Linkoping Studies in Science and Technology Thesis No. 872
The Use of Platform Dampers to Reduce Turbine Blade Vibrations
Martin H. Jareland
INSTITUTE OF TECHNOLOGY LINKOPINOS UNIVERSITET
Division of Machine Design Department of Mechanical Engineering LinkopingUniversity, SE-581 83 Linkoping, Sweden
Linkoping2001 ISBN 91-7219-990-3 ISSN 0280-7971 LiU-TEK-LIC-2001:09 Printed in Sweden by UniTryck Linkoping, 2001 DISCLAIMER
Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. ABSTRACT
Friction damping is commonly used in jet engines to reduce the vibration level of the blades and thereby increase the reliability of the engine. This thesis deals with a specific type of friction damper denoted platform damper, which is frequently used in turbine stages. A platform damper is a piece of metal located in a cavity underneath two adjacent blade platforms. It is pressed against the platforms by centrifugal force and friction forces arise in the contacts when a relative motion between the platforms occurs. In this thesis, a number of phenomena regarding platform dampers are investigated and discussed. This is performed both experimentally and theoretically. In the simulations, friction interface models valid for both macroslip and microslip are used. Macroslip means that slipping occurs in the whole contact interface and microslip means that slipping occurs in only part of the interface. The latter is most likely in the contacts between the platform damper and the blade platforms due to the high normal force and the small motions. The first paper deals with mistuning of bladed disks due to variations in the properties of the platform dampers and the closely related topic wear of the dampers. This study indicates that damper mistuning can greatly affect the blade vibrations and that damper and blade mistuning constitutes a more severe case than blade mistuning alone. It is also found that wear of the contact areas can lead either to an increase or decrease in the resonance amplitude of the blades in the studied configuration. In the second paper, so-called cottage-roof dampers are studied. Cottage-roof dampers are a type of platform damper with inclined contact surfaces. The inclination leads to a varying normal load, which complicates the analysis. A model including this effect is presented and simulations are performed both in the time and frequency domain. A parametric study is performed with the aim of finding the optimal damper design with respect to damper mass, inclination of contact surfaces, damper body stiffness and coefficient of friction. It is found that an increase in the inclination and the coefficient of friction results in a lower optimal damper mass, which is beneficial. The third paper presents a series of experiments performed for tuning a simulation model for a platform damper with curved contact areas. The model is tuned by selecting a suitable coefficient of friction and tangential stiffness for the friction interface model. A number of other topics are also investigated, such as repeatability of an experiment, comparison of new and used platform dampers and the change in surface structure on the contact areas. The overall conclusion is that wear of the contact areas probably leads to a decrease in the coefficient of friction, which implies a change in damper performance.
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PREFACE 'd
This thesis is part of the research project “Friction damping of blade vibration. Part 2” carried out during the period January 1998 - December 2000 at the Division of Machine Design, Department of Mechanical Engineering, Linkoping University. The project was performed in co-operation with Volvo Aero Corporation, Trollhattan, and was financially supported by the National Aeronautical Research Program under grant NFFP-348. I am deeply grateful to my supervisor, Professor Karl-OIof Olsson, head of the Division of Machine Design for his encouragement and enthusiasm. I have appreciated all the interesting discussions we have had and the critical review of my work that he has performed. Dr Gabor Csaba, my project leader at Volvo Aero Corporation during 1998 1999, has supported and encouraged my work. I appreciate his great knowledge within the field of friction damping. Dr Gabor Csaba has also collaborated on Paper 1.1 would also like to thank Dr David Lindstrom, Volvo Aero Corporation, who has been my project leader during 2000. A great advantage in this research project has been access to experimental data A for validating the simulations. Mr Magnus Andersson and Mr Kent Holmedahl, Volvo Aero Corporation, have provided experimental data as well as many valuable answers to the questions that have arisen. I would also like to thank Mr Anthony Stanbridge, Imperial College, London, for his support and assistance during the experimental work presented in Paper HI. The reference group for my research project has provided a unique frame of i expertise and I wish to thank all the members of this group. I would like to thank all my colleagues at the Division of Machine Design for providing an inspiring and friendly environment. Dr Bjorn Larsson and Dr Hakan Wettergren have assisted in a large part of this work by acting as discussion \ partners and providing wide knowledge in the field of structural dynamics. I would also like to thank Dr Hakan Wettergren for his ability to see solutions to any kind of question. Finally, this thesis could not have been written without the support and encouragement given by my parents, my Ingela, my brother and my sister. I also like to thank all my friends for encouraging my research.
