The Relevance of Damper Pre-Optimization and Its Effectiveness on the Forced Response of Blades

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Chiara Gastaldi ◽  
Teresa M. Berruti ◽  
Muzio M. Gola
Keyword(s):  
Turbine Blades ◽  
Time Integration ◽  
Optimization Procedure ◽  
Forced Response ◽  
Contact Forces ◽  
Test Case ◽  
Equilibrium Equations ◽  
Bending Modes ◽  
The One ◽  
High Level

The purpose of this paper is to propose an effective strategy for the design of turbine blades with underplatform dampers (UPDs). The strategy involves damper “pre-optimization,” already proposed by the authors, to exclude, before the blades-coupled nonlinear calculation, all those damper configurations leading to low damping performance. This paper continues this effort by applying pre-optimization to determine a damper configuration which will not jam, roll, or detach under any in-plane platform kinematics (i.e., blade bending modes). Once the candidate damper configuration has been found, the damper equilibrium equations are solved by using both the multiharmonic balance method (MHBM) and the direct-time integration (DTI) for the purpose of finding the correct number of Fourier terms to represent displacements and contact forces. It is shown that contrarily to non-preoptimized dampers, which may display an erratic behavior, one harmonic term together with the static term ensures accurate results. These findings are confirmed by a state-of-the-art code for the calculation of the nonlinear forced response of a damper coupled to two blades. Experimental forced response functions (FRF) of the test case with a nominal damper are available for comparison. The comparison of different damper configurations offers a “high-level” validation of the pre-optimization procedure and highlights the strong influence of the blades mode of vibration on the damper effectiveness. It is shown that the pre-optimized damper is not only the most effective but also the one that leads to a faster and more flexible calculation.

The Relevance of Damper Pre-Optimization and its Effectiveness on the Forced Response of Blades

2017 ◽  
Author(s):  
Chiara Gastaldi ◽  
Teresa M. Berruti ◽  
Muzio M. Gola
Keyword(s):  
Turbine Blades ◽  
Time Integration ◽  
Optimization Procedure ◽  
Forced Response ◽  
Contact Forces ◽  
Design Stage ◽  
Geometrical Parameters ◽  
Test Case ◽  
Equilibrium Equations ◽  
Contact Points

The paper presents a calculation procedure for the design of turbine blades with underplatform dampers. The procedure involves damper “pre-optimization” before the coupled calculation with the blades. The pre-optimization procedure excludes, since the early design stage, all those damper configurations leading to low damping performance. Pre-optimization involves plotting a design “damper map” with forbidden areas, corresponding to poorly performing damper geometries and admissible design areas, where effective solutions for the damper shape can be explored. Once the candidate damper configurations have been selected, the damper equilibrium equations are solved by using both the multi-harmonic balance (MHB) method, and the direct time integration method (DTI). Direct time integration of the damper dynamic equations is implemented in order to compute the trend of the contact forces in time and the shape of the hysteresis cycles at the different contact points. Based on these trends, the correct number of Fourier terms to represent the contact forces on the damper is chosen. It is shown that one harmonic term together with the static term, are enough in the MHB calculation of a pre-optimized damper. The proposed method is applied to a test case of a damper coupled with two blades. Experimental forced response functions of the test case with a nominal damper are available for comparison. The purpose of this paper is to show the effectiveness of the “damper maps” in excluding all those damper configurations, leading to undesirable damper behavior and to highlight the strong influence of the blades mode of vibration on the damper effectiveness. From the comparison of dampers with different geometrical parameters, the pre-optimized damper proved to be not only the most effective, in terms of damping capability, but also the one that leads to a faster and more flexible calculation of the damper, coupled with the blades.

