A Method for the Calculation of Friction Damping in Blade Root Joints

2010 ◽  
Author(s):  
Stefano Zucca ◽  
Christian M. Firrone ◽  
Muzio Gola
Keyword(s):  
Dynamic Balance ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Contact Model ◽  
Friction Damping ◽  
Friction Forces ◽  
Blade Root ◽  
Modal Density ◽  
Numerical Solver ◽  
High Modal Density

In turbomachinery, the complete detuning of turbine blades in order to avoid high cycle fatigue damage due to resonant vibration is often unfeasible due to the high modal density of bladed disks. To obtain reliable predictions of resonant stress levels of turbine blades, accurate modelling of friction damping is mandatory. One of the most common sources of friction damping in turbine blades is the blade root, where energy is dissipated by friction due to microslip between the blade and the disk contact surfaces held in contact by the centrifugal force acting on the blade. In this paper a method is presented to compute the friction forces occurring at blade root joints and to evaluate their effect on the blade dynamics. The method is based on an upgraded version of the state-of-the-art contact model, currently used for the non-linear dynamic analysis of turbine blades. The upgraded contact model is implemented in a numerical solver based on the harmonic balance method able to compute the steady-state dynamic response of turbine blades. The proposed method allows solving the static and the dynamic balance equations of the blade and of the disk, without any preliminary static analysis to compute the static loads acting at the contact interfaces.

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.

Friction Damping of Hollow Airfoils: Part II—Experimental Verification

1998 ◽  
Vol 120 (1) ◽  
pp. 126-130 ◽  
Author(s):  
Y. M. EL-Aini ◽  
B. K. Benedict ◽  
W.-T. Wu
Keyword(s):  
Essential Element ◽  
Forced Response ◽  
Friction Damping ◽  
Modal Density ◽  
Speed Range ◽  
Manufacturing Tolerances ◽  
Hollow Cavity ◽  
Microslip Friction ◽  
High Modal Density ◽  
Damping Model

The use of hollow airfoils in turbomachinery applications, in particular fans and turbines, is an essential element in reducing the overall engine weight. However, state-of-the-art airfoil geometries are of low aspect ratio and exhibit unique characteristics associated with plate like modes. These modes are characterized by a chordwise form of bending and high modal density within the engine operating speed range. These features combined with the mistuning effects resulting from manufacturing tolerances make accurate frequency and forced response predictions difficult and increase the potential for High Cycle Fatigue (HCF) durability problems. The present paper summarizes the results of an experimental test program on internal damping of hollow bladelike specimens. Friction damping is provided via sheet metal devices configured to fit within a hollow cavity with various levels of preload. The results of the investigation indicate that such devices can provide significant levels of damping, provided the damper location and preload is optimized for the modes of concern. The transition of this concept to actual engine hardware would require further optimization with regard to wear effects and loss of preload particularly in applications where the preload is independent of rotational speed. Excellent agreement was achieved between the experimental results and the analytical predictions using a microslip friction damping model.

The Vibration Characteristics of Steam Turbine Blades with New Friction Damping Structures

2013 ◽  
Vol 312 ◽  
pp. 268-272
Author(s):  
Jun Wu ◽  
Rui Shan Yuan ◽  
Peng Fei Zhao ◽  
Yong Hui Xie
Keyword(s):  
Finite Element ◽  
Steam Turbine ◽  
Contact Surface ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Equivalent Stiffness ◽  
Friction Damping ◽  
Element Analysis ◽  
Steam Turbine Blades ◽  
Stiffness And Damping

The hysteresis curves that show the relationship between the tangential friction force and relative displacement of the contact surface were measured. The equivalent stiffness and damping of the friction contact surface under different normal loads were computed by harmonic balance method (HBM). The finite element model of steam turbine blades with new friction damping structures was established. The effects of friction between the contact surfaces were considered by using spring damping elements to connect the friction damper and the blade. The equivalent stiffness and damping which were calculated by the experiment results were applied to the spring damping elements under different rotational speeds. Based on the natural frequencies which were computed by finite element analysis, the Campbell diagram of the whole blades was obtained. The results showed that there were no 3-coincide points in the working speed range.

Optimization of the Contact Geometry Between Turbine Blades and Underplatform Dampers With Respect to Friction Damping

2002 ◽  
Author(s):  
Lars Panning ◽  
Walter Sextro ◽  
Karl Popp
Keyword(s):  
Contact Area ◽  
Turbine Blades ◽  
Contact Geometry ◽  
Contact Forces ◽  
Real Contact Area ◽  
Friction Damping ◽  
Roughness Effects ◽  
Blade Vibration ◽  
Friction Forces ◽  
Damping Effect

The blades of rotating compressor or turbine disks are subjected to fluctuating fluid forces that cause blade vibrations. To avoid high resonance stresses, in many applications additional damping is introduced into the bladed disk assembly by means of friction damping devices such as underplatform dampers. These are mounted between adjacent turbine blades and pressed onto the platforms due to centrifugal forces to dissipate energy by the generated friction forces due to relative motions between the damper and the neighboring blades. In real turbomachinery applications, the rotating blades are subjected to spatial vibrations caused by a complex blade geometry and distributed excitation forces acting on the airfoil. Therefore, a spatial model is presented including an appropriate spatial contact model to predict the generalized contact forces acting between the damper and the blades accurately. Six degrees of freedom are considered for each contact between the damper and the respective neighboring blades. Roughness effects are considered that determine the real contact area with respect to the nominal contact area. Different spatial blade vibration modes are investigated with regard to the friction damping that is provided by the underplatform damper. To gain the maximum damping effect, the damper mass is optimized at different working conditions of the assembly like the excitation amplitudes and the engine order. Furthermore, the influence of the contact geometry upon the damping potential is investigated in detail including the damper as well as the blade platform geometry. In practice, different damper geometries are in operation. Studies will be presented that prove the capability of the developed model to compare the effectiveness of different damper and blade platform geometries. Asymmetric platform angles leading to different contact conditions at the left and right damper contact, respectively, are studied in detail to improve the damping effect.