, i Martin Jareland /j. Linkoping University February 2001
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CONTENTS
Introduction 1 Jet engine 1 Blade design 2 Platform dampers 5 Modelling of friction interfaces 7 Simulation of bladed disk assemblies 11
Summary of Appended Papers 13 Paper I: Friction Damper Mistoning of a Bladed Disk and Optimization with Respect to Wear 13 Paper II: A Parametric Study of a Cottage-Roof Damper and Comparison with Experimental Results 13 Paper HI: Experimental Investigation of a Platform Damper with Curved Contact Areas 14
References 15
Appendix 17 Nomenclature 17
Paper I: 19 Friction Damper Mistiming of a Bladed Disk and Optimization with Respect to Wear
Paper II: 43 A Parametric Study of a Cottage-Roof Damper and Comparison with Experimental Results
Paper III: 67 Experimental Investigation of a Platform Damper with Curved Contact Areas
APPENDED PAPERS
Paper I: Jareland M. H., Csaba G., Friction Damper Mistiming of a Bladed Disk and Optimization with Respect to Wear, presented at ASME Turbo Expo ‘00, Munich, Germany, May 8-11 2000, paper 2000-GT-363
Paper II: Jareland M. H., A Parametric Study of a Cottage-Roof Damper and Comparison with Experimental Results, accepted for presentation at ASME Turbo Expo ‘01, New Orleans, Louisiana, USA, June 4-7 2001, paper 2001-GT-275
Paper III: Jareland M. H., Experimental Investigation of a Platform Damper with Curved Contact Areas, submitted to ASME 2001 Design Engineering Technical Conferences, Pittsburgh, Pennsylvania, USA, September 9-12 2001
Printing errors found in the original versions of the papers have been corrected and the layout of the text and figures has also been changed in some papers. 1
INTRODUCTION
This chapter provides a short introduction to the field of blade vibrations in jet engines and the use of friction damping to control vibration levels. The most common types of friction damping device are presented and the simulation models most frequently used are discussed.
JET ENGINE An example of a military jet engine is shown in Fig. 1. This engine, the RM12, is used in the Gripen fighter aircraft, manufactured by SAAB Aerospace, Linkoping, Sweden. It is based on the General Electric F404 and is further developed and manufactured by Volvo Aero Corporation, Trollhattan, Sweden.
