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Structures and Dynamics

2010;():1-10. doi:10.1115/GT2010-22039.

A numerical model developed by Thorat & Childs [1] has indicated that the conventional frequency independent model for labyrinth seals is invalid for rotor surface velocities reaching a significant fraction of Mach 1. A theoretical one-control-volume (1CV) model based on a leakage equation that yields a reasonably good comparison with experimental results is considered in the present analysis. The numerical model yields frequency-dependent rotordynamic coefficients for the seal. Three real centrifugal compressors are analyzed to compare stability predictions with and without frequency-dependent labyrinth seal model. Three different compressor services are selected to have a comprehensive scenario in terms of pressure and molecular weight (MW). The molecular weight is very important for Mach number calculation and consequently for the frequency dependent nature of the coefficients. A hydrogen recycle application with MW around 8, a natural gas application with MW around 18, and finally a propane application with molecular weight around 44 are selected for this comparison. Useful indications on the applicability range of frequency dependent coefficients are given.

Commentary by Dr. Valentin Fuster
2010;():11-23. doi:10.1115/GT2010-22058.

This paper presents an analysis of the experimental and theoretical methods used to study rotordynamic characteristics of short staggered labyrinth gas seal. Two experimental identification procedures referred to as static and dynamic methods are presented. The static method allows determining direct and cross-coupled stiffness coefficients of the seal by integrating measured circumferential pressure distribution in cavities at various shaft eccentric positions. In the dynamic method, identification of stiffness and damping coefficients is based on the rotor excitation using a magnetic actuator and utilizes the effect of alternation of rotor vibrations due to aerodynamic forces acting in the seal. The experimental results obtained by the static and dynamic methods demonstrate an apparent discrepancy most of all in the direct stiffness coefficients. A CFD-based model of the seal is used to predict rotordynamic coefficients and to analyze the discrepancies between the static and dynamic measurements. The seal forces are calculated in two ways similar to the experimental procedures. The predictions are in good agreement with experimental results obtained by both measurement techniques. The effects of pressure differential, inlet swirl, shaft rotational speed, shaft eccentricity, and inflow cavity on seal stiffness and damping are presented. The discrepancies between different methods must be kept in mind while studying rotordynamic characteristics of seals.

Commentary by Dr. Valentin Fuster
2010;():25-32. doi:10.1115/GT2010-22072.

It has been previously proposed that a low-speed rotor balancing procedure can be suitable for supercritical shafting (GT2008-50077). That paper documented the necessity of taking into account nodal locations in the bending mode shapes of a supercritical rotor when designing an optimum balance process for such a rotor. This is due to the fact that balance correction forces (or for that matter, any forces) have the least impact when applied near the nodes of a particular mode. This result led to consideration that node location optimization could help with another issue, i.e. the excitation of backward excited whirl modes in a counter-rotating system. When designing a two rotor gas turbine, there are distinct advantages to having the two rotors turn in opposite directions. Among these are the ability to shorten and lighten the engine by reducing the length of the engine since a row of static turning vanes can be eliminated. The engine can be further lightened by inclusion of an inter-shaft bearing which eliminates static bearing support structure. Additional reduction in gyroscopic maneuver loads and deflections can also be achieved, thus resulting in multiple benefits to a counter-rotating system with an inter-shaft bearing. Unfortunately, the excitation of backward whirl modes of one rotor, which would normally not be a major concern in a co-rotating engine, can be a significant issue when excited in such a counter-rotating engine through the inter-shaft bearing, which serves as a conduit for forces from the other rotor. However, the logic of the earlier statement regarding the effectiveness of forces applied at, or near, a nodal point led to the hypothesis that optimizing the nodal locations relative to the interface points between the rotors could minimize the responsiveness of the system. This led to the hypothesis that by optimizing the node placement relative to the inter-shaft bearing, it should be possible to minimize the excitation of the backward modes. This paper examines that proposition and demonstrates that considering this aspect during the design of such an engine could lead to significant benefit in terms of minimized dynamic responses.

Commentary by Dr. Valentin Fuster
2010;():33-40. doi:10.1115/GT2010-22147.

The intent of this paper is to illustrate how rotor dynamics analysis can be an effective tool to improve rotor dynamic characteristics. Analytical methods, such as undamped critical speeds, unbalance response and stability (damped eigenvalues) analysis are used to evaluate the vibration characteristics of rotating machinery. Advanced rotor dynamics software is capable of generating and analyzing rotor models. By removing undesirable sources of instability and ensuring reliable separation margin, rotor-stability improvement is validated. This study presents an overhung rotor with a proven stable operating history; however, higher power requirements and changes in components resulted in a potential resonant condition of concern. Based on the rotor dynamics analysis outputs, design changes were implemented to ensure the rotor will meet API’s vibration acceptance limits. After evaluating different design alternatives using computer modeling, a change in the inboard bearing diameter proved to be the best solution for attaining smooth operation. Although this paper focuses mainly on the analysis performed on an overhung rotor, the methodology used can be applied to any rotating equipment. It is clear that rotor dynamics analysis is a powerful instrument for predicting operating behavior, thus allowing for necessary changes in analytical modeling and ensuring more stable machines.

Commentary by Dr. Valentin Fuster
2010;():41-47. doi:10.1115/GT2010-22185.

This paper focuses on the casing geometry of High Pressure Compressors. It is common practice to use damper seals, typically the hole pattern type, at the balance piston to ensure the stability of the compressor when compressing fluids with high density levels. Special attention must be paid to the clearance of the hole pattern seal which must be kept convergent at all operating conditions because a clearance divergence can lead to a rotor dynamic instability of the compressor. Furthermore, the clearance must be kept as low as possible to reduce the leakage losses through the balance piston. Therefore, extensive Fine Element Analyses are performed to determine the mechanical casing deflections in operation and hence, the correct clearance behaviour of such damper seals. This paper discusses the history of the casing design during the last ten years and compares the configurations with respect to the clearance distribution along the damper seal length. To validate the analytical predictions, leakage and stability measurements (using a magnetic shaker) are performed for these high pressure compressors during the full-load, full-pressure testing. This paper presents the stability measurements carried out on two compressors (390 bar and 655 bar discharge pressure) and compares the results.

Commentary by Dr. Valentin Fuster
2010;():49-60. doi:10.1115/GT2010-22199.

This study investigated the rigidity and contact state of joint structures that influenced the rotor dynamic characteristics and imbalance response, and the curve for variable structure parameters and the external load. The consideration of rotor joint structures dynamics design was also discussed. The finite-element models were established by using 3D solid elements and surface-to-surface nonlinear contact elements between the interfaces for numerical analysis. The rotor dynamic characteristics were affected by the rigidity of joint structures, and the rotor imbalance response was affected by the contact state of the interfaces. The experimentation for measuring the static rigidity and dynamic contact state of bolted joints with different experimental cycles were performed. Both numerical simulation and experimental results showed that: Firstly, the stiffness of joint structures was not constant. There was a critical load Fcr , when the external load was less than Fcr , the stiffness of joint structures was K1 ; when the external load was more than Fcr , the bend stiffness of joint structures would drop to K2 . The critical load Fcr was influenced by the length of interfaces and preload. Secondly, the contact state of joint structure interfaces varied after a long time of operating with alternating loads. The rotor imbalance was increased by fatigue damage accumulation and irreversible deformation. The study results show that the rigidity and contact state of joint structures vary with external loads and geometry structures, and would affect the rotor system operating. It is advisable to consider the influence of the position, structural parameter and external load of the rotor joint structures on aero-engine structure dynamics design.

Commentary by Dr. Valentin Fuster
2010;():61-67. doi:10.1115/GT2010-22223.

This paper discusses issues related with constructing a numerical model that will be used to predict the performance of a radial lip seal with surface texture on the shaft. 2-D Reynolds equation with JFO cavitation condition is solved to obtain the hydrodynamic fluid pressure of the lubricant. Finite element method is used to calculate the solid deformation. Different material properties like linear elasticity, hyperelasticity are suggested. The mutual influence between the fluid pressure and the solid deformation is also considered. Fluid pressure is relaxed due to the deformation of the lip seal. Different factors both in physics and numerical aspects that may influence the accuracy of the simulation are discussed. A simulation case is conducted and compared to previously published experiment results. Wear mechanisms and their influence on the simulation are briefly discussed.

Commentary by Dr. Valentin Fuster
2010;():69-79. doi:10.1115/GT2010-22227.

A flat-plate tester was used to measure the friction-factor behavior for a hole-pattern-roughened surface apposed to a smooth surface. The tests were executed to characterize the friction-factor behavior of annular seals that use a roughened-surface stator and a smooth rotor. Friction factors were obtained from measurements of the mass flow rate and static pressure measurements along the smooth and roughened surfaces. In addition, dynamic pressure measurements were made at four axial locations at the bottom of individual holes and at facing locations in the smooth plate. The test facility is described, and a procedure for determining the friction factor is reviewed. Three clearances were investigated: 0.635, 0.381, and 0.254 mm. Tests were conducted with air at three different inlet pressures (84, 70, and 55 bars), producing a Reynolds numbers range from 50,000 to 700,000. Three surface configurations were tested including smooth-on-smooth, smooth-on-hole, and hole-on-hole. The hole-pattern plates are identical with the exception of the hole depth. For the smooth-on-smooth and smooth-on-hole configurations, the friction factor remains largely constant or increases slightly with increasing Reynolds numbers. The friction factor increases as the clearance between the plates increases. The test program was initiated to investigate a “friction-factor jump” phenomenon cited by Ha et al. in 1992 in test results from a flat-plate tester where, at elevated values of Reynolds numbers, the friction-factor began to increase steadily with increasing Reynolds numbers. They tested apposed honeycomb surfaces. For the present tests, the phenomenon was also observed for tests of apposed roughened surfaces but was not observed for smooth-on-smooth or smooth-on-rough configurations. When the phenomenon was observed, dynamic pressure measurements showed a peak-pressure oscillation at the calculated Helmholtz frequency of the holes.

Topics: Friction , Flat plates
Commentary by Dr. Valentin Fuster
2010;():81-90. doi:10.1115/GT2010-22277.

Rotating machinery in transportation systems experiences intermittent excitation from road conditions. Internal combustion (IC) engines exert (multiple) periodic load excitations into passenger vehicle turbochargers, for example. Too large base motions can produce severe rotor-bearing system damage, even failure. The paper shows the reliability of a rotor-hybrid gas bearing system to withstand intermittent base foundation motions induced by a shaker. The test rig consists of a rigid rotor, 190mm in length, 0.825 kg in mass, and 28.6 mm in diameter, supported on two hybrid, flexure pivot tilting pad type, gas bearings. The whole system, weighing 48 kg, is supported on two soft coil springs and its lowest natural frequency is just ∼5 Hz. The rod connecting the shaker to the base plate is not affixed rigidly to the test rig base. The rod merely pushes on the base plate and hence the induced based motions are intermittent with multiple impacts and frequencies. The base induced motions are at a low main frequency (5–12 Hz) relative to the operating speed of the rotor-bearing system (max. 35 krpm). The recorded rotor responses, relative to the bearing housings, also contain the main excitation frequency and its super harmonics; and because of the intermittency of the base motions, it also excites the rotor-bearing system natural frequency, in particular when the gas bearings are supplied with a low feed pressure. Predicted rotor dynamic displacements induced by the base excitations show reasonable agreement with the test data.

Commentary by Dr. Valentin Fuster
2010;():91-100. doi:10.1115/GT2010-22315.

A nonlinear mathematical model for the rotordynamics of the rotor under the influence of the leakage air flow through a labyrinth seal was established in the present study. An interlocking seal was chosen for study. The rotor-bearing-seal system with four degrees of freedom was modeled as Jeffcot rotor subject to the aerodynamic force induced by the leakage flow through the interlocking seal and the oil-film force induced by the oil flow in the journal bearing. Particular attention was placed on the spatio-temporal variation of the aerodynamic force on the rotor surface in the coverage of the seal clearance and the cavity volume, which was specifically delineated by using Muzynska model and the perturbation analysis, respectively. The governing equation of the rotordynamics, into which the aerodynamic force integrated over all seal clearances and cavity volumes was incorporated together with the oil-film force, was solved by using the fourth-order Runge-Kutta method to obtain the orbit of the whirling rotor. Stability of the rotating rotor was inspected by using the orbital motions and the phase trajectories. The influence of the leakage air flow through the interlocking seal on the whirling rotor was described in terms of the rotating speed and the seal clearance. The results convincingly demonstrate that the destabilization of the rotor-bearing-seal system was reduced due to the aerodynamic force induced by the leakage air flow through the interlocking seal.

Topics: Bearings , Rotors , Leakage
Commentary by Dr. Valentin Fuster
2010;():101-111. doi:10.1115/GT2010-22393.

The accuracy of the dynamic analysis of rotor systems incorporating squeeze film damper (SFD) bearings is typically limited by a trade-off between the capabilities and the computational cost of the bearing model used. Simplified solutions to the Reynolds equation such as short and long bearing models, and their variants, while providing rapid solution, significantly restrict the general applicability of the solutions. Numerical solutions to the Reynolds equation allow its solution in full form, with a variety of boundary conditions. Solving the Reynolds equation numerically imposes a significant computational cost on the dynamical analysis, rendering it computationally prohibitive for industrial applications. To surmount this problem, the present paper develops the use of Chebyshev polynomial fits to mimic the hydrodynamic relationship obtained through the finite difference (FD) solution of the incompressible Reynolds equation. In order to overcome limitations of previous interpolation approaches, the proposed method has three features: (i) a reduced number of input variables with a clearly defined finite range; (ii) interpolation of the pressure rather than the bearing force; (iii) division of the pressure function into its static and dynamic parts. These manipulations allow for efficient and accurate identification in the presence of cavitation and the presence of the groove, feed-ports and end-plate seals. The ability of Chebyshev polynomials to rapidly reproduce results obtained using FD routines is demonstrated. The advanced bearing models developed are proven to give more accurate results than alternative analytical bearing models when compared to experimental results.

Commentary by Dr. Valentin Fuster
2010;():113-122. doi:10.1115/GT2010-22435.

A maneuver and acceleration analysis is a standard way to predict the structural displacements, clearance closures, and shaft and bearing loading due to aircraft turn rates and accelerations in airborne gas turbine engines. The industry standard practice is to perform these analyses assuming the acceleration and turn rates are steady-state. This gives rise to a static analysis in which the applied loads are a function of the aircraft turn rate, the aircraft translational accelerations, and the aircraft rotational accelerations. A method is presented for predicting static maneuver and acceleration lateral deflections and accompanying loads for airborne gas turbine engines with non-linear supports. The non-linear supports might include connections to ground and/or connections between various components of the rotor-structure system. These potential connections include squeeze-film-dampers (SFDs), clearance in rolling-element bearings, clearance stops in spring cages, rubs between rotors and shrouds, rubs between shafts, or supports modeled as non-linear (cubic) springs. The advantage of the method over traditional transient analysis is that the displaced shape (and accompanying shafting, bearing, and structure loads) can be found using an iterated static solution algorithm such that the transient solution is avoided. The algorithm allows for fast design trade studies when clearance closure and associated shafting/structure/bearing loads are part of the maneuver/acceleration analysis.

Topics: Gas turbines
Commentary by Dr. Valentin Fuster
2010;():123-133. doi:10.1115/GT2010-22440.

Metal mesh foil bearings (MMFB) are an inexpensive compliant gas bearing type that aims to enable high speed, high temperature operation of small turbomachinery. A MMFB with an inner diameter of 28.00 mm and length of 28.05 mm is constructed with low cost and common materials. The bearing incorporates a copper mesh ring, 20% in compactness and offering large material damping, beneath a 0.127mm thick preformed top foil. Prior experimentation (published papers) provide the bearing structure force coefficients and the break away torque for bearing lift off. Presently, the MMFB replaces a compressor in a small turbocharger driven test rig. Impact load tests aid to identify the direct and cross-coupled rotor dynamic force coefficients of the floating MMFB while operating at a speed of 50 krpm. Tests conducted with and without shaft rotation show the MMFB direct stiffness is less than its structural (static) stiffness, ∼25% lower at an excitation frequency of 200 Hz. The thin air film acting in series with the metal mesh support, and separating the rotating shaft and the bearing inner surface while airborne, reduces the bearing stiffness. The equivalent viscous damping is nearly identical with and without shaft rotation. The identified loss factor, best representing the hysteretic type damping from the metal mesh, is high at ∼0.50 in the frequency range 0–200 Hz. This magnitude reveals large mechanical energy dissipation ability from the MMFB. The measurements also show appreciable cross directional motions from the unidirectional impact loads, thus generating appreciable cross coupled force coefficients. Rotor speed coast down measurements reveal pronounced subsynchronous whirl motion amplitudes locked at distinct frequencies. The MMFB stiffness hardening nonlinearity produces the rich frequency forced response. The synchronous as well as subsynchronous motions peak while the shaft traverses its critical speeds. The measurements establish reliable operation of the test MMFB while airborne.

Topics: Force , Metals , Stress , Bearings
Commentary by Dr. Valentin Fuster
2010;():135-145. doi:10.1115/GT2010-22508.

Gas foil bearings offer several advantages over traditional bearing types that make them attractive for use in high-speed turbomachinery. They can operate at very high temperatures, require no lubrication supply (oil pumps, seals, etc), exhibit very long life with no maintenance, and once operating airborne, have very low power loss. The use of gas foil bearings in high-speed turbomachinery has been accelerating in recent years, although the pace has been slow. One of the contributing factors to the slow growth has been a lack of analysis tools, benchmarked to measurements, to predict gas foil bearing behavior in rotating machinery. To address this shortcoming, NASA Glenn Research Center (GRC) has supported the development of analytical tools to predict gas foil bearing performance. One of the codes has the capability to predict rotordynamic coefficients, power loss, film thickness, structural deformation, and more. The current paper presents an assessment of the predictive capability of the code, named XLGFBTH©. A test rig at GRC is used as a simulated case study to compare rotordynamic analysis using output from the code to actual rotor response as measured in the test rig. The test rig rotor is supported on two gas foil journal bearings manufactured at GRC, with all pertinent geometry disclosed. The resulting comparison shows that the rotordynamic coefficients calculated using XLGFBTH© represent the dynamics of the system reasonably well, especially as they pertain to predicting critical speeds.

