Identification of Dynamic Characteristics of Gas Foil Thrust Bearings Using Base Excitation

Gas foil bearings (GFBs) have clear advantages over oil-lubricated and rolling element bearings, by virtue of low power loss, oil-free operation in compact units, and rotordynamic stability at high speeds. However, because of the inherent low gas viscosity, GFBs have lower load capacity than the other bearings. In particular, accurate measurement of load capacity and dynamic characteristics of gas foil thrust bearings (GFTBs) is utmost important to widening their applications to high performance turbomachinery. In this study, a series of excitation tests were performed on a small oil-free turbomachinery with base excitations in the rotor axial direction to measure the dynamic load characteristics of a pair of six-pad, bump-type GFTBs, which support the thrust collar. An electromagnetic shaker provided dynamic sine sweep loads to the test bench (shaking table), which held rigidly the turbomachinery test rig for increasing excitation frequency from 10 Hz to 200 Hz. The magnitude of the shaker dynamic load, represented as an acceleration measured on the test rig, was increased up to 9 G (gravity). An eddy current sensor installed on the test rig housing measured the axial displacement (or vibrational amplitude) of the rotor thrust collar during the excitation tests. The axial acceleration of the rotor relative to the test rig was calculated using the measured displacement. A single degree-of-freedom base excitation model identified the frequency-dependent dynamic load capacity, stiffness, damping, and loss factor of the test GFTB for increasing shaker dynamic loads and increasing bearing clearances. The test results show that, for a constant shaker force and the test GFTB with a clearance of 155 μm, an increasing excitation frequency increases the dynamic load carried by the test GFTB, i.e., bearing reaction force, until a certain value of the frequency where it jumps down suddenly because of the influence from Duffing’s vibrations of the rotor. The bearing stiffness increases and the damping decreases dramatically as the excitation frequency increases. Generally, the bearing loss factor ranges from 0.5 to 1.5 independent of the frequency. As the shaker force increases, the bearing dynamic load, stiffness, damping, and loss factor increase depending on the excitation frequency. Interestingly, the agreements between the measured GFTB dynamic load versus the thrust runner displacement, the measured GFTB static load versus the structural deflection, and the predicted static load versus the thrust runner displacement are remarkable. Further tests with increasing GFTB clearances of 155, 180, 205, and 225 μm revealed that the vibrational amplitude increases and the jump-down frequency decreases with increasing clearances. The bearing load increases, but the bearing stiffness, damping, and loss factor decrease slightly as the clearance increases. The test results after a modification of the GFTB by rotating one side bearing plate by 30° relative to the other side bearing plate revealed insignificant changes in the dynamic characteristics. The present dynamic performance measurements provide a useful database of GFTBs for use in microturbomachinery.

Comparison of Two Numerical Algorithms for Computing the Effects of Mistuning of Fan Flutter

The aim of this paper is to study the effects of mistuning on fan flutter and to compare the prediction of two numerical models of different fidelity. The high fidelity model used here is a three-dimensional, whole assembly, time-accurate, viscous, finite-volume compressible flow solver. The Code used for this purpose is AU3D, written in Imperial College and validated for flutter computations over many years. To the best knowledge of authors, this is the first time such computations have been attempted. This is due to the fact that, such non-linear aeroelastic computations with mistuning require large amount of CPU time and cannot be performed routinely and consequently, faster (low fidelity) models are required for this task. Therefore, the second model used here is the aeroelastic fundamental mistuning model (FMM) and it based on an eigenvalue analysis of the linearized modal aeroelastic system with the aerodynamic matrix calculated from the aerodynamic influence coefficients. The influence coefficients required for this algorithm are obtained from the time domain non-linear Code by shaking one blade in the datum (tuned) frequency and mode. Once the influence coefficients have been obtained, the computations of aero damping require minimal amount of CPU time and many different mistuning patterns can be studied. The objectives of this work are to: 1. Compare the results between the two models and establish the capabilities/limitations of aeroelastic FMM, 2. Check if the introduction of mistuning would bring the experimental and computed flutter boundaries closer, 3. Establish a relationship between mistuning and damping. A rig wide-chord fan blade, typical of modern civil designs, was used as the benchmark geometry for this study. All the flutter analyses carried out in this paper are with frequency mistuning, but the possible consequences of mistuned mode shapes are briefly discussed at the end of this paper. Only the first family of modes (1F, first flap) is considered in this work. For the frequency mistuning analysis, the 1F frequency is varied around the annulus but the 1F mode shapes remain the same for all the blades. For the mode shape mistuning computations, an FE analysis of the whole assembly different mass blades is performed. The results of this work clearly show the importance of mistuning on flutter. It also demonstrates that when using rig test data for aeroelastic validation of CFD codes, the amount mistuning present must be known. Finally, it should be noted that the aim of this paper is the study of mistuning and not steady/unsteady validation of a CFD code and therefore minimal aerodynamic data are presented.

