Research Papers: Gas Turbines: Structures and Dynamics

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

[+] Author and Article Information
Hans-Peter Hackenberg

MTU Aero Engines AG,
Munich 80995, Germany
e-mail: hans-peter.hackenberg@mtu.de

Andreas Hartung

MTU Aero Engines AG,
Munich 80995, Germany
e-mail: andreas.hartung@mtu.de

1Note that in this plot, the origin is not the bottom left corner.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received November 28, 2015; final manuscript received December 31, 2015; published online March 15, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(8), 082502 (Mar 15, 2016) (12 pages) Paper No: GTP-15-1554; doi: 10.1115/1.4032664 History: Received November 28, 2015; Revised December 31, 2015

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.

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Fig. 1

Typical airfoil stress measurement: Frequency content and vibratory stress amplitude along engine order

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Fig. 2

Engine order response amplitude as function of excitation frequency

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Fig. 3

Response envelopes of transient sweep through a resonance for two different sweep velocities (example for fn = 1000 Hz, ζ = 0.02)

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Fig. 4

Response envelopes of transient sweep through a resonance for different values of the reduced sweep velocity κ (example for fn = 1000 Hz, ζ = 0.01)

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Fig. 5

Response envelopes of transient sweep through a resonance for different values of damping ζ at equal reduced sweep velocity κ (example for fn = 1000 Hz, κ = 50)

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Fig. 6

Ratio of maximum amplitude to the stationary response amplitude versus reduced sweep velocity

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Fig. 7

Ratio of estimated damping ratio to its exact value versus reduced sweep velocity

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Fig. 8

Frequency shift parameter (see Eq. (18)) versus reduced sweep velocity

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Fig. 9

Estimate for reduced sweep velocity versus exact value of reduced sweep velocity

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Fig. 10

Ratio of amplitude of second maximum to maximum amplitude as function of reduced sweep velocity

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Fig. 11

Three-dimensional analysis of resonance passage for a bladed disk at four different sweep velocities

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Fig. 12

Three-dimensional analysis results plotted against the curves obtained for a 1DOF system (Figs. 68 and 10)

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Fig. 13

1DOF resonance passage example (fn = 1000 Hz, ζ = 0.001, and κ = 100)

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Fig. 14

Short-time FFT to analyze signal of the 1DOF-system resonance passage from Fig. 13

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Fig. 15

Strain gauge measurement of a turbine vane stage, recording of stress signal versus time

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Fig. 16

Frequency content of strain gauge signal (Fig. 15) and gauge response along engine order (dashed lines indicate reduced response frequency range considered in Fig. 20)

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Fig. 17

Use of 1DOF system results (Figs. 610) to determine the reduced sweep velocity κ and the dependent quantities

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Fig. 18

Result of 1DOF model analysis processed with short-time FFT using the same processing parameters as in Fig. 16

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Fig. 19

Strain gauge measurement versus 1DOF model results comparison (left: time signal of measured or predicted stress and right: engine order response from FFT analysis)

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Fig. 20

FFT analysis result of strain gauge signal using a fine frequency resolution (frequency range is zoomed into, indicated by the dashed lines in Fig. 16)



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