Topics: Bearings , Modeling
Commentary by Dr. Valentin Fuster
2010;():147-155. doi:10.1115/GT2010-22522.

The simulation of internal airflow within turbine blade cooling channels can be useful in understanding the interactions between the operating temperatures, the coolant flow and its effectiveness, and the angular velocity of the blade. A rotating heat rig was designed as a meso-scale testing device to help understand these relationships within the confines of a lab. The first phase of the device was the use of a tubular shaft specimen which was mounted in series with the axis of rotation of the rig. The pipe was externally heated with the use of NiCr resistive wire to simulate the operating temperatures of a turbine blade. The heating element and the rotation of the sample were controlled digitally. Important design considerations were made such as accurate temperature control, modal changes as a function of varying temperature, and accurate bearing life estimates. As a part of carrying out this research, it was determined that none of the analytical models from literature were capable of predicting the critical speed of a shaft with non-uniform temperature distribution. Models based on Rayleigh’s method, Dunkerley’s method, and finite element analysis were created to estimate the critical speeds of the device. The analytical model that was developed makes up for the short comings of existing approaches.

Commentary by Dr. Valentin Fuster
2010;():157-166. doi:10.1115/GT2010-22561.

Squeeze Film Dampers (SFDs) are bearings that support large motion amplitudes when traversing rotor-bearing systems critical speeds. Actual practice demands bearings with operating conditions of low oil supply pressure and high frequency. In open-ended SFDs, large amplitudes of journal motion draw air into the film gap. The air ingested and entrapped results in a bubbly mixture that affects the dynamic performance and the overall damping capability of the SFDs. Diaz and San Andrés [11] developed a model to predict the amount of air ingested into SFDs with open-ends. They proposed an innovative non-dimensional number to estimate the amount of air entrapped in the film gap, but their analytical results are limited to short length bearings. Mendez et al. [13] extended the results of Diaz and San Andrés to finite length bearings, devising a Finite Volume Method (FVM) scheme. Even though their research presented new and significant results, they lack wider applicability that includes different geometries or boundary conditions. The present research proposes the solution of the Reynolds equation by the finite element method. Results computed by this formulation explore non-dimensional maps for determination of the amount of entrapped air. The results show that for fixed lubricant properties the amount of entrapped air depends exclusively on three dimensionless parameters: feed-squeeze flow number, length to diameter ratio, and dimensionless orbit radius.

Topics: Dampers
Commentary by Dr. Valentin Fuster
2010;():167-174. doi:10.1115/GT2010-22565.

Small size, light weight and high speed are remarkable characteristics of modern small aero-engines. The rotor components of engine are always series connected by spline joints or face tooth joints, so dynamic interaction of different rotor components have to be taken into account in aero-engine vibration analysis. Firstly, a modal analysis of the integral series connected rotor is performed as well as the analysis of each rotor components including fan rotor, compressor rotor and turbo rotor. The result captures the effects of the rotor components on the integral rotor, the modes of the integral rotor are composed of the modes of the rotor components and the coupled modes of them. Secondly, one special characteristic of this rotor is that No.3, 4, and 5 compressor disks and compressor shaft is interference connected initially. Based on calculation of connecting state, two models of the compressor rotor are presented, including a model with connecting state effects and a general model without connecting state effects, and a rotordynamic analysis is performed with the two models. The effect of the connecting state between shaft and disks of compressor rotor on rotordynamics is captured, as well as the true critical speeds and vibration modes. Thirdly, due to different assembly state and variable mechanical force, typical parameters which affect rotordynamics directly, such as rotor support stiffness and joints structure stiffness are not constant. A sensitivity analysis of critical speeds and vibration modes with respect to typical parameters (joints structure stiffness) is performed with finite difference method, two approaches are carried out, including relative sensitivity analysis and absolute sensitivity analysis. The effect of the parameters on rotordynamics is captured, as well as the variation range of critical speed. Finally, the analysis of test data validates the author’s method.

Commentary by Dr. Valentin Fuster
2010;():175-185. doi:10.1115/GT2010-22667.

This paper presents ongoing investigations on calculation and measurement of rotordynamic coefficients for brush-labyrinth gas seals. The seals are tested on static and dynamic test rigs to measure leakage, pressure distribution, and seal specific forces. To predict seal performance a full three-dimensional eccentric CFD model is considered. Rotordynamic coefficients are calculated using the whirling rotor method. The bristle pack of the brush seal is modeled using the porous medium approach. The prediction results show some deviations in absolute values of stiffness and damping coefficients in comparison with the experimental values, but the trends are similar. Comparing with a staggered labyrinth seal, the brush seal improves rotordynamic characteristics in most cases. Position of the brush seal in sealing configuration has a great influence on the stiffness and damping coefficients, while leakage performance remains relatively unaffected. The capability of the brush seal model based on the porous medium approach to predict rotordynamic coefficients is discussed.

Commentary by Dr. Valentin Fuster
2010;():187-194. doi:10.1115/GT2010-22763.

Development and field testing of a low cost expander/generator system that incorporates a high performance, high-speed permanent magnet generator and low loss magnetic bearings is described. The expander/generator is part of a waste heat recovery system based on the Organic Rankine Cycle. The waste heat system can recover energy from a wide variety of heat sources including: landfill gas, reciprocating engine exhaust, solar, geothermal, boilers, and other industrial processes. The varying frequency voltage supplied by the generator is connected to the grid using an active/active power electronics package that can deliver power at 400–480 VAC (50 or 60 Hz). Active magnetic bearings (AMB) were chosen for the application because they can operate directly in the working fluid, have low losses, and provide high reliability and remote monitoring capabilities. The expander operates between 20,000 and 26,500 rpm depending on the energy available from the heat source. The first field unit was installed in April, 2009 at a biogas site. The system design, test results, and magnetic bearing operating experience are discussed.

Commentary by Dr. Valentin Fuster
2010;():195-205. doi:10.1115/GT2010-22803.

Considered here is the effect of multistage coupling on the dynamics of a rotor consisting of eight bladed discs on a solid shaft. Each bladed disc had a different number of rotor blades. Free vibrations were examined using finite element representations of rotating single blades, bladed discs, and the entire rotor. In this study, the global rotating mode shapes of flexible tuned bladed discs-shaft assemblies were calculated, taking into account rotational effects, such as centrifugal stiffening. The thus obtained natural frequencies of the blade, the shaft, the bladed disc, and the entire shaft with discs were carefully examined to discover resonance conditions and coupling effects. This study found that the flexible modes of the tuned bladed discs affected by shaft motion were those with zero, one and two nodal diameters. In these modes shaft deflection was clearly visible. In forced vibration analysis a different EO excitation was applied for each stage. The importance of using models with different numbers of blades on each disc is apparent when compared with earlier results concerning discs with identical numbers of blades. Here the model of 8 discs with an equal number of blades on each disc is referred to as (Model 1), and the model of 8 discs with a different number of blades on each disc is referred to as (Model 2).

Topics: Disks
Commentary by Dr. Valentin Fuster
2010;():207-216. doi:10.1115/GT2010-22908.

Development of a novel train torsional vibration monitoring approach utilizing system modal analysis has been reported in this paper. Common use of high power electric helper machines especially in large turbocompressor strings together with LCI speed control system characteristics dramatically increase the risk of machinery torsional vibration problems. Contemporary, industry-wide accepted measurement technologies (strain gage with telemetry, optical probes, laser) fit well the test needs but their lack of ruggedness and durability as well as problematic installation impacting machine operation don’t allow to consider them for the long-term monitoring applications. The authors present a methodology which allows to evaluate alternating torque amplitudes in different string sections based on standard instrumentation installed on a train. The approach adopted in this paper relies heavily on modal representation of dynamic system, being analyzed. Described calculation method utilizes results of such analysis along with gas turbine speed pick-up signal spectrum. Robustness and accuracy of the proposed technique was benchmarked against test data coming from several LNG production train measurement campaigns, where the alternating torque was measured by means of standard measurement systems. Authors present the results of such verification together with prospective system applications.

Commentary by Dr. Valentin Fuster
2010;():217-226. doi:10.1115/GT2010-22941.

Rotating machines that include geared shaft-trains can be affected by a dynamic behaviour that is influenced by coupling effects between lateral and torsional vibrations. These latter vibrations are rarely measured by means of permanent probes in industrial machines; therefore these phenomena can be often pointed out only by detecting abnormal harmonic components in the frequency spectrum of the lateral vibrations measured during common monitoring activities. Then, the diagnosis of the occurrence of coupling effects between torsional and lateral vibrations can be supported by the results provided by model-based techniques. In this paper the results of the analysis of the dynamic behaviour of a small power unit that was affected by abnormal lateral vibrations caused by the excitation of torsional normal modes of the geared shaft-train are shown and discussed.

Commentary by Dr. Valentin Fuster
2010;():227-233. doi:10.1115/GT2010-22946.

This paper describes in detail the case history of a steam turbine affected by very high level of vibrations. Spectral analysis showed that the turbine shaft exhibited high sub-synchronous harmonic components. The analysis of the machine dynamic behavior, fully described here, allowed excluding some causes of instability like steam whirl or oil whirl/whip. The cause of the abnormal vibration level was ascribed to fluttering phenomena that affected some shoes of one of the “load on pad-type” four-pad tilting-pad journal bearings on which the rotor was supported. This abnormal behaviour was caused by the assembling error of the bottom shoe. Moreover, when approaching the operating speed, it was rather difficult to obtain a suitable convergent oil-film on the lateral pads. This reason, as well as the periodic changes of the journal position inside the bearing caused by the shaft synchronous vibrations due to the turbine residual imbalance, generated the excitation of sub-synchronous vibrations of both pads and shaft.

Commentary by Dr. Valentin Fuster
2010;():235-240. doi:10.1115/GT2010-22954.

The dynamics of a rotor supported in Gas Foil Bearings is strongly influenced by stiffness and damping properties of the bearings. In order to obtain the structural stiffness properties of Gas Foil Bearings, a coupled finite element method (FEM) is developed in this paper. The compressible gas lubricated Reynolds equation is transformed into a typical elliptic partial differential equation and solved by FEM. The elastic deformation equation and the contact boundary conditions between foils are solved by nonlinear contact finite method. A generalized numerical solving method for the elasto-aerodynamically coupled lubrication problem in the foil bearing is given with mesh mapping relationship between the two kind of finite element solving process above mentioned. The structural stiffness of the foil bearings with different parameters is estimated by using the numerical method. It is helpful to decide the structural parameters of the foil bearing.

Topics: Bearings , Stiffness
Commentary by Dr. Valentin Fuster
2010;():241-251. doi:10.1115/GT2010-22966.

The paper presents the results of the experimental analysis of static and dynamic characteristics of a generation 1 foil bearing of 38.1 mm diameter and L/D = 1. The test rig is of floating bearing type, the rigid shaft being mounted on ceramic ball bearings and driven up to 40 krpm. Two different casings are used for start-up and for measurement of dynamic coefficients. In its first configuration, the test rig is designed to measure the start-up torque. The foil bearing casing is made of two rings separated by a needle bearing for enabling an almost torque free rotation between the foil bearing and the static load. The basic results are the start up torque and the lift off speed. In its second configuration a different casing is used for measuring the impedances of the foil bearing. Misalignment is a problem that is minimized by using three flexible stingers connecting the foil bearing casing to the base plate of the test rig. The test rig enables the application of a static load and of the dynamic excitation on the journal bearing casing, and can measure displacements, forces and accelerations. Working conditions consisted of static loads comprised between 10 N and 50 N and rotation frequencies ranging from 260 Hz to 590 HZ. Excitation frequencies comprised between 100 Hz are 600 Hz are applied by two orthogonally mounted shakers for each working condition. Stiffness and damping coefficients are identified from the complex impedances and enable the calculation of natural frequencies. The experimental results show that the dynamic characteristics of the tested bearing have a weak dependence on the rotation speed but vary with the excitation frequency.

Commentary by Dr. Valentin Fuster
2010;():253-262. doi:10.1115/GT2010-22981.

Implementation of gas foil bearings (GFBs) into micro gas turbines requires careful thermal management with accurate measurements verifying model predictions. This two-part paper presents test data and analytical results for a test rotor and GFB system operating hot (157°C max. rotor OD temperature). Part 1 details the test rig and measurements of bearing temperatures and rotor dynamic motions obtained in a hollow rotor supported on a pair of 2nd generation GFBs, each consisting of a single top foil (38.14 mm ID) uncoated for high temperature operation, and five bump strip support layers. An electric cartridge (max. 360°C) loosely installed inside the rotor (1.065 kg, 38.07 mm OD, and 4.8 mm thick) is a heat source warming the rotor-bearing system. While coasting down from 30 krpm to rest, large elapsed times (50∼70 s) demonstrate rotor airborne operation, near friction free; and, while traversing the system critical speed at ∼13 krpm, the rotor peak motion amplitude decreases as the system temperature increases. In tests conducted at a fixed rotor speed of 30 krpm, while the shaft heats, a cooling gas stream of increasing strength is set to manage the temperatures in the bearings and rotor. The effect of the cooling flow, if turbulent in character, is most distinctive at the highest heater temperature. For operation at a lower heater temperature condition, however, the cooling flow stream demonstrates a very limited effectiveness. The measurements demonstrate the reliable performance of the rotor-GFB system when operating hot. The test results, along with full disclosure on the materials and geometry of the test bearings and rotor, serve to benchmark a predictive tool. A companion paper (Part 2) compares the measured bearing temperatures and the rotor response amplitudes to predictions.

Commentary by Dr. Valentin Fuster
2010;():263-271. doi:10.1115/GT2010-22983.

Implementation of gas foil bearings (GFB) in micro gas turbines relies on physics based computational models anchored to test data. This two-part paper presents test data and analytical results for a test rotor and GFB system operating hot. A companion paper (Part 1) describes a test rotor-GFB system operating hot to 157°C rotor OD temperature, presents measurements of rotor dynamic response and temperatures in the bearings and rotor, and including a cooling gas stream condition to manage the system temperatures. The second part briefs on a thermoelastohydrodynamic (TEHD) model for GFBs performance and presents predictions of the thermal energy transport and forced response, static and dynamic, in the tested gas foil bearing system. The model considers the heat flow from the rotor into the bearing cartridges and also the thermal expansion of the shaft and bearing cartridge and shaft centrifugal growth due to rotation. Predictions show that bearings’ ID temperatures increase linearly with rotor speed and shaft temperature. Large cooling flow rates, in excess of 100 L/min, reduce significantly the temperatures in the bearings and rotor. Predictions, agreeing well with recorded temperatures given in Part 1, also reproduce the radial gradient of temperature between the hot shaft and the bearings ID, largest (37°C/mm) for the strongest cooling stream (150 L/min). The shaft thermal growth, more significant as the temperature grows, reduces the bearings operating clearances and also the minimum film thickness, in particular at the highest rotor speed (30 krpm). A rotor finite element (FE) structural model and GFBs force coefficients from the TEHD model are used to predict the test system critical speeds and damping ratios for operation at increasing shaft temperatures. In general, predictions of the rotor imbalance show good agreement with shaft motion measurements acquired during rotor speed coastdown tests. As the shaft temperature increases, the rotor peak motion amplitudes decrease and the system rigid-mode critical speed increases. The computational tool, benchmarked by the measurements, furthers the application of GFBs in high temperature oil-free rotating machinery.

Commentary by Dr. Valentin Fuster
2010;():273-282. doi:10.1115/GT2010-23028.

During fault conditions, rotor displacements in magnetic bearing systems may potentially exceed safety/operating limits. Hence it is a common design feature to incorporate auxiliary bearings adjacent to the magnetic bearings for the prevention of rotor/stator contact. During fault conditions the rotor may come into contact with the auxiliary bearings, which may lead to continuous rub type orbit responses. In particular, forward rub responses may become persistent. This paper advances the methodology by considering an actively controlled auxiliary bearing system. An open-loop control strategy is adopted to provide auxiliary bearing displacements that destabilize established forward rub orbit responses. A theoretical approach is undertaken to identify auxiliary bearing motion limits at which forward rub responses become unstable. Experimental validation is then undertaken using a rotor/active magnetic bearing system with an actively controlled auxiliary bearing system under piezoelectric actuation. Two different operating speeds below the first bending mode of the rotor are considered and the applied harmonic displacements of the auxiliary bearing are shown to be effective in restoring contact free levitation.

Commentary by Dr. Valentin Fuster
2010;():283-292. doi:10.1115/GT2010-23035.

In this paper, a horizontal flexible rotor supported on two deep groove ball bearings is theoretically investigated for instability and chaos. The system is bi-periodically excited. The two sources of excitation are: rotating imbalance and self excitation due to varying compliance effect of ball bearing. A generalized Timoshenko beam FE formulation, which can be used for both flexible and rigid rotor systems with equal effectiveness, is developed. The novel scheme proposed in the literature to analyze quasi-periodic response is coupled with the existing non-autonomous shooting method and thus modified; shooting method is used to obtain steady state quasi-periodic solution. The eigenvalues of monodromy matrix provide information about stability and nature of bifurcation of quasi-periodic solution. The maximum value of Lyapunov exponent is used for quantitative measure of chaos in the dynamic response. The effect of three parameters, viz.: rotating unbalance, bearing clearance and rotor flexibility, on unstable and chaotic behaviour of horizontal flexible rotor is studied. Interactive effects between the three parameters are examined in detail in respect of rotor system instability and chaos, and finally the range of parameters is established for the same.

Commentary by Dr. Valentin Fuster
2010;():293-298. doi:10.1115/GT2010-23051.

This paper is to study how presence of cracks affects ground-based vibration response of a spinning cyclic symmetric rotor via a numerical simulation. A reference system used in this study is a spinning disk with four pairs of brackets, representing a 4-fold cyclic symmetric rotor. A crack with a variable depth is introduced at one of the eight disk-bracket interfaces. Both radial and circumferential cracks are simulated. The ground-based vibration response of the spinning disk-bracket system is simulated using an algorithm introduced by Shen and Kim [1]. Compared with a perfectly cyclic symmetric rotor, the crack introduces additional resonances when the crack size is large enough. Frequencies of these additional resonances can be predicted accurately and may be used as a way to detect presence of cracks. In addition, the additional resonances are more prominent for the circumferential crack than the radial crack.