Non-Invasive Parameter Identification in Rotordynamics via Fluid Film Bearings: Linking Active Lubrication and Operational Modal Analysis

In recent years, theoretical and experimental efforts have transformed the conventional tilting-pad journal bearing (TPJB) into a smart mechatronic machine element. The application of electromechanical elements into rotating systems makes feasible the generation of controllable forces over the rotor as a function of a suitable control signal. The servovalve input signal and the radial injection pressure are the two main parameters responsible for dynamically modifying the journal oil film pressure and generating active fluid film forces in controllable fluid film bearings. Such fluid film forces, resulting from a strong coupling between hydrodynamic, hydrostatic and controllable lubrication regimes, can be used either to control or to excite rotor lateral vibrations. If non-invasive forces are generated via lubricant fluid film, in situ parameter identification can be carried out, enabling evaluation of the mechanical condition of the rotating machine. Using the lubricant fluid film as a non-invasive calibrated shaker is troublesome, once several transfer functions among mechanical, hydraulic and electronic components become necessary. In this framework the main original contribution of this paper is to show experimentally that the knowledge about the several transfer functions can be bypassed by using output-only identification techniques. The manuscript links controllable (active) lubrication techniques with operational modal analysis, allowing for in-situ parameter identification in rotordynamics, i.e. estimation of damping ratio and natural frequencies. The experimental analysis is carried out on a rigid rotor-level system supported by one single pair of pads. The estimation of damping and natural frequencies is performed using classical experimental modal analysis (EMA) and operational modal analysis (OMA). Very good agreements between the two experimental approaches are found. Maximum values of the main input parameters, namely servovalve voltage and radial injection pressure, are experimentally found with the objective of defining ranges of non-invasive perturbation forces.

Micromechanics-Based Fracture Risk Assessment Using Integrated Probabilistic Damage Tolerance Analysis and Manufacturing Process Models

Materials engineering and damage tolerance assessment have traditionally been performed as disjoint processes involving repeated tests that can ultimately prolong the time required for certification of new materials. Computational advances have been made both in the prediction of material properties and probabilistic damage tolerance analysis, but have been pursued primarily as independent efforts. Integrated computational materials engineering (ICME) has the potential to significantly reduce the time required for development and insertion of new materials in the gas turbine industry. A manufacturing process software tool called DEFORM™ has been linked with a probabilistic damage tolerance analysis (PDTA) software tool called DARWIN® to form a new capability for ICME of gas turbine engine components. DEFORM simulates rotor manufacturing processes including forging, heat treating, and machining to compute residual stress and strain, track anomaly location, and predict microstructure including grain size and orientation. DARWIN integrates finite element stress analysis results, fracture mechanics models, material anomaly data, probability of anomaly detection, and inspection schedules to compute the probability of fracture of a gas turbine engine rotor as a function of operating cycles. Previous papers have focused on probabilistic modeling of residual stresses in DARWIN based on manufacturing process training data from DEFORM. This paper describes recent efforts to extend the probabilistic link between DEFORM and DARWIN to enable modeling of residual strain, average grain size, and ALA (unrecrystalized) grain size as random variables. Gaussian Process modeling is used to estimate the relationship among model responses and material processing parameters. These random variables are applied to microstructure-based fatigue crack nucleation and growth models for use in probabilistic risk assessments. The integrated DARWIN-DEFORM capability is demonstrated for a representative engine disk model which illustrates the influences of manufacturing-induced random variables on component fracture risk. The results provide critical insight regarding the potential benefits of integrating probabilistic computational material processing models with probabilistic damage tolerance-based risk assessment.

Numerical Investigation of Tip Clearance Flow Induced Flutter in an Axial Research Compressor

A flutter phenomenon was observed in a 1.5-stage configuration at the Darmstadt transonic compressor. This phenomenon is investigated numerically for different compressor speeds. The flutter occurs for the second eigenmode of the rotor blades and is caused by tip clearance flow which is able to pass through multiple rotor gaps at highly throttled operating points. The vibration pattern during flutter is accompanied by a pressure fluctuation pattern of the tip clearance flow which is interacting with the blade motion causing the aeroelastic instability. The velocity of the tip clearance flow fluctuation is about 50% of the blade tip speed for simulation and experiment and also matches the mean convective velocity inside the rotor gap. This is consistent for all compressor speeds. From this investigations, general guidelines are drawn which can be applied at an early stage during compressor design to evaluate the susceptibility to this kind of blade vibration.

