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An advanced design of sandwichstructures does not only require the knowledge of the global stress- and deformation behavior, but also the knowledge of the local effects, such as load singularities and the loss of stability caused by the short wave wrinkling of one (bending) or both (pressure) sandwich skins.Based on the nonlinear theory for sandwich shells with seven kinematic degrees of freedom, introduced from Kühhorn and Schoop an improved theory for plane sandwich shells with eight degrees of freedom will be presented, enabling a much better representation of the sandwich core behavior.Due to consideration of quadratic core thickness and linear core shear strain as well as longitudinal core deformation an improved prediction of the wrinkling behavior is succeeded even for thick cores and thin skins.The kinematic quantities as well as the nonlinear-differential equations and the simplified equations of first order theory resulting from them are given.Finally applying the well known classical problems of stability loaded by pressure and bending, the efficiency of this 8 DOF-theory ist demonstrated. A comparison with a detailed finite element (plain strain) calculation shows the high quality of these results.The presented sandwich theory characterized by eight degrees of freedom enables the calculation of nearly all essential sandwich phenomena even for thick cores.
Auf Grund der im Rahmen eines Testfluges subjektiv durch den Piloten festgestellten hohen Schwingungsamplituden wird das dynamische Verhalten eines Ultraleichtflugzeugmotors inklusive der Motoraufhängung untersucht. Hierin wir der numerische Teil der Untersuchun-gen durch eine finite Elemente Simulation abgedeckt, in deren Rahmen die wesentlichen Ei-genschwingformen der Antriebseinheit samt Motorträger identifiziert wurden. Ergänzend mit den Ergebnissen einer experimentellen Modalanalyse und Betriebsschwingungsmessungen konnten wesentliche Informationen gewonnen werden, aus denen als Maßnahme zur Schwin-gungsreduzierung die Erhöhung der Schwungradmasse abgeleitet wurde.
An advanced design of sandwichstructures does not only require the knowledge of the global stress- and deformation behavior, but also the knowledge of the local effects, such as load singularities and the loss of stability caused by the short wave wrinkling of one (bending) or both (pressure) sandwich skins.Based on the nonlinear theory for sandwich shells with seven kinematic degrees of freedom, introduced from Kühhorn and Schoop an improved theory for plane sandwich shells with eight degrees of freedom (position vector r, director d, and intensity factors az1, az2 for including core flexibility) will be presented, enabling a much better representation of the sandwich core behavior.Due to consideration of quadratic core thickness and linear core shear strain as well as longitudinal core deformation an improved prediction of the wrinkling behavior is succeeded even for thick cores and thin skins.The kinematic quantities as well as the nonlinear-differential equations achieved from the principle of virtual work and the simplified equations of first order theory resulting from them are given.Finally applying the well known classical problems of stability loaded by pressure and bending, the efficiency of this 8 DOF-theory is demonstrated. A comparison with a detailed finite element (plain strain) calculation shows the high quality of these results.The presented sandwich theory characterized by eight kinematic degrees of freedom is valid for arbitrary displacements, rotations and moderat strains enables the calculation of nearly all essential sandwich phenomena even for thick cores.
Ökonomische und ökologische Bedürfnisse verlangen von modernen Konstruktionen sowohl eine hochintegrative Bauweise als auch eine massive Gewichtseinsparung. Dies führt zu neuen Leichtbaukonstruktionen mit einem stetig zunehmenden Anteil an Faserverbundlösungen. Die hierbei eröffnete Möglichkeit, kraftfluß- und beanspruchungsgerecht auszulegen, erschließt sich erst vollständig durch die sichere Anwendung moderner FE-Programme wie beispielsweise ABAQUS. Nutzt man darüber hinaus die Möglichkeit der flexiblen Script-Programmierung, so lassen sich wirkungsvolle Effizienzsteigerungen durch die gezielte Erstellung spezifischer Eingabemenüs und Ausgaberoutinen erreichen. Dieser Beitrag veranschaulicht an Hand eines ausgeführten und getesteten CFK-Modellflügels unter Biegebeanspruchung, die Vorgehensweise bei Verwendung von ABAQUS und der Script-Sprache Python.
