One of the common failure modes of the diesel engine turbochargers is high-cycle fatigue of the turbine-wheel blades. Mistuning of the blades due to the casting process is believed to contribute to this failure mode. A laser vibrometer is used to characterize mistuning for a population of turbine wheels through the analysis of the blade-response to piezo-speaker induced noise. The turbine-wheel design under investigation is radial and is typically used in 6-12L diesel engine applications. FRFs and resonance frequencies are reviewed and summarized. The study includes test results for a paddle wheel that represents a perfectly tuned system and acts as a reference. A discrete mass-spring model is developed for the paddle wheel and the model suitability is tested against measured data. Density randomization is applied to model mistuning in the turbine wheels. Frequency mistuning and relative amplitude modelling for blade modes is found in good agreement with the data, however the mass-spring model over-predicts amplitude-amplification factors for a population of radial-turbine wheels, especially with regard to hub-dominant modes. A continuous twisted-blade model is developed in Matlab using finite-element techniques. Experimental data is shown to have good agreement with the twisted-blade model. Whitehead’s maximum amplitude-amplification prediction using RMS value for a tuned amplitude value is calculated, and the turbine-wheel response is found to fit within the theoretical limit. Different mistuning patterns are studied using the twisted-blade model. Maximum and minimum response patterns are identified and recommended.

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abstract: Monte Carlo simulations are traditionally carried out for the determination of the amplification of forced vibration response of turbomachine/jet engine blades to mistuning. However, this effort can be computationally time consuming even when using the various reduced order modeling techniques. Accordingly, some investigations in the past have focused on obtaining simple approximate estimates for this amplification. In particular, two of these have proposed the use of harmonic patterns of the blade properties around the disk as an approximate alternative to the many random patterns of Monte Carlo analyses. These investigations, while quite encouraging, have relied solely on single degree of freedom per sector models of the rotor. In this light, the overall focus of the present effort is a revisit of harmonic mistuning of rotors focusing first the confirmation of the previously obtained findings with a more detailed model of the blisk in both conditions of an isolated blade-dominated resonance and of a veering between blade and disk dominated modes. The latter condition cannot be simulated by a single degree of freedom per sector model. Further, the analysis will consider the distinct cases of mistuning due to variations of material properties (Young's modulus) and geometric properties (geometric mistuning). In the single degree of freedom model, both mistuning types are equivalent but they are not, as demonstrated here, in more realistic models. The difference arises because changes in geometry induce not only changes in natural frequencies of the blades alone but of their modes and the importance of these two sources of variability is discussed with both Monte Carlo simulation and harmonic mistuning results. The present investigation focuses also on the possible extension of the harmonic mistuning concept and of its quantitative information that can be derived from such analyses. From it, a novel measure of blade-disk coupling is introduced and assessed in comparison with the coupling index introduced in the past. In conclusions, the low cost of harmonic mistuning computations in comparison with full Monte Carlo simulations is demonstrated to be worthwhile to elucidate the basic behavior of the mistuned rotor in a random setting. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2014

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<p>Two state of the art finite element reduction techniquespreviously validated against the direct finite element method,one based on classical modal analysis and another based oncomponent mode synthesis, are applied for efficient mistunedfree vibration and forced response analysis of several bladeddisk geometries. The methods are first applied to two testcases in order to demonstrate the differences in computationalefficiency as well as to validate the methods againstexperimental data. As previous studies have indicated, nonoticeable differences in accuracy are detected for the currentapplications, while the method based on classical modalanalysis is significantly more efficient. Experimental data(mistuned frequencies and mode shapes) available for one of thetwo test cases are compared with numerical predictions, and agood match is obtained, which adds to the previous validationof the methods (against the direct finite element method).</p><p>The influence of blade-to-blade coupling and rotation speedon the sensitivity of bladed disks to mistuning is thenstudied. A transonic fan is considered with part span shroudsand without shrouds, respectively, constituting a high and alow blade-to-blade coupling case. For both cases, computationsare performed at rest as well as at various rotation speeds.Mistuning sensitivity is modelled as the dependence ofamplitude magnification on the standard deviation of bladestiffnesses. The finite element reduction technique based onclassical modal analysis is employed for the structuralanalysis. This reduced order model is solved for sets of randomblade stiffnesses with various standard deviations, i.e. MonteCarlo simulations. In order to reduce the sample size, thestatistical data is fitted to a Weibull (type III) parametermodel. Three different parameter estimation techniques areapplied and compared. The key role of blade-to-blade coupling,as well as the ratio of mistuning to coupling, is demonstratedfor the two cases. It is observed that mistuning sensitivityvaries significantly with rotation speed for both fans due toan associated variation in blade-to-blade coupling strength.Focusing on the effect of one specific engine order on themistuned response of the first bending modes, it is observedthat the mistuning sensitivity behaviour of the fan withoutshrouds is unaffected by rotation at its resonant condition,due to insignificant changes in coupling strength at thisspeed. The fan with shrouds, on the other hand, shows asignificantly different behaviour at rest and resonant speed,due to increased coupling under rotation. Comparing the twocases at resonant rotor speeds, the fan without shrouds is lessor equally sensitive to mistuning than the fan with shrouds inthe entire range of mistuning strengths considered.</p><p>This thesis’scientific contribution centres on themistuning sensitivity study, where the effects of shrouds androtation speed are quantified for realistic bladed diskgeometries. However, also the validation of two finite elementreduction techniques against experimental measurementsconstitutes an important contribution.</p>