High pressure Low pressure Afterburner turbine turbine
High pressure Exhaust ;1 Fan compressor Combustor nozzle Figure 1. The RM12 jet engine manufactured by Volvo Aero Corporationfor the Gripen fighteraircraft developed by SAAB Aerospace. The principle of a jet engine is that the inlet air is compressed by the fan and the high pressure compressor, see Fig. 1. Fuel is injected and the mix of air and fuel is •X burned in the combustor. The fan and compressor are driven by the turbines, which are powered by the exhaust from the combustor. The remaining exhaust passes out through the exhaust nozzle and generates the thrust that drives the aircraft forward. Some of the inlet air is only compressed in the fan and mixed with the exhaust after the turbines. The amount of air that is not active in the combustor is defined by the I 2 The Use of Platform Dampers to Reduce Turbine Blade Vibrations by-pass ratio. The military jet engine shown in Fig. 1 has a low by-pass ratio compared to commercial jet engines, which often have a high by-pass ratio. Military jet engines are commonly equipped with an afterburner, see Fig. 1. In this case, fuel is injected into the mix of exhaust and by-pass air, after the turbines. The mix is combusted in the afterburner, which leads to a significant increase in thrust and also fuel consumption. Guide vanes are located in front of each stage to control the flow. These may be fixed or variable. The guide vanes generate the main excitation mechanism of the blades, a periodic excitation force. This is also often referred as rotor/stator interaction. It is commonly assumed that the excitation force is monofrequent and that its angular velocity is a multiple of the angular velocity of the rotor. The number of excitation periods during one revolution of the bladed disk is denoted the engine order. The excitation force on an arbitrary blade, j, is given by the following expression
e/o = (i) where Qa is the excitation force amplitude, co is the excitation frequency and cp is the interblade phase angle. The excitation frequency is given as co = EOQ. (2) where the EO denotes the engine order and Q is the angular velocity of the rotor. The interblade phase angle is find as
BLADE DESIGN The blades in a jet engine have largely varying designs depending on weather they are used in the fan, compressor or turbine. Turbine blades must withstand significantly elevated temperatures and high gas loads, and are for example made as single crystalline components and air cooled in the RM12. Fan blades on the other hand, must withstand a high centrifugal load, which is often the most critical design criterion for this type of blade. The fan blades are large and have a slim design compared to the turbine blades. Often, they are also highly twisted. Due to their slim design, so-called part span shrouds are commonly used in fan stages. The first fan stage in the RM12 is designed with part span shrouds, see Fig. 2. A part span shroud is simply a protrusion on both sides of the blade airfoil and forms a discontinuous connection between adjacent blades. Introduction 3
The contact interface in a part span shroud generally has a plane shape and is loaded by the untwist of the blades due to centrifugal force when the jet engine is running. The effects of the part span shrouds on the blade dynamics are a significant increase in stiffness and also an increase in damping due to rubbing in the contacts.
Figure 2. The fan in the RM12 jet engine. 4 The Use of Platform Dampers to Reduce Turbine Blade Vibrations
An example of a turbine blade is shown in Fig. 3. It can be seen that the airfoil is not as twisted as in a fan blade. A fir tree attachment of the blade to the disk is used in this case. This increases the contact area between the blade and the disk, and is used when there is a risk of creep or if the centrifugal load on the attachment is high.
Figure 4 shows a turbine blade with an outer platform. This particular blade is used in a turbine powering a pump in a rocket engine. The outer platform prevents gas leakage and can also be used for controlling the vibration level of the blades. A good introduction to the field of blade dynamics in engines is provided by Srinivasan [1]. The textbook by Rao [2] includes detailed discussions of the characteristics of blade vibrations in turbomachinery. Introduction 5
Outer platform
Blade to disk Friction damper attachment cavity
Figure 4. Turbine blade with outer platform.
PLATFORM DAMPERS The vibration level of the blades at resonance is controlled by three main types of damping: aeroelastic, material and friction damping. The work presented in this thesis focuses on friction damping, which can be found at a number of locations in a bladed disk: • In the blade-to-disk attachment • At specific platform dampers • At part span shroud contacts • At the outer platforms of the blades The main type of friction damping studied in this thesis is that generated by a platform damper, which in principle is a piece of metal located in a cavity underneath the platforms of two adjacent blades. The platform damper is pressed against the platforms by the centrifugal force and friction forces arise when a relative motion between the platforms occurs. A review of friction damping in bladed disks is provided by Griffin [3]. This thesis is concerned only with so- called blade-to-blade platform dampers, which means that the damper is in contact with two adjacent blade platforms. Another group of platform dampers is the blade-to-ground dampers, where the damper is in contact with one blade platform and is connected to a rigid structure, e.g. the disk. 6 The Use of Platform Dampers to Reduce Turbine Blade Vibrations
An example of a platform damper is shown in Fig. 5. This damper is used in the first turbine stage of the RM8B jet engine manufactured by Volvo Aero Corporation. The contacts between the damper and the blades occurs through a number of line contacts. Some disadvantages of this damper design are the complex shape, tendency to perform a rolling motion and that the damper causes wear of the contact area on the platforms.
