Multiharmonic Analysis and Design of Shroud Friction Joints of Bladed Disks Subject to Microslip

2012 ◽  
Author(s):  
Malte Krack ◽  
Anna Herzog ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek ◽  
Christian Siewert ◽  
...  
Keyword(s):  
Contact Area ◽  
Turbine Blades ◽  
Synthesis Method ◽  
Forced Response ◽  
Internal Resonances ◽  
Bladed Disks ◽  
Normal Contact ◽  
Analysis And Design ◽  
Contact Points ◽  
Highly Nonlinear

Vibration reduction of turbine blades by means of friction damping in shroud joints is a well-established technology in the field of turbomachinery dynamics. Three-dimensional contact constraints in the shroud coupling can induce highly nonlinear dynamics in the bladed disk assembly. Moreover, large normal contact stresses, which are typical for this application, necessitate the consideration of microslip effects. This study focuses on the accurate prediction of the forced response of tuned bladed disks subject to friction joints. In order to account for extended friction interfaces, the contact area is discretized into several contact points. Microslip behavior is explicitly enforced by a non-uniform normal pressure distribution. Local elastic properties of the contact area are accurately captured in the reduced order model of the structure by employing a component mode synthesis method. The steady-state forced response is efficiently computed using a Multi-Harmonic Balance ansatz. Thus, it is possible to study and explain the occurrence of internal resonances. Planar Coulomb friction and unilateral normal contact conditions are considered in terms of the Dynamic Lagrangian formulation. The normal preload of the shroud interface is varied in order to study the effect on vibration amplitude and resonance frequency.

Effects of Contact Interface Parameters on Vibration of Turbine Bladed Disks With Underplatform Dampers

2011 ◽  
Author(s):  
C. W. Schwingshackl ◽  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Structural Integrity ◽  
Turbine Blades ◽  
Contact Interface ◽  
Bladed Disks ◽  
Normal Contact ◽  
Input Parameters ◽  
Software Codes ◽  
Model Setup ◽  
Interface Parameters ◽  
Underplatform Damper

The design of high cycle fatigue resistant bladed disks requires the ability to predict the expected damping of the structure in order to evaluate the dynamic behaviour and ensure structural integrity. Highly sophisticated software codes are available today for this nonlinear analysis but their correct use requires a good understanding of the correct model generation and the input parameters involved to ensure a reliable prediction of the blade behaviour. The aim of the work described in this paper is to determine the suitability of current modelling approaches and to enhance the quality of the nonlinear modelling of turbine blades with underplatform dampers. This includes an investigation of a choice of the required input parameters, an evaluation of their best use in nonlinear friction analysis, and an assessment of the sensitivity of the response to variations in these parameters. Part of the problem is that the input parameters come with varying degrees of uncertainty, since some are experimentally determined, others are derived from analysis and a final set are often based on estimates from previous experience. In this investigation the model of a commercial turbine bladed disc with an underplatform damper is studied and its first flap, first torsion and first edgewise modes are considered for 6EO and 36EO excitation. The influence of different contact interface meshes on the results is investigated, together with several distributions of the static normal contact loads to enhance the model setup and hence increase accuracy in the response predictions of the blade with an underplatform damper. A parametric analysis is carried out on the friction contact parameters and the correct setup of the nonlinear contact model to determine their influence on the dynamic response and to define the required accuracy of the input parameters.

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 Bladed Disks in Cyclic Symmetry With Underplatform Dampers

2006 ◽  
Author(s):  
Stefano Zucca ◽  
Juan Borrajo ◽  
Muzio M. Gola
Keyword(s):  
Contact Stiffness ◽  
Harmonic Balance Method ◽  
Rigid Bodies ◽  
Forced Response ◽  
Numerical Code ◽  
Algebraic Equations ◽  
Bladed Disks ◽  
Disk Model ◽  
Normal Contact ◽  
Linear Algebraic Equations

In this paper a methodology for forced response calculation of bladed disks with underplatform dampers is described. The FE disk model, supposed to be cyclically symmetric, is reduced by means of Component Mode Synthesis and then DOFs lying at interfaces are further reduced by means of interface modes. Underplatform dampers are modeled as rigid bodies translating both in the radial and in the tangential direction of the engine. Contacts between blade platforms and damper are simulated by means of contact elements characterized by both tangential and normal contact stiffness, allowing partial separation of contact surfaces. Differential equilibrium equations are turned in non-linear algebraic equations by means of the Harmonic Balance Method (HBM). The methodology is implemented in a numerical code for forced response calculation of frictionally damped bladed disks. Numerical calculations are performed to evaluate the effectiveness of both the reduced order model and the underplatform model in simulating the dynamic behavior of bladed disks in presence of underplatform dampers.

