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.

Improved Low Cycle Fatigue Analysis for Ni-Based Turbine Nozzles

The requirements for cleaner energy have driven industrial gas turbines manufacturers to increase firing temperatures and improve cooling of nozzles. The application of high temperature alloys having adequate thermo-mechanical requirements is critical, as assessed by low cycle fatigue performance. The effect of higher firing temperatures combined with higher cooling efficiencies has lead to operating cycles where the level of plastic strain imparted define component life. The capability of material models to account for non-linear effects such as ratchetting or shakedown, cyclic hardening or softening as well as Bauschinger or relaxation effects have been highlighted in this context. Neglecting these effects can lead to over and under-conservative life assessment analysis, while accounting for them using standard multilinear material models lead to convergence issues in finite element analysis. In this paper, Chaboche viscoplastic model has been applied to a transient structural of a first stage gas turbine nozzle. Fitting of the model based on experimental mechanical test data on MAR-M-247 alloy will be described, followed by an overview of how the model may be implemented to a benchmark nozzle thermo-mechanical transient analysis. Finally the details how the Chaboche-type model has provided up to 50% decrease in computation time when compared to using a standard multi-linear material modelling approach.

Transient Characteristics of a Dual-Rotor System With Intershaft Bearing Subjected to Mass Unbalance and Base Motions During Start-Up

Using Newmark-Hilber-Hughes-Taylor (Newmark-HHT) integration method, transient characteristics of the dual-rotor system with an intershaft bearing subjected to mass unbalance and base motions during start-up are illustrated. Rotary inertia, gyroscopic moment, shear deformation, mass unbalance and deterministic base motions are considered. Due to variable angular velocities, additional stiffness matrices associated with rotating angular accelerations are also introduced in the equations of motion. The effects of base motion parameters on the dynamic characteristics of the dual-rotor system are discussed, including base axial rotation, lateral rotations, and harmonic translations. The results show that base axial rotation significantly changes the transient critical speeds and resonant amplitudes of the dual-rotor system. In the case of base lateral rotation, the center of the orbit is no longer on the bearing centerline, but with a dynamic offset. When increasing the rotating speeds, the dynamic offset becomes greater. Unlike base lateral rotation, base harmonic translation doesn’t result in dynamic offset, but it amplifies response amplitudes over the entire range of rotating speed. In conclusion, it provides a flexible approach with high efficiency and good expandability to predict transient responses of dual-rotor systems under base motions, and to prevent dual-rotor systems against potential excessive vibration in the design phase.

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.