High cycle fatigue (HCF) failure has been studied extensively over the last two decades. Its impact on jet engines is severe enough that may result in engine losses and even life losses. The main requirement for fatigue life predictions is the stress caused by mechanical vibrations. One of the factors which have major impact on the vibratory stresses of bladed disk assemblies is a phenomenon called &ldquo / mistuning&rdquo / which is defined as the vibration localization caused by the loss of cyclic periodicity which is a consequence of inter&amp / #8208 / blade variations in structural properties. In this thesis, component mode synthesis method (CMSM) is combined with nonlinear forced response analysis in modal domain. Newton&amp / #8208 / Raphson and arc length continuation procedures are implemented for the solution. The component mode synthesis method introduces the capability of imposing mistuning on the modal properties of each blade in the assembly. Forced response analysis in modal domain reduces the problem size via mode truncation. The main advantage of the proposed method is that it is capable of calculating nonlinear forced response for all the degrees&amp / #8208 / of&amp / #8208 / freedom at each blade with less computational effort. This makes it possible to make a stress analysis at resonance conditions. The case studies presented in this thesis emphasize the importance of number of modes retained in the reduced order model for both CMSM and nonlinear forced response analysis. Furthermore, the results of the case studies have shown that both nonlinearity and mistuning can cause shifts in resonance frequencies and changes in resonance amplitudes. Despite the changes in resonance conditions, the shape of the blade motion may not be affected.

<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>

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.

Bladed disks are critical structural components in jet engines and other turbomachinery. The nominal design for a bladed disk is typically assumed to have identical blades. However, there are always small, random variations in the blade properties due to manufacturing tolerances, material defects, and operational wear. These blade-to-blade discrepancies, called mistuning, can have a dramatic effect on bladed disk vibration. In particular, mistuning can cause localization of the response in a small region of the bladed disk, leading to higher blade stress and high-cycle fatigue concerns. While comprehensive analytical and computational studies of mistuning have been performed, relatively few experimental investigations have been conducted. The primary objective of this research is to experimentally investigate the fundamental structural dynamics of mistuned bladed disks, and to achieve a physical understanding of mistuning effects by accounting for the influence of important phenomena that have been largely neglected in previous mistuning models and system identification algorithms. First, a systematic experimental approach is presented to validate a new mistuning identification and model updating algorithm for single-piece bladed disks, or blisks. It is shown that only a few system response measurements taken at resonant frequencies are required to identify the blade stiffness mistuning parameters and the model updating parameters referred to as cyclic modeling error. By incorporating a model updating procedure, the accuracy of the mistuning identification results are significantly improved. Second, an alternative approach for vibration testing of many mistuning patterns is proposed and validated. In particular, varying the external forcing function provided to the blades is used to mimic the influence of structural blade property mistuning on the vibration response. Since it is much easier and more efficient to vary the external excitation than to physically alter the blades, this work opens the possibility of running an experimental analogue of a Monte Carlo simulation. Finally, the mistuning identification method is extended to also identify the forcing amplitude and phase applied to each blade. This approach shows promise as a powerful tool for accelerating calibration procedures, as well as for improving the accuracy and capability of experimental methods for bladed disks.

Crack initiation and propagation in the bladed disks of aero-engines caused by high-cycle fatigue under cyclic loads could result in the breakdown of the engines if not detected at an early stage. Although a number of fault detection methods have been reported in the literature, it still remains very challenging to develop a reliable online technique to accurately diagnose defects in bladed disks. One of the main challenges is to characterize signals contaminated by noises. These noises caused by very dynamic engine operation environment. This work presents a new technique for engine bladed disk crack detection, which utilizes advanced analysis of clearance and time-of-arrival signals acquired from blade tip sensors. This technique involves two stages of signal processing: 1) signal pre-processing for noise elimination from predetermined causes; and 2) signal post-processing for characterizing crack initiation and location. Experimental results from the spin rig test were used to validate technique predictions.

