Mistuning Modeling and its Validation for Small Turbine Wheels

The production of bladed structures, e.g. turbine and compressor wheels, is a subject of statistical scatter. The blades are designed to be identical but differ due to small manufacturing tolerances. This so called mistuning can lead to increased vibration amplitudes compared to the ideal tuned case. The object of this study is to create and validate numerical models to evaluate such mistuning effects of turbine wheels for automotive turbocharger applications. As a basis for the numerical analysis vibration measurements under stand-still conditions were carried out by using a laser surface velocimeter (LSV). The scope of this investigation was to identify the mistuning properties of the turbine wheels namely the frequency deviation from the ideal, cyclic symmetrical tuned system. Experimental modal analyses as well as blade by blade measurements were performed. Moreover 3D scanning techniques were employed to determine geometric deviations. Numerical FE models and a simplified multi degree of freedom model (EBM) were created to reproduce the measured mistuning effects. The prediction of mode localization and the calculated amplitude amplification were evaluated. The best results were obtained with a FE model that employs individual sectorial stiffnesses. The results also indicate that the major contribution to mistuning is made by material inhomogeneities and not by geometric deviations from ideal dimensions. With the adjusted FE model a probabilistic study has been performed to investigate the influence of the mistuning on the amplitude amplification factor. It has been found that at a certain level of mistuning the amplification factor remains constant or slightly decreases. By introducing intentional mistuning a lower sensitivity as well as a decrease of the amplitude amplification could be achieved.

Regeneration-Induced Forced Response in Axial Turbines

The regeneration of highly loaded turbine blades causes small variations of their geometrical parameters. To determine the influence of such regeneration-induced variances of turbine blades on the nozzle excitation, an existing air turbine is extended by a newly designed stage. The aerodynamic and the structural dynamic behavior of the new turbine stage are analyzed. The calculated eigenfrequencies are verified by an experimental modal analysis and are found to be in good agreement. Typical geometric variances of overhauled turbine blades are then applied to stator vanes of the newly designed turbine stage. A forced response analysis of these vanes is conducted using a uni-directional fluid-structure interaction approach. The effects of geometric variances on the forced response of the rotor blade are evaluated. It is shown that the vibration amplitudes of the response are significantly higher for some modes due to the additional wake excitation that is introduced by the geometrical variances e.g. 56 times higher for typical MRO-induced variations in stagger-angle.

Measurement and Prediction of the Dynamic Characteristics of a Large Turbine Tilting-Pad Bearing Under High Circumferential Speeds

The identification results for the linear dynamic coefficients of a K-C model for a large tilting-pad bearing in load between pad configuration are presented for specific bearing loads between 1.0 and 2.0 MPa and circumferential speeds of 39 m/s and 78 m/s. The bearing with a double tilting support is lubricated by spray-bars and can be described by the following specifications: Five pads, 0.23 nominal preload, 60% offset, 56° pad arc angle, 500 mm inner diameter, 350 mm pad length and 1.28 per mill relative bearing clearance. The test rig and the test procedure are described in detail. For the determination of the dynamic coefficients, a harmonic force is induced by two unbalance-vibration generators being attached to the frame of the rig. The relative movement between bearing and shaft is detected by proximity probes between bearing housing and shaft. The bearing forces are identified by measurements of the entire film pressure distribution in both circumferential and axial direction. In the post processing of the data, the dynamic force components are determined by a Fourier-analysis. This procedure is well-established for fixed-pad bearings. However, the uncertainties of its capabilities for tilting-pad bearings are investigated and discussed in this study. The theoretical analyses with the code COMBROS are based on a calculation of linear perturbations for the predicted static properties. The measurement and the calculation procedures show very good agreement for fixed-pad bearings. For a tilting-pad bearing the results differ with increasing frequency ratio and rotational speed. The experimental results show very poor frequency dependence in load direction and a very high one in the orthogonal direction. Theoretically, the influence of the frequency ratio is comparable in both planes and pretty low due to the pivot offset and the high effective preload. While good agreement for the measured and predicted K-C model can be observed at the lower rotational and vibrational frequency the correspondence becomes worse with the increase of both. The identification procedure uses the fluid film force to determine the dynamic coefficients and assumes that this is equal to the load on the bearing in every time step. The results indicate that the experimental identification is uncertain due to the elasticity of the double tilting bearing support and the initiated dynamic effects of it. An improvement of the measurement that also identifies the limitation of the current procedures as well as simplifications in the theoretical analyses are discussed.

