Method for balancing rotating machinery

For balancing a body that is rotatable about an elongated axis of rotation, said body having a plurality of stages distributed along its length which are correspondingly rotatable about said axis, with at least one stage (f) of said plurality of stages being accessible for physically applying a balancing weight (.DELTA.WGT.sub.f) thereto, said balancing weight having a certain magnitude (.vertline..DELTA.WGT.sub.f .vertline.) and angular orientation (.phi..sub.f), a method of determining the optimum magnitude and angular orientation for said balancing weight (.DELTA.WGT.sub.f), comprising:

• (1) providing at least one vibration sensor that is operative to sense vibration at a certain pickup location (i) relative to said body as said body rotates;
• (2) using said sensor to measure as-built vibration (U.sub.i) at said pickup location (i) as said body is rotated at varying rates of rotation (RPMs) within and across a certain range of RPMs, said as-built vibration (U.sub.i) having both a magnitude (.vertline.U.sub.i .vertline.) and phase (.phi..sub.i), and determining from said measured vibration (U.sub.i) a maximum as-built vibrational amplitude (U.sub.max) at said pickup location (i) for said range of RPMs;
• (3) arbitrarily selecting a desired vibrational amplitude (D) at said pickup location (i) that is less than the maximum as-built vibrational amplitude (U.sub.max) determined in the preceding step;
• (4) calculating a common limit of angular orientations for said range of RPMs for placing said balancing weight (.DELTA.WGT.sub.f) on said accessible stage (f) of said body, said limit defining a minimum range where said angular orientation (.phi..sub.f) of said balancing weight (.DELTA.WGT.sub.f) must be positioned relative to said accessible stage (f), in order to reduce the magnitude of vibration at said pickup location (i) to a level that is at or below said desired vibrational amplitude (D);
• (5) calculating a lower and higher limit of weight magnitude (.vertline..DELTA.WGT.sub.f .vertline.) for said balancing weight (.DELTA.WGT.sub.f) for any angular orientation (.phi..sub.f) of said balancing weight (.DELTA.WGT.sub.f) that is within the common limit calculated in the preceding step, said lower and higher limits of weight magnitude defining a range of weight magnitudes within which said magnitude (.vertline..DELTA.WGT.sub.f .vertline.) of said balancing weight (.DELTA.WGT.sub.f) must fall in order to reduce vibration at said pickup location (i) to a level that is at or below said desired vibrational amplitude (D), including using the following equation:
• ##EQU5## wherein:
• X=.DELTA.WGT.sub.f * Cos .phi..sub.f
• Y=.DELTA.WGT.sub.f * Sin .phi..sub.f
• R.sub.if =predetermined influence coefficient at pickup location (i) as a result of as-built unbalance at accessible stage (f), such influence coefficient having a predetermined magnitude and phase (.PSI..sub.if)
• .theta.=.phi..sub.i -.PSI..sub.if
• (6) calculating the best achievable balanced vibrational amplitude (D.sub.min-max) at pickup location (i) from the range of lower and higher limits of weight magnitude calculated in the preceding step;
• and
• (7) selecting the balancing weight magnitude (.vertline..DELTA.WGT.sub.f .vertline.) and angular orientation (.phi..sub.f) that provides D.sub.min-max, and applying said selected weight to said accessible stage (f).