Nonlinear Dynamics and Combination Resonance of a Flexible Turbine Blade with Contact and Friction of Shrouds

Author:

Li Hua1,Yuan Gaofei2,Yu Zifeng1,Wang Yuefang34,Marmysh Dzianis5

Affiliation:

1. China Oil & Gas Pipeline Network Corporation, Beijing 100020, China

2. National Key Laboratory of Helicopter Aeromechanics, China Helicopter Research and Development Institute, Jingdezhen 333001, China

3. Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China

4. State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Dalian 116023, China

5. Department of Theoretical and Applied Mechanics, Belarus State University, 220030 Minsk, Belarus

Abstract

Flexible shrouded blades are commonly adopted in the last stages of steam turbines where complicated dynamical behavior can be induced by dry friction force generated on contacting interfaces between adjacent shrouds and the geometric nonlinearity due to the structural flexibility of the blades. In this paper, combination resonance caused by contact and friction forces generated on shroud interfaces is investigated, which is a concurrence of 1:3 internal resonance involving the first and second modes in the flapwise direction and the primary resonance of the first flapwise mode. The stiffness and damping at the contact interface are obtained by linearizing the contact and friction forces between shrouds through the harmonic balance method. The vibrating blade is modeled as a beam with a concentrated mass of which the responses under the combination resonance are solved through the multiple-scale method. Sensitivities of response with respect to the angle of shrouds, contact stiffness and rotation speed are illustrated, and the influences of these parameters on the periodicity and amplitudes of steady responses are demonstrated. The parametric regions where the combination resonance occurs are pointed out. Finally, parametric analyses are presented to show how the amplitude–frequency relation of the multiple-scale solutions under the combination resonance vary with detuning and design parameters. The present research provides a designing basis for improving the dynamic performance of flexible shrouded blades and suppressing vibrations of blades by adjusting structural parameters in practical engineering.

Funder

International Cooperation Fund Project of DBJI, Dalian University of Technology

Free Exploration Project of the State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment

National Science and Technology Major Project

Publisher

MDPI AG

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