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Research Papers: Gas Turbines: Structures and Dynamics

Multiharmonic Forced Response Analysis of a Turbine Blading Coupled by Nonlinear Contact Forces

[+] Author and Article Information
Christian Siewert1

Institute of Dynamics and Vibration Research, Leibniz Universität Hannover, Appelstraße 11, 30171 Hannover, Germanysiewert@ids.uni-hannover.de

Lars Panning

Institute of Dynamics and Vibration Research, Leibniz Universität Hannover, Appelstraße 11, 30171 Hannover, Germanypanning@ids.uni-hannover.de

Jörg Wallaschek

Institute of Dynamics and Vibration Research, Leibniz Universität Hannover, Appelstraße 11, 30171 Hannover, Germanywallaschek@ids.uni-hannover.de

Christoph Richter

Steam Turbine Engineering, Siemens AG-Energy Sector, Rheinstraße 100, 45478 Mülheim an der Ruhr, Germanychristoph-hermann.richter@siemens.com

1

Corresponding author.

J. Eng. Gas Turbines Power 132(8), 082501 (May 26, 2010) (9 pages) doi:10.1115/1.4000266 History: Received April 14, 2009; Revised September 08, 2009; Published May 26, 2010; Online May 26, 2010

In turbomachinery applications, the rotating turbine blades are subjected to high static and dynamic loads. The static loads are due to centrifugal stresses and thermal strains whereas the dynamic loads are caused by the fluctuating gas forces resulting in high vibration amplitudes, which can lead to high cycle fatigue failures. Hence, one of the main tasks in the design of turbomachinery blading is the reduction in the blade vibration amplitudes to avoid high dynamic stresses. Thus, coupling devices like underplatform dampers and tip shrouds are applied to the blading to reduce the vibration amplitudes and, therefore, the dynamic stresses by introducing nonlinear contact forces to the system. In order to predict the resulting vibration amplitudes, a reduced order model of a shrouded turbine blading is presented including a contact model to determine the nonlinear contact forces. To compute the forced response, the resulting nonlinear equations of motion are solved in the frequency domain using the multiharmonic balance method because of the high computational efficiency of this approach. The transformation from the time domain into the frequency domain is done by applying Galerkin’s method in combination with a multiharmonic approximation function for the unknown vibration response. This results in an algebraic system of nonlinear equations in the frequency domain, which has to be solved iteratively in order to compute the vibration response. The presented methodology is applied to the calculation of the forced response of a nonlinear coupled turbine blading in the frequency domain.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Low pressure steam turbine blading with a shroud coupling (courtesy of Siemens AG-Energy Sector)

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Figure 2

Cyclic symmetric shrouded blade model

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Figure 3

Schematic view of the segment model with the used coordinate systems

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Figure 4

One-dimensional contact model with normal load variation

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Figure 5

Diagram of the AFT/HFT method

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Figure 6

Model of a shrouded turbine blading

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Figure 7

Nodal diameter map of the analyzed shrouded turbine blading

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Figure 8

Response for different values of the normal preload (spatial periodicity m=1)

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Figure 9

Response for a different number of harmonics (spatial periodicity m=1, normal preload fn,p=50 N)

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Figure 10

Response for a different number of harmonics (spatial periodicity m=3, initial gap g=0.1 mm)

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Figure 11

Relative displacement response in normal direction for a different number of harmonics (spatial periodicity m=3, gap g=0.1 mm)

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Figure 12

Relative displacement response for different values of the coefficient of friction (spatial periodicity m=3, gap g=0.1 mm)

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Figure 13

Response for different values of the contact stiffness (spatial periodicity m=3, gap g=0.1 mm)

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