Commentary by Dr. Valentin Fuster
2010;():299-308. doi:10.1115/GT2010-23084.

Application of two smart materials, namely shape memory alloy (SMA) and magnetorheological fluid (MRF) for rotor vibration control is explored to control the synchronous vibration of rotors crossing resonance condition. First a single degree of freedom system is analyzed to study the effect of SMA and MR fluid damper individually, and then the simulations are repeated to find the feasibility of using the two smart materials simultaneously. An MRF damper is designed, fabricated and installed on a rotor system. The fabricated MR damper is tested and an ANFIS model is trained to predict the damper force in the simulations carried out. The experimental rotor model is analyzed using finite element method in Matlab™. Simulations are carried out to study the effect of MR damper on rotor vibration response. Experimental results obtained from the rotor model with the fabricated MRF damper show considerable reduction in peak vertical amplitude as the current in the MR damper coils is increased. A good correlation between the theoretical and experimental results is observed.

Commentary by Dr. Valentin Fuster
2010;():309-318. doi:10.1115/GT2010-23091.

It is well known that zero and one nodal diameter (k = 0 and k = 1) modes of a blade system interact with the shaft system. The former is coupling with torsional and/or axial shaft vibrations, and the latter with bending shaft vibrations. This paper deals with the latter. With respect to k = 1 modes, we discuss experimentally and theoretically in-plane blades and out-of-plane blades attached radially to a rotating shaft. We found that when we excited the shaft at the rotational speed of Ω = |ωb ωs | (where ωb = blade natural frequency, ωs = shaft natural frequency and Ω = rotational speed), the exciting frequency ν = ωs induced shaft-blade coupling resonance. In addition, in the case of the in-plane blade system, we encountered an additional resonance attributed to deformation caused by gravity. In the case of the out-of-plane blade system, we experienced two types of abnormal vibrations. One is the additional resonance generated at Ω = ωb / 2 due to the unbalanced shaft and the anisotropy of bearing stiffness. The other is a flow-induced self-exited vibration caused by galloping due to the cross-section shape of the blade tip, because this instability disappeared at the rotation test inside a vacuum chamber. Both occurred at the same time, and both led to the entrainment phenomenon, which was identified by our own frequency analysis technique.

Commentary by Dr. Valentin Fuster
2010;():319-326. doi:10.1115/GT2010-23120.

Dynamic characteristics of a 600MW steam turbine rotor model supported by cylindrical bearings and elliptical bearings were investigated respectively. Differences between the linear and nonlinear characteristics of rotor-bearing systems were studied by numerical simulations, and the performances of rotor systems using different bearings were also presented. Dynamic tests were performed on the 600MW turbine generator group model test rig, while sustained by different types of bearings, to study the oil whirl and whip phenomenon. Comparisons of the numerical results with experimental data show that the nonlinear model is more accurate than the linear model, and the elliptical bearing has the advantage of better dynamic stability over cylindrical bearings.

Topics: Stability , Bearings , Rotors
Commentary by Dr. Valentin Fuster
2010;():327-337. doi:10.1115/GT2010-23127.

This paper briefly describes the rotor dynamic analysis requirements in the API standards for process centrifugal compressors, induction motors and gearboxes. The paper also presents an example for each equipment type where the dynamic analysis performed by the manufacturer during the design stage in accordance with these standards identified critical aspects that were concerning to the purchase. The paper also highlights the measures taken to alleviate the purchaser’s concerns, the vibration behavior of these machines after commissioning and some lessons learned from these cases. The first case is for a 4,744 kW (6,400 HP) centrifugal gas compressor running at 11,889 rpm. The dynamic analysis shows that the compressor will run above its fist critical speed estimated at 5,400 rpm and below its second critical speed estimated at 20,600 rpm that is 16% less than the second multiple of the running speed. The analysis also shows that the second mode is lightly damped with an amplification factor equal to 116. The second case is for a 2,984 kW (4000 HP) induction motor running at 3,600 rpm. The dynamic analysis shows that the motor will run at almost twice its first critical speed. The first critical speed is estimated at 1,750 rpm with high amplification factor equal to 99. Also, the second critical speed is estimated at 7,400 rpm which is less than 5% from twice the line frequency and the second multiple of the running speed. The third case is for a 4,744 kW (6,400 HP) helical gearbox. The dynamic analysis shows the existence of a critical speed for the gear wheel rotor that coincides with the pinion rotor running speed at 50%–100% load range.

Commentary by Dr. Valentin Fuster
2010;():339-347. doi:10.1115/GT2010-23152.

The objective of the present work is the study of the rubbing failure between fan stator vanes and the spacer ring of a Turbo-Fan Engine. The similar failures appeared 2 times in this small turbo-fan engine. The failure mechanism is analysed, in which kinds of factors that could influence the clearance between the rotor and the stator are taken into account. The failure is analysed by means of both test characterizations and numerical simulation techniques. Firstly, a finite element model of the spline joints is used to calculate the stiffness of the fan-rotor considering the influence of locating surface clearance. Secondly, a traveling wave vibration analysis of the spacer ring is performed, as well as the analysis of the stator vane. Finally, the analysis of the vibration test data is performed. The test characterizations and numerical simulation results indicate that, for Engine-1, the large 2×vibration shows a rotor misalignment, at the same time the traveling wave resonance of the spacer ring occurs, these cause the appearance of the failure. For Engine-2, the failure is caused by the rotor unbalance vibration. Some improvement measures are proposed to avoid this failure.

Topics: Engines , Failure , Turbofans
Commentary by Dr. Valentin Fuster
2010;():349-361. doi:10.1115/GT2010-23218.

A Reynolds-averaged Navier-Stokes (RANS) solver developed in-house was used to simulate grazing channel flow past single and multiple cavities. The objective of this investigation was to predict fluid instabilities in hole-pattern stator seals. The numerical results generated with the RANS solver showed good agreement with those obtained using a commercial Large Eddy Simulation (LES) code. In addition, the numerical results agreed well with experimental data. Rossiter’s formula, a popular semi-empirical model used to predict frequencies of hole-tone acoustic instabilities caused by grazing fluid flow past open cavities, was modified using the RANS solver results to allow for its application to channel flows. This was done by modifying the empirical constant κ, the ratio of vortex velocity and the freestream velocity. The dominant frequencies predicted using the Rossiter’s formula with the new κ value matched well the experimental data for hole-pattern stator seals. The RANS solver accurately captured the salient features of the flow/acoustic interaction and predicted well the dominant acoustic frequencies measured in an experimental investigation. The flow solver also provided detailed physical insight into the cavity flow instability mechanism.

Topics: Resonance , Cavities , Stators
Commentary by Dr. Valentin Fuster
2010;():363-371. doi:10.1115/GT2010-23243.

Oil-free turbochargers (TCs) will increase power and efficiency of internal combustion (IC) engines, sparking ignition (SI) and compression ignition (CI), without engine oil lubricant feeding and scheduled maintenance. Implementing gas foil bearings (GFBs) into passenger vehicle TCs enables compact, light weight, oil-free systems along with accurate shaft motions, while engine oil lubricated TCs with floating ring bearings (FRBs) are prone to show severe sub synchronous motions over a wide range of shaft speeds due to instability. The paper presents static load-deflection tests of TC GFB structure, and rotordynamic performance measurements of an oil-free TC unit supported on test GFBs. Three metal shims inserted under the bump-strip layers and in contact with the bearing housing create a mechanical preload, which induces a hydrodynamic wedge in the assembly radial clearance to generate more film pressure for the shimmed GFB. Static load-deflection tests estimate the assembly radial clearances of the shimmed GFB smaller than that of the original GFB. Model predictions agree well with test data. The discrepancy between the model predictions and test data is attributed to fabrication inaccuracy of the top foil and bump strip layers. The rotordynamic TC test rig is driven by pressurized air. The test TC rotor, of 335 gram weight and 117 mm length, is coated using commercially available wear-resistant solid lubricant, Amorphous M, to prevent severe wears during start up and shutdown in the absence of an air film. Pressure sensors measure the driving turbine inlet air pressure and a control valve changes the air mass flow manually. A pairs of optical proximity probes positioned orthogonally at the compressor end record the lateral rotor motions. Rotordynamic test results show that the shimmed GFB attenuates significantly the large amplitude of subsynchronous whirl motions arising for the original GFBs. Mechanical preloads, which determine the assembly radial clearance of the shimmed GFB, causes the increase in the rotor-bearing system natural frequency.

Commentary by Dr. Valentin Fuster
2010;():373-382. doi:10.1115/GT2010-23246.

Synchronous vibration in rotor systems having bearings, seals or other elements with non-linear stiffness characteristics is prone to amplitude jump when operating close to critical speeds as there may be two or more possible whirl responses for a given unbalance condition. This paper describes research on the use of active control methods for eliminating this potentially undesirable behavior. A control scheme based on direct feedback of rotor-stator interaction forces is considered. Model based conditions for stability of low amplitude whirl, derived using Lyapunov’s direct method, are used as a basis for synthesizing controller gains. Subsidiary requirements for existence of a static feedback control law that can achieve stabilization are also explained. An experimental validation is undertaken on a flexible rotor test rig where non-linear rotorstator contact interaction can occur across a small radial clearance in one transverse plane. A single radial active magnetic bearing is used to apply control forces in a separate transverse plane. The experiments confirm the conditions under which static feedback of the measured interaction force can prevent degenerate whirl responses so that the low amplitude contact-free orbit is the only possible steady-state response. The gain synthesis method leads to controllers that are physically realizable and can eliminate amplitude jump over a range of running speeds.

Commentary by Dr. Valentin Fuster
2010;():383-388. doi:10.1115/GT2010-23267.

In aerodynamic bearings, since the supporting air film is generated by rotor motion, there is no support at the start of motion. As in all such bearings, there is dry rubbing until the rotor achieves sufficient speed to lift-off. Thus, the lower the lift-off speed, the less will be the rubbing and so the greater will be the life of the bearing. This paper focuses on the theoretical prediction of lift-off speed in aerodynamic compliant foil journal bearings based on a generalized solution of elasto-aerodynamically coupled lubrication for compliant foil bearings. A computational method is presented which is used to predict the lift-off speed in aerodynamic foil journal bearings with eccentricity ratio greater than or equal to 1.0. Special emphasis is placed on investigating the effects of the load imposed on the bearing, the nominal radial clearance and the bearing radius on the lift-off speed. The numerical results obtained indicate that lift-off speed decreases with the decrease of load and nominal radial clearance, but with an increase in bearing radius. The eccentricity ratios are all greater than 1.0 at the lift-off speed for the aerodynamic compliant foil journal bearings used in this study.

Commentary by Dr. Valentin Fuster
2010;():389-398. doi:10.1115/GT2010-23368.

This paper is concerned the stability and bifurcation of a flexible rod-fastening rotor bearing system (FRRBS). Here the shaft is considered as an integral or continuous structure and be modeled by using Timoshenko beam-shaft element which can take the effects of axial load into consideration. And using Hamilton’s principle, model tie rods distributed along the circumference as a constant stiffness matrix and an add-moment which caused by unbalanced pre-tightening forces. Then the model is reduced by a component mode synthesis method, which can conveniently account for nonlinear oil film forces of the bearing. This study focuses on the influence of nonlinearities on the stability and bifurcation of T periodic motion of the FRRBS subjected to the influence of mass eccentricity. The periodic motions and their stability margin are obtained by shooting method and path-following technique. The local stability and bifurcation behaviors of periodic motions are obtained by Floquet theory. The results indicate that mass eccentricity and unbalanced pre-tightening forces of tie rods have great influence on nonlinear stability and bifurcation of the T periodic motion of system, cause the spillover of system nonlinear dynamics and degradation of stability and bifurcation of T periodic motion.

Commentary by Dr. Valentin Fuster
2010;():399-408. doi:10.1115/GT2010-23482.

The paper describes an experimental assessment of the transient performance of a multi-objective adaptive approach to the control of flexible rotors previously presented by the authors. The approach is applicable to any form of controllable bearings or actuators. In the case reported here, the rotor is supported by active magnetic bearings (AMBs). The theory underlying the controller is outlined: the objectives include minimization of the forces transmitted to the base while restricting rotor vibrations to a user-defined limit. A third objective is to prevent rotor contact with the auxiliary bearings used to protect the active elements. These three objectives are met by a two-stage weighting strategy followed by the adaptive control of two parameters that automatically and continuously adjust the weightings of individual objective functions to satisfy user defined performance criteria.

Commentary by Dr. Valentin Fuster
2010;():409-420. doi:10.1115/GT2010-23553.

This paper discusses the application of squeeze-film dampers in series with the tilting pad bearings of a large centrifugal compressor. The compressor was first factory tested with non-damper bearings and there was some subsynchronous vibration. Damper bearings were installed and the subsynchronous vibration was gone. The compressor shipped with damper bearings. Analytical and test results will be presented for both rotor dynamic systems. Design considerations in the use of squeeze-film dampers with tilting pad journal bearings will be reviewed.

Topics: Compressors , Dampers
Commentary by Dr. Valentin Fuster
2010;():421-430. doi:10.1115/GT2010-23585.

A large alternator/flywheel/motor train is employed as part of the power system for the ALCATOR C-MOD experiment at the MIT Plasma Fusion Center. The alternator is used to provide peak pulse power of 100 MW to the magnets employed in the fusion experiment. The flywheel diameter is 3.3m and the alternator is 1.8 m in diameter. After being driven up to full speed over a long period of time by a 1491 kW motor, the alternator is rapidly decelerated from approximately 1800 rpm to 1500 rpm during a 2 second interval. This sequence is repeated about six times per working day on average. A full lateral rotordynamic analysis of the including the rotors, fluid film bearings and unbalanced motor magnetic force was carried to assess the effects of rotor modifications in the alternator shaft bore. This paper provides a more detailed analysis of a complicated rotor train than is often performed for most rotors. Critical speeds, stability and unbalance response were evaluated to determine if lateral critical speeds might exist in the operating speed range in the existing or modified rotor train and if unbalance levels were within acceptable ranges. Critical speeds and rotor damping values determined for the rotor system with the existing and modified rotor. The first critical speed at 1069 rpm is an alternator mode below the operating speed range. The second critical speed is also an alternator mode but, at 1528 rpm, is in the rundown operating speed range. The third critical speed is a flywheel mode at 1538 rpm, also in the rundown operating speed range but well damped. The predicted highest rotor amplitude unbalance response level is at 1633 rpm, again in the operating speed range. Direct comparisons were made with measured bearing temperature values, with good agreement between calculations and measurements. Stress levels in the rotor were evaluated and found to be well below yield stress levels for the material for both original and modified rotors. Comparisons we carried out between standard vibration specifications and measured vibration levels which indicated that the third critical speed amplification factors were much higher than API standards indicate they should have been. Corrective actions to reduce unbalance were taken for the modified rotor.

Topics: Engines , Flywheels , Trains
Commentary by Dr. Valentin Fuster
2010;():431-442. doi:10.1115/GT2010-23609.

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to non-synchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are considered using a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced non-synchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

Commentary by Dr. Valentin Fuster
2010;():443-452. doi:10.1115/GT2010-23619.

The successful industrial application of flexible rotors supported on active magnetic bearings (AMBs) requires careful attention not only to rotordynamic design aspects, but also to electromagnetic and feedback control design aspects. This paper describes the design, construction and modeling process for an AMB test rig which contains a 1.23m long flexible steel rotor, with a mass of 44.9 kg and two gyroscopic disks. The rotor typifies a small industrial centrifugal compressor designed to operate above 12,000 rpm and the first bending natural frequency. There are four AMBs — two AMBs at the shaft ends to support the shaft with a combined load capacity of 2600N and two additional AMBs at the mid and quarter spans to allow for the application of simulated destabilizing fluid or electromagnetic forces to the rotor. Simulated aerodynamic cross coupling stiffness values are to be applied to the rotor through these two internal AMBs with the goal of developing stabilizing robust controllers. The unique design allows multiple support and disturbance locations providing the ability to represent a variety of machine configurations, e.g., between bearing and overhung designs. The shaft transfer function in lateral movement has been developed with finite element model and then verified by experimental frequency response measurements. Models for the power amplifiers, position sensors, signal conditioning and data converter hardware were developed, verified experimentally and included in the overall system model. A PID controller was developed and tuned to levitate the rotor and enable further system characterization.

Commentary by Dr. Valentin Fuster
2010;():453-462. doi:10.1115/GT2010-23683.

Oil-free foil bearing technology has advanced intermittently over the years, driven by research efforts to improve both steady-state and dynamic performance characteristics, namely: load capacity, stiffness, and damping. Bearing designs are thus classified according to “generation”, with first-generation bearings being the most primitive. This paper presents an experimental evaluation of a first- and a second-generation foil bearing, and aims to provide the high-fidelity data necessary for proper validation of theoretical predictive models of foil bearing performance. The aforementioned test bearings were fabricated in-house, and are both 70mm in diameter with an aspect ratio of 1; bearing manufacturing details are provided. The work makes use of a facility dedicated to measuring both the steady-state and dynamic properties of foil bearings under a variety of controlled operating conditions. The bearing under test is placed at the midspan of a horizontal, simply-supported, stepped shaft which rotates at up to 60krpm. Static and dynamic loads of up to 3500N and 450N (respectively) can be applied by means of a pneumatic cylinder and two electrodynamic shakers. The bearings’ structural (static) stiffnesses are highly nonlinear, and this affects the accuracy of the dynamic coefficient determination. Both dynamic stiffness and damping are found to vary nonlinearly with excitation frequency, and are over-predicted by a structural experimental evaluation — the film plays an important role in bearing dynamics. The second-generation bearing is found to have a higher load capacity, dynamic stiffness, and damping than the first-generation bearing.

Commentary by Dr. Valentin Fuster
2010;():463-472. doi:10.1115/GT2010-23802.