Figure 5. Platform damper for a turbine stage in a military jet engine. For the current case, a new damper was developed. Figure 6 shows a schematic view of the new damper. The overall shape of the new damper is much simpler than the older design, which makes it less expensive. The configuration with inclined contact surfaces on the platforms and the curved contact areas on the damper makes the damper self-centering when subjected to centrifugal force. Also a softer material is selected for the damper than for the blade. This leads to wear of the damper instead of the platforms, which is beneficial. The performance of both the old and new damper designs, discussed here, has been investigated by Csaba and Andersson [4].
Platform 1 Platform 2
Figure 6. Schematic view of platform damper with curved contact areas. A specific type of platform damper is the so-called cottage-roof damper, which often also is called wedge damper. Two examples of cottage-roof dampers are shown in Fig. 7. The characteristic feature of this type of damper is the inclined contact areas. This implies that the vibration motion of the blade is not parallel to the plane of the contact, which leads to a variation in the normal force on the contacts during a vibration cycle. The analysis of this damper type is complicated by this fact. The cottage-roof dampers shown in Fig. 7 are designed for the turbine stage, shown in Fig. 4. The main difference between the two dampers is the weight. Introduction 7
The lighter damper, shown to the right, is designed for experiments in a test rig with a limited excitation level.
Figure 7. Cottage-roof dampers.
MODELLING OF FRICTION INTERFACES The most commonly used model for friction contacts is the macroslip model, which implies that the contact is either stuck or fully slipping. This model has been used for simulation of platform dampers by Muszynska and Jones [5], Griffin [6] and Yang and Menq [7, 8]. A macroslip element consists of a friction contact in series with a spring, see Fig. 8. The friction contact is assumed to follow the Coulomb friction law, which implies that the interface is stuck until the force through the spring exceeds the limiting friction force. A limitation of the macroslip model is that no energy is dissipated for small motions in the contact, which implies a force lower than the limiting friction force. The main advantage is that the model is relatively straightforward.
F
Figure 8. Macroslip element and corresponding hysteresis loop. For a platform damper, the displacements are small and the normal force high. It is therefore most likely that partial slip will occur in the contact, which is denoted microslip. The hysteresis loop for a case including microslip is shown in Fig. 9. It should be noted that the microslip model should follow the Coulomb friction law when the limiting friction force is reached. Microslip has been included in dynamic analysis of turbine stages with platform dampers by authors such as Csaba [4, 9-11], Menq et al. [12,13] and Sanliturk et al. [14]. 8 The Use of Platform Dampers to Reduce Turbine Blade Vibrations
Figure 9. Microslip element and corresponding hysteresis loop. The microslip model used in paper I and II is the so-called Bar model presented by Csaba [9]. The foundation of this friction interface model can be found in a model presented by Menq et al. [12]. The basic idea in both Menq’s and Csaba ’s models is to include the elasticity of at least one of the components in contact and assume that the contact area has a rectangular shape. Csaba introduced a load intensity, q, described by a quadratic function
?(*) = go + g24~"-2~~ (4) where the load intensity coefficients q0 and q2 are defined in Fig. 10 and l is the total length of the bar. Figure 10 shows the case during an initial loading. When a force F is applied at the end of the bar, the bar is extended and a friction force will occur under the extended part, zone B in Fig. 10. By assuming linear elasticity for the bar and stating equilibrium for the forces acting on the bar, the equations for the displacement and the force at the end of the bar can be derived. The force and the displacement at the end of the bar during an initial loading are
F{A) = [LlA(q0 + qj2A - |a2J) (5)
x |—► u
Figure 10. The Bar model (top).The slip zone (B) and the stuck zone (A) during an initial loading (bottom). In the case where A = 0, the bar is at rest. When the force F is increased, the amount of slip increases and finally when A = 1, the entire contact interface is slipping and macroslip is present. In other words, a value of the amount of slip between 0 and 1 means that partial slip is present, which is named microslip. In a general case, when both microslip and macroslip are present, a further definition is needed. In the case of macroslip, the friction force can be found by setting the amount of slip equal to unity in Eq. (5). If the total vibration amplitude is denoted ua, the displacement in macroslip can be calculated as “rn = «<,-«(!) (8) For the case when both microslip and macroslip are present, the amount of slip is defined as
