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Research Papers

Influence of Geometric Design Parameters Onto Vibratory Response and High-Cycle Fatigue Safety for Turbine Blades With Friction Damper

[+] Author and Article Information
Matthias Hüls

Siemens AG,
Mellinghofer Straße 55 45473,
Mülheim a. d. Ruhr 45473, Germany
e-mail: matthias.huels@siemens.com

Lars Panning-von Scheidt

Institute of Dynamics and Vibration Research,
Leibniz University Hannover,
Hannover 30167, Germany
e-mail: panning@ids.uni-hannover.de

Jörg Wallaschek

Institute of Dynamics and Vibration Research,
Leibniz University Hannover,
Hannover 30167, Germany
e-mail: wallaschek@ids.uni-hannover.de

1Corresponding author.

Manuscript received June 22, 2018; final manuscript received June 25, 2018; published online December 4, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(4), 041022 (Dec 04, 2018) (10 pages) Paper No: GTP-18-1290; doi: 10.1115/1.4040732 History: Received June 22, 2018; Revised June 25, 2018

Among the major concerns for high aspect-ratio, turbine blades are forced and self-excited (flutter) vibrations, which can cause failure by high-cycle fatigue (HCF). The introduction of friction damping in turbine blades, such as by coupling of adjacent blades via under platform dampers, can lead to a significant reduction of resonance amplitudes at critical operational conditions. In this paper, the influence of basic geometric blade design parameters onto the damped system response will be investigated to link design parameters with functional parameters like damper normal load, frequently used in nonlinear dynamic analysis. The shape of a simplified turbine blade is parameterized along with the under platform damper configuration. The airfoil is explicitly included into the parameterization in order to account for changes in blade mode shapes. For evaluation of the damped system response, a reduced-order model for nonlinear friction damping is included into an automated three-dimensional (3D) finite element analysis (FEA) tool-chain. Based on a design of experiments approach, the design space will be sampled and surrogate models will be trained on the received dataset. Subsequently, the mean and interaction effects of the geometric design parameters onto the resonance amplitude and safety against HCF will be outlined. The HCF safety is found to be affected by strong secondary effects onto static and resonant vibratory stress levels. Applying an evolutionary optimization algorithm, it is shown that the optimum blade design with respect to minimum vibratory response can differ significantly from a blade designed toward maximum HCF safety.

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Figures

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Fig. 1

Definition of blade and underplatform damper design parameters

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Fig. 2

Classical relation between resonance amplitude U and frequency fres at nominal stimulus s=snom (normalized to uncoupled system response) and damper mass md. The optimum damper mass is indicated by md,opt.

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Fig. 3

Definition of airfoil section design parameter

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Fig. 4

Effect of normalized airfoil parameters on hub (0) and tip (1) section

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Fig. 5

Resonance amplitude U as function of stimulus s and equivalent logarithmic decrement damping Λ (damping performance curves) for first bending type vibrational motion

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Fig. 6

Fully meshed model of baseline blade design, disk, blade-root, and indicated monitor node position

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Fig. 8

Two-dimensional planar damper FEA model for calculation of force–displacement hysteresis curves

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Fig. 9

Force–displacement hysteresis curves and estimation of contact stiffness

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Fig. 10

High-cycle fatigue capacity utilization for baseline design, determined from allowable and resonant vibratory stress

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Fig. 11

Exemplary visualization of Box–Behnken (training data) and Latin-hypercube (test data) sampling for three factors x1,x2,x3

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Fig. 12

Exemplary calculation of MAE of polynomial surrogate model on Latin-hypercube test-dataset for resonance amplitude at nominal stimulus U(s=snom)

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Fig. 13

Main effects of design parameter onto resonance amplitude of first bending type vibrational motion at nominal stimulus U(s=snom) and resonant vibratory stress σv,vib(s=snom). Results shown based on polynomial regression and Kriging surrogate model.

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Fig. 14

Main effects of design parameter onto allowable vibratory stress σ¯allow at HCF critical node and locally minimum HCF capacity utilization at nominal stimulus. Results shown based on polynomial regression and Kriging surrogate model.

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Fig. 15

(a) Pareto front of optimization of normalized resonance amplitude of first bending type deflection at nominal stimulus U(s=snom) and normalized maximum available equivalent logarithmic decrement damping. (b) Pareto front of optimization of normalized HCF capacity utilization of first bending type deflection at nominal stimulus HCF(s=snom) and normalized maximum available equivalent logarithmic decrement damping.

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Fig. 16

Normalized performance curves for minimization of resonance amplitude, baseline and minimization of HCF capacity utilization

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Fig. 17

Optimum design parameter for minimization of resonance amplitude and minimization of HCF capacity utilization

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