Investigation into balancing of high-speed flexible shafts by compensating balancing sleeves

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 of ii concentrated 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

An investigation into the balancing of high speed, flexible shafts by external application of compensating balancing sleeves

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

Passive control of critical speeds of a rotating shaft using eccentric sleeves: model development (GT2016-58155)

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

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

Mathematical development and modelling of a counter balance compensating sleeve for the suppression of lateral vibrations in high speed flexible couplings

High speed drive shafts are traditionally balanced using trim balance weights applied to the shaft ends. This paper considers the development and theoretical analysis of a novel and alternative strategy of balancing long flexible coupling shafts, whereby the trim balancing weights are applied by the means of a pair of 'Balancing Sleeve' arms that are integrally attached to each end of the coupling shaft. The trim balance weights are intended to apply a corrective centrifugal force to the coupling shaft in order to limit shaft end reaction forces. With increasing speed, the magnitude of the corrective force also increases due to the flexibility of the balance sleeve. This thereby counteracts the increased coupling shaft unbalance resulting from its own flexibility. Additionally, it is also found that the mechanism imparts a corrective bending moment to the coupling shaft ends, which has a tendency to limit deflection. The methodology is modelled as a rotating simply supported shaft with uniform eccentricity and allows application to the problem of drivetrain balancing of sub-15MW industrial gas turbines. Results show that reaction loads can theoretically be reduced from 10,000 N to approximately zero. The bending moment applied to the shaft is also shown to reduce shaft deflection theoretically to zero. In practical applications this will be unrealistic and achievable results show deflection theoretically reduced by half. Analysis of the balance sleeve feasibility is considered through use of a three-dimensional finite element model. Further to this paper, the aim is to develop a full dynamic model of both shaft and counterbalance sleeve, with verification coming from scaled, experimental test facilities. Copyright © 2013 by ASME

Mathematical development and modelling of a counter balance compensating sleeve for the suppression of lateral vibrations in high speed flexible couplings

High speed drive shafts are traditionally balanced using trim balance weights applied to the shaft ends. This paper considers the development and theoretical analysis of a novel and alternative strategy of balancing long flexible coupling shafts, whereby the trim balancing weights are applied by the means of a pair of 'Balancing Sleeve' arms that are integrally attached to each end of the coupling shaft. The trim balance weights are intended to apply a corrective centrifugal force to the coupling shaft in order to limit shaft end reaction forces. With increasing speed, the magnitude of the corrective force also increases due to the flexibility of the balance sleeve. This thereby counteracts the increased coupling shaft unbalance resulting from its own flexibility. Additionally, it is also found that the mechanism imparts a corrective bending moment to the coupling shaft ends, which has a tendency to limit deflection. The methodology is modelled as a rotating simply supported shaft with uniform eccentricity and allows application to the problem of drivetrain balancing of sub-15MW industrial gas turbines. Results show that reaction loads can theoretically be reduced from 10,000 N to approximately zero. The bending moment applied to the shaft is also shown to reduce shaft deflection theoretically to zero. In practical applications this will be unrealistic and achievable results show deflection theoretically reduced by half. Analysis of the balance sleeve feasibility is considered through use of a three-dimensional finite element model. Further to this paper, the aim is to develop a full dynamic model of both shaft and counterbalance sleeve, with verification coming from scaled, experimental test facilities. Copyright © 2013 by ASME.</p

Functional gastrointestinal disorders are associated with the joint hypermobility syndrome in secondary care: a case-control study

The work was funded by a charitable grant from the Pseudo-obstruction Research Trust, as well as a grant from Bowel and Cancer Research and Ehlers-Danlos Syndrome Support UK. Neither of these charities had any role in the study design; in the collection, analysis, and interpretation of data; in the writing of the report; nor in the decision to submit the article for publication