This paper presents the identification of the rotordynamic force coefficients for a direct lubrication five-pad and four-pad tilting pad bearing. The bearing is 110 mm in diameter with an L/D of 0.4. The experiments include load-on-pad (LOP) and load-between-pad (LBP) configurations, with a 0.5 and 0.6 pivot offset, for rotor speeds ranging from 7500 rpm to 15000 rpm. The bearing force coefficients are identified from multiple frequency excitations (20 to 300 Hz) exerted on the bearing housing by a pair of hydraulic shakers, and are presented as a function of the excitation frequency, rotor speed, for a 300 kPa unit load. The experimental results also include temperatures at the trailing edge of three pads. The direct force coefficients, identified from curve-fits of the complex dynamic stiffness, are frequency independent if considering an added mass term much smaller than the test device modal mass. The force coefficients from the four-pad bearing load-between-pad configuration show similar coefficients in the loaded and orthogonal direction. On the other hand, as expected, the five-pad bearing load-on-pad shows larger coefficients (∼25%) in the loaded direction. The maximum pad temperature recorded for the 0.5 pivot offset configurations are up to 20° C higher than those associated to the 0.6 offset configuration. Results from a predictive code are within 50% of the experimental results for the direct stiffness coefficients and within 30% for the direct damping coefficients.

Topics: Force , Stress , Bearings
Commentary by Dr. Valentin Fuster
2010;():473-480. doi:10.1115/GT2010-23812.

Modern rotating machinery is prone to fatigue cracks due to the severe working and continuously varying loading conditions. To avoid failure of the rotating systems due to these cracks, the system needs to be continuously monitored. The reliability of the machinery can be enhanced with the fault identification at the early stages of their occurrence. Model based methods are used for crack identification in rotating systems successfully. Model based methods are of different types. One of the methods, the equivalent loads minimization method is studied here. It has a limitation that the error in identified crack depth increases with decrease in number of measured vibrations. In the present work, the theoretical fault model loads used in least squares minimization algorithm are transformed using modal expansion to reduce error in the identified fault parameters. The crack is identified accurately even in the case of less number of measured vibrations. The method is applied for crack identification in a centrifugal pump rotor using transverse vibrations. The results presented are obtained purely from FEM simulations.

Commentary by Dr. Valentin Fuster
2010;():481-489. doi:10.1115/GT2010-22262.

A compressor blade failure was experienced at the 69 MW gas turbine of a combined cycle (C.C.) unit after four years operation since the last overhaul (January 2005). The unit accumulated 27,000 service hours and 97 start-ups since the last overhaul. This unit consists of four gas turbine stages and 19 compressor stages and operates at 3600 rpm. In 2006, the unit was equipped with a fogging system at the compressor air inlet duct to increment unit power output during high ambient temperature days (hot days). These fog water nozzles were installed upstream of the compressor inlet air filter without any water filter/catcher before the water spray nozzles. Three unit failure events occurred at small periods, which caused forced outage. The first failure occurred in December 2008, a second event in March 2009 and the third event in May 2009. Visual examination carried out after the first failure event indicated that the compressor vanes (diaphragms) had cracks in their airfoils initiating at blade tenons welded to the diaphragm outer shroud at stages 3, 8, 9, 10 and 11. Also, many stationary vanes and moving blades at each stage of the compressor showed foreign object damage (FOD) and fractures at the airfoil. Visual examination performed for the second failure event after 60 unit operation hours indicated that many compressor vanes (diaphragms) and moving blades had FOD at the airfoil. This was attributed to fractures of the fogging system water spray nozzle, which were then induced to the compressor flow path channel at high velocity causing the above-mentioned damage. Visual examination completed upon the third failure event after two unit startup attempts indicated damage of compressor stationary vanes and moving blades principally at stages 12 to 16, and also stages 17 to 19. The damage consisted of airfoil fracture in stationary vanes and moving blades, FOD, moving blade tip rubbing, and bending of stationary vanes, moving blades and diaphragm shrouds. A laboratory evaluation of stationary vane tenon fracture indicated a high cycle fatigue (HCF) failure mechanism, and crack initiation was accelerated by corrosion picks on blade surfaces due to high humidity air generated by the fogging system. Stationary vane damage was caused by a rotating stall phenomenon, which generates vibratory stresses in stationary vanes and moving blades during unit start-ups. During the third failure event, stationary vane HCF damage was highly accelerated due to pre-existent partial fractures in tenons generated during previous failure events, which had not been detected by non-destructive tests. Stationary vane and moving blade failure was also influenced by high tenon brittleness in stationary vanes and moving blades generated during manufacture by welding (diaphragms) and repair welding (moving blades) without adequate post-weld heat treatment (stress relieving). A compressor stationary vane and moving blade failure evaluation was completed. This investigation included cracked blade metallographic analysis, unit operation parameter analysis, history-of-events analysis, and crack initiation and propagation analysis. This paper provides an overview of the compressor failure investigation, which led to identification of the HCF failure mechanism generated by rotating stall during unit start-ups, highly accelerated by corrosion generated by the fogging system and influenced by high stationary vane and moving blade brittleness as the primary contribution to the observed failure.

Commentary by Dr. Valentin Fuster
2010;():491-498. doi:10.1115/GT2010-22320.

The axial thrust load of a turbocharger is generated due to the pressure differential between the compressor and turbine. Changes in compressor and turbine geometry and variations in test conditions can influence the thrust load. Once the axial force exceeds the loading capacity limit of a thrust bearing, the balance of the thrust bearing system cannot be maintained, which may lead to a catastrophic failure of the turbocharger. In this paper, a fault diagnosis of a turbocharger that experienced a catastrophic failure during flow bench testing is analyzed. A detailed analysis of a turbocharger thrust load, based on empirical formulae and CFD verification, is presented. The thrust prediction at high rotation speed is helpful for further flow bench testing and to avoid the future turbocharger failure.

Commentary by Dr. Valentin Fuster
2010;():499-504. doi:10.1115/GT2010-22355.

Single crystal superalloy turbine blades exhibit anisotropic behaviors, and the stress at the fir-tree root often reaches the yield stress of the material when the turbine operates at the peak rotational speed and at the maximum temperature. The nonlinear behavior of the material character at these operating conditions poses a significant challenge to prediction of the blade behavior using the conventional linear elastic fracture mechanics approach. In this paper a fracture mechanics analysis was performed for a single crystal turbine blade using the J-integral concept. First of all, the elastic-perfectly plastic J-integral and CTOD was used to correlate with the fatigue crack growth rates obtained in a single crystal blade in [100] and [110] directions, with the [001] direction as the loading direction under typical service conditions. The weight function method was used to evaluate the stress intensity factor for a crack growing along the serration bottom of the blade fir-tree root under small-scale yielding conditions and the crack growth analysis was performed using the correlated fatigue crack growth data. In addition, crack growth simulations were also performed using the Zencrack software. The simulated crack growth profile was compared with the actual crack profile on the component.

Commentary by Dr. Valentin Fuster
2010;():505-510. doi:10.1115/GT2010-22425.

One of the main reasons of engine failure is foreign object damage (FOD) of compressor blades. Engine manufactures are constantly searching for blade endurance increasing methods. The problem solution requires investigation in the field of the structural factor effects on the blade damageability. The paper describes numerical analysis method of the damage process. Based on “the typical damage case” concept, this method can simulate typical blade damages: dents, tears, notches. The numerical analysis is performed by the finite element method (FEM). Material behavior is described with an elastic-plastic strain rate dependent model. Blade damage numerical model is thoroughly verified by the results of special experiments. To implement the experimental modeling, actual blades were damaged, a special experimental setup based on a pneumatic gun being used. The foreign object kinematic parameters before and after the impact, a blade leading edge displacements and residual deformation fields registered in the experiment are used as verification criteria for the numerical model. The blade leading edge thickness and a foreign object energy effect on the blade damageability is investigated. The research showed there are some foreign object kinetic energy critical values at which the damage mechanism and type are changed.

Commentary by Dr. Valentin Fuster
2010;():511-520. doi:10.1115/GT2010-22532.

Anisotropic creep-damage modeling has become an increasingly important prediction technique in both the aerospace and industrial gas turbine industries. The introduction of tensorial damage mechanics formulations in modeling tertiary creep behavior has lead to improved predictions of the creep strain that develops due to anisotropic grain structures and the induced anisotropy that occurs with intergranular damage. A number of isotropic creep-damage rupture time prediction models have been developed in literature; however, few rupture time prediction models for tensorial anisotropic creep-damage are available. In this paper, a rupture time model for anisotropic creep-damage of transversely isotropic materials is derived. Comparison with the Larson-Miller parameter, Monkman-Grant relation, and Kachanov-Rabotnov continuum damage mechanics (CDM) approach shows improved creep rupture time predictions for multiaxial conditions and material rotations. A parametric study of the rupture time predicted under various states of equivalent stress and material orientations is performed to demonstrate the robustness of the new formulation.

Topics: Creep , Rupture
Commentary by Dr. Valentin Fuster
2010;():521-527. doi:10.1115/GT2010-22547.

A multi-axial prediction method is used to calculate the fatigue life of components under pure torsion loading. The general life prediction method was developed based on the understanding that the total accumulated strain energy density in a fatigue and monotonic processes is the same. Due to this understanding, the fatigue life prediction method has been used to calculate fatigue cycles of components experiencing either uniaxial, transverse shear, or multi-axial loads. This manuscript extends the capability of the multi-axial prediction method by calculating the fatigue life of components under pure torsion loads. This calculation is possible because the maximum applied shear stress from a pure torsion load can be observed as two normal principal stresses. Based on some unusual results from experimental torsion fatigue, it was assumed that a linear misalignment was present in the experimental setup. With the inclusion of this correction, a comparison between experimental torsion fatigue results and the energy-based prediction method further affirms the capability to determine fatigue life cycles in a multi-axial loading state.

Commentary by Dr. Valentin Fuster
2010;():529-537. doi:10.1115/GT2010-22647.

An energy-based fatigue life prediction framework for calculation of torsional fatigue life and remaining life has been developed. The framework for this fatigue prediction method is developed in accordance with our previously developed energy-based axial and bending fatigue life prediction approaches, which state: the total strain energy dissipated during a monotonic fracture and cyclic processes is the same material property, where each can be determined by measuring the area underneath the monotonic true stress-strain curve and the area within a hysteresis loop, respectively. The energy-based fatigue life prediction framework is composed of the following entities: (1) development of a shear fatigue testing procedure capable of assessing strain energy density per cycle in a pure shear stress state and (2) incorporation of an energy-based fatigue life calculation scheme to determine the remaining fatigue life of in-service gas turbine materials subjected to pure shear fatigue.

Topics: Fatigue
Commentary by Dr. Valentin Fuster
2010;():539-548. doi:10.1115/GT2010-22741.

Since E class gas turbines manufactured by Ansaldo Energia are approaching their typical life limits for their planned life cycle (100.000 EOH or 3000 start up) a detailed approach has been developed and carried out in order to guarantee main components for a life extension. This approach has become very important in order to overcome the adopted conservative design approach developed in the seventies taking into account an “ideal reference engine” and therefore focusing on the real engine featured by its history and its component peculiarity. This paper presents a complete life analysis approach which includes experimental tests, FEM analysis and life prediction for the gas turbine model AE94.2, using the 170MW-class 3000 rpm.

Commentary by Dr. Valentin Fuster
2010;():549-555. doi:10.1115/GT2010-22802.

Blade failures in gas turbine engines often lead to the loss of all downstream stages and it can have a dramatic effect on the availability of the turbine engines. This paper presents the analysis of an in service failure of a first stage gas turbine blade. The premature failure of the blade, made of nickel-base superalloy Inconel 738 LC, occurred after a service life of 8,127 EOH with normal start/stop and caused extensive damage to the unit. Crack growth mechanism has been evaluated based on macroscopic and microscopic observations of the fracture surfaces. Chemical analyses were carried out to identify the possible causes of the failures by examining anomalies in the chemical composition and microstructure analysis through SEM observations. The analysis of the different regions of fracture surface shows that crack propagation is mainly related to fatigue mechanism. Typical fatigue striations could be identified under a homogeneous oxide layer. The crack propagation occurred in the pressure-suction side direction and the initial crack origin is located on the missing part near leading edge area. The impact marks on the first stage leading edge of the blade and the general damage of the turbine give indication that the crack initiation was caused by an impact of a broken piece from first stage vanes or another object of unknown source.

Commentary by Dr. Valentin Fuster
2010;():557-567. doi:10.1115/GT2010-23095.

High cycle fatigue is the most common cause of failure in gas turbine engines. Different design tools have been developed to predict number of cycles to failure for a component subjected to fatigue loads. An energy-based fatigue life prediction framework was previously developed in recent research for prediction of axial and bending fatigue life at various stress ratios. The framework for the prediction of fatigue life via energy analysis was based on a new constitutive law, which states the following: the amount of energy required to fracture a material is constant. A finite element approach for uniaxial and bending fatigue was developed by authors based on this constitutive law. In this study, the energy expressions that construct the new constitutive law are integrated into minimum potential energy formulation to develop a new QUAD-4 finite element for fatigue life prediction. The newly developed QUAD-4 element is further modified to obtain a plate element. The Plate element can be used to model plates subjected to biaxial fatigue including bending loads. The new QUAD-4 element is benchmarked with previously developed uniaxial tension/compression finite element. The comparison of Finite element method (FEM) results to existing experimental fatigue data, verifies the new finite element development for fatigue life prediction. The final output of this finite element analysis is in the form of number of cycles to failure for each element in ascending or descending order. Therefore, the new finite element framework can predict the number of cycles to failure at each location in gas turbine engine structural components. The new finite element provides a very useful tool for fatigue life prediction in gas turbine engine components. The performance of the fatigue finite element is demonstrated by the fatigue life predictions from Al6061-T6 aluminum and Ti-6Al-4V. Results are compared with experimental results and analytical predictions.

Commentary by Dr. Valentin Fuster
2010;():569-580. doi:10.1115/GT2010-23311.

Constitutive modeling has proven useful in providing accurate predictions of material response in components subjected to a variety of operating conditions; however, the high number of experiments necessary to determine appropriate constants for a model can be prohibitive, especially for more expensive materials. Generally, up to twenty experiments simulating a range of conditions are needed to identify the material parameters for a model. In this paper, an automated process for optimizing the material constants of the Miller constitutive model for uniaxial modeling is introduced. The use of more complex stress, strain, and temperature histories than are traditionally used allows for the effects of all material parameters to be captured using significantly fewer tests. A graphical user interface known as uSHARP was created to implement the resulting method, which determines the material constants of a viscoplastic model using a minimum amount of experimental data. By carrying out successive finite element simulations and comparing the results to simulated experimental test data, both with and without random noise, the material constants were determined from 75% fewer experiments. The optimization method introduced here reduces the cost and time necessary to determine constitutive model constants through experimentation. Thus it allows for a more widespread application of advanced constitutive models in industry and for better life prediction modeling of critical components in high-temperature applications.

Commentary by Dr. Valentin Fuster
2010;():581-590. doi:10.1115/GT2010-23440.

Many critical components in turbocharger are subjected to rapid temperature changes during operations. Thermal gradient within these components produces internal stresses and the repetition of these thermal cycles may cause a component to fail due to Thermal Mechanical Fatigue (TMF). Turbine Wheel, Turbine Housing and Manifold are subjected to TMF; these are the most expensive components of the turbocharger and have very complex geometric shapes. The maximum exhaust gas temperature could reach 1050°C. To assess TMF failure, it is very critical to accurately estimate metal temperature of these components subjected to complex duty cycles where exhaust gas temperatures vary significantly with time. Evaluating metal temperature and stress components from finite element analysis for complex duty cycles is a very time consuming process, particularly for complex geometries and approximately requires more than 3 weeks of time to complete analysis for different field complex duty cycles (driving conditions: city, highway and road). Several of these analysis cases are required to consider the impact of the real driving condition. In the present work we have developed an analytical methodology that is accurate and faster to predict the metal temperature and stresses in turbocharger components for complex duty cycles. This method was applied to evaluate the fatigue damage of turbine housing under actual condition.

Commentary by Dr. Valentin Fuster
2010;():591-599. doi:10.1115/GT2010-22083.

The geometric parameters of manufactured compressor blades do not exactly comply with the design intention. These deviations result from the abrasion of the forging and milling machines as well as variations of the material properties or the blank part geometries. Using probabilistic methods, the geometric deviations can be considered within the design process. This paper presents the results of a probabilistic High-Cycle-Fatigue investigation under consideration of the geometric parameter scatter of the entire compressor blade. Based on a previous paper of the authors, the geometric parametrization as well as the process chain to apply the geometric scatter to an existing FE-mesh was supplemented by the radii and the geometric dimensions of the compressor blade root. Thus, the impact of all geometric parameter scatter on the High-Cycle-Fatigue strength, the eigenfrequencies and the mode shapes can be evaluated.

Commentary by Dr. Valentin Fuster
2010;():601-610. doi:10.1115/GT2010-22129.

Mistuning affects forced response of bladed disks drastically; therefore, its identification plays an essential role in the forced response analysis of realistic bladed disk assemblies. Forced response analysis of mistuned bladed disk assemblies has drawn wide attention of researchers but there are a very limited number of studies dealing with identification of mistuning, especially if the component under consideration is a blisk (integrally bladed disk). This paper presents two new methods to identify mistuning of a rotor from the assembly modes via utilizing neural networks. It is assumed that a tuned mathematical model of the rotor under consideration is readily available, which is always the case for today’s realistic bladed disk assemblies. In the first method, a data set of selected mode shapes and natural frequencies is created by a number of simulations performed by mistuning the tuned mathematical model randomly. A neural network created by considering the number of modes, is then trained with this data set. Upon training the network, it is used to identify mistuning of the rotor from measured data. The second method further improves the first one by using it as starting point of an optimization routine and carries out an optimization to identify mistuning. To carry out identification analysis by means of the proposed methods, there are no limitations on the number of modes or natural frequencies to be used. Thus, they are suitable for incomplete data as well. Moreover, since system modes are used rather than blade alone counterparts, the techniques are ready to be used for analysis of blisks. Case studies are performed to demonstrate the capabilities of the new methods, using two different mathematical models to create training data sets; a lumped-parameter model and a relatively realistic reduced order model. Throughout the case studies, the effects of using incomplete mode families and random errors in assembly modes are investigated.

