The Impact of Excitation and Mode Shape on Non-Linear Blade Vibrations

2020 ◽  
Author(s):  
Johannes Linhard ◽  
Andreas Hartung ◽  
Stefan Schwarz ◽  
Hans-Peter Hackenberg ◽  
Mateusz Sienko
Keyword(s):  
Mode Shape ◽  
Optical Measurement ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Vibration Measurement ◽  
Numerical Predictions ◽  
Non Linear ◽  
Strain Gauge Measurements ◽  
The Impact

Abstract Recently, reliable non-linear dynamic solvers for the analysis of frictionally coupled turbine blades have been developed which are based on either Higher Harmonic Balance Method or Non-linear Modal Analysis. One of these tools is OrAgL which was developed by Institute of Dynamics of Vibrations (Leibniz University of Hannover) and Institute of Aircraft Propulsion Systems (University of Stuttgart). In [1], the rig and engine validation results of with OrAgL performed forced response analyses have been published: The main aim of this paper was the comparison of non-linear numerical predictions (amplitude, frequencies) with the blade-to-blade averaged values of optical measurement results obtained using MTU’s non-contact vibration measurement system for shrouded turbine blades (BSSM-T). Detailed analyses and validations performed over the last two years showed several novel aspects of validation such as the comparison with strain gauge measurements. Moreover, a better understanding of the impact of excitation (magnitude and load distribution over the airfoil) as well as of the impact of the mode shape on the formation of saturation regimes is now possible. The results obtained from the analyses of real turbine blades are presented in this work.

Non-Linear Dynamics of Steam Turbine Blades With Shroud: Numerical Analysis and Experiments

2012 ◽  
Author(s):  
Stefano Zucca ◽  
Muzio M. Gola ◽  
Francesco Piraccini
Keyword(s):  
Frequency Domain ◽  
Steam Turbine ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Low Pressure ◽  
Forced Response ◽  
Numerical Code ◽  
Accurate Information ◽  
Normal Contact ◽  
Non Linear

The prediction of the aeromechanical behavior of low-pressure blades represents one of the main challenges in the Steam Turbine Industry. The evaluation of forced response and damping is critical for the reliability of new designs and usually requires expensive validation campaigns such as Wheel Box Tests (WBT). A WBT consists of one or more blade rows assembled on a rotor and spun at the desired rotating speed in a vacuum cell, with synchronous excitation provided by various sources. The WBT provides accurate information about the blade modes frequency, the alternating response level, and allows the evaluation of the mechanical damping. Given the large effort in terms of costs and time associated to the experimental activity, the possibility to rely on the output of a numerical code either during the first steps of a new design or to investigate the effect of minor changes to a current design would be extremely beneficial to the development of future products. In order to compute the non-linear forced response of shrouded blades of steam turbines, custom numerical solvers must be developed, since commercial finite element (FE) solvers do not perform this kind of analysis in the frequency domain. In this paper, the forced response of a blade with shrouds of a low pressure steam turbine is computed and numerical results are compared with the experimental Wheel Box Tests performed at GE Oil & Gas. The calculations require a three-step procedure: in the first step, a non-linear static analysis is performed in ANSYS® in order to compute the actual contact area on the shroud surface and the distribution of static normal loads, then a reduced order model of the blade is generated in ANSYS® taking into account the stiffening effect on the blade of the pre-stress due to the centrifugal force, finally the reduced model is imported in a numerical code and the non-linear forced response of the blade is computed. The numerical code solves the balance equations of the system in the frequency domain, by means of the Harmonic Balance Method, imposing cyclic symmetry boundary conditions of the system. An interpolation procedure is implemented in order to manage the non-perfectly matching meshes of the shroud contact surfaces, while the tangential and normal contact stiffness is computed with a numerical model based on the contact mechanics principles. The numerical and the experimental results around some of the critical resonances of the system are compared in order to assess the reliability and accuracy of the numerical tool for its future implementation in the mechanical design practice of the blades.

