A Bladed Disk Reduction Technique That Captures Variation in Blade Stiffness and Blade Root Joint Contacts

In practice, a bladed disk will always have variations, known as mistuning, which is a focus of a significant amount of research within the turbomachinery industry. When mistuning is present, the forced response of the system often shows localized amplification of the blade deflection amplitudes when compared to a tuned system. In order to quickly perform a significant number of simulations containing mistuning, reduced order models (ROMs) have been developed where the mistuning can be introduced efficiently in the reduced space. Previously, mistuning had been introduced to bladed disks in the form of natural frequency shifts in the blades, and separately from contact uncertainties in the blade root joint and also separately from the various forms of small and large geometric mistuning. This work introduces a method to efficiently model multiple types of mistuning sources so that any interactions that may result can be studied. This work focuses on cases with stiffness and contact mistuning which are due to design tolerances, manufacturing processes, assembly procedures, material variability, and wear. The technique in this work utilizes the Craig-Bampton component mode synthesis that is applied to the uncoupled blade and disk sector. Small stiffness mistuning is applied by directly adjusting the modulus of elasticity within the uncoupled blade portion of the ROM. The degrees of freedom at the contacts are reduced using a modal basis based on the Gram-Schmidt Interface technique. A numerical validation of the developed methods is performed for cases including small and large stiffness mistuning and contact mistuning using a finite element model of a simplified rotor.