Analytical and Experimental Investigation of the Coupled Bladed Disk/Shaft Whirl of a Cantilevered Turbofan

The structural dynamics of a rotating flexible blade-rigid disk-flexible cantilevered shaft system is analytically and experimentally investigated. A simple analytical model yields the equations of motion expressed in the rotating frame, which show that the blade one nodal diameter modes dynamically couple to the rigid body whirling motion of the shaft-disk system. The blade modes higher than one nodal diameter are uncoupled from the shaft-disk dynamics. Nondimensionalization of the coupled equations of motion yield the criteria for the propensity and magnitude of the interaction between the bladed disk and shaft-disk modes. The analytical model was then correlated with the results of a structural dynamic experiment performed on the MIT Aeroelastic Rotor, a fan similar in design to a modern high bypass ratio shroudless turbofan. A special whirl excitation apparatus was used to excite both forward and backward asynchronous whirl, in order to determine the natural frequencies of the system. The agreement between the predicted and experimental natural frequencies is good and indicates the possibility of significant interaction of the one nodal diameter blade modes with the shaft-disk modes.