<p>This research investigates the forced response of mistuned rotor blades that can lead to excessive vibration, noise, and high cycle fatigue failure in a turbomachine. In particular, an embedded rotor in the Purdue Three-Stage Axial Compressor Research Facility is considered. The prediction of the rotor forced response contains three key elements: the prediction of forcing function, damping, and the effect of frequency mistuning. These computational results are compared with experimental aerodynamic and vibratory response measurements to understand the accuracy of each prediction.</p><p>A state-of-the-art time-marching computational fluid dynamic (CFD) code is used to predict the rotor forcing function. A highly-efficient nonlinear frequency-domain Harmonic Balance CFD code is employed for the prediction of aerodynamic damping. These allow the compressor aerodynamics to be depicted and the tuned rotor response amplitude to be predicted. Frequency mistuning is considered by using two reduced-order models of different levels of fidelity, namely the Fundamental Mistuning Model (FMM) and the Component Mode Mistuning (CMM) methods. This allows a cost-effective method to be identified for mistuning analysis, especially for probabilistic mistuning analysis.</p><p>The first topic of this work concerns the prediction of the forcing function of the embedded rotor due to the periodic passing of the neighboring stators that have the same vane counts. Superposition and decomposition methods are introduced under a linearity assumption, which states that the rotor forcing function comprises of two components that are induced by each neighboring stator, and that these components stay unchanged with only a phase shift with respect to a change in the stator-stator clocking position. It is found that this assumption captures the first-order linear relation, but neglects the secondary nonlinear effect which alters each stator-induced forcing functions with respect to a change in the clocking position.</p><p>The second part of this work presents a comprehensive mistuned forced response prediction of the embedded rotor at a high-frequency (higher-order) mode. Three steady loading conditions are considered. The predicted aerodynamics are in good agreement with experimental measurements in terms of the compressor performance, rotor tip leakage flow, and circumferential distributions of the stator wake and potential fields. Mistuning analyses using FMM and CMM models show that the extremely low-cost FMM model produces very similar predictions to those of CMM. The predicted response is in good agreement with the measured response, especially after taking the uncertainty in the experimentally-determined frequency mistuning into consideration. Experimentally, the characteristics of the mistuned response change considerably with respect to loading. This is not very well predicted, and is attributed to un-identified and un-modeled effects. A significant amplification factor over 1.5 is observed both experimentally and computationally for this higher-order mode.</p> / Dissertation

One of the most important problems that plague turbomachinery rotors is the existence of rogue blades -- lone blades that exhibit unexpected fatigue failure. It has been recognized that rotor mistuning might be the cause of rogue blades through a phenomenoncalled normal mode localization, whereby vibration energy is confined to a few blades of the assembly. The goals of this dissertation are (1) to achieve a thorough understanding of the fundamental mechanisms governing mistuning effects, (2) the development of mathematical models of turbomachinery rotors suitable for mistuning analysis, and (3) the development of techniques for designers interested in the mistuning sensitivity of a particular rotor design.

This dissertation provides numerical studies to improve bladed disk assembly design for preventing blade high cycle fatigue failures. The analyses are divided into two major subjects. For the first subject presented in Chapter 2, the mechanisms of transonic fan flutter for tuned systems are studied to improve the shortcoming of traditional method for modern fans using a 3D time-linearized Navier-Stokes solver. Steady and unsteady flow parameters including local work on the blade surfaces are investigated. It was found that global local work monotonically became more unstable on the pressure side due to the flow rollback effect. The local work on the suction side significantly varied due to nodal diameter and flow rollback effect. Thus, the total local work for the least stable mode is dominant by the suction side. Local work on the pressure side appears to be affected by the shock on the suction side. For the second subject presented in Chapter 3, sensitivity studies are conducted on flutter and forced response due to frequency mistuning and aerodynamic asymmetry using the single family of modes approach by assuming manufacturing tolerance. The unsteady aerodynamic forces are computed using CFD methods assuming aerodynamic symmetry. The aerodynamic asymmetry is applied by perturbing the influence coefficient matrix. These aerodynamic perturbations influence both stiffness and damping while traditional frequency mistuning analysis only perturbs the stiffness. Flutter results from random aerodynamic perturbations of all blades showed that manufacturing variations that effect blade unsteady aerodynamics may cause a stable, perfectly symmetric engine to flutter. For forced response, maximum blade amplitudes are significantly influenced by the aerodynamic perturbation of the imaginary part (damping) of unsteady aerodynamic modal forces. This is contrary to blade frequency mistuning where the stiffness perturbation dominates. / Dissertation