Stability in a Twisted Periodic Blade System with Cracks

摘要

This paper investigates the variations in dynamic stability of a cracked rotating periodic bladed disk assembly. A bladed disk composed of periodically shrouded blades is used to simulate the coupled periodic structure. To study mode localization, a number of apparently identical blades are distributed periodically around a rigid hub. For simplicity, the rigid hub is considered to be attached to a rigid shaft. The modal localization equations of the rotating cracked assembly are formulated using Hamilton's principle and Galerkin's method. The regions of instability in this cracked assembly are identified by means of the multiple scales perturbation method. The numerical results indicate that the modal localization effect introduced by local blade cracks destabilizes the shrouded blade group. One additional instability band at the localization frequency is introduced from the local crack. Furthermore, it is shown that the stability regions of a cracked rotating bladed disk assembly are significantly dependent on the rotational speed, shroud stiffness, and crack depth.