3D Numerical Friction Contact Model and Its Application to Nonlinear Blade Damping

2010 ◽  
Author(s):  
Weiwei Gu ◽  
Zili Xu
Keyword(s):  
Friction Coefficient ◽  
Nonlinear Vibration ◽  
Fourier Transforms ◽  
Three Dimensional ◽  
Harmonic Balance Method ◽  
Static Friction ◽  
Contact Model ◽  
Friction Contact ◽  
Friction Forces ◽  
Discrete Fourier Transforms

A three dimensional numerical friction contact model is proposed to investigate the nonlinear vibration of damped blade. The model describes the discrete friction forces in the time domain. By using Discrete Fourier Transforms, the discrete friction forces can be transformed into a series of harmonic functions which are used to solve the nonlinear vibration of damped blade in the frequency domain. The difference between static friction coefficient and dynamic friction coefficient is considered in the model. To consider microslip effect, an array of spring-slider contact pairs (friction contact model) is distributed on the contact surfaces. Additionally, the effect of area of the contact surface on the vibration of damped blade can be studied by altering the number of the contact pairs. Finally, the nonlinear vibration of a real turbine blade with shrouded friction dampers is solved using the proposed friction contact model, Multi-Harmonic Balance Method and Receptance Method.

scholarly journals Friction Damping of Hollow Airfoils: Part II — Experimental Verification

1996 ◽  
Author(s):  
Yehia M. El-Aini ◽  
Barry K. Benedict ◽  
Wen-Te Wu
Keyword(s):  
Essential Element ◽  
Forced Response ◽  
Friction Damping ◽  
Modal Density ◽  
Hollow Blade ◽  
Speed Range ◽  
Manufacturing Tolerances ◽  
Hollow Cavity ◽  
High Modal Density ◽  
Damping Model

The use of hollow airfoils in turbomachinery applications, in particular fans and turbines, is an essential element in reducing the overall engine weight. However, state–of–the–art airfoil geometries are of low aspect ratio and exhibit unique characteristics associated with plate–like modes. These modes are characterized by a chordwise form of bending and high modal density within the engine operating speed range. These features combined with the mistuning effects resulting from manufacturing tolerances make accurate frequency and forced response predictions difficult and increase the potential for High Cycle Fatigue (HCF) durability problems. The present paper summarizes the results of an experimental test program on internal damping of hollow blade–like specimens. Friction damping is provided via sheet metal devices configured to fit within a hollow cavity with various levels of preload. The results of the investigation indicate that such devices can provide significant levels of damping provided the damper location and preload is optimized for the modes of concern. The transition of this concept to actual engine hardware would require further optimization with regard to wear effects and loss of preload particularly in applications where the preload is independent of rotational speed. Excellent agreement was achieved between the experimental results and the analytical predictions using a micro–slip friction damping model.

Power Flow and Energy Sharing between an Oscillator and a Continuous Receiver Structure

2011 ◽  
Vol 189-193 ◽  
pp. 1914-1917
Author(s):  
Lin Ji
Keyword(s):  
High Frequency ◽  
Power Flow ◽  
Energy Analysis ◽  
Statistical Energy Analysis ◽  
Coupled Subsystems ◽  
Modal Density ◽  
Vibration Problems ◽  
Energy Sharing ◽  
High Modal Density ◽  
Vibration Modeling

A key assumption of conventional Statistical Energy Analysis (SEA) theory is that, for two coupled subsystems, the transmitted power from one to another is proportional to the energy differences between the mode pairs of the two subsystems. Previous research has shown that such an assumption remains valid if each individual subsystem is of high modal density. This thus limits the successful applications of SEA theory mostly to the regime of high frequency vibration modeling. This paper argues that, under certain coupling conditions, conventional SEA can be extended to solve the mid-frequency vibration problems where systems may consist of both mode-dense and mode-spare subsystems, e.g. ribbed-plates.

Studies on Determination of Natural Frequencies of Industrial Turbine Blades

1995 ◽  
Author(s):  
Mahesh M. Bhat ◽  
V. Ramamurti ◽  
C. Sujatha
Keyword(s):  
Steam Turbine ◽  
Dynamic Behavior ◽  
Turbine Blade ◽  
Natural Frequencies ◽  
Complex Structure ◽  
Turbine Blades ◽  
Blade Root ◽  
Steam Turbine Blade ◽  
Manufacturing Tolerances

Abstract Steam turbine blade is a very complex structure. It has geometric complexities like variation of twist, taper, width and thickness along its length. Most of the time these variations are not uniform. Apart from these geometric complexities, the blades are coupled by means of lacing wire, lacing rod or shroud. Blades are attached to a flexible disc which contributes to the dynamic behavior of the blade. Root fixity also plays an important role in this behavior. There is a considerable variation in the frequencies of blades of newly assembled turbine and frequencies after some hours of running. Again because of manufacturing tolerances there can be some variation in the blade to blade frequencies. Determination of natural frequencies of the blade is therefore a very critical job. Problems associated with typical industrial turbine bladed discs of a 235 MW steam turbine are highlighted in this paper.

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.

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