(9) «(1) With this minor extension, the Bar model is valid for both microslip and macroslip. This is important because both microslip and macroslip are normally present during one vibration cycle for a real platform damper. A limitation of the Bar model is that it is only valid for one dimensional relative motion over the contact. This is usually no problem in the simulation of platform dampers, due to the fact that the motion is generally in one direction. The main disadvantage of the Bar model might be to identify the geometric parameters, especially the cross-section area of the bar, for a real contact. Platform dampers have also been modelled with discrete friction interface models based on the Hertzian solution for the contact, see Csaba [15], Sextro et al. 10 The Use of Platform Dampers to Reduce Turbine Blade Vibrations
[16] and Panning et al. [17]. These models are more general than the Bar model discussed above, in the sense that they can simulate a general relative motion over the contact. In paper HI, a discrete friction interface model is used. This model is denoted the Brush model and has been developed by Csaba [15]. The basic idea in the Brush model is to divide the friction interface into a number of discrete contact points, or bristles, each with a stiffness in the normal and the tangential direction. This is shown on the left in Fig. 11, where each discrete contact is represented by a spring.
Figure 11. The Brush model in two dimensions (left) and damper model (right). The stiffnesses in the normal and the tangential directions for a bristle are given by the following expressions
(10)
k, = y tE*Ab /b (11) where E*, Ab and b are the combined modulus, bristle contact area and the shorter semi-axis for the Hertzian solution without friction. The quantities y„ and yt are non-dimensional stiffness coefficients. The coefficient yn can be set so that either the maximum pressure or the contact area corresponds to the Hertzian solution for the contact, see Csaba [15]. The coefficient yt is an uncertain parameter that normally has to be found by experiment due to the lack of theoretical models. The force in the tangential direction over bristle k is found as
k{(w(k, l)-v(&, 1)) if kf(w(k, 1) - v(fc, 1)) < P/nto (12 ) F/nW if kt{w(k, 1) - v(k, 1)) > \Lfn{k) where w and v are the coordinates for the contact point and the bristle attachment point, respectively. The normal force on bristle k is fn(k). The first case in Eq. (12) corresponds to a tangential force lower than the limiting friction force and the second case corresponds to a slipping bristle. The Brush model is capable of simulating a general motion over the contact and includes both microslip and macroslip. A limitation, with the model used in Paper HI, is that it is only valid for contacts with curved contact areas, due to the fact that the properties of the bristles are given by the Hertzian solution for the contact. Introduction 11
SIMULATION OF BLADED DISK ASSEMBLIES Turbine stages with platform dampers have been studied by a number of researchers. A commonly used method for modelling of turbine stages is to represent the turbine blades with abeam model, see Fig. 12. In this case, the blades are modelled with four elements. Beam element number 1 represents the blade neck and is connected to the disk through a torsional stiffness kdisk. The disk is assumed to be rigid. Element 2 represents the blade platform and elements 3 and 4 represent the airfoil of the blade. The platform dampers are modelled with two friction interfaces connected by a stiffness representing the elasticity of the platform damper body.
Blade j-1 Blade j Blade j+1
Damper j-1 Damper j Damper j+1
Figure 12. Beam model of a turbine stage with platform dampers. The equation of motion for the system shown in Fig. 12 is + [C]« + [*]{*} = {Q} + {P} (13) where [M], [C] and [K] are the mass, damping and stiffness matrices, respectively. The harmonic excitation force {Q} is applied at the node between element 3 and 4. The nonlinear force from the platform dampers on the blade platforms are included in the vector {P}. The equation of motion Eq. (13) is a nonlinear differential equation due to the nonlinear friction force in {P}. This equation can be solved either in the time domain by numerical integration or in the frequency domain by Fourier series expansion of the nonlinear force. The time domain solution gives a high accuracy in the result, but is time-consuming. It is therefore unsuitable for use in a parametric study, for example. The frequency domain solution normally agrees well with the time domain solution but is much faster, see for example Csaba [11] or Sanliturk et al. [18]. If the fundamental term alone is included in the series expansion, it is denoted the harmonic balance method, HBM, and if higher harmonics are also included, it is denoted the higher order harmonic balance 12 The Use of Platform Dampers to Reduce Turbine Blade Vibrations method, HHBM. A detailed description of HBM, HHBM and similar techniques is given by Ferreira [19]. A key issue in designing of a platform damper is selection of the mass. The optimal mass is the mass that minimises the resonance amplitude for the blade. In Fig. 13, the resonance amplitude for the blade tip is shown as a function of the centrifugal force for a typical case.