Initiiert durch die im Rahmen eines Testfluges subjektiv durch den Piloten festgestellten hohen Schwingungsamplituden wird das dynamische Verhalten eines Ultraleichtflugzeugmotors inklusive der Motoraufhängung untersucht. Hierin wir der numerische Teil der Untersuchungen durch eine finite Elemente Simulation abgedeckt, in deren Rahmen die wesentlichen Eigenschwingformen der Antriebseinheit samt Motorträger identifiziert wurden. Ergänzend mit den Ergebnissen einer experimentellen Modalanalyse und Betriebsschwingungsmessungen konnten wesentliche Informationen gewonnen werden, aus denen als Maßnahme zur Schwin-gungsreduzierung die Erhöhung der Schwungradmasse abgeleitet wurde.
Simulation fluidgedämpfter Strukturschwingungen mittels partitionierter Fluid-Struktur-Kopplung
(2005)
Theoretische und experimentelle Untersuchungen von Schaufelschwingungen bei Verdichterintegralrädern
(2006)
Verstimmungsuntersuchungen am Laufrad (Blisk) eines modernenFlugtriebwerk-Hochdruckverdichters
(2011)
Analysis of oxygen exchange-limited transport and chemical stresses in perovskite-type hollow fibers
(2012)
Radial turbine wheels designed as blade integrated disks (blisk) are widely used in various industrial applications. However, related to the introduction of exhaust gas turbochargers in the field of small and medium sized engines, a sustainable demand for radial turbine wheels has come along. Despite those blisks being state of the art, a number of fundamental problems, mainly referring to fluid-structure-interaction and, therefore, to the vibration behavior, have been reported. Aiming to achieve an enhanced understanding of fluid-structure-interaction in radial turbine wheels, a numerical method, able to predict forced responses of mistuned blisks due to aerodynamic excitation, is presented. In a first step, the unsteady aerodynamic forcing is determined by modeling the spiral casing, the stator vanes, and the rotor blades of the entire turbine stage. In a second step, the aerodynamic damping induced by blade vibration is computed using a harmonic balance technique. The structure itself is represented by a reduced order model being extended by aerodynamic damping effects and aerodynamic forcings. Mistuning is introduced by adjusting the modal stiffness matrix based on results of blade by blade measurements that have been performed at rest. In order to verify the numerical method, the results are compared with strain-gauge data obtained during rig-tests. As a result, a measured low engine order excitation was found by modeling the spiral casing. Furthermore, a localization phenomenon due to frequency mistuning could be proven. The predicted amplitudes are close to the measured data.
It is important to steadily refine lightweight designs with regard to saving resources and energy in common with good economic efficiency.
Thin structured sheet metals offer significantly improved component stiffnesses in addition to an upgraded buckling behavior compared to flat, unstructured sheet metals.
By using a distortion energy based homogenization method it is possible to develop a mechanical surrogate model which describes effective mean properties. The accurate selection of symmetric and periodic boundaries enables to determine the required parameters. The conditions are contemplated on elementary cells whose structural mechanical behavior is representative for the elastic behavior of large structures. By doing this, the amount of elements can be reduced and thus the calculating time of large components can considerably be saved.
For an efficient surrogate model it is required to analyze and compare numerical with experimental investigations. Some different versions of optimization will be tested to get better approximation of the data.
As a result of more balanced blade aspect ratios of modern blade-integrated disks (blisks), interactions between disk-dominated and blade-dominated modes are becoming more and more important, especially if blade mistuning is considered. The specific vibration behavior in these transition regions is characterized by a mix of both fundamental mode types into “coupled” modes. In this paper, numerical and experimental investigations based on a front high-pressure compressor (HPC) blisk stage were carried out in order to determine the effect of blade mistuning on those regions in detail. At this, effects like mode localization and amplitude magnification are found to be weakened in an integer frequency-veering zone. Contrary to this, blisks are very sensitive to mistuning in regions of pure blade-dominated mode families with high modal density.
