On the Importance of Shear Deformation, Rotatory Inertia, and Coriolis Forces in Turbine Blade Vibrations

1986 ◽  
Vol 108 (2) ◽  
pp. 319-324 ◽  
Author(s):  
K. A. Ansari
Keyword(s):  
Shear Deformation ◽  
Turbine Blade ◽  
Normal Modes ◽  
Functional Method ◽  
Lumped Parameter Model ◽  
Rotatory Inertia ◽  
Blade Vibration ◽  
Coriolis Forces ◽  
Analysis Technique ◽  
Blade Vibrations

This paper is concerned with the significance of the effects of shear deformation, rotatory inertia, and Coriolis forces in the analysis of turbine blade vibrations. Since these are quite pronounced at the high frequency ranges encountered in turbine blade vibration problems, they should not be overlooked although their inclusion paves the way for a complicated nonlinear analysis. An approximate analysis technique is presented which involves an application of the stationary functional method using the normal modes of a discretized model. Numerical results for a typical blade are obtained and discussed. An advantage of this analysis as applied to a lumped parameter model is that nonlinear modes higher than the fundamental can also be easily computed and assessed.

On the Importance of Shear Deformation, Rotatory Inertia and Coriolis Forces in Turbine Blade Vibrations

1983 ◽  
Author(s):  
Khyruddin Akbar Ansari
Keyword(s):  
Shear Deformation ◽  
Turbine Blade ◽  
Normal Modes ◽  
Functional Method ◽  
Lumped Parameter Model ◽  
Rotatory Inertia ◽  
Blade Vibration ◽  
Coriolis Forces ◽  
Analysis Technique ◽  
Blade Vibrations

This paper is concerned with the significance of the effects of shear deformation, rotatory inertia and Coriolis forces in the analysis of turbine blade vibrations. Since these are quite pronounced at the high frequency ranges encountered in turbine blade vibration problems, they should not be overlooked although their inclusion paves the way for a complicated nonlinear analysis. An approximate analysis technique is presented which involves an application of the stationary functional method using the normal modes of a discretized model. Numerical results are obtained and discussed. It is noted that a definite advantage of applying this technique to a lumped parameter model is that nonlinear modes higher than the fundamental can also be easily generated.

Sparse Reconstruction Method of Non-Uniform Sampling and its Application in Blade Tip Timing System

2020 ◽  
Author(s):  
Jie Tian ◽  
Xiaopu Zhang ◽  
Yong Chen ◽  
Peter Russhard ◽  
Hua Ouyang
Keyword(s):  
Compressive Sensing ◽  
Sparse Reconstruction ◽  
Reconstruction Method ◽  
Blade Vibration ◽  
Uniform Sampling ◽  
Blade Vibrations ◽  
Timing Data ◽  
Blade Tip ◽  
Simultaneous Identification ◽  
Multi Mode

Abstract Based on the blade vibration theory of turbomachinery and the basic principle of blade timing systems, a sparse reconstruction model is derived for the tip timing signal under an arbitrary sensor circumferential placement distribution. The proposed approach uses the sparsity of the tip timing signal in the frequency domain. The application of compressive sensing in reconstructing the blade tip timing signal and monitoring multi-mode blade vibrations is explored. To improve the reconstruction effect, a number of numerical experiments are conducted to examine the effects of various factors on synchronous and non-synchronous signals. This enables the specific steps involved in the compressive sensing reconstruction of tip timing signals to be determined. The proposed method is then applied to the tip timing data of a 27-blade rotor. The results show that the method accurately identifies the multi-mode blade vibrations at different rotation speeds. The proposed method has the advantages of low dependence on prior information, insensitivity to environmental noise, and simultaneous identification of synchronous and non-synchronous signals. The experimental results validate the effectiveness of the proposed approach in engineering applications.

Interaction Between Coriolis Forces and Mistuning on a Cyclic Symmetric Structure With Geometrical Nonlinearity

2020 ◽  
Author(s):  
Anthony Tacher ◽  
Fabrice Thouverez ◽  
Jason Armand
Keyword(s):  
Standing Wave ◽  
Geometrical Nonlinearity ◽  
Numerical Approach ◽  
Travelling Wave ◽  
Lumped Parameter Model ◽  
Coriolis Forces ◽  
High Speeds ◽  
Symmetric Structure ◽  
Lumped Parameter ◽  
Cyclic Symmetric

Abstract An investigation of the interaction between Coriolis forces and mistuning on a cyclic symmetric structure is presented in this paper. The sensitivity of the eigenvalues and eigenvectors to mistuning is first studied with the perturbation method. A lumped parameter model is used to perform a modal analysis using a numerical approach after which geometrical nonlinearity is added to compare behavior with the linear case. Two different modes are thoroughly investigated for different rotational speeds, the first with an eigenvalue isolated from the others and the second presenting a frequency veering zone. The evolution from a standing wave domination at low speeds to a travelling wave domination at high speeds is observed for the isolated mode, whereas a standing wave domination remains around the veering zone for the second mode studied. It is also shown that the geometrical nonlinearity reinforces the mistuning effect versus the Coriolis forces.

scholarly journals Friction Damper Optimisation: Simulation of Rainbow Tests

1999 ◽  
Author(s):  
Kenan Y. Sanliturk ◽  
David J. Ewins ◽  
Robert Elliott ◽  
Jeff S. Green
Keyword(s):  
Harmonic Balance Method ◽  
Lumped Parameter Model ◽  
Friction Damper ◽  
Blade Vibration ◽  
Friction Dampers ◽  
Lumped Parameter ◽  
Engine Order ◽  
Resonance Response ◽  
Theoretical Predictions ◽  
Different Characteristics