CFD Investigation on the Rotordynamic Characteristics of Shroud Leakage Flow in High Pressure Steam Turbine

We conducted a computational fluid dynamics (CFD) study to investigate the rotordynamic characteristics of the shroud labyrinth seal of a high-pressure steam turbine. Four different CFD models were constructed to investigate the appropriate modeling approach for evaluating the seal force of an actual steam turbine because shroud seals are generally short with fewer fins and the effect of surrounding flow field is thought to be large. The four models are a full model consisting of a 1-stage stator/rotor cascade and a labyrinth seal over the rotor shroud, a guide-vane model to simulate the condition similar to seal element experiments, and two other simplified models. The calculated stiffness coefficients of the four models did not agree and fell into two groups. Through careful investigations of flow fields, it was found that the difference could be explained by the circumferential mass flow distribution at the seal inlet and the mass flow bias rate is an important factor in evaluating the seal force of a turbine shroud. The results also indicate that the rotordynamic characteristics obtained from seal element experiments may differ from those of actual turbines, especially in short seals.

Aeroelastic Investigation of a Transonic Research Compressor

The trend in modern compressor design is towards higher stage loading and less structural damping, resulting in increased flutter risk. The understanding of the underlying aeroelastic effects, especially at highly loaded BLISK rotors, is small. This paper reports on the analysis of flutter phenomena in a modern transonic compressor. The geometry examined here is the one-and-a-half stage transonic research compressor operated by Technische Universität Darmstadt. High blade deflections recorded during throttling measurements point to an aerodynamic excitation. Therefore, numerical investigations are carried out using the CFD-Code TRACE developed at the German Aerospace Center (DLR). Simulations are compared to measured compressor speed lines to validate the steady state results. The open source Finite Element code CalculiX is used to simulate the rotor blade eigenmodes and -frequencies. The results are then used in time-linearized calculations to determine the onset of flutter. These calculations confirm that there is an aerodynamic excitation of the first torsional eigenmode and blade flutter is at risk. A sensitivity study is carried out to further investigate the aerodynamic conditions under which structural vibrations become unstable and to identify influencing factors.

Efficient Techniques for the Computation of the Nonlinear Dynamics of a Foil-Air Bearing Rotor System

The foil-air bearing (FAB) plays a key role in the development of high speed, economical and environmentally friendly oil-free turbomachinery. However, FABs are known to be capable of introducing undesirable nonlinear effects into the dynamic response of a rotor-bearing system. This necessitates a means for calculating the nonlinear response of rotor systems with FABs. Up to now, the computational burden introduced by the interaction of the dynamics of the rotor, air film and foil structure has been overcome by uncoupling these three subsystems, introducing the potential for significant error. This paper performs the time domain solution of a simple rotordynamic system without uncoupling the state variables. This solution is then used as a reference for the verification of two proposed novel methods for reducing the computational burden: (a) use of harmonic balance; (b) use of Galerkin transformation. The applicability and accuracy of these two methods is illustrated on a simple symmetric rotor-FAB system.

A Novel Weldless Foils-Case Attachment for Gas Foil Bearings

Gas Foil Bearings (GFB) have a wide field of applications, from air cycle machines to microturbomachinery. A GFB basically consists of a foil (top foil) that lies over a corrugated foil (bump foil) that acts as a compliant spring. The rotation of the shaft introduces the fluid into the bearing and the pressure generated into the gap between the shaft and the top foil supports the rotor. The foils are attached to the case in a fixed point; usually they are welded to the bearing case. In addition to being rather cumbersome to build, this welded union is a potential point of failure. This work presents a new proposal of foils and case union. Foils are not welded to the case; they are placed or slid into a groove which avoids the strain concentration. This also permits the replacement of any foil in case of damage and to change the bump foil to modify the load capacity or the rotordynamic coefficients if required. The proposed assembly is experimentally tested by measuring its static stiffness in different radial directions of the fixed point. Results for static stiffness are presented and discussed.