"5 0.8
a 0.6 ::
Centrifugal Force Figure 13. Optimal centrifugal force fora platform damper. It is clearly seen that an optimal damper mass exists and that the optimal platform damper significantly reduces the resonance amplitude compared to the case without platform damper. For a damper mass lower than optimal, macroslip dominates in the friction interfaces and the platform damper can only provide a small amount of stiffness and damping to the system. For a damper mass higher than optimal, microslip has a greater influence on the resonance amplitude. In these cases, the platform dampers provide a significant amount of stiffness to the system, but on the other hand a small amount of damping, due to the small amount of slip in the contacts. The optimal damper is the one that provides an optimal amount and combination of stiffness and damping to the system. 13
SUMMARY OF APPENDED PAPERS
PAPER I: FRICTION DAMPER MISTUNING OF A BLADED DISK AND OPTIMIZATION WITH RESPECT TO WEAR Friction damper mistiming is an area in which less research has been done compared to blade mistuning of bladed disks. Inspection of contact areas on used platform dampers indicates that their environment varies widely. This is mostly due to geometric imperfections of the damper and contact surfaces on the blades, as well as to variations in mechanical properties of the blades. In this paper, a parametric study is performed to investigate the effects of damper mistuning on blade vibrations. A friction interface model valid for both microslip and macroslip, the Bar model, is used to model the contacts between the blade platforms and the dampers. The result indicates that damper mistuning greatly affects the blade vibrations. It is also found that the optimal damper is the same for the tuned and the mistimed case. A comparison of blade and damper mistuning is also performed. Numerical data for the first turbine stage in the RM8B jet engine are used, together with data from engine-tests performed by Volvo Aero Corporation. The result indicates that blade and damper mistuning together constitutes a more severe case than blade or damper mistuning alone. A topic closely related to mistuning of bladed disks is wear of platform dampers, which is also studied in this paper. For a tuned bladed disk, the result demonstrates that the resonance amplitude may either increase or decrease, depending on the properties of the damper. The wear process is also investigated for an initially blade mistimed case, where the mistuning pattern for a real turbine stage is used. The simulation results are compared with engine-tests and similarities between the theoretical and experimental results are found. The final conclusion is that it is important to know how the damper will perform when it is in use and becomes worn.
PAPER II: A PARAMETRIC STUDY OF A COTTAGE-ROOF DAMPER AND COMPARISON WITH EXPERIMENTAL RESULTS Platform dampers with inclined contact surfaces are studied in this paper. This type of damper is often called cottage-roof damper or wedge damper. The inclination of the contact surfaces leads to variation in the normal load, which complicates the analysis of such dampers. In the damper model presented, the contacts are modelled with a friction interface model valid for both microslip and macroslip, the Bar model, and the 14 The Use of Platform Dampers to Reduce Turbine Blade Vibrations possibility of varying normal loads on them is included. An important parameter for the performance of the damper is the elasticity of the damper body, which is also included in the model. A comparison between solving the equation of motion in the frequency domain and in the time domain is performed. It is shown that the frequency domain solution with the fundamental frequency alone generally gives a result close to the time domain solution. The simulation model is compared with experimental data for the first stage in the Vulcain 2 LOX turbine, which is designed for powering the liquid oxygen pump in the Vulcain 2 engine for the Ariane 5 launcher. It is found that the reduction in the resonance amplitudes agrees well for the tested dampers. A parametric study is performed to find the optimal damper shape and mass. The studied parameters are inclination of the contact surfaces, coefficient of friction, damper mass and damper body stiffness. It is found that an increase in inclination of the contact surface and an increase in the coefficient of friction both lead to a reduction in the optimal damper mass. An increase in the damper body stiffness results in a decrease of the resonance amplitude of the blade tip, particularly for high damper masses. The result of the parametric study greatly improves the knowledge of how an optimal platform damper should be designed.
