In industries like the aircraft gas turbine, trans-critical or super-critical operating speeds are quite common, and rotating machinery must be mass produced with very demanding precision in balance effectiveness, generally without recourse to high-speed balance procedures. A procedure has been developed which permits high-speed multi-plane (i.e., three or more plane) balance correction to be made on rotors in simple conventional low-speed balance machines (Patent Applied For). The procedure accomplishes most of the benefits of actual high-speed or modal or true multi-plane balancing by utilizing other known or available data on the particular rotor’s generic dynamic behavior (i.e., its natural or critical mode shapes) and data on the particular rotor’s generic design and manufacture (i.e., its perceived generic patterns of unbalance distribution). For (N) balance planes, the procedure involves the specification of a Balancing Rule wherein a sequence of (J) low speed balance steps is specified (where J equals the integer part of [(N + 7)/2]). At each of these steps, some fraction (called a Balancing Factor) of the measured two plane unbalance vectors is applied to one or two of the other balance correction planes, before final correction is made on the last two correction planes themselves. A procedure is derived to predetermine those (I) Balance Factors (where I equals [N-2]). The procedure involves an iterative sequence for computing the optimized Balance Factors, with convergence driven by the Newton Raphson procedure, and requires the specification of (I) pairs of generic unbalance distributions and natural mode shapes. The analytically derived Balancing Factors are designed to null the vibration response of the rotor excited by each of the specified generic unbalance distributions at the critical speed associated with the specified mode shape with which the generic unbalance distribution is paired.

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