The Interaction Between Mistuning and Friction in the Forced Response of Bladed Disk Assemblies

1985 ◽  
Vol 107 (1) ◽  
pp. 205-211 ◽  
Author(s):  
J. H. Griffin ◽  
A. Sinha
Keyword(s):  
Gas Turbine ◽  
Turbine Blades ◽  
Forced Response ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Resonant Response ◽  
Friction Dampers ◽  
Bladed Disk ◽  
The Impact ◽  
Slip Force

This paper summarizes the results of an investigation to establish the impact of mistuning on the performance and design of blade-to-blade friction dampers of the type used to control the resonant response of turbine blades in gas turbine engines. In addition, it discusses the importance of friction slip force variations on the dynamic response of shrouded fan blades.

scholarly journals Modeling of Friction Contact and its Application to the Design of Shroud Contact

1996 ◽  
Author(s):  
Been-Der Yang ◽  
Chia-Hsiang Menq
Keyword(s):  
Friction Force ◽  
Normal Load ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Effective Stiffness ◽  
Force Model ◽  
Friction Forces ◽  
Friction Joint ◽  
Stiffness And Damping

Designers of aircraft engines frequently employ shrouds in turbine design. In this paper, a variable normal load friction force model is proposed to investigate the influence of shroud-like contact kinematics on the forced response of frictionally constrained turbine blades. Analytical criteria are formulated to predict the transitions between slick, slip, and separation of the interface so as to assess the induced friction forces. When considering cyclic loading, the induced friction forces are combined with the variable normal load so as to determine the effective stiffness and damping of the friction joint over a cycle of motion. The harmonic balance method is then used to impose the effective stiffness and damping of the friction joint on the linear structure. The solution procedure for the nonlinear response nf a two-degree-of-freedom oscillator is demonstrated. As an application, this procedure is used to study the coupling effect of two constrained forces, friction force and variable normal load, on the optimization of the shroud contact design.

A Contact Model for Nonlinear Forced Response Prediction of Turbine Blades: Calculation Techniques and Experimental Comparison

2008 ◽  
Author(s):  
Christian M. Firrone ◽  
Marco Allara ◽  
Muzio M. Gola
Keyword(s):  
Normal Load ◽  
Contact Stiffness ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Model ◽  
Experimental Comparison ◽  
Normal Contact ◽  
Contact Models

Dry friction damping produced by sliding surfaces is commonly used to reduce vibration amplitude of blade arrays in turbo-machinery. The dynamic behavior of turbine components is significantly affected by the forces acting at their contact interfaces. In order to perform accurate dynamic analysis of these components, contact models must be included in the numerical solvers. This paper presents a novel approach to compute the contact stiffness of cylindrical contacts, analytical and based on the continuous contact mechanics. This is done in order to overcome the known difficulties in simultaneously adjusting the values of both tangential and normal contact stiffness experimentally. Monotonic loading curves and hysteresis cycles of contact forces vs. relative displacement are evaluated as a function of the main contact parameters (i.e. the contact geometry, the material properties and the contact normal load). The new contact model is compared with other contact models already presented in literature in order to show advantages and limitations. The contact model is integrated in a numerical solver, based on the Harmonic Balance Method (HBM), for the calculation of the forced response of turbine components with friction contacts, in particular underplatform dampers. Results from the nonlinear numerical simulations are compared with those from validation experiments.

Forced Response of Interlocked Vane Segments: Numerical Predictions and Experimental Results

2006 ◽  
Author(s):  
Stefano Zucca ◽  
Sergio Filippi ◽  
Fabio Droetti ◽  
Muzio M. Gola
Keyword(s):  
Tangential Force ◽  
Harmonic Balance Method ◽  
Outer Radius ◽  
Forced Response ◽  
Experimental Results ◽  
Numerical Code ◽  
Friction Forces ◽  
Normal Contact ◽  
Numerical Predictions ◽  
Local Compliance

Resonant vibrations affect fatigue life of vane segments. Friction damping is employed to reduce vibration amplitude. When vane segments are assembled, they are twisted so that lower platforms are in contact. The sum of displacements of the two ends of the lower platform after twisting is defined ‘interlocking’. Different ‘interlocking’ values correspond to different values of normal contact force. When interlocked vanes vibrate under external force excitation, energy is dissipated by friction forces at lower platform contacts providing damping to the system. The aim of this paper is the experimental validation of a numerical code for forced response calculation of interlocked vane segments. Since friction forces depend on relative displacements of bodies in contact, the system is nonlinear. System force response is computed by means of Harmonic Balance Method (HBM). Contact model implemented in the code is characterised by tangential and normal stiffness to take into account local compliance of the contact area. Gross slip occurs when the instantaneous ratio of tangential force to normal force is equal to the friction coefficient. Also effect of microslip is taken in account. The experimental set-up used to validate the code is made of a vane segment fixed at the outer radius to an aluminium frame and in contact with two supports at the inner radius. Comparison between the numerical predictions and experimental results is performed for different values of interlocking (i.e. force normal to the contact).

