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.