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.

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.

Effects of Contact Interface Parameters on Vibration of Turbine Bladed Disks With Underplatform Dampers

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
C. W. Schwingshackl ◽  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Structural Integrity ◽  
Nonlinear Modeling ◽  
Turbine Blades ◽  
Contact Interface ◽  
Bladed Disks ◽  
Normal Contact ◽  
Input Parameters ◽  
Software Codes ◽  
Interface Parameters ◽  
Underplatform Damper

The design of high cycle fatigue resistant bladed disks requires the ability to predict the expected damping of the structure in order to evaluate the dynamic behavior and ensure structural integrity. Highly sophisticated software codes are available today for this nonlinear analysis, but their correct use requires a good understanding of the correct model generation and the input parameters involved to ensure a reliable prediction of the blade behavior. The aim of the work described in this paper is to determine the suitability of current modeling approaches and to enhance the quality of the nonlinear modeling of turbine blades with underplatform dampers. This includes an investigation of a choice of the required input parameters, an evaluation of their best use in nonlinear friction analysis, and an assessment of the sensitivity of the response to variations in these parameters. Part of the problem is that the input parameters come with varying degrees of uncertainty because some are experimentally determined, others are derived from analysis, and a final set are often based on estimates from previous experience. In this investigation the model of a commercial turbine bladed disk with an underplatform damper is studied, and its first flap, first torsion, and first edgewise modes are considered for 6 EO and 36 EO excitation. The influence of different contact interface meshes on the results is investigated, together with several distributions of the static normal contact loads, to enhance the model setup and, hence, increase accuracy in the response predictions of the blade with an underplatform damper. A parametric analysis is carried out on the friction contact parameters and the correct setup of the nonlinear contact model to determine their influence on the dynamic response and to define the required accuracy of the input parameters.

The Calculation of the Forced Response of Shrouded Blades With Friction Contacts and its Experimental Verification

2000 ◽  
Author(s):  
Walter Sextro
Keyword(s):  
Dry Friction ◽  
Turbine Blades ◽  
Life Time ◽  
Normal Pressure ◽  
Tangential Direction ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Model ◽  
Spatial Motion ◽  
Normal Contact

Shrouds with a frictional interface are used to reduce the dynamic stresses in turbine blades. Due to dry friction energy is dissipated, which can be used to decrease vibration amplitudes and, hence, to increase the life time of turbine blades. The spatial motion of the blades results in a spatial motion of the contact planes. Due to the non-linearity of the problem, the contact planes are discretized. For each contact area, the developed contact model is used to calculate the corresponding tangential and normal contact forces. This contact model includes the roughness of the contact surfaces, the normal pressure distribution due to roughness, the stiffnesses in normal and tangential direction and dry friction. Due to the roughness of the contact planes the normal contact forces and the contact stiffnesses in normal and tangential direction are nonlinear dependent on the relative displacements in the normal direction. This effect is verified by experiments. An experiment with one shrouded blade and two non-Hertzian contacts is used to verify the developed contact model and the calculation method. The comparison between measured and calculated frequency response functions for bending and torsional vibrations of the blade show a very good agreement. A bladed disk assembly with shrouds is investigated and optimized with respect to the vibration amplitudes and alternating stresses. Varying the normal contact force best damping effects are obtained. Separation of the contacts leads to an increase of the alternating stresses and, thus, has to be avoided.

Regeneration-Induced Forced Response in Axial Turbines

2013 ◽  
Author(s):  
Jens Aschenbruck ◽  
Christopher E. Meinzer ◽  
Linus Pohle ◽  
Lars Panning-von Scheidt ◽  
Joerg R. Seume
Keyword(s):  
Turbine Blades ◽  
Forced Response ◽  
Response Analysis ◽  
Geometrical Parameters ◽  
Turbine Stage ◽  
Structural Dynamic ◽  
Air Turbine ◽  
Axial Turbines ◽  
Interaction Approach ◽  
Stagger Angle

The regeneration of highly loaded turbine blades causes small variations of their geometrical parameters. To determine the influence of such regeneration-induced variances of turbine blades on the nozzle excitation, an existing air turbine is extended by a newly designed stage. The aerodynamic and the structural dynamic behavior of the new turbine stage are analyzed. The calculated eigenfrequencies are verified by an experimental modal analysis and are found to be in good agreement. Typical geometric variances of overhauled turbine blades are then applied to stator vanes of the newly designed turbine stage. A forced response analysis of these vanes is conducted using a uni-directional fluid-structure interaction approach. The effects of geometric variances on the forced response of the rotor blade are evaluated. It is shown that the vibration amplitudes of the response are significantly higher for some modes due to the additional wake excitation that is introduced by the geometrical variances e.g. 56 times higher for typical MRO-induced variations in stagger-angle.