A Resonance Tracking Algorithm for the Prediction of Turbine Forced Response With Friction Dampers

2000 ◽  
Author(s):  
C. Bréard ◽  
J. S. Green ◽  
M. Vahdati ◽  
M. Imregun
Keyword(s):  
Rotor Blade ◽  
Turbine Blades ◽  
Turbine Rotor ◽  
Forced Response ◽  
Rotor Blades ◽  
Test Case ◽  
Friction Damper ◽  
Blade Vibration ◽  
Frequency Shifts ◽  
Friction Dampers

This paper presents an iterative method for determining the resonant speed shift when non-linear friction dampers are included in turbine blade roots. Such a need arises when conducting response calculations for turbine blades where the unsteady aerodynamic excitation must be computed at the exact resonant speed of interest. The inclusion of friction dampers is known to raise the resonant frequencies by up to 20% from the standard assembly frequencies. The iterative procedure uses a viscous, time-accurate flow representation for determining the aerodynamic forcing, a look-up table for evaluating the aerodynamic boundary conditions at any speed, and a time-domain friction damping module for resonance tracking. The methodology was applied to an HP turbine rotor test case where the resonances of interest were due to the 1T and 2F blade modes under 40 engine-order excitation. The forced response computations were conducted using a multi-stage approach in order to avoid errors associated with “linking” single stage computations since the spacing between the two bladerows was relatively small. Three friction damper elements were used for each rotor blade. To improve the computational efficiency, the number of rotor blades was decreased by 2 to 90 in order to obtain a stator/rotor blade ratio of 4/9. However, the blade geometry was skewed in order to match the capacity (mass flow rate) of the components and the condition being analysed. Frequency shifts of 3.2% and 20.0% were predicted for the 1T/40EO and 2F/40EO resonances in about 3 iterations. The predicted frequency shifts and the dynamic behaviour of the friction dampers were found to be within the expected range. Furthermore, the measured and predicted blade vibration amplitudes showed a good agreement, indicating that the methodology can be applied to industrial problems.

Range of Variability in the Dynamics of Semi-Cylindrical Friction Dampers for Turbine Blades

2008 ◽  
Author(s):  
Stefano Zucca ◽  
Daniele Botto ◽  
Muzio M. Gola
Keyword(s):  
Degrees Of Freedom ◽  
Turbine Blades ◽  
Numerical Test ◽  
Forced Response ◽  
Numerical Code ◽  
Test Case ◽  
Force Coefficient ◽  
System A ◽  
Flat Side ◽  
Fatigue Failures

Under-platform dampers are used to reduce resonant stresses in turbine blades to avoid high cycle fatigue failures. In this paper a model of semi-cylindrical under-platform damper (i.e. with one flat side and one curved side) for turbine blades is described. The damper kinematics is characterized by three degrees of freedom (DOFs): in-plane translations and rotation. Static normal loads acting on the damper sides are computed using the three static balance equations of the damper. Non-uniqueness of normal pre-loads acting on the damper sides is highlighted. Implementation of the model in a numerical code for the forced response calculation of turbine blades with under-platform dampers shows that non-uniqueness of normal pre-loads leads to non-uniqueness of the forced response of the system. A numerical test case is presented to show the capabilities of the model and to analyze the effect of the main system parameters (damper mass, excitation force, coefficient of friction and damper rotation) on the damper behavior and on the system dynamics.

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.

Assessment of a 3D Linear Euler Flutter Prediction Tool Using Sector Cascade Test Data

2005 ◽  
Author(s):  
Hans Ma˚rtensson ◽  
Damian M. Vogt ◽  
Torsten H. Fransson
Keyword(s):  
Turbine Blades ◽  
Tip Clearance ◽  
Mode Shapes ◽  
Test Case ◽  
Prediction Tool ◽  
Reduced Frequency ◽  
3D Geometry ◽  
Annular Sector ◽  
Lp Turbine ◽  
Bending Modes

An assessment and validation of a numerical prediction tool for flutter are made using new experimental data from experiments on turbine blades in a sector cascade. The 3D geometry is that of a low-pressure (LP) turbine blade with twist and a profile that changes along span in an annular sector cascade. The numerical model is a linear harmonic Euler equation solver. Rig results are obtained for the blade by oscillating 1 blade out of 7 in the annular sector cascade. The blade is oscillated in the rig using a mechanical type of actuator to control the mode. The mode shapes in the rig consist of torsion and bending modes around a pivot mechanism fixed inside the hub end wall. The frequencies obtained in the rig are in the range up to 219 Hz, or reduced frequency based on full chord k = 0.5, which covers the range of useful reduced frequencies typically found in turbine designs. Under reference running conditions the unsteady pressure responses are found qualitatively in line with the experiment. The test case is shown to be challenging to the numerical tool in terms of effects of tip clearance as well as off-design effects. In order to improve results tip clearance modeling and inclusion of viscous terms are identified as key factors.