Commentary by Dr. Valentin Fuster
2010;():611-616. doi:10.1115/GT2010-22169.

The paper presents the results of a probabilistic creep life study on F5001P turbine discs and demonstrates the importance of using physics based probabilistic damage modeling techniques to deal with life prediction uncertainty in forged components. In physics based modeling, the influence of individual microstructural or thermal-mechanical loading factors on metallurgical crack initiation can also be studied with relative ease. In a previous study, Life Prediction Technologies Inc.’s (LPTi’s) prognosis tool known as XactLIFE™ was successfully used to conduct deterministic analysis to establish the fracture critical location of F5001P first stage discs under steady state loads. In this paper, the variability in life is further established as a function of prior austenite grain size. The analysis used typical engine operating data from the field in terms of engine speed and average exhaust gas temperature (EGT). The primary objectives of the case study are to show how prognosis can allow a user to assess fleet reliability for engine specific operating conditions. The lower bound deterministic creep life and probabilistic creep life at 0.1% cumulative probability of failure are very close in magnitude.

Topics: Creep , Turbines , Disks
Commentary by Dr. Valentin Fuster
2010;():617-628. doi:10.1115/GT2010-22484.

The present paper addresses a non-deterministic CFD simulation of a high-pressure compressor (HPC) stage. The investigation focuses on the determination of the influence of the manufacturing scatter of compressor blades on the aerodynamic performance of the analyzed HPC stage. A set of 150 blades was scanned using an optical 3D digitizer to obtain a three-dimensional point cloud representing the surface of the blades. Classical profile parameters were identified at several sections of constant spanwise coordinate. The radial stacking of these parameters forms a parameter vector that constructs the airfoil model of each scanned blade. Consequently these parameters were used to define the geometric variability of the entire measured blade set. A statistical analysis of the distribution of these parameters defines the input data of the probabilistic 3D CFD simulation. The Monte-Carlo method is used to identify the scatter of the performance values of the HPC stage and their sensitivity to the geometric variability of profile parameters.

Commentary by Dr. Valentin Fuster
2010;():629-638. doi:10.1115/GT2010-22548.

The maintenance and reliability of aircraft engines is strongly influenced by the environmental and operating conditions they are subjected to in service. A probabilistic tool has been developed to predict shop visit arisings and respective maintenance workscope that depends on these factors. The tool contains a performance model of the engine and a number of physics-based damage mechanisms (at piece part level). The performance model includes variation of performance relevant parameters due to production scatter and delivers the conditions to determine the deterioration of the individual parts. Shop visit maintenance is modeled as a result of limitations to engine operation, e.g. reaching TGT limit, or mechanical deterioration. The influence of maintenance actions on engine performance is determined on component basis. The maintenance strategy can consist of proactive and reactive maintenance elements. The decision of repair or replacement of any single part is implemented through a sum of different logic rules in the model. The loading capacity scatter depends on the engine type and is operator independent. It is represented via data-driven distribution functions, in which the probabilities of failure, repair and replacement for each part are specified depending on the number of reference flight cycles. The loading variation is considered through a physics-based cycle weighting. The developed tool runs a Monte Carlo simulation in which a fleet of engines is modeled through their respective lifetime of maintenance and performance deterioration. Using an example it is shown that the model can describe the effects of varying environmental and operating conditions on part damage, and therefore engine maintenance cost and reliability.

Commentary by Dr. Valentin Fuster
2010;():639-648. doi:10.1115/GT2010-22708.

Service lives for critical rotating parts in aero engine gas turbines are declared using deterministic lifing calculations based on fixed point values of key mechanical properties and factors to allow for the scatter. However, novel probabilistic lifing algorithms have been developed, which are able to take into account the degree of scatter in the material properties throughout the component. Process simulation software has been developed to predict the material flow, residual stresses, microstructure and properties in components during the disc forging operations to ensure robust manufacturing routes. This allows the changes in the materials microstructure, and the mechanical property variation throughout the component, to be predicted as the crack initiation and propagation properties are significantly dependent on the grain structure. These two strains of research have been combined in an attempt to increase the reliability of service life predictions through modelling the scatter in the mechanical properties resulting from manufacturing variation. Results will be presented which indicate that significant life benefits can be obtained by adopting a location specific lifing method based on this approach.

Commentary by Dr. Valentin Fuster
2010;():649-658. doi:10.1115/GT2010-22736.

In the design of gas turbine engines, the analysis of nonlinear vibrations of mistuned and frictionally damped blade-disk assembly subjected to random excitation is highly complex. The transitional probability density function (PDF) for the random response of nonlinear systems under white or coloured noise excitation (delta-correlated) is governed by both the forward Fokker-Planck (FP) and backward Kolmogorov equations. This paper presents important improvement and extensions to a computationally efficient higher order, finite difference (FD) technique for the solution of higher dimensional FP equation corresponding to a two degree of freedom nonlinear system representative of vibration of tip shrouded frictionally damped bladed disk assembly subjected to Gaussian white noise excitation. Effects of friction damping on the mean square response of a blade are investigated. The friction coefficient of the damper is assumed to be a function of the sliding velocity of the contact surface. The effects of stiffness and damping mistuning on the forced response of frictionally damped bladed disk are investigated. Numerical studies are presented for a pair of mistuned blades of cyclic assemblies. The response and reliability of a blade subjected to random excitation is also obtained. With time averaged probability density as an invariant measure, the probability of large excursion in case of damping mistuning is also presented. The results of the FD method are validated by comparing with Monte Carlo Simulation (MCS) results.

Commentary by Dr. Valentin Fuster
2010;():659-666. doi:10.1115/GT2010-23007.

This paper reports the results of an investigation focused on identifying the necessary steps required to develop a probabilistic fracture mechanics-based methodology for treating high-cycle fretting fatigue in military engine disks. The current methodology based on finite-element method (FEM) modeling, analytical contact stress analysis, and probabilistic fracture mechanics for analyzing low-cycle fretting fatigue is highlighted first. Incorporation of high-frequency vibratory stress cycles into a composite mission profile containing mostly low-cycle stresses requires the use of the Campbell diagram and the need to identify the mode shape, frequency, and forcing function for blade excitation induced by stator wake, flutter or rotating stall. Forced response computation methods for addressing these phenomena in the literature are reviewed to assess their applicability for integration with a contact stress analysis and a probabilistic fracture mechanics life-prediction code. This overview identifies (1) a promising path for combining vibratory stress computation, FEM structural modeling, contact stress analysis, and probabilistic fracture mechanics for treating high-cycle fretting fatigue at the attachment region of engine disks, and (2) a new approach for treating high-cycle fretting fatigue due to vibratory stresses separately from low-cycle fretting fatigue at various positions of a fan-speed profile.

Commentary by Dr. Valentin Fuster
2010;():667-672. doi:10.1115/GT2010-23099.

An approach has been considered for analysis of forced vibrations for randomly mistuned bladed discs. It is based on stochastic reduced basis method and hypothesis of locally distributed mistuning, which could realise in blade-to-blade joints due to the deviation at the assemblage technology. The method gives an essential possibility to make an analysis using one sector model and allows for this case to use of industrial-size sector models of bladings. The numerical researches of steady-state forced vibrations of randomly mistuned bladed disk of a 3-rd stage low pressure cylinder of a steam turbine have been done.

Topics: Vibration
Commentary by Dr. Valentin Fuster
2010;():673-682. doi:10.1115/GT2010-23569.

An effort has been ongoing to integrate manufacturing process simulations with probabilistic structural analyses in order to capture the important impacts of manufacturing uncertainties on component stress levels and life. A physics-based manufacturing process simulation code has been linked to the NESSUS structural analysis code to analyze annular deformation resistance welding manufacturing process. This paper describes the methodology developed to perform this integration, including an example. Although this effort is underway, particularly for fuller integration of a probabilistic analysis, the progress to date has been encouraging and a software interface that implements the methodology has been developed. The purpose of this paper is to report this development.

Commentary by Dr. Valentin Fuster
2010;():683-693. doi:10.1115/GT2010-23618.

Some rotor-grade gas turbine engine materials may contain multiple types of anomalies such as voids and inclusions that can be introduced during the manufacturing process. The number and size of anomalies can be very different for the various anomaly types, each of which may lead to premature fracture. The probability of failure of a component with multiple anomaly types can be predicted using established system reliability methods provided that the failure probabilities associated with individual anomaly types are known. Unfortunately, these failure probabilities are often difficult to obtain in practice. In this paper, an approach is presented that provides treatment for engine materials with multiple anomalies of multiple types. It is based on previous work that has extended to address the overlap among anomaly type failure modes using the method of Kaplan-Meier, and is illustrated for risk prediction of a nickel-based superalloy. The results can be used to predict the risk of general materials with multiple types of anomalies.

Topics: Gas turbines
Commentary by Dr. Valentin Fuster
2010;():695-703. doi:10.1115/GT2010-23780.

Due to uncertainty in design, manufacturing and operating processes, the initial prediction of a machine’s useful life is often quite different from that of the actual machine. In this paper, we utilize the Bayesian technique to incorporate the field data with the initial predictions in order to improve the prediction. The field data is interpreted in terms of the probability of having defective hardware, and then the likelihood function is generated from the binomial distribution. Since the predictions incorporate field experience, as time progresses and more data becomes available the probabilistic predictions are continuously updated. This results in a continuous increase of confidence and accuracy of the prediction. The resulting distributions can then be used directly in risk analysis, maintenance scheduling, and financial forecasting by both manufacturers and operators of heavy-duty gas turbines. This presents a quantification of the real time risk for direct comparison with the volatility of the power market.

Commentary by Dr. Valentin Fuster
2010;():705-713. doi:10.1115/GT2010-22046.

The results of non linear modeling of mechanical damped behavior of fan bladed disk are presented in the paper. A combined test/modeling strategy dedicated to the prediction of behavior of bladed disk in all operating flight range is proposed. The proposed methodology is applied on 2 configurations: firstly, on a well known fan stage (wide chord titanium blade with curvilinear attachment) and secondly, on a new one based on woven composite technology. This strategy needs to perform efficient and precise modal tests able to measure as well as possible the damping parameters. The test procedure is set up after trying of different test configurations: the robustness/repeatability of measure is verified and the scatter is quantified. A non linear tool (Snecma in-house code) is used to predict the behavior of the test configuration and allows the identification of damping parameters. These damping parameters are then used to assess the dissipative behavior in operating conditions. This tool is based on DLFT method derived from classical harmonic balance method and allows fast calculations of NL responses. The results presented illustrate the quality of tests measurement and the validity of the non linear model used to predict the characterized physics. The calibration is based on the damping parameters updated on a wide test configurations.

Topics: Disks
Commentary by Dr. Valentin Fuster
2010;():715-722. doi:10.1115/GT2010-22048.

This paper presents a method for determination of case load by modeling blade-on-casing incursions using a moving load, finite element based approach. The blade is represented as a load moving at constant speed, imparting both tangential and radial forces to the casing. This approach also forms the basis for future work in the determination of the blade tip forces during such an event. A description of the future work required to use this approach to determine blade tip forces is presented.

Commentary by Dr. Valentin Fuster
2010;():723-728. doi:10.1115/GT2010-22051.

This paper describes a numerical approach to compute the passage through the resonance with one of the natural frequencies and provides analytical proof of this. The numerical approach was used to compute the resonance passage of a turbine blade. The results are compared with complete resonance passages of a simplified multi body model and showed a very good agreement with the test results. In addition some parameter studies, such as structure damping resonance passage time and excitation amplitude, are presented.

Commentary by Dr. Valentin Fuster
2010;():729-737. doi:10.1115/GT2010-22090.

Ceramic coatings applied by air plasma spray or electron beam techniques as thermal barrier coatings or to improve the erosion or corrosion resistance of blades in gas turbine engines are found to add damping to the system. However, such coatings display non-linear mechanical properties in that the Young’s modulus and the measure of damping are dependent on the amplitude of cyclic strain. To account for the coating nonlinearity, a new methodology for predicting blade response was developed and applied to an actual component coated with a titania-alumina blend ceramic infiltrated with a viscoelastic material. Resonant frequencies, mode shapes, and the forced response of a one blade segment of an integrated disk from a fan stage rotor were computed and compared with results from bench tests. Predicted frequencies agreed satisfactorily with measured values; predicted and observed values of system damping agreed to within 10%. The results of these comparisons are taken to indicate that it is possible to use laboratory-determined material properties together with an iterative finite element analysis to obtain satisfactory predictions of the response of an actual blade with a nonlinear coating.

Topics: Coatings , Blades
Commentary by Dr. Valentin Fuster
2010;():739-747. doi:10.1115/GT2010-22093.

Experiments to determine the effects of turbomachinery fan blade damping concepts such as passively shunted piezoelectric materials on blade response are ongoing at the NASA Glenn Research Center. A vertical rotor is suspended and excited with active magnetic bearings (AMBs) usually in a vacuum chamber to eliminate aerodynamic forces. Electromagnetic rotor excitation is superimposed onto rotor PD-controlled support and can be fixed to either a stationary or rotating frame of reference. The rotor speed is controlled with an air turbine system. Blade vibrations are measured using optical probes as part of a Non-Contacting Stress Measurement System (NSMS). Damping is calculated from these measurements. It can be difficult to get accurate damping measurements using this experimental setup and some of the details of how to obtain quality results are seemingly nontrivial. The intent of this paper is to present those details.

Commentary by Dr. Valentin Fuster
2010;():749-756. doi:10.1115/GT2010-22105.

A new mistuning identification method based on the Subset of Nominal Modes (SNM) theory for the integrally bladed disk is presented. In this approach, steady-state responses from experiments are used as input parameters for identification without requiring the knowledge of the applied forces. This makes the input data more reliable and reduces the measurement difficulty. The method is especially suitable for the bladed disk situation in which the high modal density or relatively high damping leads the isolation of normal modes more difficult. The submatrix method enables the definition of mistuning parameters more freely and adds the model modification function to this identification method. The improved identification method introduced in this paper could simultaneously identify both the blade mistuning parameters and tuned natural frequencies to avoid the adverse influences of the errors in tuned natural frequencies and greatly increase the accuracy of identified mistuning. Finally, numerical example of a fan bladed disk is preformed to validate the effectiveness of the proposed identification method.

Topics: Disks
Commentary by Dr. Valentin Fuster
2010;():757-766. doi:10.1115/GT2010-22128.

Forced response analysis of bladed disk assemblies plays a crucial role in rotor blade design, and therefore has been investigated by researchers extensively. However, due to lack of computation power, several studies in the literature utilize either linear mistuned models which are short of capturing nonlinear effects, or non-linear tuned models which do not catch the effects of mistuning. Studying the combined effect of the two, namely non-linearity and mistuning, is relatively recent and generally conducted with methods whose convergence and accuracy depend highly on the number of degrees of freedom related with the non-linear elements. In this paper, a new approach is proposed to predict forced response of frictionally damped mistuned bladed disk assemblies in modal domain. A friction element, which enables normal load variation and separation of the contact interface, is utilized to determine the non-linear contact forces in three-dimensional space, and harmonic balance method is used to obtain a relationship between the non-linear contact forces and the relative motion. As mistuning phenomenon destroys the cyclic symmetry, modeling the whole assembly rather than a sector of it is necessary, which increases the number of non-linear elements required considerably. In the proposed approach, the analysis is carried out in modal domain where the differential equations of motions are converted to a set of non-linear algebraic equations using harmonic balance method and modal superposition technique. Thus, the number of non-linear equations to be solved is proportional to the number of modes retained, rather than the number of degrees of freedom related with the nonlinear elements. Therefore, the proposed approach can be applied to realistic bladed disk models without increasing the number of non-linear equations. Moreover, to accomplish this it is not required to use a reduced order model in the method suggested. Two case studies are presented to illustrate the implementation of the method: a lumped parameter bladed disk model and an academic bladed disk model with shrouds.

Topics: Disks
Commentary by Dr. Valentin Fuster
2010;():767-777. doi:10.1115/GT2010-22146.

To guarantee a faultless operation of a turbine it is necessary to know the dynamic performance of the machine especially during start-up and shut-down. In this paper the vibration behaviour of a low pressure model steam turbine which has been intentionally mistuned is investigated at the resonance point of an eigenfrequency crossing an engine order. Strain gauge measurements as well as tip timing analysis have been used, whereby a very good agreement is found between the methods. To enhance the interpretation of the data measured, an analytical mass-spring-model, which incorporates degrees of freedom for the blades as well as for the rotor shaft, is presented. The vibration amplitude varies strongly from blade to blade. This is caused by the mistuning parameters and the coupling through the rotor shaft. This circumferential blade amplitude distribution is investigated at different operating conditions. The results show an increasing aerodynamic coupling with increasing fluid density, which becomes visible in a changing circumferential blade amplitude distribution. Furthermore the blade amplitudes rise non-linearly with increasing flow velocity, while the amplitude distribution is almost independent. Additionally, the mechanical and aerodynamic damping parameters are calculated by means of a non-linear regression method. Based on measurements at different density conditions, it is possible to extrapolate the damping parameters down to vacuum conditions, where aerodynamic damping is absent. Hence the material damping parameter can be determined.

Topics: Pressure , Turbines
Commentary by Dr. Valentin Fuster
2010;():779-789. doi:10.1115/GT2010-22166.

The turbomachinery industry continually struggles with the adverse effects of contact rubs between airfoils and casings. The key parameter controlling the severity of a given rub event is the contact load produced when the airfoil tips incur into the casing. These highly non-linear and transient forces are difficult to calculate and their effects on the static and rotating components are not well understood. To help provide this insight, experimental and analytical capabilities have been established and exercised through an alliance between GE Aviation and The Ohio State University Gas Turbine Laboratory. One of the early findings of the program is the influence of blade flexibility on the physics of rub events. The focus of this paper is to quantify the influence of airfoil flexibility through a novel modeling approach that is based on the relationship between applied force duration and maximum tip deflection. Results from the model are compared to experimental results, providing sound verification.

Topics: Deflection , Airfoils
Commentary by Dr. Valentin Fuster
2010;():791-798. doi:10.1115/GT2010-22202.

