Dynamic analysis and design strategies for mistuned bladed disks

Bladed disks are used in many important engineering applications, including turbine engine rotors. Typically, each disk-blade sector in a bladed disk is assumed to be identical, and the bladed disk is analyzed based on a single sector model. However, due to manufacturing tolerances, operational wear, and other unavoidable factors, an actual bladed disk always has discrepancies among individual sectors, called mistuning. Even small mistuning can alter dramatically the vibration response of a bladed disk compared to the ideal, tuned system. In particular, the vibration energy may be concentrated in a few blades, leading to increased stress levels and fatigue problems. Moreover, since mistuning destroys cyclic symmetry, the whole assembly model must be analyzed, which is computationally expensive. In this work, a new reduced-order vibration modeling technique for mistuned bladed disks is presented. This is called the component mode mistuning (CMM) method, and it allows for easy implementation of mistuning and yields more efficient and accurate reduced order models (ROMs) compared to previous methods. Based on the CMM method, a mistuning identification technique is also developed. In order to account for the difference between an actual bladed disk and the finite element model, the concept of cyclic modeling error is introduced in the CMM formulation, and a model updating procedure is implemented to compensate for this error. As a result, the identification method becomes more accurate and robust. In addition, because the increase in maximum blade response due to mistuning is used for design safety evaluation, two methods for calculating the upper bound of this response amplification are presented. Then, as a design strategy for significantly reducing the worst-case amplification, the use of intentional mistuning in a nominal design is investigated. Based on key observations from an analysis of vibration energy flow in bladed disks, some guidelines are proposed for reducing the design space for intentional mistuning patterns, so that an optimal or near-optimal pattern can be found without requiring an expensive optimization process. Finally, a novel reduced-order modeling technique is presented for a system subject to large, geometric mistuning or design changes. A ROM constructed by this new technique shows fast convergence and excellent accuracy in capturing the motion of a system featuring large deviations from the original design, which cannot be handled with existing small-mistuning ROMs.