The Impact of Blade Loading and Unsteady Pressure Bifurcations on Low-Pressure Turbine Flutter Boundaries

2015 ◽  
Author(s):  
Joshua J. Waite ◽  
Robert E. Kielb
Keyword(s):  
Mode Shape ◽  
Pressure Ratio ◽  
Low Pressure ◽  
Forced Response ◽  
Blade Loading ◽  
Unsteady Pressure ◽  
Aerodynamic Damping ◽  
Low Pressure Turbine ◽  
Reduced Frequency ◽  
The Impact

The three major aeroelastic issues in the turbomachinery blades of jet engines and power turbines are forced response, non-synchronous vibrations, and flutter. Flutter primarily affects high-aspect ratio blades found in the fan, fore high-pressure compressor stages, and aft low-pressure turbine (LPT) stages as low natural frequencies and high axial velocities create smaller reduced frequencies. Often with LPT flutter analyses, physical insights are lost in the exhaustive quest for determining whether the aerodynamic damping is positive or negative. This paper underlines some well known causes of low-pressure turbine flutter in addition to one novel catalyst. In particular, an emphasis is placed on revealing how local aerodynamic damping contributions change as a function of unsteady (e.g. mode shape, reduced frequency) and steady (e.g. blade torque, pressure ratio) parameters. To this end, frequency domain RANS CFD analyses are used as computational wind tunnels to investigate how aerodynamic loading variations affect flutter boundaries. Preliminary results show clear trends between the aerodynamic work influence coefficients and variations in exit Mach number and back pressure, especially for torsional mode shapes affecting the passage throat. Additionally, visualizations of qualitative bifurcations in the unsteady pressure phases around the airfoil shed light on how local damping contributions evolve with steady loading. Final results indicate a sharp drop in aeroelastic stability near specific regions of the pressure ratio indicating a strong correlation between blade loading and flutter. Passage throat shock behavior is shown to be a controlling factor near the trailing edge, and like critical reduced frequency, this phenomenon is shown to be highly dependent on the vibratory mode shape.

Interaction of Concurrent Forced Response and Flutter Phenomena in a Compressor Stage

2017 ◽  
Author(s):  
Zhiping Mao ◽  
Robert E. Kielb
Keyword(s):  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Rotor Blades ◽  
Single Frequency ◽  
Response Frequency ◽  
Unsteady Pressure ◽  
Aerodynamic Damping ◽  
Frequency Domain Methods ◽  
The Impact

This paper studies a subsonic compressor case with concurrent forced response and flutter by using the Harmonic Balance method, and was inspired by historical experimental data. Forced response was observed when the rotating speed was approaching a crossing on the Campbell diagram, where flutter appeared to be suppressed. CFD simulations are conducted by using a quasi-3D configuration at the mid-span of one stage of a 3.5-stage compressor. Due to the constraint of frequency domain methods, the research is conducted in the vicinity of the 1T-44EO crossing with a small frequency shift between flutter frequency and external excitation frequency. The influence from flutter to forced response is observed: a one-way crosstalk at forced response frequency is observed, presented as the anomaly of unsteady velocity and unsteady pressure near the rear section of rotor blades and in the rotor wake region. The anomaly is speculated as the presence of increasing intensity of shedding vortices induced by the vibration of the blade. To further prove the impact of this viscous effect, a numerical experiment was performed with inviscid rotor blades. In contrast to the crosstalk at forced response frequency, no obvious influence on the unsteady behavior is detected at the flutter frequency, and this observation is confirmed at multiple vibration amplitudes. Considering the relationship between unsteady pressure at flutter frequency and aerodynamic damping, we conclude the influence of forced response on the aerodynamic damping is negligible. In addition, a linearity of unsteady pressure at the flutter frequency vs. vibration amplitude is uncovered. The discoveries provide a proof to linearity assumption and single-frequency simplification widely adopted by industry in flutter simulations.

