Effectiveness Testing of an Inverse Method for Balancing Nonlinear Rotordynamic Systems

Modern aero-engine structures typically have at least two nested rotors mounted within a flexible casing via squeeze-film damper (SFD) bearings. The inaccessibility of the HP rotor under operational conditions motivates the use of a non-invasive inverse problem procedure for identifying the unbalance. Such an inverse problem requires prior knowledge of the structure and measurements of the vibrations at the casing. Recent work by the authors reported a non-invasive inverse method for the balancing of rotordynamic systems with nonlinear squeeze-film damper (SFD) bearings, which overcomes several limitations of earlier works. However, it was not applied to a common practical configuration wherein the HP rotor is mounted on the casing via just one weak linear connection (retainer spring), with the other connections being highly nonlinear SFDs. The analysis of the present paper considers such a system. It explores the influence of the condition number and how it is affected as the number of sensors and/or measurement speeds is increased. The results show that increasing the number of measurement speeds has a far more significant impact on the conditioning of the problem than increasing the number of sensors. The balancing effectiveness is reasonably good under practical noise level conditions, but significantly lower than obtained for the previously considered simpler configurations.

Rotordynamics Experimental Validation of a Sliding-Blade Architecture for an Inside-Out Ceramic Turbine

The integration of monolithic ceramic blades into sub-megawatt microturbines is a low-cost option for increasing Turbine Inlet Temperature and efficiency. The Inside-Out Ceramic Turbine (ICT) is a promising concept for the integration of ceramic blades by loading each blades in compression using a carbon-polymer composite rim to convert the blade radial loads to tangential hoop stress. High tangential velocities lead to elevated radial displacement of the rim and, therefore, the rotor hub needs to be able to maintain the contact with the blades for a large range of radial displacements. This displacements comes with hub structural challenges and rotordynamics considerations. For these reasons, blade tip speed have been previously limited to about 360 m/s. This paper presents a hub design that allows high radial displacement using the combination of inclined blade roots, inclined hub grooves and an axial spring. The contact between the blade root and the hub is maintained through the inclined planes by the axial forces from the spring creating internal friction in the rotor that can induce sub-synchronous rotordynamics instabilities. The onset of instabilities is investigated experimentally with cold spin tests of a simplified ICT prototype. The results first show that the concept remains stable up to the maximum speed tested of 127 kRPM (tip speed of 387 m/s) if the spring is designed such that it remains in contact with the blade roots at all time. On the other hand, when reducing the preload sufficiently to test the limits of the concept, the rotor first mode became unstable at 120 kRPM resulting in failure of the prototype. These results suggest that, provided a sufficient spring preload to prevent excessive relative motion, the blades can reach the desired radial displacements, removing the main constraint on ICT tip speed.

Analysis of Rotordynamic and Thermodynamic Performance of a Multistage Centrifugal Compressor Operating in the Minimum Flow Region

In this paper both rotordynamic and thermodynamic analysis of a multistage centrifugal compressor running with one or more stages in post-stall condition are presented. The purpose of this study is to demonstrate the machine can operate stable and safe in such condition (i.e. stable condition means the head vs. flow operating curve shall have negative slope and safe means a vibration free machine). This allows to extend the operating range at lower flow with respect to the current day-by-day design practice. Experimental results from ASME PTC10 Class 2 test carried out on a seven-stage compressor are shown to validate the analysis.

Improved Empirical Identification of the Inverse Model of a Squeeze-Film Damper Bearing Based on a Recurrent Neural Network

Most recently proposed techniques for inverse rotordynamic problems seek to identify the unbalance on a rotor using a known structural model and measurements from externally mounted sensors only. Such non-intrusive techniques are important for balancing rotors that cannot be accessed under operational conditions because of temperature or space restrictions. The presence of nonlinear bearings, like squeeze-film damper (SFD) bearings used in aero-engines, complicates the solution process of the inverse rotordynamic problem. In certain practical aero-engine configurations, the solution process requires a substitute for internal instrumentation to quantify the SFD journal vibration. This can be provided by an inverse model of the SFD bearing which outputs the time history of the relative vibration of the SFD journal relative to its housing, for a given input time history of the SFD force. This paper focuses on the inverse model of the SFD and presents an improved methodology for its identification via a Recurrent Neural Network (RNN) trained using experimental data from a purposely designed rig. The novel application of chirp excitation via two orthogonal shakers considerably improves both the quality of the training data and the efficiency of its generation, relative to an earlier preliminary work. Validation test results show that the RNNs can predict the journal displacement time history with reasonable accuracy. It is therefore expected that such an inverse SFD model would serve as a reliable component in the solution of the wider inverse problem of a rotordynamic system.

