The analysis presented in the paper considers industrial shaft machinery that rotates at high speeds, specifically the rotating shaft in sub-15MW industrial gas turbine units, typically used for power generation or mechanical drive purposes. Operation of such machinery is accompanied by vibration, attributable in part to mass unbalance due to asymmetry and manufacturing imperfection in the rotating shaft, resulting in forces being exerted on surrounding structures [1
]. It is vitally important to ensure that such forces are controlled by eliminating the geometric unbalance of the rotor where possible. Primarily this is achieved through design and high tolerances in manufacture [2
]. Nevertheless, this is frequently insufficient and other means of reducing vibration levels are necessary post-manufacture.
Safe operation is ensured by adherence to regulation, such as API 671, which dictates that, in the case of a flexible coupling shaft, the lateral critical speed (LCS) margin should be 1.5 times the maximum operating speed [3
]. Therefore, the flexible coupling shaft design is dictated by the LCS margin, resulting in couplings, which are more flexible than would otherwise be desirable. This in turn results in shafts that are difficult to dynamically balance across a wide range of operating speeds. As such, rotor unbalance is a commonly encountered issue in rotating machinery, requiring periodic remediation. Vibration-based identification and characterization of rotor unbalance and other faults in rotating machines has been the subject of numerous studies [5
]. A model-based method for the estimation of multi-plane unbalance and misalignment in a rotating shaft from a single machine rundown was proposed by Sinha et al. [6
]. The method was applied to a small, experimental test-rig, with a sensitivity analysis showing the robustness of the method, particularly with regard to phase estimation. Sudhakar et al. proposed a model based methodology for the identification of rotor unbalance in an experimental rotor bearing system utilizing two approaches: equivalent loads minimization and vibration minimization [7
]. Considering errors in phase and amplitude estimation, it was concluded that the combined equivalent loads and vibration minimization method was more effective than the equivalent loads minimization method alone. More recently, a method for the identification and optimization of unbalance parameters in rotor-bearing systems was proposed by Yao et al. [8
]. The method combined a modal expansion approach with optimization algorithms and allowed for the identification of the axial location of the unbalance, as well as its magnitude and phase, showing good agreement with experimental observations.
Once the degree of residual unbalance in the rotor in terms of amplitude and phase has been established, conventional corrective balancing techniques then involve the addition or subtraction of mass at specified locations [9
]. 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
By this means, the trim balance mass applies a corrective centrifugal force to the drive shaft to limit the shaft end-reaction forces. The balancing sleeves are flexible by design; as such, the magnitude of the correcting forces is greater at higher speeds due to the increasingly eccentric position of the trim balance mass. The sleeves also impart a corrective bending moment to the rotating shaft, which has a beneficial tendency to limit the shaft deflection [13
]. However, the addition of mass to the system in the form of a sleeve can result in a change in the natural frequency and hence the critical speed of the system. Significant research is required to analyze the behavior of the system due to the addition of the eccentric sleeves prior to embedding them into engines. From this analysis, additional passive control characteristics may be identified.
In this paper, the critical speeds of a rotating shaft fitted with eccentric balance sleeves are identified from a scaled, high speed experimental test facility. The results are compared with the results of dynamic finite element simulations. It is shown that the stiffness of the sleeves must be accommodated when considering passive control characteristics critical speeds of a rotating shaft using eccentric sleeves.