipliers to impose orbit and/or weight constraints; these constraints are combined with the least squares minimization process to provide a set of coupled equations that result in a single solution form for determining correction weights. Proper selection of constraints results in the capability to: (1) balance higher speeds without disturbing previously balanced modes, thru the use of modal trial weight sets; (2) balance off-critical speeds; and (3) balance decoupled modes by use of a single balance plane. If no constraints are imposed, this solution form reduces to the general weighted least squares influence coefficient method. A test facility used to examine the use of the general constrained balancing procedure and application of modal trial weight ratios is also described.