Rotordynamic Performance Measurements and Predictions of a Rotor Supported on Multilayer Gas Foil Journal Bearings for Microturbomachinery

This paper presents rotordynamic performance measurements of multilayer gas foil journal bearings (GFJBs) supporting the rotor of oil-free microturbomachinery, and a comparison with the model predictions. A series of rotor coast-down tests from 60 krpm were conducted to compare the rotordynamic performances of three previously developed multilayer GFJBs: types A, B, and C. During the tests, two sets of orthogonally positioned displacement sensors recorded the horizontal and vertical rotor motions, and an axially positioned displacement sensor measured the thrust of the runner axial motion. The test results revealed that the type C GFJBs have a superior rotordynamic capability over the other types. The additional coast-down tests from 100 krpm for the type C showed that the synchronous motions of the rotor are dominant at up to ∼50 krpm, but that large amplitudes of subsynchronous motion associated with the natural frequency of a rotor-GFJB system occur above this speed. Thermal transient response measurements were conducted using four k-type thermocouples at increasing rotor speeds of 20 to 100 krpm with increments of 10 krpm. The operation time required to establish steady-state temperatures was approximately 25 min for each speed. For most of the speeds tested, the front GFJB near the rotor impeller end showed the lowest temperatures, and both the rear GFJB near the thrust runner end and the permanent magnet (PM) motor showed the highest temperatures. The GFTB showed the lowest temperature at low speeds of below 50 krpm, and the highest temperature at the top speed of 100 krpm owing to the increasing axial load caused by the impeller force. The measured impeller pressure and motor output power increased nonlinearly with the increasing rotor speed and fits best with the second-order and third-order polynomial equations, respectively. The measured axial displacement revealed that the rotor moved axially up to ∼ 270 μm toward the impeller side as the speed increased to 100 krpm. Further experiments using a decrease in radial clearance of 30 μm demonstrated a suppression of the large amplitude of the subsynchronous rotor motion to a certain degree. In addition, the onset speed of the subsynchronous motions increased to 80 krpm for the type C GFJBs with the decrease in the radial clearance. Rotordynamic model predictions with the predicted GFJB stiffness and damping coefficients were benchmarked against the test data. The predicted natural frequencies, onset speed of instability (OSI) where the damping ratio became negative, and synchronous rotor response versus speed agreed reasonably with the measured whirl frequencies of the subsynchronous motions, the onset speed of subsynchronous motions (OSS), and the filtered synchronous rotor motion versus speed, respectively. The predictions also showed that the OSI increased from 50 krpm to 80 krpm with a decrease in the radial clearance, thus validating the present rotordynamic model.

Transient Lift-Off Test Results for an Experimental Hybrid Bearing in Air, Simulating a Liquid Hydrogen Turbopump Start Transient

Start-transient testing of a hybrid (combined hydrostatic and hydrodynamic action) bearing supplied with air was completed, providing an indication of its performance while operating in a compressible fluid medium. The test start transients were modeled after Rocket Engine Transient Simulation Software (ROCETS) predictions for start-transient behavior of running speed ω(t) and bearing supply pressure Ps(t). The top test speed was 15 krpm. The ramp rate, supply pressure Ps values at 15 krpm, constant bearing unit load magnitude w0, and load orientation (load-on-recess LOR or load-on-land LOL) were varied. Five different load-case combinations were carried out (separately) for LOR and LOL load configurations with ramp rates varying from 2206 rpm/s to 8824 rpm/s. The target pressures at 15 krpm varied from 5.32 bars to 18.25 bars. The tested bearing dimensions were: L = D = 38.1 mm, and Cr =.0635 mm. Lift-off occurs due to the increase in Ps (ω dependent) and was defined as the point of departure towards the center of the bearing with increasing ω while the rotor remained 0.00254 mm (0.1 mils) above the bearing surface. This method is limited by the inability to accurately measure an established operating bearing clearance. Evaluation of the lift-off Ps versus applied unit load w0 supports the following conclusions: (1) Lift-off Ps is approximately a linear function of w0, (2) Changing the ramp rate while keeping constant the specified Ps at 15 krpm has no significant impact, (3) Lowering the limit Ps at 15 krpm may reduce the lift-off Ps value, and (4) The LOR start-transient cases required a higher lift-off speed and lift-off Ps values than the corresponding LOL start-transient cases.