PAPER III: EXPERIMENTAL INVESTIGATION OF A PLATFORM DAMPER WITH CURVED CONTACT AREAS The main objectives of this study are to improve and verify the Brush model, which is a friction interface model for curved contacts. This is achieved mainly through a series of experiments performed at Imperial College, London, with the RM8B high pressure turbine platform damper. This resulted in a more precisely tuned simulation model for this damper. A number of other topics are also investigated, such as repeatability of an experiment, comparison of new and used dampers, and changes in the surface structure on the contact areas due to wear. A similar set of experiments has earlier been performed with the current damper. It was then found that the experiments and simulations did not agree as desired and therefore a new set of experiments and simulations was suggested. The new simulations, presented in this paper, agree well with the new experiments, in which the normal force was held constant and the excitation force was varied. If a new damper is compared with a damper that has been used in a series of experiments, it is found that the resonance shifts to a lower frequency and that the amplitude increases. This is probably caused by a decrease in the coefficient of friction due to wear of the contact surfaces. One of the main conclusions is that changes in the surface structure of the damper due to wear greatly influence the experimental results. Hence, it is difficult to tune the model, using the experimental results, in order to simulate damper performance under the conditions existing in the jet engine. 15
REFERENCES
[1] Srinivasan A. V., 1997, “Flutter and Resonant Vibration Characteristics of Engine Blades”, ASME Turbo Expo ‘97, Orlando, Florida, USA, June 2-5 1997, paper 97-GT-533 [2] Rao J. S., 1991, “Turbomachine Blade Vibration ”, John Wiley & Sons Limited, West Sussex, England, ISBN 0-470-21764-2 [3] Griffin J. H., 1990, “A Review of Friction Damping of Turbine Blade Vibration ”, International Journal of Turbo and Jet Engines, Vol. 7, pp. 297 307 [4] Csaba G., Andersson M., 1997, “Optimization of Friction Damper Weight, Simulation and Experiments”, ASME Turbo Expo ‘97, Orlando, Florida, USA, June 2-5 1997, paper 97-GT-115 [5] Muszynska A., Jones D. I. G., 1983, “On Tuned Bladed Disk Dynamics: Some Aspects of Friction Related Mistiming”, J. of Sound and Vibration, Vol. 86(1), pp. 107-128 [6] Griffin J. H., 1980, “Friction Damping of Resonant Stresses in Gas Turbine Engine Airfoils”, J. of Vibration and Acoustics”, Vol. 112(2), pp. 175-182 [7] Yang B. D., Menq C. H., 1997, “Characterization of Contact Kinematics and Application to the Wedge Dampers in Turbomachinery Blading, Part I: Stick- Slip Contact Kinematics”, ASME Turbo Expo ‘97, Orlando, Florida, USA, June 2-5 1997, paper 97-GT-19 [8] Yang B. D., Menq C. H., 1997, “Characterization of Contact Kinematics and Application to the Wedge Dampers in Turbomachinery Blading, Part II: Prediction of Forced Response and Experimental Verification”, ASME Turbo Expo ‘97, Orlando, Florida, USA, June 2-5 1997, paper 97-GT-20 [9] Csaba G., 1995, “Microslip Friction Damping with Special Reference to Turbine Blade Vibrations ”, LiU-Tek-Lic-1995:09, ISBN 91-7871-507-5, Linkoping University, Sweden [10] Csaba G., 1995, “Friction Damping of Turbine Blade Vibrations Using a Microslip Model”, J. of Machine Vibration, Vol. 4, pp. 2-7 [11] Csaba G., 1998, “Forced Response Analysis in Time and Frequency Domain of a Timed Bladed Disk with Friction Dampers”, J. of Sound and Vibration, Vol. 214(3), pp. 395-412 [12] Menq C.