Experimental and Analytical Investigations of a Low Pressure Model Turbine During Forced Response Excitation

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.

On the Frequency Response of a Spinning Disk With Large Deformations

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.

Impact of Frequency Dependence of Gas Labyrinth Seal Rotordynamic Coefficients on Centrifugal Compressor Stability

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.

Theoretical Prediction of the Lift-Off Speed in Aerodynamic Compliant Foil Journal Bearings

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.

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness and Different Pad Preloads

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.

Evaluation of High-Order Resonance of Blade Under Wake Excitation

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.

Maximum Amplification of Blade Response in Mistuned Multi Stage Assemblies

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)+…)/2, where Ni are the number of blades on the stages and gi = FiTMi−1Fi with Fi 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.

Exploration of NDE Properties of AMB Supported Rotors for Structural Damage Detection

This paper addresses self-diagnostic properties of AMB (active magnetic bearing) supported rotors for on-line detection of the transverse crack on a rotating shaft. In addition to pure levitation, the rotor supporting bearing also serves as an actuator that transforms current signals additionally injected into the control loop into the superimposed specially selected excitation forces into the suspended rotor. These additional excitations induce combination frequencies in the rotor response, providing unique signatures for the presence of crack. The background of theoretical modeling, experimental and computer simulation results for the AMB supported cracked rotor with self-diagnostic excitation forces are presented and discussed.

Failure Investigation of the 69 MW Gas Turbine of Combined Cycle Unit

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.

Destabilization of Forward Rub in Rotor Magnetic Bearing Systems Using Actively Controlled Auxiliary Bearings

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.