Generalised analysis of compensating balancing sleeves with experimental results from a scaled industrial turbine coupling shaft

The paper furthers the analysis of a recently proposed balancing methodology for high-speed, flexible shafts. This mechanism imparts corrective balancing moments, having the effect of\ud simulating the fixing moments of equivalent double or single encastre mounted shafts. This is shown to theoretically eliminate/nullify the 1st lateral critical speed (LCS), and thereby facilitate safe operation with reduced LCS margins. The paper extends previously reported research to encompass a more generalised case of multiple, concentrated, residual imbalances, thereby facilitating analysis of any imbalance distribution along the shaft. Solutions provide greater insight of the behaviour of the balancing sleeve concept, and the beneficial implications for engineering design. Specifically: 1) a series of concentrated imbalances can be regarded as an equivalent level of uniform eccentricity, and balance sleeve compensation is equally applicable to a generalised unbalanced distribution, 2) compensation depends on the sum of the applied balancing sleeve moments and can therefore be achieved using a single balancing sleeve (thereby simulating a single encastre shaft), 3) compensation of the 2nd critical speed, and to a lesser extent higher orders, is possible by use of two balancing sleeves, positioned at shaft ends, 4) the concept facilitates on-site commissioning of trim balance which requires a means of adjustment at only one end of the shaft, 5) the Reaction Ratio, RR, (simply supported/ encastre), is independent of residual eccentricity, so that the implied benefits resulting from the ratio (possible reductions in the equivalent level of eccentricity) are additional to any balancing procedures undertaken prior to encastre simulation. Analysis shows that equivalent reductions in the order of 1/25th, are possible. Experimental measurements from a scaled model of a typical drive coupling employed on an industrial gas turbine package, loaded asymmetrically with a concentrated point of imbalance, are used to support the analysis and conclusions