Effects of centrifugal stiffening and spin softening on nonlinear modal characteristics of cyclic blades with impact–friction coupling

Abstract

This paper aims to interpret the coupling modal properties of cyclic blades under impact–friction interactions and their evolution mechanism versus operating points. Therefore, a coupling analytical model of cyclic blades is developed based on a Lagrange method and the assumed mode method (AMM), after considering centrifugal stiffening, spin softening, stagger angle, and twist angle. Then a mixed modal analysis method (MMAM) for this analytical model is extended by combining the extended periodic motion concept (EPMC) with AMM. Wherein a classic alternating frequency/time method (AFT) and the continuation method are employed to overcome the numerical divergence problem. Then damped nonlinear normal modes (dNNMs), including eigenfrequencies, modal damping ratios, and mode shapes, of the coupling system with shroud joints are finally computed and discussed under different excitation levels and contact conditions through a modal synthesis algorithm. After that, the influence laws of centrifugal stiffening and spin softening on the dNNMs are explored to reveal its evolution mechanism versus operation speeds. Finally, the Campbell diagrams of dNNMs are successfully obtained to discuss the effects of the impact–friction coupling on critical speeds (CSs) of the shrouded blades system.