Piezoelectric Networks for Vibration Suppression of Mistuned Bladed Disks

2007 ◽  
Vol 129 (5) ◽  
pp. 559-566 ◽  
Author(s):  
Hongbiao Yu ◽  
K. W. Wang
Keyword(s):  
Vibration Suppression ◽  
Periodic Structures ◽  
Electric Circuit ◽  
Forced Response ◽  
Bladed Disks ◽  
Vibration Localization ◽  
Network Concept ◽  
Engine Order ◽  
The Individual ◽  
Local Circuits

Extensive investigations have been conducted to study the vibration localization phenomenon and the excessive forced response that can be caused by mistuning in bladed disks. Most previous researches have focused on analyzing∕predicting localization or attacking the mistuning issue via mechanical tailoring. Few have focused on developing effective vibration control methods for such systems. This study extends the piezoelectric network concept, which has been utilized for mode delocalization in periodic structures, to the control of mistuned bladed disks under engine order excitation. A piezoelectric network is synthesized and optimized to effectively suppress vibration in bladed disks. One of the merits of such an approach is that the optimum design is independent of the number of spatial harmonics, or engine orders. Local circuits are first formulated by connecting inductors and resistors with piezoelectric patches on the individual blades. Although these local circuits can function as conventional damped absorber when properly tuned, they do not perform well for bladed disks under all engine order excitations. To address this issue, capacitors are introduced to couple the individual local circuitries. Through such networking, an absorber system that is independent of the engine order can be achieved. Monte Carlo simulation is performed to investigate the effectiveness of the network for a bladed disk with a range of mistuning level of its mechanical properties. The robustness issue of the network in terms of detuning of the electric circuit parameters is also studied. Finally, negative capacitance is introduced and its effect on the performance and robustness of the network is investigated.

Aeroelastic Analysis of NREL Wind Turbine

2017 ◽  
Author(s):  
Yaozhi Lu ◽  
Fanzhou Zhao ◽  
Loic Salles ◽  
Mehdi Vahdati
Keyword(s):  
Numerical Model ◽  
Wind Turbine ◽  
Wind Turbines ◽  
Gas Turbines ◽  
High Cycle Fatigue ◽  
Turbine Blades ◽  
Measured Data ◽  
Forced Response ◽  
Cycle Fatigue ◽  
Aeroelastic Analysis

The current development of wind turbines is moving toward larger and more flexible units, which can make them prone to fatigue damage induced by aeroelastic vibrations. The estimation of the total life of the composite components in a wind turbine requires the knowledge of both low and high cycle fatigue (LCF and HCF) data. The first aim of this study is to produce a validated numerical model, which can be used for aeroelastic analysis of wind turbines and is capable of estimating the LCF and HCF loads on the blade. The second aim of this work is to use the validated numerical model to assess the effects of extreme environmental conditions (such as high wind speeds) and rotor over-speed on low and high cycle fatigue. Numerical modelling of this project is carried out using the Computational Fluid Dynamics (CFD) & aeroelasticity code AU3D, which is written at Imperial College and developed over many years with the support from Rolls-Royce. This code has been validated extensively for unsteady aerodynamic and aeroelastic analysis of high-speed flows in gas turbines, yet, has not been used for low-speed flows around wind turbine blades. Therefore, in the first place the capability of this code for predicting steady and unsteady flows over wind turbines is studied. The test case used for this purpose is the Phase VI wind turbine from the National Renewable Energy Laboratory (NREL), which has extensive steady, unsteady and mechanical measured data. From the aerodynamic viewpoint of this study, AU3D results correlated well with the measured data for both steady and unsteady flow variables, which indicated that the code is capable of calculating the correct flow at low speeds for wind turbines. The aeroelastic results showed that increase in crosswind and shaft speed would result in an increase of unsteady loading on the blade which could decrease the lifespan of a wind turbine due to HCF. Shaft overspeed leads to significant increase in steady loading which affects the LCF behaviour. Moreover, the introduction of crosswind could result in significant dynamic vibration due to forced response at resonance.

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