This paper presents a simple analysis method for predicting vibration response characteristics of a bladed disk with continuous ring type structure losing a shroud or a shroud and a stab between two blades. This loss introduces a mistuning of the system and the whole bladed disk model must be used to conduct the study. However, the vibration modes change regularly from a sine and a cosine mode, if the bladed disk consists of many blades. By utilizing this phenomenon, the simple formulation of vibration response of a bladed disk can be derived. Second, the parametric study on the vibration response characteristics of a bladed disk losing a shroud or a shroud and a stab is carried out extensively, utilizing the analysis method proposed here. From the calculated results, the vibration response characteristics of a bladed disk are clarified for both of resonant vibration and random vibration. Lastly, the results calculated by the simple analysis method proposed are compared with the results obtained from FEA (Finite Element Analysis) in order to verify the validity of the analysis method.

Topics: Vibration , Disks
Commentary by Dr. Valentin Fuster
2010;():799-807. doi:10.1115/GT2010-22216.

This work develops a time domain coupled fluid-structure computational model that predicts dynamic blade stresses in a rotating centrifugal compressor. Although, much research has been performed on axial flow turbomachinery, little has been published for radial machines such as centrifugal compressors and radial inflow turbines. This research develops a time domain coupled fluid-structure computational model using commercially available codes. The model couples the codes unidirectionally, where pressures are transferred to the structural code during the transient solution, and the fluid mesh remains unaffected by the structural displacements. Models are developed for the compressor at blade resonant conditions. The model is then validated with a rotating test of a centrifugal compressor instrumented with blade mounted strain gauges. The test rig is an open loop rig that utilizes an unshrouded centrifugal compressor with a vaneless diffuser. The strain gauge signals are passed through a high gain, low noise amplifier that is mounted on the compressor rotor. This work not only develops a unidirectionally coupled fluid-structure model capable of predicting dynamic strains, but also provides valuable experimental data that can be used for future research and validation cases of fluid-structure interaction (FSI) models.

Commentary by Dr. Valentin Fuster
2010;():809-817. doi:10.1115/GT2010-22292.

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.

Topics: Friction , Damping , Blades
Commentary by Dr. Valentin Fuster
2010;():819-826. doi:10.1115/GT2010-22353.

To enhance the Steam Turbine product line rotating speed and efficiency, GE Company has developed a new generation of high rotating speed Steam Turbine Low Pressure (LP) Sections named HS family (see also Cosi at al., [1.]). The master component of the family, and its smallest size, is the 4-stage LP section HS8, capable of variable speed operation up to 11250 rpm. The aeromechanical validation of HS8 was carried out in two steps: a full-scale rotating test in a vacuum chamber (so called wheel Box Test, WBT) and a full-size test vehicle campaign in steam (Low Pressure Development Turbine, LPDT). During both tests the 4-stage rotors were equipped with a reliable system of strain gages and thermocouples. Aim of the present paper is to present an overview of the experimental results and post-processed data from both tests. Measured blades modes frequencies, responses and quality factors from both WBT and LPDT are described and compared, and the behavior of these parameters at different mass-flows and backpressures is explored. Then, interesting results from the comparison of damping (or Q factors), in WBT and LPDT test are presented. Finally, a methodology for nodal diameter configuration identification is described. To the best of authors’ knowledge the present paper is the deepest investigation about damping in WBT and prototypical test for steam turbine last stage blades.

Commentary by Dr. Valentin Fuster
2010;():827-835. doi:10.1115/GT2010-22385.

A discrete microslip friction contact model, which can consider time-dependent/space-related normal load, has been established to investigate the contact kinematics in the contact interfaces between adjacent blade shrouds. The model extends the capability of Csaba’s model in dealing with the situation of variant normal load. A Fast Anti-alias Fourier transform (FAFT) is introduced to the alternating frequency/time domain method (AFT) to improve the accuracy of spectrum analysis and extend analysis spectrum range. The developed friction model and the modified AFT are applied to calculate nonlinear vibration for a simplified shrouded blade, and the effect of parameters on resonant frequency and amplitude of shrouded blade are investigated and discussed. Comparing with existing variable normal load macroslip model, the model proposed here has the mathematically tractable characteristic and can be easily used. Combining with the AFT method, it is suitable for the analysis of complex system with multiple variables and degrees of freedom, and it can meet the engineering need.

Topics: Stress , Blades
Commentary by Dr. Valentin Fuster
2010;():837-843. doi:10.1115/GT2010-22386.

The damping characteristics of blade with loosely assembled dovetail attachment are investigated experimentally. An experimental method and a test rig were presented to study the blade damping characteristics. In the measurement system, an external force is imposed on blade, to simulate the centrifugal force of blade. The dynamic responses of a group of simulation blades with different dovetail attachment angles were measured in consideration of variable simulation centrifugal force. The damping characteristics of a compressor blade with dovetail attachment were measured too. Some conclusions can be drawn from the experimental results. The resonant frequency increases with the centrifugal force, gradually reaches a certain value. The amplitude of resonant response decreases at the beginning and then increases with the centrifugal force increasing, there exists a special centrifugal force on which the effect of dry friction damping is the best. The change rate of the blade response in the range of neighboring optimal centrifugal force is obviously influenced by the dovetail angle. From the results of the last stage blade of compressor, we can find that the resonant amplitude retains a low level when the centrifugal force is from 1.5kN to 4kN.

Topics: Damping , Blades
Commentary by Dr. Valentin Fuster
2010;():845-854. doi:10.1115/GT2010-22388.

The study intends to simulate the process of the blade tip amplitude calculation by the tip-timing method. An attention is focused on tip-timing measurements for detection of a cracked blade from the bladed disk forced response. The cracked blade is considered within frameworks of the bladed disk dynamic model that takes into account mistuning presence. Nonlinear formulation of a crack behavior is done with the harmonic balance method in its combination with the contact analysis that allows simulation of crack breathing. In order to make the cracked blade detection process evident, the crack length and location are set in such a way as to produce the cracked blade frequency localization. Reconstruction of the blade tip amplitudes is attained with the arriving time of measured probes of the blade tips. The results are compared with the blade forced response obtained by the bladed disk dynamic model. A possibility is also considered how to reconstruct time-history of the bladed disk forced response with tip-timing data.

Commentary by Dr. Valentin Fuster
2010;():855-864. doi:10.1115/GT2010-22447.

Determination of the amplification factor due to mistuning is an important task for the safe design of turbomachinery, specially for blisk-design with low mechanical damping. The complexity of the environment effects increases from measurements in the laboratory to measurements in test rigs and engines. Also the uncertainties of the boundary conditions increase. In this paper measurements of the amplification factors due to mistuning at various conditions are presented, starting from simple lab measurements up to rig measurements. Calculations with a Reduced-Order Code based on measured frequency distributions and FEM are performed and compared with the measurements. For the determination of the amplification factor a mistuning rig with travelling wave excitation was built. For a small demo-blisk the amplification factor was determined. Then a real blisk was tested. Afterward, the same blisk was built into a two-stage axial compressor rig. Here, tip-timing measurements were performed under rig conditions (centrifugal force, flow conditions). As tip-timing measures the vibration amplitude of each single airfoil, an amplification factor can be determined for each resonance.

Commentary by Dr. Valentin Fuster
2010;():865-877. doi:10.1115/GT2010-22463.

The motivation for the usage and a further development of blade integrated disk (blisk) technology is driven by a rising demand for efficient, economical and environment-friendly aero engines. In contrast to conventional bladed disks with separated blade and disk design, blisks are either manufactured from solid or disk and blades are assembled by friction welding. Due to an optimized stress distribution, the integrated design leads to potentially higher maximum rotational speeds of the HP-shaft and thus to an improved pressure ratio. This fact offers the opportunity to reduce the number of blades or even to save whole compressor stages. In order that a significant mass-reduction is achieved, which is increased since heavy blade-disk connections of the conventional design are not necessary anymore. Apart from the advantages of the integrated design, the vibration behaviour of a real blisk is more sophisticated compared to the conventional bladed disk design. Due to the very low mechanical damping, effects like mode-localization and amplitude magnification can lead to high cycle fatigue problems of such complex structures. Extensive experimental and numerical investigations are carried out considering a real rotor-stage 1 blisk of the Rolls-Royce E3E/1 demonstrator-HPC. In order to identify “blade individual frequencies” and “blade individual damping”- values, a new patented blade by blade measurement method is used, that provides FRFs characterized by an unique resonance, as known from SDOF-systems. Based on the adjusted FE-model, numerical and experimental investigations of the vibration behaviour in the frequency range of splitted double eigenvalues are carried out. In doing so the expressions “travelling wave” and “standing waves” are commonly used to characterize the eigenmodes and forced modes of vibration respectively. The splitting of eigenvalues could be proved and a novel criterion to distinguish travelling and standing waves is introduced.

Topics: Waves
Commentary by Dr. Valentin Fuster
2010;():879-887. doi:10.1115/GT2010-22479.

Can-annular combustion systems for gas turbines are complex assemblies of relatively thin components made of heat resistant alloys or superalloys. The thermal environment requires minimal structural constraints in order to accommodate deformation due to thermal growth and expansion. As a result, the systems have the potential to be rich in modes within the range of combustion dynamic frequencies. The natural frequencies of the system are extremely sensitive to variations in contact, damping and thickness. Combustion dynamic frequencies vary, to some extent, from can-to-can and engine-to-engine. Frequencies can also change with ambient conditions, engine load and emissions tuning. Tuning the design to avoid resonant frequencies can be extremely difficult or impractical. A method for determining which modes are likely to be responsive to combustion drivers, for obtaining approximate response magnitudes, for identifying limiting locations, and for comparing two design concepts, would be a great aid to combustion system designers. An analytical technique is proposed for scaling modal stresses. This technique, hereafter referred to as modal stress efficiency scaling (or the acronym MOSES), includes the effect of the efficiency with which a traveling sine wave couples with structural modes of differing wavelengths. Excitation is assumed to come from stationary waves impacting exposed surfaces simultaneously as well as waves traveling in all 3 orthogonal directions. Excitation due to base motion in 3 axis is also considered. In order to quickly evaluate multiple sources of excitation, this technique assumes the driver is at resonance. It is assumed that the modes are widely spaced so no modal superposition is considered. As a result of these simplifications, the response is simple rather than complex. No phase relationships are calculated. The result is the mode shape scaled by the calculated efficiency factor. The method was applied to a combustion system component with a history of cracking, and a low emissions redesign expected to eliminate the problem. The technique identified modes most likely to be excited, and predicted substantially lower responses and stresses in the new design. Results were validated through instrumented engine testing conducted with multiple accelerometers and pressure transducers on engines with each design. Acceleration measurements from these tests confirmed MOSES’s identification of the harmful response and demonstrated the robustness of the redesigned component. The MOSES technique is demonstrated to be a useful tool for root cause analysis as well as for design of combustion hardware.

Commentary by Dr. Valentin Fuster
2010;():889-898. doi:10.1115/GT2010-22498.

The Asymptotic Mistuning Model (AMM) is a recently introduced simplified method for the analysis of mistuning effects in the vibration characteristics of bladed disks. It is derived directly from the full mistuned bladed disk using an asymptotic expansion that exploits the smallness of the mistuning and the damping. The results from the AMM have been previously successfully verified using a simple 1-D mass-spring model. In this paper we validate the accuracy of AMM for the prediction of the effect of mistuning in realistic configurations. To this end, we perform a quantitative comparison between the AMM results and those from a detailed finite element method (FEM) numerical simulation of a complete mistuned bladed disk, for several mistuning patterns and forcing conditions. We also emphasize and comment the useful information provided by the AMM about the essential mechanisms involved in the mistuning effects on the vibration of cyclic structures.

Topics: Disks
Commentary by Dr. Valentin Fuster
2010;():899-904. doi:10.1115/GT2010-22526.

To reduce the vibration levels in a complex structure, the designer often needs to know how the vibrations in one part of a structure are transmitted to other parts at each interface of the connected components. A lumped-mass method and component mode synthesis is used to evaluate the power flow for vibrations in low-frequency range. The model mass and stiffness matrices are portioned into substructures separated by the interfaces whose power flow should be evaluated. The vibration modes of the substructure are divided into constrained and fixed interface modes corresponding to the interface and interior degree of freedoms, respectively. The effective interface mass criterion is used to rank the most dynamic important modes at each interface. The most important modes are preserved in a reduced model for computing the power flow. A numerical example of a linear system is used to illustrate the application of the new technique.

Commentary by Dr. Valentin Fuster
2010;():905-915. doi:10.1115/GT2010-22619.

To meet the highest compressor efficiency and resonance free operation, the design process of a modern compressor blade requires several iterations between the aerodynamic and mechanical integrity disciplines. The 1D beam theories, usually used in the concept design process, do not consider the local flexibility of a flat, tapered and twisted geometry of an axial compressor airfoil. Therefore, chord-wise bending resonances of the compressor blade, excited by flow field upstream and downstream, cannot be predicated in a reliable manner. In the paper, firstly the sensitivity of compressor blade vibrations is analysed in terms of airfoil design parameters, rotor coupling effects, and mistuning phenomena. Owing to high bending stiffness of a welded shaft, a numerical CWB tool is developed mainly for reliable predictions of chord-wise bending resonances of the compressor blade in the design process. Finally, the tool reliability is demonstrated by a good agreement of the numerical and experimental resonance frequencies, which have been measured with the tip-timing system at the front stage of the axial compressor in the field. Regarding the measured compressor bladed disc, the numerical sensitive study is carried out to determine an impact of contact uncertainties in the blade root on the computed resonance frequencies. The paper shows how physical uncertainties of the root contact and airfoil mistuning are involved in practical manner into the design process of compressor blades. In the design process, the presented CWB tool allows for fast and reliable mitigation of chord-wise bending resonances, which requires the collective solution between the aerodynamics and mechanical integrity disciplines, as it is illustrated in this paper.

Commentary by Dr. Valentin Fuster
2010;():917-929. doi:10.1115/GT2010-22681.

This work is devoted to the study of non linear dynamics of structures with cyclic symmetry under geometrical nonlinearity using the harmonic balance method (HBM). In order to study the influence of the non-linearity due to large deflection of blades a simplified model has been developed. It leads to nonlinear differential equations of the second order, linearly coupled, in which the nonlinearity appears by cubic terms. Periodic solutions in both free and forced cases are sought by the HBM coupled with an arc length continuation and stability analysis. In this study, a specific attention has been paid to the evaluation of nonlinear modes and to the influence of excitation on dynamic responses. Indeed, several cases of excitation have been analyzed: punctual one and tuned or detuned low engine order. The paper shows that for a localized, or sufficiently detuned, excitation, several solutions can coexist, some of them being represented by closed curves in the Frequency-Amplitude domain. Those different kinds of solution meet up when increasing the force amplitude, leading to forced nonlinear localization. As the closed curves are not tied with the basic nonlinear solution they are easily missed. They were calculated using a sequential continuation with the force amplitude as a parameter.

Commentary by Dr. Valentin Fuster
2010;():931-937. doi:10.1115/GT2010-22698.

Stator vanes which are found at different stages in axial compressors are subject to major aerodynamic load fluctuations, due to cyclic excitations induced by the wakes of the rotors located upstream and also due to the pressure waves generated by the blade rows located downstream. In a vibratory fatigue context, it is important to ensure the structural strength of these stator vanes. A new technology of monoblock sectorised stator vanes has been developed to provide an easier manufacturing process and lower costs; in return, cyclic symmetry properties, which make the prediction studies easier, are lost in this case. Besides, these kinds of monoblock sectors are characterized by low damping which increases the criticality of the blade modes localization. The division into sectors of stator vanes creates a high density of eigenmodes in some short frequency ranges; this phenomenon is accompanied by non-negligible modal participations of neighbouring eigenmodes. Moreover, stator vanes sectors have shown a strong sensitivity to mistuning, making their vibratory behaviour prediction more difficult by means of deterministic prediction methods. In this paper, a phenomenological approach is followed to quantify the mistuning. Thus, several sensitivity to mistuning numerical studies were performed. They allowed to have first results about the relative predictable errors that could be done, depending on the mistuning. Some engine tests were also performed with gauges-equipped stator vanes sectors.

Topics: Stators
Commentary by Dr. Valentin Fuster
2010;():939-948. doi:10.1115/GT2010-22725.

An algorithm to generate a reduced order model of a multi-stage rotor in which each stage has a different number of blades has been developed. It is shown that a reduced order model can be developed on the basis of tuned modes of certain bladed disks which can be easily obtained via sector analyses. Further, it is shown that reduced order model can also be obtained when blades are geometrically mistuned. This algorithm is similar to the modified modal domain analysis, which has been recently developed for a single-stage bladed rotor with geometric mistuning. The validity of this algorithm is shown for the finite element model of a two-stage bladed rotor. In addition, the statistical distributions of peak maximum amplitudes and natural frequencies of a two-stage rotor are generated via Monte Carlo simulations for different patterns of geometric mistuning.

Commentary by Dr. Valentin Fuster
2010;():949-957. doi:10.1115/GT2010-22786.

Gas turbines incorporate throughout the engine many labyrinth air seals, which can suffer vibration excitation from a number of potential sources. This paper presents an analytical study of an example design of seal, for which vibration test data were available. Understanding of the observed vibration displacements was gained from (i) an investigation of the forcing excitation mechanism and (ii) non-linear vibration analysis of the seal structure, including estimates of work extracted by frictional contacts (mechanical damping). This paper presents only the mechanical damping analysis as an example of an industrial application of advanced multi-harmonic balance non-linear vibration techniques. The paper includes an overview of the non-linear model construction, including sensitivity studies in model reduction and contact element parameter choices. Once established, it is shown how the vibration model is used to assess the performance of a ring damper for the labyrinth seal in relation to the background mechanical damping provided by contact with adjacent components. The damping is a function of both friction coefficient and displacement amplitude and it is shown how the robustness of the damper design relates to friction assumptions.

Topics: Damping
Commentary by Dr. Valentin Fuster
2010;():959-969. doi:10.1115/GT2010-22801.