Crack initiation and propagation in the bladed disks of aero-engines caused by high-cycle fatigue under cyclic loads could result in the breakdown of the engines if not detected at an early stage. Although a number of fault detection methods have been reported in the literature, it still remains very challenging to develop a reliable online technique to accurately diagnose defects in bladed disks. One of the main challenges is to characterize signals contaminated by noises. These noises caused by very dynamic engine operation environment. This work presents a new technique for engine bladed disk crack detection, which utilizes advanced analysis of clearance and time-of-arrival signals acquired from blade tip sensors. This technique involves two stages of signal processing: 1) signal pre-processing for noise elimination from predetermined causes; and 2) signal post-processing for characterizing crack initiation and location. Experimental results from the spin rig test were used to validate technique predictions.

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). 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. 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. / NR 20140805

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Steam turbine rotor is a very complicated assembly, typically consists of several rotor rows. Due to design limitations and increasing demands on the efficiency of the steam turbines, it is practically impossible to avoid all of the resonant states. The significant vibrations can occur, for example, due to passing resonance state during turbine start up or run out. In the worst case the turbine operates state is close to the resonance state of the rotor row. This leads to the significant oscillation of the bladed disk, and may results in the blade (or blade to disk joints) high cycle fatigue. These parts are highly loaded components and any cracks are unacceptable. Therefore it is absolutely necessary to damp vibration by using, for example, passive damping elements. The damping element analyzed in this thesis is a strap with an isosceles trapezoidal cross section, which is placed in the circumferential dovetail groove in the blade segmental shrouding. The sliding between the contact surfaces leads to the dissipation of energy which causes decreasing of undesirable vibrations. The main aim is to design the optimal dimensions of the strap cross-section with a view to the most effective damping of vibration for a particular turbine operating state. Considered bladed disk has 54 blades which are coupled in 18 packets by segmental shrouding. The damping element is paced in circumferential dovetail groove created in the shrouding. This type of damping element is suitable especially for damping vibrations in the axial direction and only with the mode shape with the nodal diameters. The modal properties of the bladed disk are influenced by the sliding distance. Since the friction force depends on centrifugal force acting on the damping element and on the angle of the side walls of the strap and groove, the sliding distance can be influenced by the damping element dimensions. During the optimization process the best possible size of middle width, height and angle of damping element cross-section is searched. The strap weight, contact area size and flexural stiffness of damping element can be influenced by these parameters. Their change has also impact on the size of the contact pressure and thus on the size of relative motion as well. As stated previously, the damping efficiency is influenced by the relative motion between the damping element and shrouding. Numerical simulation in time domain is very time-consuming, especially for systems containing nonlinearities. In order to verify dynamic behavior of the computational model with the passive friction element in numerical simulations, the simplified model is created. The model is created in the ANSYS environment. The main requirement imposed on this model is to have as small number of degrees of freedom as possible, so the time needed to perform the simulation is reduced to a minimum. To satisfy this requirement the simplified model is a cantilever beam with rectangular cross section. The dovetail groove is created in this model in longitudinal direction. In this groove is damping element. In addition to damping element dimensions optimization, the influence of each design variable on model dynamic behavior is studied. The results are verified experimentally. Experiment also shows other interesting results that confirm the damping element influence on the modal characteristics. The gained knowledge is used to optimize the dimensions of the damping element in the model of the bladed disk.

Because blades in jet engine compressors are subject to dynamic loads based on the engine's speed, it is essential that the blades are properly "tuned" to avoid resonance at those frequencies to ensure safe operation of the engine. The tuning process can be time consuming for designers because there are many parameters controlling the geometry of the blade and, therefore, its resonance frequencies. Humans cannot easily optimize design spaces consisting of multiple variables, but optimization algorithms can effectively optimize a design space with any number of design variables. Automated blade tuning can reduce design time while increasing the fidelity and robustness of the design. Using surrogate modeling techniques and gradient-free optimization algorithms, this thesis presents a method for automating the tuning process of an airfoil. Surrogate models are generated to relate airfoil geometry to the modal frequencies of the airfoil. These surrogates enable rapid exploration of the entire design space. The optimization algorithm uses a novel objective function that accounts for the contribution of every mode's value at a specific operating speed on a Campbell diagram. When the optimization converges on a solution, the new blade parameters are output to the designer for review. This optimization guarantees a feasible solution for tuning of a blade. With 21 geometric parameters controlling the shape of the blade, the geometry for an optimally tuned blade can be determined within 20 minutes.