Friction dampers have been used to reduce turbine blade vibration levels for a considerable period of time. However, optimal design of these dampers has been quite difficult due both to a lack of adequate theoretical predictions and to difficulties in conducting reliable experiments. One of the difficulties of damper weight optimisation via the experimental route has been the inevitable effects of mistuning. Also, conducting separate experiments for different damper weights involves excessive cost. Therefore, current practice in the turbomachinery industry has been to conduct so-called ‘rainbow tests’ where friction dampers with different weights are placed between blades with a predefined configuration. However, it has been observed that some rainbow test results have been difficult to interpret and have been inconclusive for determining the optimum damper weight for a given bladed-disc assembly. A new method of analysis — a combination of Harmonic Balance Method and structural modification approaches — is presented in this paper for the analysis of structures with friction interfaces and the method is applied to search for qualitative answers about the so-called ‘rainbow tests’ in turbomachinery applications. A simple lumped-parameter model of a bladed-disc model was used and different damper weights were modelled using friction elements with different characteristics. Resonance response levels were obtained for bladed discs with various numbers of blades under various engine-order excitations. It was found that rainbow tests, where friction dampers with different weights are used on the same bladed-disc assembly, can be used to find the optimum damper weight if the mode of vibration concerned has weak blade-to-blade coupling (the case where the disc is almost rigid and blades vibrate almost independently from each other). Otherwise, it is very difficult to draw any reliable conclusion from such expensive experiments.

Influence of Trailing-Edge Geometry on Hydraulic-Turbine-Blade Vibration Resulting From Vortex Excitation

1960 ◽  
Vol 82 (2) ◽  
pp. 103-109 ◽  
Author(s):  
Gunnar Heskestad ◽  
D. R. Olberts
Keyword(s):  
Boundary Layer ◽  
Turbine Blade ◽  
Vortex Shedding ◽  
Hydraulic Turbine ◽  
Trailing Edge ◽  
Blade Vibration ◽  
Edge Geometry ◽  
Blade Thickness ◽  
Vortex Induced Vibrations ◽  
Approach Velocity

A study was made to determine effects of trailing-edge geometry on the vortex-induced vibrations of a model blade designed to simulate the conditions at the trailing edge of a hydraulic-turbine blade. For the type of trailing-edge flow encountered, characterized by a thick boundary layer relative to the blade thickness, the vortex-shedding frequency could not be represented by any modification of the Strouhal formula. The amplitude of the induced vibrations increased with the strength of a vortex in the von Karman vortex street of the wake; one exception was provided by a grooved edge, which is discussed in some detail. For a particular approach velocity, the vortex strength is primarily a function of the ratio of distance between separation points to boundary-layer thickness, the degree of “shielding” between regions of vortex growth, and frequency of vortex shedding.

Acoustic Resonance in an Axial Multistage Compressor Leading to Non-Synchronous Blade Vibration

2020 ◽  
Author(s):  
Anne-Lise Fiquet ◽  
Agathe Vercoutter ◽  
Nicolas Buffaz ◽  
Stéphane Aubert ◽  
Christoph Brandstetter
Keyword(s):  
Acoustic Waves ◽  
High Speed ◽  
Numerical Study ◽  
Acoustic Resonance ◽  
Structural Vibration ◽  
Wave Number ◽  
Blade Vibration ◽  
Acoustic Modes ◽  
Blade Vibrations ◽  
Circumferential Wave

Abstract Significant non-synchronous blade vibrations (NSV) have been observed in an experimental three-stage high-speed compressor at part-speed conditions. High amplitude acoustic modes, propagating around the circumference and originating in the highly loaded Stage-3 have been observed in coherence with the structural vibration mode. In order to understand the occurring phenomena, a detailed numerical study has been carried out to reproduce the mechanism. Unsteady full annulus RANS simulations of the whole setup have been performed using the solver elsA. The results revealed the development of propagating acoustic modes which are partially trapped in the annulus and are in resonance with an aerodynamic disturbance in Rotor-3. The aerodynamic disturbance is identified as an unsteady separation of the blade boundary layer in Rotor-3. The results indicate that the frequency and phase of the separation adapt to match those of the acoustic wave, and are therefore governed by acoustic propagation conditions. Furthermore, the simulations clearly show the modulation of the propagating wave with the rotor blades, leading to a change of circumferential wave numbers while passing the blade row. To analyze if the effect is self-induced by the blade vibration, a noncoherent structural mode has been imposed in the simulations. Even at high vibration amplitude the formerly observed acoustic mode did not change its circumferential wave number. This phenomenon is highly relevant to modern compressor designs, since the appearance of the axially propagating acoustic waves can excite blade vibrations if they coincide with a structural eigenmode, as observed in the presented experiments.

Symmetric Flexural Vibrations of a Clamped Circular Disk

1956 ◽  
Vol 23 (2) ◽  
pp. 319
Author(s):  
H. Deresiewicz
Keyword(s):  
Shear Deformation ◽  
Frequency Spectrum ◽  
Transverse Shear ◽  
Circular Disk ◽  
Transverse Shear Deformation ◽  
Axially Symmetric ◽  
Rotatory Inertia ◽  
Flexural Vibrations ◽  
Clamped Edges

Abstract The frequency spectrum is computed for the case of free, axially symmetric vibrations of a circular disk with clamped edges, using a theory which includes the effects of rotatory inertia and transverse shear deformation.

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