-H., Bielak J., Griffin J. H., 1986, “The Influence of Microslip on Vibratory Response, Part I: A New Microslip Model”, J. of Sound and Vibration, Vol. 107(2), pp. 279-293 [13] Menq C.-H., Bielak J., Griffin J. H., 1986, “The Influence of Microslip on Vibratory Response, Part II: A Comparison with Experimental Results”, J. of Sound and Vibration, Vol. 107(2), pp. 295-307 16 The Use of Platform Dampers to Reduce Turbine Blade Vibrations
[14] Sanliturk K. Y., Ewins D. J., Stanbridge A. B., 1999, “Underplatform Dampers for Turbine Blades: Theoretical Modelling, Analysis and Comparison with Experimental Data”, ASME Turbo Expo ‘99, Indianapolis, Indiana, USA, June 7-10 1999, paper 99-GT-335 [15] Csaba G., 1999, “Modelling of a Microslip Friction Damper Subjected to Translation and Rotation”, ASME Turbo Expo ‘99, Indianapolis, Indiana, USA, June 7-10 1999, paper 99-GT-149 [16] Sextro W., Popp K., Wolter L, 1997, “Improved Reliability of Bladed Disks due to Friction Dampers”, ASME Turbo Expo ‘97, Orlando, Florida, USA, June 2-5 1997, paper 97-GT-189 [17] Panning L., Sextro W., Popp K., 2000, “Optimization of Interblade Friction Damper Design”, ASME Turbo Expo ‘00, Munich, Germany, May 8-11 2000, paper 2000-GT-541 [18] Sanliturk K. Y., Imregun M., Ewins D. J., 1997, “Harmonic Balance Vibration Analysis of Turbine Blades with Friction Dampers”, Trans. ASME, J. of Vibration and Acoustics, Vol. 119, pp. 96-103 [19] Ferreira J. V., 1998, “Dynamic Response Analysis of Structures with Nonlinear Components”, Doctoral Thesis at the Dept, of Mechanical Engineering, Imperial College of Science, Technology and Medicine, London, UK, pp. 30-66 17
APPENDIX
NOMENCLATURE Locally used notations are defined where they are used.
Mathematical Symbols [] Matrix {} Column vector d/dt " d2/dt2 i
Latin Symbols A Cross-section area [C] Damping matrix Equivalent viscous damping coefficient Normalized equivalent viscous damping coefficient E9 Modulus of elasticity for the damper [Ei Dynamic stiffness matrix EO Engine order {Edatjip} Friction damper force vector F Force at end of the bar Fc Centrifugal force % Friction force Normal force H Surface hardness j Blade index IK] Stiffness matrix k Coefficient of wear ^damp Damper body stiffness kdisk Torsional stiffness in blade attachment keq Equivalent stiffness coefficient keq Normalized equivalent stiffness coefficient l Stiffness in macroslip element Bristle stiffness in normal direction kt Bristle stiffness in tangential direction l Length of bar m Number of macroslip elements [M] Mass matrix 18 The Use of Platform Dampers toReduce Turbine Blade Vibrations
N Normal force on bar Hb Number of blades {P} Platform force vector {Qi Excitation force vector a Load intensity #2 Load intensity coefficients Rj Limiting friction force in macroslip element S State variable t Time T Period u Displacement at end of the bar um Displacement in macroslip V Amount of removed material V Displacement over friction damper w Platform displacement W Dissipated energy X Displacement
Greek Symbols a Inclination of contact surface y„.Yt Non-dimensional stiffness coefficients 8 Length of slip zone A Amount of slip V- Coefficient of friction
Angular velocity of the rotor
Subscripts a Amplitude amp Amplitude d Force function is decreasing i Force function is increasing j Blade index m Macroslip n Fourier component