Assessment of Blade Mistuning Effects via Power Flow Analysis of Tuned Bladed Disks

An efficient method is proposed for the early assessment of bladed disk designs with respect to blade mis-tuning effects. Structural and material differences among blades, known as blade mistuning, often cause sig-nificant increases in blade forced vibration amplitudes relative to ideal (tuned) bladed disks, and such effects are most pronounced when the blades and the disk share vibration energy actively. In this paper, it is shown that the flow of vibration energy between the blades and the disk of tuned bladed disks can be used to char-acterize disk-blade dynamic interaction, and consequently it is proposed as a means to assess blade mistuning effects. Power flow is first calculated for a simple lumped-parameter model, and it is shown to provide a phys-ical explanation for the sharp increases in blade forced response amplitudes that take place when disk-blade dynamic interactions are strong. The power flow analysis is then extended to parametric design studies of finite element models for industrial bladed disks. The calculation of coupling power flow between the blade and the disk segment for a nominal bladed disk sector is shown to enable the rapid, albeit approximate, assessment of mistuning effects on blade vibration response for the nominal bladed disk design as well as for a variety of alternate designs obtained by varying disk structural parameters. The power flow analysis tool developed in this paper solely requires tuned system information, and thus it provides an inexpensive alternative to detailed statistical analyses of mistuned system response, such as Monte Carlo simulations. It seems particularly well suited to the design optimization of bladed disks with respect to minimizing blade mistuning effects. I