A Computational Parametric Analysis of the Vibration of a Three-Spool Aero-Engine Under Multifrequency Unbalance Excitation

The integration of squeeze-film dampers (SFDs) in aero-engine assemblies is a highly cost-effective means of introducing damping in an otherwise lightly damped structure. However, their deployment requires careful unbalance response calculations that take due account of the SFDs' nonlinearity, particularly when they are unsupported by a centralizing spring. Until recently, such calculations were prohibitive due to the large number of assembly modes that typically need to be considered. This problem has been overcome by the authors through the novel impulsive receptance method (IRM) and the receptance harmonic balance method (RHBM), which efficiently solve the nonlinear problem in the time and frequency domains, respectively. These methods have been illustrated on a realistic twin-spool engine and have been shown to be effective for both single frequency unbalance excitation (unbalance on a single rotor) and multifrequency unbalance (MFU) excitation (unbalance on both rotors). In the present paper, the methods are applied to a realistic three-spool engine and the aims are twofold: (i) to present some preliminary results of a parametric study into a three-spool aero-engine assembly and (ii) to propose a technique that makes use of both IRM and RHBM in producing the speed responses under MFU excitation (from all three rotors) with a realistic speed relation between the rotors. The latter technique is necessary since the speed ratio will vary along a realistic speed characteristic and the authors have previously solved the twin-spool MFU problem under a constant speed ratio condition. The approach used here is to approximate the speed characteristic by one in which the speed ratios are ratios of low integers, enabling the use of RHBM to finish off (to steady-state) time-transient solutions obtained through IRM. The parameter study shows that the application of simple bump-spring supports to selected, otherwise unsupported, SFDs along with slight sealing should have a beneficial effect on the dynamic response of aero-engines with heavy rotors.