Application of Simplified Parametric Model to Estimate Fan Blade-Out Response

A six-degree-of-freedom non-linear model is developed using Lagrange’s equation. The model is used to estimate transient fan-stage dynamic response during a fan-blade-out event in a turbo fan engine. The coupled degrees of freedom in the model include the fan whirl in the fan plane, the torsional response of the fan and low-pressure turbines (LPTs) about the engine centerline, the radial position of the released blade fragment, and the angular rotation of the trailing blade from its free state due to acceleration of the released blade. The released blade is assumed to slide radially outward along the trailing blade without friction. The external loading applied to the system includes fan imbalance, the remaining fan blades machining away the rub strip, rubbing of the blades with the fan case, and slowly-varying torques on the low pressure (LP) spool as engine performance degrades. The machining of the abradable imparts tangential loading on the fan blades as momentum is transferred to the liberated rub strip material. After application of the initial conditions including angular positions, angular velocities, released blade fragment position, and torsional wind-up, the governing equations are integrated forward in time from the instant the blade fragment is released. A reasonable match to test data is shown. Parameters affecting the fan-system response are varied to study the impact on fan peak lateral whirl amplitude, peak LP shaft torque, and peak loading on the trailing blade. It is found that the rub strip and mass eccentricity have the strongest influence on the LP shaft torsional loading. It is found that mass eccentricity has the largest influence on peak fan whirl. It is also found that released blade mass and attachment stiffness have the largest influence on the trailing blade loading.

Investigation of Fan Blades Vibration due to Blade/Casing Rubbing Interactions Using In-Plane Two-Dimensional Model

Interactions between casings and bladed-disks of modern turbofan engines may occur through various mechanisms: casing distortions, rotor vibrations and casing vibrations to name a few. These interactions might lead to nonlinear blade vibrations, which could then induce severe damages to both structures. The impacts of casing vibrations on the vibration behaviors of engine blades are studied in this paper. A two-dimensional in-plane model is established in this paper. Fan blade, disk and casing are modeled using beam element. Craig-Bampton model reduction is applied to simplify the model. Penalty method mixed with golden section method is created and used for contact treatments. The interaction is initiated by the external forces acting on the casing. The casing is excited to two-, three- and four-nodal diameter vibration patterns, respectively. In order to capture the core of the problem, contact forces applied to the casing, and casing damping are neglected. Steady casing vibrations could thus be generated. Blade vibrations are calculated in a wide rotating speed range, maximum amplitudes are recorded and studied. The results show that the bladed-disk will have several vibration peaks in the calculated rotating speed range. To figure out the physical mechanisms of these peaks, Fourier spectrums as well as different bladed-disk materials are introduced. Almost all vibration peaks can be explained by three kinds of mechanisms found and summarized in this paper. Two of them are related to travelling waves and the third is related to harmonics. Speed and frequency margins that are related to blade-tip-rub induced vibrations are defined and analyzed. The findings and ideas shown in this paper can be used as a reference in engine preliminary structural design to avoid potential blade tip-rub induced damages.

Some Aspects of Operated Blades HCF Analysis: Rejuvenation and Life Estimation

The lifecycle of modern industrial gas turbines can reach hundred thousand hours and usually the turbine blades need to be replaced. The use of super alloys and application of advanced coatings makes the cost of turbine lifecycle rather high. The methods for blade rejuvenation and life extension are based on the analysis of the main defects which can considerably reduce blade strength. The effect of long operation and typical defects in turbine blades has been studied in correlation with HCF. The decrease of blades HCF under the effect of operation has been considered as the result of influence of mechanical and thermal factors. The influence of FOD on the blade HCF strength is studied. Some random defects in turbine blades which resulted in HCF decreasing and blade failure are considered. The rejuvenation heat treatment for the blades of ZhS6K and EI893 and its positive effect on metal properties is demonstrated. The ultrasonic shot peening for operated blades have been considered. It is demonstrated that HCF strength of blades after shot peening is about 25–30% higher. Relaxation of compressing stresses in operation is shown as not essential. The remaining life of operated blades can be estimated using the correlation of endurance limit and run time.

