Nonlinear Vibration of Bladed Discs

Over the years, finite element software has taken an increasingly important place in the engineering field and the aerospace sector is no exception: the verification of structural aspects with this software is now common practice. This is the background to the European research project EXPERTISE, which aims to develop tools and methodologies for the dynamic analysis of large-scale turbomachinery models, thus pioneering the virtual testing of the entire machine. This thesis project is aimed at demonstrating the potential of how finite element software can help in the design and verification of bladed discs, and how to estimate the level of vibrations due to forced response near resonance. The correct prediction of the dynamic behaviour of a bladed disc is of uttermost importance since it affects the performance of the entire aircraft engine, its reliability and maintenance as vibrations are the major cause for high cycle fatigue failure. A strongly nonlinear dynamic response can be observed during engine operation given the particular complex design of turbomachinery, thus representing a big challenge for the virtual analysis. When verifying a tuned bladed disc, the most used approach is to analyse only a single sector exploiting the cyclic symmetry hypothesis, thus reducing the computational cost. During this work, modal analysis of tuned system has been carried out in the open-source software CalculiX to determine the prestressed modes and build the SAFE diagram, a widely used tool which helps to find resonances, thus indicating to the designer which of them should be checked. The results obtained in CalculiX have been compared to the one in the Rolls-Royce in-house software SC03 and ANSYS for validation. Then a reduced model based on free modes and FRF matrix has been built by extracting the mode shapes with CalculiX. The nonlinear forced response is computed using harmonic balance method. Today's computational power is not nearly enough to estimate the response of the whole model thus only a handful of degrees of freedom are retained in the reduced order model. The nonlinear forced response curve has been computed using the Imperial College in-house code FORSE. The proposed approach has been applied to a bladed-disc testcase provided by SAFRAN in the framework of the EXPERTISE project. The demonstrator consists of a disc with 24 shrouded blades. The nodes retained in the reduced order model nodes are selected at the interface between two blades, where the cause of the major nonlinearities is the friction due to contact. The ROM has been validated first comparing the mode shapes with the MAC then checking the estimated response. Finally, a sensitivity analysis of the characteristics most affecting the nonlinear behaviour, such as contact parameters, shroud geometry or the type of elements used, has been carried out.