Influence of mechanical mistuning on the forced response of a turbine cascade

An experimental investigation has been conducted in the non-rotating annular test facility of the "Laboratoire de Thermique Appliquée et de Turbomachines" (LTT), "École Polytechnique Fédérale de Lausanne" (EPFL). The influence of frequency mistuning and modeshape mistuning on the forced response of a turbine cascade is thereby determined. The 20 turbine blades of the cascade are excited by gusts generated using a strutted rotor with 13 elliptical bars providing a 13th engine order excitation pattern. The blades vibrate in their first eigenmode, corresponding to either a bending vibration or a torsion vibration. The frequency mistuning study has been carried out for the cascade with a first vibration mode in torsion. The frequency mistuning is introduced by adding or removing mass. A case with a weak (case T1) and a strong random frequency mistuning (case T2) are studied. For the modeshape mistuning study the blades used exhibit a first eigenmode in bending. The modeshape mistuning is introduced by changing the bending direction, using three different directions in the experimental setup. A datum case and two mistuned case are studied: The blades all vibrate in a direction normal to the chord for the datum case, called case B0. For the first mistuned case B1, the bending direction is varied alternately from blade to blade by plus or minus 10°. The second mistuned case B2 corresponds to a random variation of the bending direction. The motions of all blades as well as the unsteady pressure distributions on selected blade surfaces are recorded during the forced response measurements. In order to quantify the forcing function, the unsteady pressure distribution is measured in a second test setup with clamped blades, allowing the isolation of the effects of motion-induced unsteady pressures. Specific objective of this work is to study the influence of mistuning of the structural properties on the forced response of a turbine cascade. Both frequency mistuning and modeshape mistuning are investigated and an attempt is made to separate their impact on the maximum vibration amplitude of the individual blades. The measurement results show that the aerodynamic force that excites the vibration comprises five significant harmonics, the first harmonic at the strut passing frequency being dominant. The dominant first harmonic leads to an aerodynamic excitation of the 13th engine order. The measured forced response amplitude plots for the frequency mistuning study show typical effects of frequency mistuning and coupling (secondary peaks). The measured forced response phase of the blade movement exhibits inter-blade phase angles that are typical for a 13th engine order excitation. The effects of frequency mistuning and coupling can be detected on the phase plots. Besides the frequency mistuning, a significant damping mistuning is present in the cascade. The damping mistuning leads to a wide scatter of maximum response amplitude. A damping factor correction is applied to the measured maximum forced response amplitudes. The corrected amplitudes are much less scattered than the uncorrected ones. The average of the maximum response amplitudes is insignificantly higher for the heavily random mistuned case T2 than for case T1. A simplified frequency mistuning model that is capable of reproducing the effects of frequency mistuning and coupling qualitatively was established. The measured forced response for the modeshape mistuning study exhibits effects of frequency and damping mistuning. The influence of the damping mistuning is eliminated by the application of a damping factor correction method. This allows a better appreciation of the modeshape mistuning on the forced response. The differences in amplitudes between the cases B0 and B1 – for the individual blades as well as for the average values – follow a periodic pattern (with same periodicity as the mistuning pattern). This is a consequence of the periodic modeshape mistuning pattern. The average of the maximum forced response amplitudes is increased for case B1 compared to case B0. Comparing base B0 to B2, the trends in differences of maximum amplitudes are not as clear as for case B0 versus B1. This is due to the non-periodic and non-symmetric mistuning pattern. Nevertheless, some trends are detectable which correlate with the absolute change in bending direction between two adjacent blades. The modeshape mistuning does not reduce the level of the forced response amplitudes for both the alternate and random modeshape mistuning pattern. The minimum, average and maximum forced response maximum amplitudes as well as their standard deviation are nearly identical for both mistuned cases B1 and B2.