The Effect of Manufacturing Variations on Unsteady Interaction in a Transonic Turbine

2017 ◽  
Author(s):  
John P. Clark ◽  
Joseph A. Beck ◽  
Alex A. Kaszynski ◽  
Angela Still ◽  
Ron-Ho Ni
Keyword(s):  
Fourier Transforms ◽  
Optical Measurement ◽  
Turbine Blades ◽  
Region Of Interest ◽  
Navier Stokes ◽  
Analysis Tool ◽  
Grid Data ◽  
Discrete Fourier Transforms ◽  
Numerical Predictions ◽  
Transonic Turbine

This effort focuses on the comparison of unsteadiness due to as-measured turbine blades in a transonic turbine to that obtained with blueprint geometries via computational fluid dynamics (CFD). A Reynolds-averaged Navier-Stokes flow solver with the two-equation Wilcox turbulence model is used as the numerical analysis tool for comparison between the blueprint geometries and as-manufactured geometries obtained from a structured light optical measurement system. The nominal turbine CFD grid data defined for analysis of the blueprint blade was geometrically modified to reflect as-manufactured turbine blades using an established mesh metamorphosis algorithm. The approach uses a modified neural network to iteratively update the source mesh to the target mesh. In this case the source is the interior CFD surface grid while the target is the surface blade geometry obtained from the optical scanner. Nodes interior to the CFD surface were updated using a modified iterative spring analogy to avoid grid corruption when matching as-manufactured part geometry. This approach avoids the tedious manual approach of regenerating the CFD grid and does not rely on geometry obtained from Coordinate Measurement Machine (CMM) sections, but rather a point cloud representing the entirety of the turbine blade. Surface pressure traces and the discrete Fourier transforms thereof from numerical predictions of as-measured geometries are then compared both to blueprint predictions and to experimental measurements. The importance of incorporating as-measured geometries in analyses to explain deviations between numerical predictions of blueprint geometries and experimental results is readily apparent. Further analysis of every casting produced in the creation of the test turbine yields variations that one can expect in both aero-performance and unsteady loading as a consequence of manufacturing tolerances. Finally, the use of measured airfoil geometries to reduce the unsteady load on a target blade in a region of interest is successfully demonstrated.

The Effect of Manufacturing Variations on Unsteady Interaction in a Transonic Turbine

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
John P. Clark ◽  
Joseph A. Beck ◽  
Alex A. Kaszynski ◽  
Angela Still ◽  
Ron-Ho Ni
Keyword(s):  
Fourier Transforms ◽  
Optical Measurement ◽  
Turbine Blades ◽  
Region Of Interest ◽  
Navier Stokes ◽  
Analysis Tool ◽  
Grid Data ◽  
Discrete Fourier Transforms ◽  
Numerical Predictions ◽  
Transonic Turbine

This effort focuses on the comparison of unsteadiness due to as-measured turbine blades in a transonic turbine to that obtained with blueprint geometries via computational fluid dynamics (CFD). A Reynolds-averaged Navier–Stokes flow solver with the two-equation Wilcox turbulence model is used as the numerical analysis tool for comparison between the blueprint geometries and as-manufactured geometries obtained from a structured light optical measurement system. The nominal turbine CFD grid data defined for analysis of the blueprint blade were geometrically modified to reflect as-manufactured turbine blades using an established mesh metamorphosis algorithm. The approach uses a modified neural network to iteratively update the source mesh to the target mesh. In this case, the source is the interior CFD surface grid while the target is the surface blade geometry obtained from the optical scanner. Nodes interior to the CFD surface were updated using a modified iterative spring analogy to avoid grid corruption when matching as-manufactured part geometry. This approach avoids the tedious manual approach of regenerating the CFD grid and does not rely on geometry obtained from coordinate measurement machine (CMM) sections, but rather a point cloud representing the entirety of the turbine blade. Surface pressure traces and the discrete Fourier transforms (DFT) thereof from numerical predictions of as-measured geometries are then compared both to blueprint predictions and to experimental measurements. The importance of incorporating as-measured geometries in analyses to explain deviations between numerical predictions of blueprint geometries and experimental results is readily apparent. Further analysis of every casting produced in the creation of the test turbine yields variations that one can expect in both aero-performance and unsteady loading as a consequence of manufacturing tolerances. Finally, the use of measured airfoil geometries to reduce the unsteady load on a target blade in a region of interest is successfully demonstrated.

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