Investigation into balancing of high-speed flexible shafts by compensating balancing sleeves
Creators: name: Knowles, Grahame
Publisher: name: University of Lincoln
Year: 2023
Subjects: H100 - General engineering

description: Engineers have been designing machines with long, flexible shafts and dealing with consequential vibration problems, caused by shaft imbalance since the beginning of the industrial revolution in the mid 1800’s. Modern machines still employ balancing techniques based on the Influence Coefficient or Modal Balancing methodologies, that were introduced in the 1930’s and 1950’s, respectively.The research presented in this thesis explores fundamental deficiencies of current trim balancing techniques and investigates novel methods of flexible attachment to provide a component of lateral compliance. Further, a new balancing methodology is established which utilizes trim balance induced bending moments to reduce shaft deflection by the application of compensating balancing sleeves. This methodology aims to create encastre simulation by closely matching the said balancing moments to the fixing moments of an equivalent, encastre mounted shaft. It is therefore significantly different to traditional methods which aim to counter-balance points of residual eccentricity by applying trim balance correction, usually at pre-set points, along a shaft.Potential benefits of this methodology are initially determined by analysis of a high-speed, simply supported, plain flexible shaft, with uniform eccentricity which shows that near elimination of the 1st lateral critical speed, (LCS) is possible, thereby allowing safe operation with much reduced LCS margins.Further study of concentrated, residual imbalances provides several new insights into the behaviour of the balancing sleeve concept: 1) a series of concentrated imbalances can be regarded simply as an equivalent level of uniform eccentricity, and balance sleeve compensation is equally applicable to a generalised unbalanced distribution consisting of any number ofiiconcentrated imbalances, 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, thereby reducing commissioning time, 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. The analysis shows that equivalent reductions of 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, support this analysis and confirms the operating mechanism of balancing sleeve compensation and also it’s potential to vastly reduce shaft deflections/ reaction loads.