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.

Forced Vibration of Elastic Structures With Friction Contacts

1999 ◽  
Author(s):  
Walter Sextro
Keyword(s):  
Relative Motion ◽  
Dry Friction ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Point Contact ◽  
Normal Pressure ◽  
Tangential Direction ◽  
Contact Model ◽  
Elastic Structures ◽  
Normal Forces

Abstract In many technical contacts energy is dissipated because of dry friction and relative motion. This can be used to reduce the vibration amplitudes. For example, shrouds with friction interfaces are used to reduce the dynamic stresses in turbine blades. The three-dimensional motion of the blades results in a three-dimensional relative motion of the contact planes. The developed Point-Contact-Model is used to calculate the corresponding tangential and normal forces for each contact element. This Point-Contact-Model includes the roughness of the contact surfaces, the normal pressure distribution due to roughness, the stiffness in normal and tangential direction and dry friction. An experiment with two non-Hertzian contacts is used to verify the developed contact model. The comparison between measured and calculated frequency response functions for three-dimensional forced vibrations of the elastic structures shows a very good agreement.

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.

Development and Experimental Validation of a Point Contact Model for Dynamical Problems With Friction

2001 ◽  
Author(s):  
Walter Sextro
Keyword(s):  
Pressure Distribution ◽  
Relative Motion ◽  
Contact Area ◽  
Point Contact ◽  
Contact Problems ◽  
Normal Pressure ◽  
Tangential Direction ◽  
Contact Model ◽  
Impact Oscillator ◽  
Normal Contact

Abstract The contact forces are dependent on many parameters, such as contact stiffnesses, surface profiles, material parameters, temperature distribution, relative motion and normal pressure distribution. These parameters can change within the contact area and from here, it is impossible to derive a general force law. The only possibility to overcome this problem is to discretize the contact areas, since in general the relative motion and the contact parameters are not constantly distributed within the contact surface. This leads to a point contact model, which has to include all main physical effects as described above, which are important, when simulating dynamical contact problems with friction. The friction model includes the main parameters such as the roughness of the contact surfaces, the nonlinear friction law, the contact stiffnesses in normal and tangential direction. The decreasing characteristic of the friction coefficient with respect to the relative velocity has to be modeled in a sufficient way. With respect to the dissipation of energy, the hysteretic behavior is studied with respect to the normal and tangential direction. Separation of the contact is included. This point contact model is be applied to real dynamical contact problems. In the first example, a simple impact oscillator with an elastic contact is used to check the overall modeling with respect to the elastic normal contact. Then, a self excited friction oscillator is investigated with respect to the tangential contact. Here, the modeling of surface waviness leads to high periodic solutions, which is also observed within the experiments. In both examples, the comparison of measurements and calculated phase plots is good. Furthermore, the influence of wear on to the surface profile, contact area and normal pressure distribution is investigated. From here, it follows, that friction leads to time dependent systems.

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.

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.

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.

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.

Experimental Friction Damping Characteristic of a Steam Turbine Blade Coupled by Shroud and Snubber at Standstill Set-Up

2012 ◽  
Author(s):  
Jun Wu ◽  
Yonghui Xie ◽  
Di Zhang ◽  
Minghui Zhang
Keyword(s):  
Steam Turbine ◽  
Turbine Blade ◽  
Rotational Speed ◽  
Damping Ratio ◽  
Turbine Blades ◽  
Contact Forces ◽  
Normal Contact ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Steam Turbine Blade

In order to avoid the high cycle fatigue which leads to the failure of turbine blades, friction structural damping has been widely used in turbine blade designs to reduce vibratory stresses by energy dissipation. A method is developed here to analyze the influence of friction structural damping on the vibration characteristics of turbine blades. Vibratory responses of a long steam turbine blade with shroud and snubber are studied. Finite element contact analysis of the steam turbine blades which are modeled in 3-D solid elements is conducted to obtain the normal contact force on the shroud contact surface and snubber contact surface of adjacent blades under five different rotational speeds (2100rpm, 2200rpm, 2413rpm, 2600rpm and 3000rpm). A rig for the tests of non-rotating turbine blade with friction damping structure is built. The normal contact forces of the shroud and snubber are applied to the blade according to numerical results. The response curves and modal damping ratios of the blade under different normal contact forces, which each one is related to a different rotational speed, are obtained. The experimental results show that with increases in rotational speed, modal damping ratio of the blade experiences an increasing period followed by a decreasing period while the resonance amplitude decreases first and then increases when there is only shroud contact. The effects are similar when there are both shroud and snubber contact. The modal damping ratio of the blade is basically identical with that of the uncoupled blade for the rotational speed above 2600rpm. For this range of rotational speed, the resonance frequency increases with the increase of rotational speed, and the changes of the resonance frequency are very trivial.