An Optimum Aero-Design Process of Turbine Blades

2002 ◽  
Author(s):  
C. Xu ◽  
R. S. Amano
Keyword(s):  
Design Process ◽  
High Efficiency ◽  
Pressure Ratio ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Optimization Procedure ◽  
Compressor Blade ◽  
Advanced Technology ◽  
Test Case ◽  
Blade Design

With the development of the advanced technology, the combustion temperature is raised for increased efficiencies. At the same time, the turbine and compressor pressure ratio and the mass flow rate rise; thus causing turbine and compressor blades turning and blade lengths increase. Moreover, the high efficiency requirements had made the turbine and compressor blade design difficult. A turbine airfoil has been custom designed for many years, but an optimization for the section design in a three-dimensional consideration is still a challenge. For a compressor blade design, standard section cannot meet the modern compressor requirements. Modern compressor design has not only needs a custom designed section according to flow situation, but also needs three-dimensional optimizations. Therefore, a good blade design process is critical to the turbines and compressors. A blade design of the turbomachines is one of the important steps for a good turbomachine design. A blade design process not only directly influences the overall machine efficiency but also dramatically impact the design time and cost. In this study, a blade design and optimization procedure was proposed for both turbine and compressor blade design. A compressor blade design was used as a test case. It was shown that the current design process had more advantages than conventional design methodology.

scholarly journals Rub-Impact Dynamics of Shrouded Blades under Bending-Torsion Coupling Vibration

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1073
Author(s):  
Shangwen He ◽  
Kunli Si ◽  
Bingbing He ◽  
Zhaorui Yang ◽  
Ying Wang
Keyword(s):  
Turbine Blades ◽  
Vibration Reduction ◽  
Forced Response ◽  
Contact Forces ◽  
Coupling Vibration ◽  
Response Characteristics ◽  
Transition Mechanism ◽  
Blade System ◽  
Aero Engines ◽  
Set Up

Shroud devices which are typical cyclic symmetric structures are widely used to reduce the vibration of turbine blades in aero engines. Asymmetric rub-impact of adjacent shrouds or aerodynamic excitation forces can excite the bending-torsion coupling vibration of shrouded blades, which will lead to complex contact motions. The aim of this paper is to study the rub-impact dynamic characteristics of bending-torsion coupling vibration of shrouded blades using a numerical method. The contact-separation transition mechanism under complex motions is studied, the corresponding boundary conditions are set up, and the influence of moments of contact forces and aerodynamic excitation forces on the motion of the blade is considered. A three-degree-of-freedom mass-spring model including two mass blocks with the same size and shape is established to simulate the bending-torsion coupling vibration, and the dynamic equations of shrouded blades under different contact conditions are derived. An algorithm based on the fourth-order Runge–Kutta method is presented for simulations. Variation laws of the forced response characteristics of shrouded blades under different parameters are studied, on the basis of which the method to evaluate the vibration reduction characteristics of the shrouded blade system when the motion of the blade is chaotic is discussed. Then, the vibration reduction law of shrouded blades under bending-torsion coupling vibration is obtained.

scholarly journals Describing the German Research Infrastructure DCOLL Based on the Criteria Defined by the One World Collection Group - a test case

2019 ◽  
Vol 3 ◽  
Author(s):  
Frederik Berger
Keyword(s):  
Natural Science ◽  
Organizational Structures ◽  
Research Infrastructure ◽  
Test Case ◽  
Digital Collections ◽  
Institutional Level ◽  
Positive Side ◽  
World Collection ◽  
The One ◽  
High Level

