Nonlinear modal analysis for blisks with friction dampers

Abstract

Dynamic analyses of nonlinear systems have become an important topic in the field of turbomachinery. In industrial turbomachinery, the friction damping is regarded as the major damping source compared to the aerodynamic damping and material damping. Contact with friction is a type of common non-conservative and non-smooth nonlinearities. The existence of various friction joints in industrial turbomachinery makes the dynamic analysis complicated. The definition of the damped Nonlinear Normal Modes (dNNMs) and various numerical approaches facilitate the infrastructure of nonlinear modal analysis for structures with friction dampers. However, the relations between dNNMs and resonant solutions in forced responses cannot be directly addressed. In this context, the purpose of the present thesis is (i) to evaluate the performance of the existing numerical approaches for computing the dNNMs of systems with non-conservative nonlinearities; (ii) to develop a new method to directly relate the dNNMs to the resonant solutions in forced response for such system; and (iii) to study the geometric influence of the friction ring dampers on their dynamic responses and damping performances. The first contribution of the present thesis is to provide a comprehensive comparison of the existing numerical approaches, including Complex Nonlinear Mode (CNM) and Extended Periodic Motion Concept (EPMC). EPMC with artificial hysteretic damping is firstly attempted and compared with the original EPMC and CNM. The advantages and limitations of each method are critically discussed. The second contribution is the development of the Extended Energy Balance Method (E-EBM), which is a numerical method used to efficiently predict the resonances using the dNNMs of a non-conservative nonlinear system. This E-EBM can be simply applied to both CNM and EPMC approaches. The third contribution is the investigation the damping performance of friction ring dampers for blisk structures, especially the geometric effects of the ring dampers. The geometric design of the ring dampers is achieved by using kriging meta-modelling to predict the dNNMs. Useful advice is proposed for the future design of friction ring dampers.