Reduced Order Models for Blade-To-Blade Damping Variability in Mistuned Blisks

A novel reduced order modeling methodology to capture blade-to-blade variability in damping in blisks is presented. This new approach generalizes the concept of component mode mistuning (CMM), which was developed to capture stiffness and mass mistuning (and did not include variability in damping among the blades). This work focuses on modeling large variability in damping. Such variability is significant in many applications and particularly important for modeling damping coatings. Similar to the CMM based studies, structural damping is used to capture the damping effects due to the mechanical energy dissipation caused by internal friction within the blade material. The steady state harmonic responses of the blades are obtained using the novel reduced order modeling methodology and are validated by comparison with simulation results obtained using a full order model in ANSYS with a maximum amplitude error of 0.3%. It is observed that there is no strong correlation between the engine order of excitation and both the variation in the response from blade to blade and the blade amplification factors. The effects of damping mistuning are studied statistically through Monte Carlo simulations. For this purpose, the blisk model is subjected to multiple traveling wave excitations. The uncertainty in the various mechanisms responsible for dissipation of energy and the uncontrollability of these dissipation mechanisms makes it difficult to assign a reliable value for the loss factor of each blade. Hence, large variations (up to ±80%) in the structural damping coefficients of the blades are simulated.