The standardized description of collections is an important means for prioritizing collection digitization on a supra-institutional level. Different organizational and systematic structures prevent easy comparison of collections sizes and foci, in order to make informed decisions on setting priorities and efficiently distributing tasks. In autumn 2018, the consortium of German Natural Sciences Collections (DCOLL), consisting of seven natural history collections holding institutions integrated as a National Research Infrastructure*1 performed a top-level description of the consortium's collections based on a subset of the criteria defined by the One World Collection Working Group (OWC). OWC is based on an initiative of the directors of the world's largest Natural Science Collections and aims at making collections and ressource allocations comparable. Categories relating to the staff structure of institutions were omitted, as those were considered sensitive and of little use for the purpose. The survey focused on collection size and geographical distribution only. Since some partners already had previously assembled the necessary data and since the OWC criteria are based on a reasonably high level, allowing the integration of heterogenous collections, the OWC dashboard presented an opportunity to achieve quick standardized results. However, as one purpose of the survey was to support decisions on the consortium's digitization strategy, arguably not the objective of OWC, a field to describe the digitization rate had to be added. Another shortcoming of the OWC dashboard for this purpose was the difficulty in subsuming some important sub-collections into the given criteria, namely digital collections (like animal sound archives) and non-biological or non-geological collections (e.g. historical objects and archives). On the positive side, the survey proved to be very helpful to indicate the consortium's collection focus in comparison with other institutions on an international level. This can provide valuable information for establishing an integrated collection development and digitization strategy on a supra-institutional level. It can be shown for example that 41% of the objects with origin from Europe in Natural Science Collections are held by DCOLL. While it may be possible to derive meaningful strategic goals from this information, it is a big challenge to implement practical objectives based on the same criteria. From a bottom-up perspective the OWC dashboard aggregates data, which were collected in a non-standardized form within institutions across organizational structures. Increasing the granularity from this level will result in an unreasonable effort. This presentation discusses the process of collecting information based on the OWC criteria and will present the collection structure of DCOLL.

Multi-Objective Synthesis Optimization of Heat Exchanger Networks With Arbitrary Topology

2008 ◽  
Author(s):  
Andrea Toffolo
Keyword(s):  
Heat Exchanger ◽  
Internal Heat ◽  
Optimization Procedure ◽  
Primary Energy ◽  
Test Case ◽  
Graph Representations ◽  
Multi Objective ◽  
Heat Exchanger Networks ◽  
High Level ◽  
Internal Heat Transfer

The synthesis of heat exchanger networks (HENs) is one of the most studied problems in process synthesis, because a high level of integration of the internal heat transfer is necessary to reduce both primary energy consumption and total costs. This work develops a methodology for the multi-objective optimization of HEN synthesis. A two-level hybrid algorithm operating on a population of candidate HEN topologies is proposed to search for the best tradeoffs between the maximization of energy recovery and the minimization of total HEN costs. The advantages deriving from graph representations of a HEN are fully exploited in order to handle topologies with arbitrary complexity and to simplify the optimization procedure required to evaluate the objective functions for a given topology. The Aromatics Plant problem, a well-known test case in the literature about HEN synthesis, is used as a test case to show the potentialities of the proposed methodology.

Effects of Static Friction on the Forced Response of Frictionally Damped Turbine Blades

1984 ◽  
Vol 106 (1) ◽  
pp. 65-69 ◽  
Author(s):  
A. Sinha ◽  
J. H. Griffin
Keyword(s):  
Steady State ◽  
Turbine Blades ◽  
Time Integration ◽  
Ground Vibration ◽  
Static Friction ◽  
Steady State Solution ◽  
Forced Response ◽  
Steady State Response ◽  
Integration Algorithm ◽  
State Response

The effect of static friction on the design of flexible blade-to-ground vibration dampers used in gas turbine engines is investigated. It is found that for γ (ratio of dynamic and static friction coefficients) less than 1, the steady-state response is essentially harmonic when the damper slip load, S, is small. However, as S increases beyond a certain value, the steady-state response ceases to be simply harmonic and, while still periodic, is a more complex waveform. The transition slip load is found to be lower for smaller γ. The maximum possible reduction in vibratory stresses increases as γ decreases. These analytical results are compared with those from the conventional numerical time integration method. In addition, an efficient time integration algorithm is described which can be used to predict the peak displacements of the transition solution without tracing the whole waveform, a useful procedure when no harmonic steady-state solution exists. The conditions under which blade response can be adequately modeled by simulating only dynamic friction are established.

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