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It is well known that asymmetric vane spacing can result in decreased levels of the excitation at specific frequencies. In this paper, the resonant response reduction of mistuned bladed disks due to asymmetric vane spacing is studied theoretically for the most probable asymmetric vane, in which the vane count of the upper and lower half is slightly different. First, a method for predicting the maximum amplitude of the mistuned bladed disk for the asymmetric vane spacing is proposed. Second, a parametric study is carried out using Monte Carlo simulation to clarify the vibration response characteristics of the mistuned bladed disk for the asymmetric vane spacing. From these results, it is concluded that asymmetric vane spacing is effective for reduction of resonant amplitudes of a mistuned bladed disk if a multi-resonance phenomenon does not appear. INTRDUCTION In a multi-stage turbo-machinery, the interaction between the vane and the blade generates the excitation force on the blade, which comes from the wake of the upstream vane or the potential field of the upstream/downstream vane. The fundamental frequency of the excitation force due to the interaction between the vane and the blade is the rotor speed multiplied by the vane count, and if the natural frequency of the blade is coincident with the frequency of the excitation force, the resonant stress of the blade may become very large and may cause a blade failure due to HCF. Besides the traditional methods to reduce the resonant stress, it is well known that the asymmetric vane spacing can result in decreased levels of the excitation force at specific frequencies [1, 2]. It seems that asymmetric vane spacing is a very effective method for controlling the blade response for variable speed engines where the axial rotor span cannot be lengthened. As for a tuned bladed disk, where dynamic properties of individual blades on a disk is the same, the reduction effect of the resonant stress due to asymmetric vane spacing has been studied theoretically and experimentally [3, 4]. However, realistic bladed disks, although designed mostly to be cyclically symmetric, are mistuned, i.e. dynamic properties of individual blades are different. In spite that such imperfections of mistuned bladed disks are usually small, it is well known that the loss of cyclic symmetry properties of the bladed disk by mistuning can drastically change the forced response levels. There are numerous papers studying the mistuning effect. In the early papers [5, 6], the forced response of mistuned bladed disk for symmetric vane spacing has been studied by use of simple spring-mass model. Modern methods of the numerical analysis are described in the recent papers [7-9]. However, as far as authors know, few studies have been carried out on the reduction effect of the forced response of the mistuned bladed disk due to asymmetric vane spacing. In this paper, the resonant response reduction of mistuned bladed disks due to asymmetric vane spacing is studied theoretically for the most probable asymmetric vane, in which the vane count of the upper and lower half is slightly different. First, a method for predicting the maximum amplitude of the mistuned bladed disk for the asymmetric vane spacing is proposed. Second, a parametric study is carried out using Monte Carlo simulation to clarify the vibration response characteristics of the mistuned bladed disk for the asymmetric vane spacing. From these results, it is concluded that asymmetric vane spacing is effective for reduction of resonant amplitudes of a mistuned bladed disk. And except for the multi-resonance phenomena, the maximum response of the mistuned bladed disk to asymmetric vane spacing can be roughly predicted by the maximum response of the mistuned bladed disk to symmetric vane spacing multiplied by the response reduction effect for free-standing blade without circumferential coupling [3]. ANALYSIS METHOD As for the asymmetric vane spacing, usually the whole vanes in the stage are equally divided into Ns segments, and the following techniques are used to make asymmetric vane spacing. (1) Vane count in Ns segments is slightly altered (Vane count method). (2) Vane count in Ns segments is equal but the vane pitch between segments is changed by shifting segments circumferentially with respect to each other (Tangential offset method). (3) All vane pitches are altered at random (Random pitch method). Although these methods are well known, it seems that only the vane count method, where the whole vanes are divided into two segments (Ns = 2, upper half and lower half) and the vane count in the upper and lower half is slightly altered, is most practical and has been applied to actual engines, taking the cost of manufacturing and maintenance, disadvantageous effect on the excitation force of the lower engine orders, and the stability of the flow such as surge into consideration. Therefore, in this paper, the analytical method for predicting the blade vibration response of the asymmetric vane spacing by use of vane count method (Ns = 2) is mainly described, but the same procedure can be used for other methods. Blade-Vane Interaction Force for Asymmetric Vane Spacing When the vane counts in the upper and lower half are N1 and N2, respectively, two kinds of blade-vane interaction analyses with 3D International Journal of Gas Turbine, Propulsion and Power Systems February 2012, Volume 4, Number 1 Copyright © 2012 Gas Turbine Society of Japan Presented at International Gas Turbine Congress 2011 Osaka, November 13-18, Osaka, Japan, IGTC2011-0065 Review completed February 7, 2012

Study on Vibration Response Reduction of Bladed Disk by Use of Asymmetric Vane Spacing (Study on Response Reduction of Mistuned Bladed Disk)