Theoretical investigation into balancing high-speed flexible shafts, by the use of a novel compensating balancing sleeve

Abstract

Traditional techniques for balancing long, flexible, high-speed rotating shafts are inadequate over a full range of shaft\ud speeds. This problem is compounded by limitations within the manufacturing process, which have resulted in increasing\ud problems with lateral vibrations and hence increased the failure rates of bearings in practical applications. There is a need\ud to develop a novel strategy for balancing these coupling shafts that is low cost, robust under typically long-term operating\ud conditions and amenable to on-site remediation. This paper proposes a new method of balancing long, flexible couplings\ud by means of a pair of balancing sleeve arms that are integrally attached to each end of the coupling shaft. Balance\ud corrections are applied to the free ends of the arms in order to apply a corrective centrifugal force to the coupling shaft\ud in order to limit shaft-end reaction forces and to impart a corrective bending moment to the drive shaft that limits shaft\ud deflection. The aim of this paper is to demonstrate the potential of this method, via the mathematical analysis of a plain,\ud simply supported tube with uniform eccentricity and to show that any drive shaft, even with irregular geometry and/or\ud imbalance, can be converted to an equivalent encastre case. This allows for the theoretical possibility of eliminating the\ud first simply supported critical speed, thereby reducing the need for very large lateral critical speed margins, as this\ud requirement constrains design flexibility. Although the analysis is performed on a sub 15 MW gas turbine, it is anticipated\ud that this mechanism would be beneficial on any shaft system with high-flexibility/shaft deflection

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

“…The presented account extends previous, special case, research 14 on compensating balancing sleeves, to demonstrate the suitability of the methodology when applied to a generalised case of a shaft loaded with a single concentrated imbalance. By extension, it is shown that the principle of superposition allows for more practical imbalance distributions to be analysed using vector addition of any number of individual concentrated imbalances, of various magnitude/position.…”

“…Shear Force Reaction Ratio, RR This can be determined more readily by considering the special case of uniform eccentricity, 14 for simply supported and encastre supported ends.…”

“…The following parameter equations are taken from a previously reported study 14 into cases of simply supported shafts, with uniform eccentricity and balance sleeve compensation.…”

“…As an alternative to the above approaches, a novel method of balancing long, flexible, high-speed drive shafts has been proposed, 14,15 where balance corrections (that are traditionally applied to the ends of the drive shaft) are applied instead to the free ends of a pair of balancing sleeve arms, integrally attached to each end of the drive shaft. The balance sleeve applies a corrective centrifugal force to the drive shaft to limit the shaft-end reaction forces.…”

On the Importance of Sleeve Flexibility in Passive Control of Critical Speeds of a Rotating Shaft Using Eccentric Sleeves

“…This is typically done using a series of fixed balancing flanges on the shaft. Knowles et al proposed an alternative method in which balance corrections are applied to the free ends of a pair of balancing sleeves, attached to each end of the rotating shaft [11,12].…”