The integration of squeeze-film dampers (SFDs) in aero-engine assemblies is a highly cost-effective means of introducing damping in an otherwise lightly damped structure. However, their deployment requires careful unbalance response calculations that take due account of the SFDs’ nonlinearity, particularly when they are unsupported by a centralising spring. Until recently, such calculations were prohibitive due to the large number of assembly modes that typically need to be considered. This problem has been overcome by the authors through the novel Impulsive Receptance Method (IRM) and the Receptance Harmonic Balance Method (RHBM), which efficiently solve the nonlinear problem in the time and frequency domains respectively. These methods have been illustrated on a realistic twin-spool engine and have been shown to be effective for both single frequency unbalance (SFU) excitation (unbalance on a single rotor) and multi-frequency unbalance (MFU) excitation (unbalance on both rotors). In the present paper, the methods are applied to a realistic three-spool engine and the aims are two fold: i) to present some preliminary results of a parametric study into a three-spool aero-engine assembly; ii) to propose a technique that makes use of both IRM and RHBM in producing the speed responses under MFU excitation (from all three rotors), with a realistic speed relation between the rotors. The latter technique is necessary since the speed ratio will vary along a realistic speed characteristic and the authors have previously solved the twin-spool MFU problem under a constant speed ratio condition. The approach used here is to approximate the speed characteristic by one in which the speed ratios are ratios of low integers, enabling the use of RHBM to finish off (to steady state) time-transient solutions obtained through IRM. The parameter study shows that the application of simple bump-spring supports to selected, otherwise unsupported, SFDs, along with slight sealing, should have a beneficial effect on the dynamic response of aero-engines with heavy rotors.

Commentary by Dr. Valentin Fuster
2010;():971-980. doi:10.1115/GT2010-22879.

The paper presents a static test rig called “Octopus” designed for the validation of numerical models aimed at calculating the nonlinear dynamic response of a bladed disk with underplatform dampers (UPDs). The test rig supports a bladed disk on a fixture and each UPD is pressed against the blade platforms by wires pulled by dead weights. Both excitation system and response measurement system are noncontacting. The paper features the design and the set-up of the noncontacting excitation generated by electromagnets placed under each blade. A travelling wave excitation is generated according to a desired engine order by shifting the phase of the harmonic force of one electromagnet with respect to the contiguous exciters. Since the friction phenomenon generated by UPDs introduces nonlinearities on the forced response, the amplitude of the exciting force must be kept constant at a known value on every blade during step-sine test to calculate Frequency Response Functions. The issue of the force control is therefore addressed since the performance of the electromagnet changes with frequency. The system calibration procedure and the estimated errors on the generated force are also presented. Examples of experimental tests that can be performed on a dummy integral bladed disk (blisk) mounted on the rig are described in the end.

Topics: Waves , Dampers , Disks
Commentary by Dr. Valentin Fuster
2010;():981-994. doi:10.1115/GT2010-23062.

This paper focuses on the determination of the maximum amplification of blade response due to mistuning in multi stage assemblies. The modal optimization strategy developed earlier in connection with single stage models is extended here to multi stage configurations. Theoretical developments are carried out first and lead to the new upper limit of (1 + N1 + N2 (g2/g1) + [[ellipsis]])/2, where Ni are the number of blades on the stages and gi = F i T Mi −1 F i with F i the force vector applied on a sector of stage i and Mi its mass matrix. For identical stages, this maximum equals the Whitehead limit observed with single stages but with the number of blades equal to sum of the numbers of blades of the coupled stages. A computational validation of the theoretical results is achieved next on both a single degree of freedom per blade model and a reduced order model of a blisk. These numerical optimization efforts confirm the theoretical developments and demonstrate that such high amplification factors can indeed be achieved with small levels of mistuning. The effects of the number of blades on the different stages, damping in the system, stage coupling strength, etc are discussed in details.

Topics: Blades
Commentary by Dr. Valentin Fuster
2010;():995-1001. doi:10.1115/GT2010-23148.

Avoiding the low-order resonances of blades is one of the main design goals for a mechanical structure designer of turbo machinery. However, we have to accept that there are resonance frequencies in the operating speed range of the blade, for the following reasons: Firstly, the natural frequencies of the blade are closely spaced sometimes, it is impossible to avoid them all. Secondly, in general, the higher of the resonance frequency, the lower the energy of resonance will be. But in recent 10 years, the high-order blade resonances present more and more frequently in turbo machinery, which induce a lot of HCF problems. As the considerations above, studies on the high-order vibration of blades become necessary and important. In the cascade, the high-order vibration of blades is mainly induced by the wakes from upstream. An obvious difference of the wake excitation from the common excitations resides in its asynchronism, that is, the maximum value of aerodynamic force from wakes at each point doesn’t appear at the same time, because except the frequency, the distribution of the aerodynamic force field depends on two parameters: not only amplitude but also phase angle. Both are functions of coordinates. In this paper, the related position in Euclidean Space between the asynchronous excitation field and the modal displacement of blade were deal with to evaluate the strength of the high-order resonance of blade. The effect of the asynchronous aerodynamic force field on the blade resonance was studied either. Finally a method for evaluation of high-order resonance of blade excited by wake fluid is proposed. A numerical case was studied either, which demonstrates that the proposed evaluation on high-order resonance is practical in engineering problem.

Topics: Resonance , Wakes , Blades
Commentary by Dr. Valentin Fuster
2010;():1003-1013. doi:10.1115/GT2010-23264.

Assembled bladed disks have many contact interfaces (blade-disk joint, blade shrouds, friction damper, etc). Because of relative displacements at these interfaces, fretting-wear can occur, which shortens the life expectancy of the structure. Moreover, vibrations that occur in bladed-disks can increase this fretting-wear phenomenon. Two previous papers in Turboexpo have introduced a numerical method based on the Dynamical Lagrangian Frequency Time algorithm (DLFT) to calculate worn geometry, especially wear of bladed-disks’ dovetail roots. Numerical investigations have illustrated the performances of this method and shown the coupling between dynamical and tribological phenomena. The basic idea of the DLFT-with-wear method is to separate time in two scales, slow scale for tribological phenomena and fast scale for dynamics. In the present paper, implicit and explicit integration schemes on the slow time scale are compared. An ad hoc prediction-correction method is used in both methods to accelerate the convergence of the non-linear solver. Numerical experiments on bladed-disk show that the implicit scheme is more appropriate to deal with fretting-wear under dynamical loading.

Commentary by Dr. Valentin Fuster
2010;():1015-1024. doi:10.1115/GT2010-23274.

The modelling of friction contact interfaces in structural dynamics attracts much interest in the gas turbine industry. In order to obtain reliable predictions of typical friction interfaces, such as encountered in under platform dampers or blade roots, accurate characteristics of friction interfaces must be provided to the analysis. It must be ensured that a sufficient number of parameters are provided, characterising all aspects of the friction contact, that the values are measured accurately, and that the contact parameters are interpreted and used correctly in the numerical modelling of the contact interfaces. This investigation demonstrates that measured friction coefficient and tangential contact stiffness are sufficient to reproduce the experimental friction interface behaviour and that these two parameters can be measured reliably in the available test rig. In combination with fine nonlinear interface meshes and accurate contact pressure representations, the measured interface behaviour of stick, micro- and macroslip is reproduced with good accuracy. The capability of modelling the microslip behaviour for the contact interface by a multitude of friction contact elements is explored and the effect of the normal stress distribution over the contact area on the microslip is studied.

Commentary by Dr. Valentin Fuster
2010;():1025-1037. doi:10.1115/GT2010-23295.

A highly accurate and computationally efficient method is proposed for reduced modelling of jointed structures in frequency domain analysis of nonlinear steady-state forced response. The method has significant advantages compared with the popular variety of mode synthesis methods or forced response matrix methods and can be easily implemented in the nonlinear forced response analysis using standard finite element codes. The superior qualities of the new method are demonstrated on a set of major problems of nonlinear forced response analysis of bladed discs with contact interfaces: (i) at blade roots; (ii) between interlock shrouds, and (iii) at under platform dampers. The numerical properties of the method are thoroughly studied on a number of special test cases.

Commentary by Dr. Valentin Fuster
2010;():1039-1051. doi:10.1115/GT2010-23299.

The newly-revealed phenomenon of reduction of forced response levels in a mistuned bladed disc to levels significantly (e.g. by a factor of two and more) lower than that of its tuned counterpart is studied in detail on an example of a realistic bladed disc. Statistical properties of the amplification factor of the mistuned forced response calculated with aero-effects included have been studied for cases of random blade mistuning and for mistuned blade rearrangements. Optimization search for the best mistuning patterns providing maximum forced response reduction effect have been performed, and the robustness of the optimum mistuning patterns has been demonstrated. The combined effect of the aerodynamic and structural damping on the response reduction is assessed. It is shown that the new phenomenon is of major practical significance and has to be taken into account in analysis of the forced response and design decisions.

Topics: Disks
Commentary by Dr. Valentin Fuster
2010;():1053-1061. doi:10.1115/GT2010-23351.

Repeating structures in the form of multiple-bladed rotors are used widely in turbomachinery. Damage to blades can have significant consequences but can be difficult to identify in normal operation. This paper introduces an approach for identifying small defects such as cracks in a repeating structure that may be applicable to the limited data obtainable from developing techniques such as blade tip-timing. In order to understand the key issues involved, this initial work involves a numerical study of a simple comb-like repeating structure rather than a bladed rotor. Changes to the system modeshapes and mode order arising from damage are related to the location and severity of damage. Damage, in the form of small, open cracks, is modelled using different techniques such as material removal, periodic reduction in modulus of elasticity of selected elements at the required location and mass modification. Damage indices based on differences in the Modal Assurance Criterion (MAC) that give a measure of the change in the modeshapes are introduced. MAC matrices are obtained using a reduced number of data points. The damage index is obtained from the Frobenius norm of MAC matrix subtracted from (1) the AutoMAC of reference model without crack and (2) the identity matrix. A clear correlation between the damage indices and crack depth / location is shown. In order to account for mistuning in real repeating structures, the performance when the assembly is subjected to inhomogeneous temperature distributions is also considered.

Commentary by Dr. Valentin Fuster
2010;():1063-1071. doi:10.1115/GT2010-23413.

A test campaign with the purpose of demonstrating new technologies introduced in the Vinci engine was performed in 2008. One of these new technologies is the blisk technology included in the LH2 fuel and LOX oxidizer pump turbines, for which Volvo Aero Corporation has the design responsibility. A challenge with blisks in rotating machinery is the risk of large amplitude vibrations due to low damping. To address the mechanical integrity of the Vinci LH2 turbine rotor blisk with respect to vibrations, an advanced blade vibration measurement system using the blade tip timing method was designed and implemented in close cooperation with the subcontractor AGILIS. The implementation of tip timing for measuring the blade vibrations of the Vinci LH2 blisk was recognized as a challenging application for this kind of measurement system. The conditions in the LH2 turbine are harsh with temperatures down to about 80 K with high pressure and hydrogen environment. Nevertheless, these challenges were systematically investigated rendering a successful implementation. The detailed analysis of the tip timing test data provided unique information for validation. More resonances than expected were confirmed. The responses, however, were modest rendering a low risk for HCF in the test. The most severe resonance in the test with respect to HCF was excited by the second stator harmonics. It was excited several times in the test campaign at about 69200 rpm. This resonance was also pointed out in the design process as being the worst one with respect to HCF. Hence, even though the test data revealed more resonances than expected, the most critical one was identified by the VAC design tool prior to the test. The agreement in predictions and test results for the critical mode was very good with respect to both frequency and response. This statement of very good agreement also applies to the frequencies associated with the other resonances in the test.

Commentary by Dr. Valentin Fuster
2010;():1073-1086. doi:10.1115/GT2010-23466.

Friction damping is one of the most exploited systems of passive control of vibration of mechanical systems. A common type of blade-to-blade friction dampers are the so-called underplatform dampers (UPDs); they are metal devices placed under the blade platforms and held in contact with them by the centrifugal force acting during rotation. The effectiveness of underplatform dampers to dissipate energy by friction and reduce vibration amplitude depend mostly on the damper geometry and material and on the static pre-loads pressing the damper against the blade platforms. The common procedure used to estimate the static pre-loads acting on underplatform dampers consists in decoupling the static and the dynamic balance of the damper. A preliminary static analysis of the contact is performed in order to compute the static pressure distribution over the damper/blade interfaces, assuming that it does not change when vibration occurs. In this paper a coupled approach is proposed. The static and the dynamic displacements of blade and underplatform damper are coupled together during the forced response calculation. Both the primary structure (the bladed disk) and the secondary structure (the damper) are modelled by finite elements and linked together by contact elements, allowing for stick, slip and lift off states, placed between each pair of contact nodes, by using a refined version of the state-of-the-art friction contact model. In order to model accurately the blade/damper contact with a large number of contact nodes without increasing proportionally the size of the set of non-linear equations to be solved, damper and blade dynamics are modelled by linear superposition of a truncated series of normal modes. The proposed method is applied to a bladed disk under cyclic symmetric boundary conditions in order to show the capabilities of the method compared to the classical decoupled approaches.

Commentary by Dr. Valentin Fuster
2010;():1087-1095. doi:10.1115/GT2010-23528.

This paper considers a rotating gas turbine engine disk. The governing equations lead to a non-linear, second order equation with thickness h as parameter. “Thin disk” assumption is made, implying plane stress conditions. In the present study, starting from the equations of equilibrium and compatibility, the author proposes the new approach of Pseudo Material Density. By introducing a pseudo material density, the problem is reduced to the Flat Disk Equation that can be solved easily. Introduction of pseudo density, however, throws up an additional equation — a fourth one — relating the pseudo density, actual density and the thickness parameter. The equation is solved to find the shape of the disk in terms of the actual density. This procedure allows modeling of the non-uniform profile disk as a disk with flat profile facilitating easier analysis. An unexpected, but important result that emerges from the present study pertains to the proof testing of rotating disks. It is shown that it is now possible to replace the external blade loading exactly with a radial extension of the disk itself.

Topics: Density , Gas turbines , Disks
Commentary by Dr. Valentin Fuster
2010;():1097-1102. doi:10.1115/GT2010-23531.

A novel method to determine the exact time period of oscillations of a class of non-linear systems is presented. Taking the bifilar pendulum as an example, and employing the conservation of total energy concept, the free oscillations of the system is studied. The governing equation of motion of a bifilar pendulum is non-linear. The integration of this equation to obtain the time period of oscillation is highly complicated and only numerical solution is available. This is because the integral is singular at the extremities of the motion where the velocity will be zero. But, what cannot be achieved by integral calculus can be obtained easily by employing the definition of velocity taught in the high school curriculum. By employing this simple mathematical trick, this intractable equation is recast in a different but exact form. This leads to the identification of what is called the “Geometric Inertia” in bifilar pendulums. This Geometric Inertia is the additional inertia displayed by the system due to the constraint imposed by the two filaments as a result of the geometry of the pendulum. In the proposed method, the total displacement of the system is considered and divided into small equal segments. At the end points of each such segment, the corresponding velocity is calculated from the energy equation. Noting that the velocities are zero at the extremities of the system, an average velocity to each segment is calculated, and this average velocity is positive in each segment. The “delta” time spent by the system in each segment is now calculated by dividing the segment length by the average velocity of that segment. (From, time = displacement/velocity). The linear sum of such “delta” times gives the time period of oscillation. As the number of segments is increased, thereby reducing the segment length, the estimate becomes increasingly accurate. The proposed approach avoids a direct integration of complex, and often singular expressions that complicate the determination of time periods of oscillations of non-linear systems.

Commentary by Dr. Valentin Fuster
2010;():1103-1116. doi:10.1115/GT2010-23610.

An experimental setup is described which permits to rotate a bladed disk in vacuum and to measure its dynamic response to excitations provided by some embedded piezoelectric actuators. A particular spatial placement of actuators associated with phase-shifting electronic circuits is set for simulating travelling wave excitations with respect to the rotating frame. The system is demonstrated on an actual high-pressure compressor (HCP) integrally bladed disk. The dynamic response of the blisk is analyzed experimentally and results are correlated with those obtained from a simplified finite elements model taking into account Coriolis effect. The paper focuses on the influence of the latter which is most of the time neglected and its implication on the forced response levels is studied into two situations without or with mistuning.

Topics: Disks
Commentary by Dr. Valentin Fuster
2010;():1117-1126. doi:10.1115/GT2010-23649.

Waste heat recovery cycles equipped with radial inflow turbines (turbo-expanders) typically dictate large pressure ratios per stage in order to increase the overall cycle efficiency. Depending on the operating conditions, supersonic flow may be reached at some location within the stage. The design of turbo-machinery in such an environment poses several challenges, the most important of which are preventing performance deterioration and High Cycle Fatigue (HCF) failure of the rotating, stressed material by avoiding resonance frequencies in the operating range. Turbo-expander wheels, being uncooled components, are generally not affected by high temperature gradients; therefore LCF (Low Cycle Fatigue) doesn’t constitute their main limiting life factor. This paper describes the process used in GE Oil & Gas to design and optimize the wheels of a 17MW double supersonic stage turbo-expander. The initial design phases, preliminary design assessments, CFD analyses and structural analysis optimization are described. Special focus is given to the modal analysis and resonance identification (i.e., Modal Cyclic Analysis) used in the design phase. A critical review of the use of the SAFE interference diagram in place of the Campbell diagram is also provided.

Commentary by Dr. Valentin Fuster
2010;():1127-1134. doi:10.1115/GT2010-23703.

In this paper, the effect of geometrical nonlinear terms, caused by a space fixed point force, on the frequencies of oscillations of a rotating disk with clamped-free boundary conditions is investigated. The nonlinear geometrical equations of motion are based on Von Karman plate theory. Using the eigenfunctions of a stationary disk as approximating functions in Galerkin’s method, the equations of motion are transformed into a set of coupled nonlinear Ordinary Differential Equations (ODEs). These equations are then used to find the equilibrium positions of the disk at different discrete blade speeds. At any given speed, the governing equations are linearized about the equilibrium solution of the disk under the application of a space fixed external force. These linearized equations are then used to find the oscillation frequencies of the disk considering the effect of large deformation. Using multi mode approximation and different levels of nonlinearity, the frequency response of the disk considering the effect of geometrical nonlinear terms are studied. It is found that at the linear critical speed, the nonlinear frequency of the corresponding mode is not zero. Results are presented that illustrate the effect of the magnitude of disk displacement upon the frequency response characteristics. It is also found that for each mode, including the effect of the geometrical nonlinear terms due to the applied load causes a separation in the frequency responses of its backward and forward traveling waves when the disk is stationary. This effect is similar to the effect of a space fixed constraint in the linear problem. In order to verify the numerical results, experiments are conducted and the results are presented.