Prediction of High-Frequency Blade Vibration Amplitudes in a Radial Inflow Turbine With Nozzle Guide Vanes

Impeller blades in radial inflow turbines are not only exposed to high thermal loads and centrifugal forces. Additional dynamic stresses occur by the aerodynamic excitation of a variety of blade and disc modes and can lead to damages by fatigue. This is a critical consideration for engines with nozzle guide vanes in particular, where excitation is caused by the interaction between guide vanes and rotor blades. This leads to high excitation frequencies, which are within the range of eigenfrequencies of the stiff impeller. Previous experimental analyses provide vibration amplitude data for resonances in a radial inflow turbine equipped with three nozzle rings with varying vane numbers. The experimental data is used for validation of numerical investigations. The numerical work presented involves the simulation of the transient flow field of the entire turbine as a first step. Aerodynamic excitation forces on the blades are derived from the results for various resonance conditions. The influence of the operating condition and the vane number is pointed out. Higher speed and lower vane number increase the amplitudes of the blade force. In a second step, the transient and spatially resolved pressure distribution is used as a boundary condition in an FE model. The damping ratio is an essential parameter in order to calculate the forced response of the structure, and it is determined from the experimental data. The damping behavior is characterized and compared to ratios derived from additional experimental studies using laser vibrometry at the non-rotating turbine wheel under ambient conditions. A disparity in the damping ratios is recovered, depending on the eigenmodes and the boundary conditions. The forced response of the structure is computed using the individual damping ratios for four resonance conditions. Harmonic analyses are conducted, applying the pressure forces from CFD. The calculated amplitudes are validated with data from strain gauge measurements under operating condition. The prediction of the vibration amplitudes shows acceptable agreement to the test data with a tendency towards lower values.

Flutter Amplitude Saturation by Nonlinear Friction Forces: An Asymptotic Approach

The computation of the friction saturated vibratory response of an aerodynamically unstable bladed-disk in a realistic configuration is a formidable numerical task, even for the simplified case of assuming the aerodynamic forces to be linear. The non-linear friction forces effectively couple different traveling waves modes and, in order to properly capture the dynamics of the system, large time simulations are typically required to reach a final, saturated state. Despite of all the above complications, the output of the system (in the friction microslip regime) is not that complex: it typically consists of a superposition of the aeroelastic unstable traveling waves, which oscillate at the elastic modal frequency and exhibit also a modulation in a much longer time scale. This large time modulation over the purely elastic oscillation is due to both, the small aerodynamic effects and the small nonlinear friction forces. The correct computation of these two small effects (small as compared with the elastic forces) is crucial to determine the final amplitude of the flutter vibration, which basically results from its balance. In this work we apply asymptotic techniques to obtain a new simplified model that gives only the slow time dynamics of the amplitudes of the traveling waves, filtering out the fast elastic oscillation. The resulting asymptotic model is very reduced and extremely cheap to simulate, and it has the advantage that it gives precise information about how the nonlinear friction at the fir-tree actually acts in the process of saturation of the vibration amplitude.

Approximate Analytical Model for Oil Film Force of Finite Length Squeeze Film Damper Under Low Reynolds Number

Squeeze film dampers (SFDs) are widely used in aero-engines and other high speed rotating machines as damping elements, owing to their remarkable damping effect. The oil-film force model of SFDs is the key to investigate the dynamic characteristics of the rotor-bearing systems involving SFDs. In this paper, the analytical solution of the oil film pressure of a finite length SFD is obtained by employing the separation of variables method to solve the Reynolds equation (at low Reynolds number) based upon the dynamic π boundary condition. The analytical expression of the oil film force is then derived by applying the integral method. The oil film force from the analytical model is compared with the results from other well-known methods, i.e. the long bearing approximation, the short bearing approximation and the finite difference method. The results clearly show that within a wider length-diameter ratio range, the newly proposed model can accurately predict the oil film characteristics of the SFDs at low Reynolds numbers.