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

The paper investigates the use of compensating balancing sleeves positioned at the shaft’s end for the balancing of high-speed flexible shafts. The balancing sleeve is a new arrangement that creates a pure balancing moment with virtually zero radial reaction forces. For comparison purposes, experimental results from previous research are used to benchmark performance and to demonstrate the benefits newly proposed topology. The new configuration is commensurate with what is required for the Power Turbine (PT) shaft of a twin shaft industrial gas turbine, with an overhung disc. The study is also aimed at bladed shafts, such as those used in high speed gas turbines/compressors, with a view to improving their volumetric efficiency by reducing the formation of relatively large tip leakage gaps caused by shaft deflection/blade wear of abradable seals. It is shown to be practically possible to separate the two main dynamic balancing functions i.e. the control of bearing reaction loads and shaft deflections, thus allowing for their independent adjustment. This enables the required balancing sleeve moment to be determined and set during low-speed commissioning i.e. before any excessive shaft deflection and resulting seal wear occurs, as is typical when final balancing is undertaken at full operational speed.

This paper considers the passive control of lateral critical speeds in high-speed rotating shafts through application of eccentric balancing sleeves. Equations of motion for a rotating flexible shaft with eccentric sleeves at the free ends are derived using the extended Hamilton Principle, considering inertial, non-constant rotating speed, Coriolis and centrifugal effects. A detailed analysis of the passive control characteristics of the eccentric sleeve mechanism and its impact on the shaft dynamics, is presented. Results of the analysis are compared with those from three-dimensional finite element simulations for 3 practical case studies. Through a comparison and evaluation of the relative differences in critical speeds from both approaches it is shown that consideration of eccentric sleeve flexibility becomes progressively more important with increasing sleeve length. The study shows that the critical speed of high-speed rotating shafts can be effectively controlled through implementation of variable mass/stiffness eccentric sleeve systems.