Unsteady Forces in Last Stage LP Steam Turbine Rotor Blades With Exhaust Hood

Several high vibration amplitude problems have been reported regarding the slender last stage blades of commercial LP steam turbines. This paper presents a numerical study of unsteady forces acting on rotor blades using ANSYS CFX. A 3D transonic viscous flow through the stator and rotor blades with an exhaust hood was modelled. The last stage was modelled as a full blade annulus, so that the axial, radial and circumferential distribution of flow patterns and blade forces could be examined. An unsteady flow analysis was conducted on a typically designed last stage and exhaust diffuser, with measured and calculated downstream static pressure distribution as the outlet boundary condition. The results showed that under off-design conditions, vortices occurred in the last stage and diffuser. Unsteady aerodynamic forces were found at high frequencies (stator passing frequencies) and low frequencies (generated from asymmetric pressure distributions behind the rotor), with the relative dominance of these forces/frequencies shifting as a function of radial span. An FFT analysis was carried out. Three sections were investigated: the hub, midspan and peripheral (tip) section. The steady pressure behind the rotor blade was compared with experimental results in the LP last stage behind the rotor blades and in a specified cross-section of the exhaust hood. The lower frequency unsteady forces had a higher relative contribution towards the tip of the blade.

The Influence of Hydrodynamic Bearing Configuration on Morton Effect

The Morton effect (ME) results from the synchronous, thermal excitation of a rotating shaft because of the uneven viscous shearing in hydrodynamic bearings and the asymmetric temperature distribution in shafts. The temperature difference bends the rotor, reducing the film thickness and increasing the thermal unbalance, which may cause excessive vibration level and unsteady phase angle. To predict the potential thermal instability from the ME, the finite element method is used to solve the transient rotordynamics and temperature distribution in the lubricant, bearing and shaft. The conventional thermal unbalance method is replaced by a more accurate thermal shaft bow model for rotordynamic analysis and the three-dimensional energy equation is utilized for the lubricant temperature prediction. Considering that the temperature change in the shaft and bearing occurs quite slowly relative to the shaft vibration deflection change, a staggered scheme is employed to assign a longer period to update the system temperature distribution and a shorter period to update the vibration orbits. Verified by a real overhung compressor model, the ME instability onset speed predicted by simulation coincides with the tested speed, at which large vibration level is observed. The hysteresis phenomenon, which is quite typical for thermal-induced vibration problems, can be caused by the ME and is demonstrated by the simulation. A stability recovery speed is confirmed, above which the vibration level and the rotor temperature difference will decrease to an acceptable level and the system will become stable. To investigate the influence of bearing configuration on ME, different bearing types including fixed pad bearings (FPBs) and tilting pad bearings (TPBs) with various pad numbers are analyzed. Meanwhile, the bearing clearance and preload intentionally remain unchanged in the comparison. Results show that despite similar critical speeds, the TPBs are better at suppressing the ME with lower average temperature and larger film thickness in the lubricant, especially at high speeds. This is due to the self-tilting ability for the TPBs to maintain a satisfactory bearing clearance. The four-pad TPBs outperform the five-pad TPBs with both lower average temperature and smaller temperature difference in the shaft considering that the effective load-carrying area is larger in the 4-pad bearings. Moreover, the asymmetric pivot offset of 0.6 is simulated to demonstrate its superiority in mitigating the ME compared with the common 0.5 offset. Considering that the ME instability occurs in the vicinity of the critical speeds in most cases, the bearing diameter-length ratio should be carefully designed to achieve a larger separation margin.

Random Vibration Analysis for Centrifugal Compressor Impellers With Unsteady Aerodynamic Excitations

Dynamic response of impeller of centrifugal compressor is studied considering pulsating pressure field on blades due to unsteady flow conditions. The aerodynamic forces on the blades are modeled as random load whose spectral characteristics are determined through computational fluid dynamic simulations in the time domain. The dynamical response in the unsteady case is solved as a random vibration problem in the frequency domain which provides useful power spectral density displacement and stress for early stage of impeller design. A semi-open impeller mounted with 19 blades is modeled using three dimensional solid finite elements. The random vibration problem of the impeller is solved through the Pseudo-Excitation Method considering spatial variance of the pressure field. A user-defined module is developed based on harmonic analysis to generate the auto power spectral density and variance of displacement and stress at 200 nodes. It is demonstrated that solving a random vibration problem through the Pseudo-Excitation Method is faster than the commonly adopted multiple-step transient analysis. It is concluded that evaluating the structural integrity of impeller solids in the regime of random vibration is a feasible and efficient approach at the early design stage of compressors.