Effect of a Planetary Gearbox on the Dynamics of a Rotor System

The dynamic analysis of rotors with bladed disks has been investigated in detail over many decades and is reasonably well understood today. In contrast, the dynamic behaviour of two rotors that are coupled via a planetary gearbox is much less well understood. The planetary gearbox adds inertia, mass, stiffness, damping and gyroscopic moments to the system and can strongly affect the modal properties and the dynamic behaviour of the global rotating system. The main objective of this paper is to create a six degrees of freedom numerical model of a rotor system with a planetary gearbox and to investigate its effect on the coupled rotor system. The analysis is based on the newly developed finite element software “GEAROT” which provides axial, torsional and lateral deflections of the two shafts at different speeds via Timoshenko beam elements and also takes gyroscopic effects into account. The disks are currently considered as rigid and the bearings are modelled with isotropic stiffness elements in the translational and rotational directions. A novel planetary gearbox model has been developed, which takes the translational and rotational stiffness and the damping of the gearbox, as well as the masses and inertias of the sun gear, ring gear, planet gears and carrier into account. A rotating system with a planetary gearbox has been investigated with GEAROT. The gearbox mass and stiffness parameters are identified as having a significant effect on the modal behaviour of the rotor system, affecting its natural frequencies and mode shapes. The higher frequency modes are found to be more sensitive to the parameter changes as well as the modes which have a higher deflection at the location of the gearbox on the rotor system. Compared with a single shaft system, the presence of a gearbox introduces new global modes to the rotor system and decouples the mode shapes of the two shafts. The introduction of a planetary gearbox may also lead to an increase or a reduction of the frequency response of the rotor system based on gear parameter values.

Steady-State Characteristics of a Dual-Rotor System With Intershaft Bearing Subjected to Mass Unbalance and Base Motions

A dual-rotor system with an intershaft bearing subjected to mass unbalance and base motions is established. Using Lagrange’s principle, equations of motion for dual-rotor system relative to moving base are derived. Rotary inertia, gyroscopic inertia, transverse shear deformation, mass unbalance, and six components of deterministic base motions are taken into account. Using state-space vector, steady-state characteristics of dual-rotor system are analyzed through dual-rotor critical speed map, mode shapes, unbalance responses considering base rotations, frequency responses due to base motions, and shaft orbits. The results show that base translations just add external force vectors, while base rotations bring on parametric system matrices and additional force vectors. Base rotations not only change natural frequencies of dual-rotor system, but also break the symmetry of dynamic characteristics in the case of base lateral rotation. Excited by base harmonic translation, resonant frequencies correspond to whirl frequencies. The orbit remains circular under base axial rotation, while it becomes elliptical with a static offset under lateral rotation and then a complicated curve due to harmonic translation. When harmonic frequency of base translation gets close to dual-rotor excitation frequencies, obvious beat vibration appears. Overrall, this flexible approach can ensure calculation accuracy with high efficiency and good expandability.

Reliability Analysis on a Turbine Disk Considering the Coupling of Multiple Failure Modes

Current probabilistic design methods mainly focus on single mode of failure, under the consideration on random variables including geometry, loading, and material properties. However, due to the complex structural characters and unevenly distributed temperature, turbine disks are always undergoing multiple potential failure modes, which should be effectively evaluated under a coupling scheme in reliability analysis. To this end, a collaborative response surface method involving multiple potential modes was established, aligning individual failure modes that were precisely evaluated via linear heteroscedastic regression analysis. To validate our model, reliability assessment was conducted on a turbine disk in turbo-shaft engine, where the coupling failure including low cycle fatigue and creep-fatigue was considered. This method can be an effective tool in the evaluation of reliability analysis involving multiple failure modes.