An Approach for Estimating the Effect of Transient Sweep Through a Resonance

Abstract

The difference of a stationary forced response situation of a turbine or compressor blade relative to a transient resonance sweep is well known and documented in the literature. Different approaches have been used to understand the effect on transient amplitude in comparison with forced response. The dependencies on damping levels and resonance passage speed have been noted. Estimates for a critical or/and maximum sweep velocity have been given. The understanding of transient response during resonance sweep is of practical importance for instance when running a certification stress test for an aircraft engine, where it needs to be decided upfront which acceleration rate (increase in rpm per second) to use to ensure that the maximum airfoil response that could be attained under stationary condition is being measured with sufficient precision. A second reason for understanding of transient response is the verification of correct, if relevant lower, component life usage during transient regimes in operation. This paper gives a proposal for a simple 1D method based on one degree-of-freedom (1DOF) system considerations for estimating the transient response dependency on the sweep velocity, damping levels, and resonance frequency. The method is verified with 3D analyses of more complex blade–disk structures, which have been validated with air jet excitation rig and aero-engine tests. Using the results of the 1DOF analysis, an estimate of the expected stationary resonance response increase can be formulated even in cases where the measured data are based on a significant deviation from the desired sweep velocity, where transient effects would be significant.

Transient Resonance Passage of a Mistuned Bladed Disk with and without Underplatform Dampers

“…As stated in [1], a transient run-up or coast-down mainly causes a frequency shift of the resonance peak along the sweep direction as well as beating following the resonance peak. This so-called ring-down or beating effect is caused by the linear system's relatively small structural damping.…”

“…Due to the ongoing need of global power generation for flexibilization, turbine blades are more frequently subject to transient resonance crossings. Typical effects that are expected from this kind of resonance passage such as ring-down and a frequency shift of the maximum amplitude, according to [1], have a significant influence on turbine blade dynamics. Furthermore, this has an impact on both the operational safety, e.g., through a possible high cycle fatigue (HCF), and the evaluation of measurements, especially the calculation of damping values.…”

Key Features of the Transient Amplification of Mistuned Systems

“…Under the cyclic symmetry condition, the vibration modes have harmonic shape, i.e. their j th components are in the form [7] GTP-20-1517 4 Carassale where r is called harmonic index and floor(•) is the rounding towards -. For the cases r=0 and r=N/2 (if N is even), the eigenvector r (s) does not exist.…”

“…where the constant C can be set to zero to select the solution that verifies A → 0 as  → −∞. Moreover, the Faddeeva function [18] GTP-20-1517 12 Carassale  = is the correct parameter that should be employed to represent the chirp rate, as it was already deduced in [4] on the basis of different arguments.…”

“…That is, the faster the crossing of the resonance, the lower the response amplification e.g. [1][2][3][4][5].…”