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Research Papers: Gas Turbines: Structures and Dynamics

Transient Forced Response Analysis of Mistuned Steam Turbine Blades During Startup and Coastdown

[+] Author and Article Information
Christian Siewert

Energy Sector,
Fossil Power Generation,
Siemens AG,
Rheinstraße 100,
Mülheim an der Ruhr 45478, Germany
email: christian.siewert@siemens.com

Heinrich Stüer

Energy Sector,
Fossil Power Generation,
Siemens AG,
Rheinstraße 100,
Mülheim an der Ruhr 45478, Germany
e-mail: heinrich.stueer@siemens.com

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received August 4, 2014; final manuscript received July 5, 2016; published online August 16, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(1), 012501 (Aug 16, 2016) (10 pages) Paper No: GTP-14-1459; doi: 10.1115/1.4034151 History: Received August 04, 2014; Revised July 05, 2016

It is well known that the vibrational behavior of a mistuned bladed disk differs strongly from that of a tuned bladed disk. A large number of publications dealing with the dynamics of mistuned bladed disks are available in the literature. The vibrational phenomena analyzed in these publications are either forced vibrations or self-excited flutter vibrations. Nearly, all published literature on the forced vibrations of mistuned blades disks considers harmonic, i.e., steady-state, vibrations, whereas the self-excited flutter vibrations are analyzed by the evaluation of the margin against instabilities by means of a modal, or rather than eigenvalue, analysis. The transient forced response of mistuned bladed disk is not analyzed in detail so far. In this paper, a computationally efficient mechanical model of a mistuned bladed disk to compute the transient forced response is presented. This model is based on the well-known fundamental model of mistuning (FMM). With this model, the statistics of the transient forced response of a mistuned bladed disk is analyzed and compared to the results of harmonic forced response analysis.

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References

Figures

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Fig. 1

Example of a Campbell diagram indicating transient synchronous forced vibration situations during speedup and coastdown

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Fig. 2

Dynamic strains measured on three blades during startup of a real turbine blading in a transient synchronous resonance situation

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Fig. 3

Full FE model of a model bladed disk with mistuned blades indicated by different gray scales

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Fig. 11

PDF and CDF of the forced response vibrations for m = 3 and σ+ = 0.5% (nMC = 5000)

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Fig. 12

PDF and CDF of the forced response vibrations for m = 3 and σ+ = 1.0% (nMC = 5000)

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Fig. 4

Nodal diameter map of the tuned bladed disk shown in Fig. 3

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Fig. 5

Natural frequencies of the mistuned model bladed disk shown in Fig. 3 (σ+ = 1.2%)

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Fig. 6

Campbell diagram of the tuned bladed disk shown in Fig. 3

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Fig. 7

Mistuned transient forced response vibrations for blade j = 3 with f˙r=1.0 Hz/s (σ+ = 1.2%)

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Fig. 8

Harmonic forced response vibrations (σ+ = 1.2%)

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Fig. 9

Transient forced response vibrations with f˙r=1.0 Hz/s (σ+ = 1.2%)

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Fig. 10

Transient forced response vibrations for startup and coastdown with f˙r=±1.0 Hz/s for the blade with the maximum response (j = 13; σ+ = 1.2%)

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Fig. 14

Amplitude magnification for different speed harmonics and speed gradients (σ+ = 1.0%; harmonic results are independent of the speed gradient)

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Fig. 15

Mistuning factors for the maximum harmonic forced response and the forced response for m = 3 (σ+=1.0 %and f˙r=1.0 Hz/s)

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Fig. 16

Mistuning factors for the maximum transient forced response and the forced response for m = 3 (σ+=1.0 % and f˙r=1.0 Hz/s)

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Fig. 13

Amplitude magnification for different speed harmonics and speed gradients (σ+ = 0.5%; harmonic results are independent of the speed gradient)

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