Commentary by Dr. Valentin Fuster
2010;():1135-1143. doi:10.1115/GT2010-23708.

For rotating disks, the effect of axisymmetric runout is of interest. This study examines the frequency characteristics of thin rotating discs subjected to axisymmetric non-flatness. The equations of motion used are based on Von Karman’s plate theory. First, the eigenfunctions of the stationary disk problem corresponding to the stress function and transverse displacement are found. These eigenfunctions produce an equation that can be used in the Gelrkin’s method. The initial nonflatness is assumed to be a linear combination of the eigenfunctions of the transverse displacement of the stationary disk problem. Since the initial non-flatness is assumed to be axisymmetric, only eigenfunctions with no nodal diameters are considered to approximate the initial runout. It is supposed that the disk bending deflection is small compared to disk thickness, so we can ignore the second-order terms in the governing equations corresponding to transverse displacement and stress function. After simplifying and discretizing the governing equations of motion, we can obtain a set of coupled equations of motion which takes the effect of initial axisymmetric runout into account. These equations are then used to study the effect of initial runout on the frequency response of the stationary disk. It is found that the initial runout increases the frequencies of the oscillations of a stationary disk. In the next step, we study the effect of initial non-flatness on the critical speed behavior of a spinning disk.

Commentary by Dr. Valentin Fuster
2010;():1145-1156. doi:10.1115/GT2010-23782.

It is well-known that the vibrational behavior of a mistuned bladed disk differs strongly from that of a tuned bladed disk. A large number of publications dealing with the dynamics of a mis-tuned bladed disk is available in the literature. Nearly all published mechanical models for a mistuned bladed disk consider the mistuning in terms of a perturbation of the mass and/or the stiffness matrix or in terms of a perturbation of the tuned system natural frequencies. Therefore, the possible effect of a damping mistuning is neglected in these models. In this paper, a model of a mistuned bladed disk with a combined damping and natural frequency mistuning is presented. This model is based on the well-known Fundamental Model of Mistuning with a novel extension to include the damping mistuning in a straight-forward way.

Commentary by Dr. Valentin Fuster
2010;():1157-1165. doi:10.1115/GT2010-23790.

Methods are developed to improve damping of compressor blades, where unconstrained and constrained damping techniques are applied to the blades to increase material damping, displaying both measurement and modeling results. Two specimens, titanium and stainless steel, are treated by aluminum oxide and epoxy coating material. Measurements of material damping of simple beam specimens without and with treatments are carried out and results show that both treatments give damping increase, where aluminum treatment is more effective for damping improvement than the corresponding epoxy treatment. The unconstrained damping layer model is used to predict the total material damping of the combined structure as well as the material damping of coating layer. Comparisons with measured results are made. The constrained-layer model is also used to optimize the damping configuration and parametric analyses are performed. Two compressor blades in titanium and stainless steel are tested in air and vacuum conditions to measure material damping and results show that difference between air and vacuum situations exists. One reason is being that the radiation loss factor produced in air condition increases damping comparing with the damping in vacuum condition. The calculation of the radiation loss factor is performed to match the measurement data and results demonstrate that the radiation loss factor is one factor and air friction is another strong factor in this case. Finally, increasing material damping gives a contribution to decrease peak stress values and therefore increase the life time of compressor blades.

Commentary by Dr. Valentin Fuster
2010;():1167-1173. doi:10.1115/GT2010-22224.

Wind tunnel experiments were carried out on NACA 0015 airfoil model to investigate the formation of laminar separation bubble on the upper surface of the airfoil by varying angle of attack from −5° to 25° with respect to the free stream velocity at constant Reynolds number varying from 0.2E06 to 0.6E06. Pressure signals were acquired from the pressure ports selected at the mid-span of the airfoil model along the chord. Static stall characteristics were obtained from the surface pressure distribution. The flow separation was found to be a trailing edge turbulent boundary layer separation preceded with a laminar separation bubble. Flow Visualizations were done by using Surface Oil flow Technique for qualitative analysis of the transition zone formed due to the presence of laminar separation bubble As the angle of attack is increased the separation bubble moves towards the leading edge of the airfoil and finally gets shredded or burst at a particular angle of attack resulting in leading edge turbulent flow separation which induces the static stall condition. The flow separation process is critically analyzed and the existence of laminar separation bubble is visualized and quantified with the increase in angle of attack and Re. Effect of Re and angle of attack on the various boundary layer and Separation bubble parameters are obtained and analyzed.

Commentary by Dr. Valentin Fuster
2010;():1175-1188. doi:10.1115/GT2010-22546.

In this paper the aerodynamics of an innovative multisplitter LP stator downstream of a high-pressure turbine stage is presented. The stator row, located inside a swan necked diffuser, is composed of 16 large structural vanes and 48 small airfoils. The experimental characterization of the steady and unsteady flow field was carried out in a compression tube rig under engine representative conditions. The one-and-a-half turbine stage was tested at three operating regimes by varying the pressure ratio and the rotational speed. Time-averaged and time-accurate surface pressure measurements are used to investigate the aerodynamic performance of the stator and the complex interaction mechanisms with the HP turbine stage. Results show that the strut blade has a strong impact on the steady and unsteady flow field of the small vanes depending on the vane circumferential position. The time-mean pressure distributions around the airfoils show that the strut influence is significant only in the leading edge region. At off-design condition (higher rotor speed) a wide separated region is present on the strut pressure side and it affects the flow field of the adjacent vanes. A complex behavior of the unsteady surface pressures was observed. Up to four pressure peaks are identified in the time-periodic signals. The frequency analysis also shows a complex structure. The spectrum distribution depends on the vane position. The contribution of the harmonics is often larger than the fundamental frequency. The forces acting on the LP stator vanes are calculated. The results show that higher forces act on the small vanes but largest fluctuations are experienced by the strut. The load on the whole stator decreases 30% as the turbine pressure ratio is reduced by approx. 35%.

Topics: Pressure , Ducts , Shapes
Commentary by Dr. Valentin Fuster
2010;():1189-1199. doi:10.1115/GT2010-22555.

A new mechanism for fan stator vane failure in turbofan engines at high speed and high loading has been identified and reported in this paper. Highly destructive vane failures have been encountered at Honeywell in one of the development fans with composite stator vanes. Measured data indicated nonlinear high amplitude vibratory response in fan stator vanes on stall side of the fan map at high speeds. Analysis showed that under certain vane steady loading vane fixity at hub could change, significantly reducing the vane natural frequency. At lower natural frequency the vane was found to be aeroelastically unstable and calculated response exhibited behavior observed during failure. An engine test was conducted to validate the role of hub fixity in vane failures. Test results showed failure to be a self-excited phenomenon and not driven by an external source of excitation. It was also shown that failures occur in vanes that are not rigidly fixed, validating the role of hub fixity in vane failures. Test results along with the analysis confirm the role of time dependent hub fixity leading to the highly destructive flutter responsible for vane failures.

Commentary by Dr. Valentin Fuster
2010;():1201-1208. doi:10.1115/GT2010-22595.

The interaction between impeller and diffuser in a high-pressure ratio centrifugal compressor is considered to have a strong influence on the unsteady flow field, the impeller response and the performance of the compressor. A computational study was performed to investigate the interactions between a backswept impeller and its downstream vaned diffuser with emphasis on the impeller response at 2 different vane settings. The unsteady computations were conducted using two different modelling levels of increasing fidelity. The computational domain included an impeller with 15 main and 15 splitter blades and 22-vane wedge diffuser. A steady-state stage calculation with a mixing-plane interface between the impeller trailing edge and the vane leading edge was conducted first to assess the performance. A whole-annulus unsteady stage calculation was conducted to study the response of the impeller. The effect of radial gap between the impeller trailing edge and the vane leading edge on the performance of the impeller was investigated in some detail. In agreement with other similar studies, the results suggest that there is an optimum value of the radius ratio for best performance.

Commentary by Dr. Valentin Fuster
2010;():1209-1219. doi:10.1115/GT2010-22745.

This paper presents the description and application of a new method for stability and forced response analyses of aerodynamically coupled blades considering the interaction of various mode families. The method, here referred as MLS (Multimode Least Square), considers the unsteady forces due to the blade motion at different modes shape families and calculates the aerodynamic matrixes by means of a least square (L2 ) approximations. This approach permits the prediction of mode families’ interaction with capabilities of structural, aerodynamic and force mistuning. A projection technique is implemented in order to reduce the computational domain. Application of the method on tuned and structural mistuned forced response and stability analyses is presented on a highly loaded transonic compressor blade. When considering structural mistuning the forced response amplitude magnification is highly affected by the change in aerodynamic damping due to mistuning. Analyses of structural mistuning without aerodynamic coupling might result in over-estimated or under-estimated response when the source of damping is mainly aerodynamic. The frequency split due to mistuning can cause that mode families’ interact due to reducing their frequencies separation. The advantage of the present method is that the effect of mode family interaction on aerodynamic damping and forced response is captured not being restricted to single mode families.

Topics: Stability , Modeling , Blades
Commentary by Dr. Valentin Fuster
2010;():1221-1233. doi:10.1115/GT2010-22756.

The influence of the Blade Count Ratio (BCR) on the aerodynamic forcing of a highly transonic compressor has been investigated. The focus has been put on the unsteady aerodynamics as well as mode excitability and thus High Cycle Fatigue (HCF) risk. A number of compressor stages were investigated that differed in blade count of the stator blade row. Time-resolved aerodynamic forcing results were acquired using a non-linear CFD approach. The results were decomposed into frequency content and combined with modal properties of the various components. It is found that the BCR is a key parameter to reduce generalized force and consequently vibratory HCF stresses. Furthermore a potential in avoiding and/or alleviating potential resonant crossings in the Campbell diagram is reported. The dependency of these aspects from BCR is largely non-linear and for the first time discussed in detail on the basis of a transonic compressor stage.

Topics: Compressors , Blades
Commentary by Dr. Valentin Fuster
2010;():1235-1245. doi:10.1115/GT2010-23037.

The effect of the structural coupling in the aeroelastic stability of a packet of low-pressure turbine vanes is studied in detail. The dynamics of a 3D sector vane is reduced to that of a simplified mass-spring model to enhance the understanding of its dynamics and to perform sensitivity studies. It is concluded that the dynamics of the simplified model retains the basic features of the finite element three-dimensional model. A linear fully coupled analysis in the frequency domain of the 3D vane sector has been conducted. It is concluded that the small structural coupling provided by the casing and the inter-stage seal is essential to explain the experimental evidences. It is shown that the use of fully coupled methods is necessary to retain the mode interaction that takes place in this type of configurations.

Commentary by Dr. Valentin Fuster
2010;():1247-1252. doi:10.1115/GT2010-23335.

A three-dimensional (3D) non-reflecting boundary condition for linearized flow solvers is presented. The unsteady aerodynamic modes at the inlet and outlet (far-field) are numerically determined by solving an eigen problem for the semi-discretized flow equations on a two-dimensional mesh. Unlike previous methods the shape of the far-field can be general and the non-uniformity of the steady flow across the far-field is considered. The calculated unsteady modes are used to decompose the unsteady flow at the far-field into modes. The direction of each mode is determined, and incoming modes are prescribed and outgoing modes are extrapolated. The results of 2D and 3D inviscid linearised flow simulations using the new boundary condition are presented.

Commentary by Dr. Valentin Fuster
2010;():1253-1261. doi:10.1115/GT2010-23376.

In the present work, an interface treatment method has been developed to extend a non-linear harmonic solution method for aeromechanic analysis in multiple blade row configurations. The main emphasis is two folds. Firstly the method will enable efficient and accurate analysis of blade aerodynamic forcing and damping characteristics under the influence of adjacent bladerows. Secondly, it will warrant that the same steady/mean base flow as defined by the aerothermal designers is used consistently in the aeromechanical analysis. For passing the harmonic disturbance across a rotor-stator interface, the present method employs the time series reconstruction in conjunction with a temporal Fourier transform. On the other hand, the consistency with a conventional steady multistage solution for the base flow is achieved by applying an extended mixing plane method. The validity and effectiveness of the method are examined and demonstrated.

Commentary by Dr. Valentin Fuster
2010;():1263-1275. doi:10.1115/GT2010-23557.

In this paper, the rotor geometries of two consecutive design loops are compared numerically with respect to aeroelastic stability. Therefore, the TRACE code of the German Aerospace Center DLR is used to compute the flutter predictions: based on a three-dimensional steady solution, the time-linearized Navier-Stokes equations are solved in order to assess the aerodynamic damping so that the critical inter-blade phase angles can be determined. Apart from the global stability behaviour the computation of local excitation per surface area is presented, facilitating the identification of stabilizing and destabilizing effects due to blade motion and flow field disturbances. Aiming for flutter-free design of compressor blades, an exemplary sensitivity analysis on the first mode is performed. Within the scope of this study, reduced frequency and mass ratio are varied and the influence of these parameters on the stability behaviour is deduced. For a tuned system, the nondimensional flutter equations are derived introducing the flutter index as aeroelastic similarity parameter. Differing tendencies of the aerodynamic work entry and the corresponding logarithmic decrement concerning flutter susceptibility are discussed in detail.

Commentary by Dr. Valentin Fuster
2010;():1277-1285. doi:10.1115/GT2010-23590.

The interaction between rotor blades and non-rotating stator blades is the most significant blade excitation mechanism in turbomachines. It is well documented in various numerical and experimental investigations for turbine cascades. Like turbine blades, also compressor blades are excited as well by potential fields of the following stator, the downstream flowfield of the stator of the previous stage or struts and incoming flow distortions. In this paper, experimental investigations of the excitation of a transonic compressor cascade due to gust generating struts upstream are presented. The experiments were performed in the test facility of non-rotating annular cascades at EPFL using a compressor cascade, which consists of 20 blades (NACA3506 profile) mounted on elastic spring suspensions for torsional motions at the midchord. For the non-rotating annular cascade, relative flow conditions similar to those present in a rotating cascade are generating by swirling the flow in front of the test test section. The struts are rotating in order to create a periodic excitation upstream of the cascade. The so generated pressure distribution on the cascade’s profiles as well as the measured vibration response of the blades are presented and compared for a pure subsonic and a transonic flow case.

Commentary by Dr. Valentin Fuster
2010;():1287-1297. doi:10.1115/GT2010-23771.

This article contains an investigation of the unsteady acoustic forcing on a centrifugal impeller due to coupled blade row interactions. Selected results from an aeromechanical test campaign on a GE Oil and Gas centrifugal compressor stage with a vaneless diffuser are presented. The most commonly encountered sources of impeller excitation due to upstream wake interaction were identified and observed in the testing campaign. A 30/rev excitation corresponding to the sum of upstream and downstream vane counts caused significant trailing edge vibratory stress amplitudes. Due to the large spacing between the impeller and the return channel vanes, this 30/rev excitation was suspected to be caused by an aero-acoustic excitation rather than a potential disturbance. The origin of this aero-acoustic excitation was deduced from an acoustic analysis of the unsteady compressor flow derived from CFD. The analysis revealed a complex excitation mechanism caused by impeller interaction with the upstream vane row wakes and subsequent acoustic wave reflection from the downstream return channel vanes. The findings show it is important to account for aero-acoustic forcing in the aeromechanical design of low pressure ratio centrifugal compressor stages.

Topics: Acoustics , Impellers , Blades
Commentary by Dr. Valentin Fuster
2010;():1299-1307. doi:10.1115/GT2010-23779.

In recent years there have been major developments in turbomachinery aeroelasticity methods. There are now greater possibilities to predict blade vibrations arising from self-excitation or inlet flow distortion. This is not only important with regard to aircraft compressor and fan blade rows, but also in the case of the last stages of steam and gas turbines working in highly loaded off-design conditions. In order to predict the unsteady pressure loads and aeroelastic behaviour of blades (including the computation of shock waves, shock/boundary layer interaction and boundary layer separation), complete Reynolds-averaged Navier-Stokes (RANS) equations are used in modelling complex and off-design cases of turbomachinery flows. In this paper the 3D RANS solver, including a modified Baldwin and Lomax algebraic eddy viscous turbulence model, is presented to calculate unsteady viscous flow through the turbine stage, while taking into account the blade oscillations but without the separating of outer excitation and unsteady effects caused by blade motion. The numerical method uses the second order by time and coordinates an explicit finite-volume Godunov’s type difference scheme and a moving H-O structured grid. The structure analysis uses the modal approach and a 3D finite element model of blade. To validate the numerical viscous code, the numerical calculation results were compared with the 11th Standard Configuration measurements. Presented here are the numerical analysis results for the aeroelastic behaviour of a steam turbine last stage with 760 mm rotor blades in a nominal and an off-design regime.

Commentary by Dr. Valentin Fuster
2010;():1309-1324. doi:10.1115/GT2010-22733.

Turbomachinery disks are highly stressed, heavy components used in virtually all axially configured gas turbines. Historically, simple plane stress models have primarily been used to quickly analyze the thickness profiles of thin compressor disks. The application of a plane stress model to a more complex system including large thermal gradients or composite materials is much less common. This paper will focus on low fidelity design studies of complex disk systems using a plane stress model. The automated design of a thick, high pressure turbine (HPT) disk with a large radial thermal gradient will be explored. This system clearly shows the limitations of a plane stress model. Discussion will focus on ways to identify and account for inaccuracies in the low fidelity turbine disk results. This paper will also explore the use of a low fidelity stress model in a fan disk design study including both isotropic and composite disk materials. This study shows that with proper assumptions, a plane stress model may be used to investigate a wide range of disk loading and geometry configurations in much less time than would be needed with higher fidelity tools. As examples, hardware from the GE E3 HPT and GE90 fan will be investigated using the disk design program T-Axi Disk. With proper assumptions and an understanding of the stress model, complex disk systems can be designed and optimized accurately at a low fidelity level. The time savings from using a low fidelity tool allows the designer to perform design studies that would be much more difficult or expensive using higher fidelity tools.