The forced response of an E3E-type high pressure compressor (HPC) blisk front rotor is analyzed with regard to varying mistuning and the consideration of the fluid-structure interaction (FSI). For that purpose, a reduced order model is used in which the disk remains unchanged and mechanical properties of the blades, namely stiffness and damping, are adjusted to measured as well as intentional blade frequency mistuning distributions. The aerodynamic influence coefficient technique is employed to model the aeroelastics. Depending on the blade mode, the exciting engine order, and aerodynamic influences, it is sought for the worst mistuning distributions with respect to the maximum blade displacement based on optimization analyses. Genetic algorithms using blade-alone frequencies as design variables are applied. The validity of the Whitehead limit is assessed in this context. In particular, the question is addressed if and how far aeroelastic effects, mainly caused by aerodynamic damping, combined with mistuning can even cause a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the interblade phase angle is the main driver for a possible response attenuation considering the fundamental as well as a higher blade mode. Furthermore, the differences to the blisk vibration response without a consideration of the flow and an increase of the disk's stiffness are discussed. Closing, the influence of pure damping mistuning is analyzed again using optimization.
The forced response of the first rotor of an engine 3E (technology program) (E3E)-type high pressure compressor (HPC) blisk is analyzed with regard to varying mistuning, varying engine order (EO) excitations and the consideration of aero-elastic effects. For that purpose, subset of nominal system modes (SNM)-based reduced order models are used in which the disk remains unchanged while the Young's modulus of each blade is used to define experimentally adjusted as well as intentional mistuning patterns. The aerodynamic influence coefficient (AIC) technique is employed to model aero-elastic interactions. Furthermore, based on optimization analyses and depending on the exciting EO and aerodynamic influences it is searched for the worst as well as the best mistuning distributions with respect to the maximum blade displacement. Genetic algorithms using blade stiffness variations as vector of design variables and the maximum blade displacement as objective function are applied. An allowed limit of the blades' Young's modulus standard deviation is formulated as secondary condition. In particular, the question is addressed if and how far the aero-elastic impact, mainly causing aerodynamic damping, combined with mistuning can even yield a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the interblade phase angle is the main driver for a possible response attenuation considering the fundamental blade mode. The results of the optimization analyses are compared to the forced response due to real, experimentally determined frequency mistuning as well as intentional mistuning.
In this paper a successful topology optimization of a centrifugally loaded aero-engine part is presented. For the topology optimization, which is a nonlinear problem due to several contact regions, a self-developed topology optimization algorithm in combination with a commercial FE-solver is used. The goal of the optimization was the reduction of stresses in the structure.
©2014 Rolls-Royce Deutschland Ltd & Co. KG. Published by Elsevier Masson SAS. All rights reserved.
The impact performance of structural components made of fibre-reinforced plastic is often one of the limiting properties during the design process. To improve the damage resistance regarding transverse low-velocity impact loading, a rubber layer (KRAIBON®) is integrated into the composite laminate of tubular carbon/epoxy specimens. Numerous impact tests, using two different rubber compounds and three different layups, are carried out. The specimens are impacted using a modified Charpy pendulum. Force–time histories have been used to determine the damage threshold load. To visualise damage such as delaminations and inter-fibre failures, the impacted samples have been examined using microsectioning.
It is shown that a significant improvement in impact damage resistance can be achieved by integrating a rubber layer into a carbon/epoxy laminate.