Measurement of Tangential Contact Stiffness in Frictional Contacts: The Effect of Normal Pressure

2011 ◽  
Vol 70 ◽  
pp. 321-326 ◽  
Author(s):  
Mehmet E. Kartal ◽  
Daniel M. Mulvihill ◽  
David Nowell ◽  
Dawid A. Hills
Keyword(s):  
Structural Integrity ◽  
Contact Stiffness ◽  
Testing Machine ◽  
Normal Pressure ◽  
Tangential Direction ◽  
Image Correlation ◽  
Tensile Testing Machine ◽  
Normal Contact ◽  
Tangential Contact ◽  
Frictional Contacts

The tangential contact stiffness of frictional interfaces affects both the vibration response and structural integrity of structures comprising frictional joints. Vibration and structural response of monolithic structures can be predicted very accurately; however, when assemblies of components involve frictional interfaces, additional damping and compliance are present due to these interfaces. These features make it more challenging to predict the vibration characteristics of assemblies with the same degree of accuracy as can be achieved for single components. If these interface properties can be determined, it should then be possible to significantly enhance current models of the vibration of engineering assemblies. Measurements of both force and displacement in the tangential direction are obtained from a series of in-line fretting tests involving flat pads with rounded corners clamped against the flat surface of a specimen which is oscillated by a hydraulic tensile testing machine. In order to measure the local displacement field very close to the contact interface, the digital image correlation (DIC) method is employed. The effect of normal contact pressure on tangential contact stiffness is investigated. Multiple experiments with the same parameters show good repeatability given the number of variables involved.

Evaluation of Friction Damping in Dovetail Root Joints Based on Dissipation Energy on Contact Surfaces

2009 ◽  
Author(s):  
Kunio Asai ◽  
Shigeo Sakurai ◽  
Takeshi Kudo ◽  
Norihiko Ozawa ◽  
Taizo Ikeda
Keyword(s):  
Contact Force ◽  
Contact Stiffness ◽  
Relative Displacement ◽  
Contact Angles ◽  
Forced Response ◽  
Contact Forces ◽  
Friction Damping ◽  
Normal Contact ◽  
Tangential Contact ◽  
Contact Surfaces

It is necessary to increase and estimate friction damping at contact interfaces to reduce vibratory stresses in turbines. The hysteresis behavior between tangential contact force and relative displacement should be precisely estimated to improve the accuracy of fiction-damping estimates. There is a difficulty in establishing a general model of hysteresis because tangential contact stiffness depends on many parameters, such as normal contact force, contact geometry, surface roughness, and wear status. We discuss a procedure to empirically calculate friction damping in dovetail root joints using the tangential contact stiffness estimated from measured natural frequencies and the micro-slip model whose coefficients were experimentally obtained from special fretting tests. Instead of the multi-harmonic balance methods, we calculated the friction damping on the basis of the energy dissipation at contact surfaces to discuss the effects of the tangential contact stiffness on several physical values, i.e., tangential and normal contact forces, natural frequency, and micro-slip. In our model, the linear forced response analysis was conducted by taking into consideration the non-linearity between the tangential contact force and the relative displacement by defining the actual and imaginary tangential contact stiffness. We confirmed that the numerically calculated damping ratios are quantitatively in very good agreement with the measured ones under different contact angles, input gravity levels, and contact forces. This indicates that if the tangential contact stiffness is accurately estimated, friction damping with our method can be precisely estimated under different test conditions. We also showed that the estimated tangential contact stiffness for dovetail root joints are smaller than those obtained by the fretting tests at high input gravity. This is probably because the contact interface partially separates during a cyclic loading in the former case; this results in the decrease of the contact area and contact stiffness.

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