Study on the Reduction of the Resonant Stress of Turbine Blades Caused by the Stage Interaction Force (Simultaneous Optimization of Blade Resonant Stress and Amount of Unbalance)

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. Especially for a bladed disk with the free-standing blade structure, it is indispensable to keep the sufficiently large safety factor in a design stage, considering the mistuning effect. Traditionally, the blade designer has adopted the following methods to reduce the resonant stress:

(1) Avoid the resonance by detuning the blade frequency or altering the vane count.

(2) Reduce the excitation force by expanding the spacing between the vane and the blade or by use of clocking.

(3) Adopt the asymmetric vane spacing.

(3) Increase the blade damping by adopting the friction damper, etc.

In addition, intentional mistuning has been used as an effective method to reduce the resonant response caused by the un-avoidable random mistuning.

Besides these above-mentioned methods, for a variable speed engine which cannot avoid the resonance, it is thought that a practical optimization method for a bladed disk with the free-standing blade structure is to sort the blades of a mistuned system so that the amplification factor is minimized. In this study, a simultaneous optimization method of the blade resonant stress and amount of unbalance causing the rotor vibration is proposed. In this method, first, the natural frequency and weight of all blades on a disk are measured. Second, a mistuned system is assembled and the analysis model is created. Then, the resonant stress and amount of unbalance of the mistuned system are analyzed. To reduce the computational time, the reduced model FMM (Fundamental Mistuning Model) is used to calculate the resonant stress of the mistuned system. The analyses of the resonant stress and amount of unbalance are carried out repeatedly, sorting the blades on a disk, and the optimal solution is explored by the Monte Carlo simulations or DDE (Discrete Differential Evolution). As an example, a mistuned bladed disk of an aero-engine is analyzed and the validity of the proposed method is verified.