Computational Fluid Dynamics is widely used for the analysis and the design of turbomachinery blade rows. A well established method is the application of semi-unstructured meshes, that uses a combination of structured meshes in the radial direction and unstructured meshes in the axial as well as the tangential direction. This takes advantage of the approximately two dimensional flow field through the blade rows, whereby a fine radial discretization, excepting the near wall region, is not necessary. Otherwise, it is possible to discretize particular regions, e.g. the leading and trailing edge regions, in the axial and tangential direction without generating unnecessary nodes in the far field. The meshing approach is based on the projection of a two dimensional unstructured mesh defined at a reference surface. Once, the two dimensional mesh is generated the projection is achieved by transfinite interpolation from the reference surface to further radial surfaces using a structured mesh. Due to the modeling of geometrical features, especially fillets, advanced methods for the generation of structured meshes and mesh smoothing algorithms are required.
The paper presents two different approaches for the generation of an appropriate structured mesh. The first is based on the solution of elliptic partial differential equations. The second approach is based on the split of the domain into fourteen appropriately arranged blocks. Furthermore, two smoothing methods for two dimensional unstructured meshes, a constrained Laplace smoothing and an optimization based approach, are presented. Regarding a more realistic representation of the geometry, methods for the modeling of cavities, variable clearance sizes and fillets are presented. Finally, a comparison of the smoothing techniques applied to a rotor passage is presented and the influence of chosen geometrical features on the flow solution is evaluated.
This contribution presents a model update procedure and its experimental validation using the example of a blade integrated disk rotor. This so called blisk is discretized using the finite element method. It is well known that numerical blisk models based on the ideal tuned design show major differences in structural dynamic behavior compared to the real rotor. In this context a modification of the mechanical simulation model should lead to a better accordance of numerical results and the real blisk characteristics. The described model update procedure utilizes data of an optical 3D measurement system. Using this data enables to identify geometric deviations between the ideal design and its real counterpart. Within the update procedure the originally tuned finite element mesh is modified in order to match the measured geometry of the real part. This is done by defining several morph regions. The outer surface nodes of these morph regions change their position along the surface normal vector until they meet the defined deviation constraint. Based on eigenvalue calculations employing free boundary conditions the sensitivity of structural dynamic behavior is shown with respect to small geometric changes. Finally computed eigenvalues and eigenvectors of the updated simulation model are compared with vibration measurement data. A laser Doppler vibrometer is used to detect the vibration responses of the impact excited structure. All experiments are carried out under technical vacuum conditions in order to minimize ambient air damping. In the context of an experimental modal analysis this low damping condition helps to identify more natural frequencies of the investigated structure. This leads to a much more efficient model validation.
Due to the demand of more and more detailed FEM simulation results of whole aero-engine models, the number of DOF of such models (Fig. 1) increases dramatically. Although the available computational power for the solution of such highly nonlinear, dynamic boundary value problems also increased during the last years, the overall computational time of these high-fidelity models for the simulation of a few milliseconds of the running engine is in the order of several weeks even on high performance clusters with thousands of CPU cores. Typically, for such highly dynamic FEM computations explicit time integration schemes are used in order to solve the equations of motion. To keep such a numerical integration stable, the time step size may not exceed a certain critical
time step size. Unfortunately, the critical time step size of an explicit time integration algorithm for the engine models under consideration is in the order of 10-8. This means that the simulation of a running engine over a time span of a few seconds results in a computational time of several years with clusters, which are available nowadays. Therefore, implicit time integration schemes, which are unconditionally stable and allow much bigger time steps, have to be used. Since in an implicit integration, in contrast to an explicit one, an equilibrium iteration is always necessary, the computational costs for an implicit time step are much higher than for an explicit time step.
Almost all commercial FE codes use the classical Newmark implicit time integration scheme. It will be shown that this algorithm fails especially for the simulation of fast rotating structures if bigger time steps are used. This is demonstrated at the example of academic examples as well as for more realistic rotor models. To overcome the problems of the Newmark integration, a 3-Point-Newmark-
Euler-Backward integration scheme [1,2] has been selected, which consists of alternating Newmark and 3-Point-Euler-Backward steps. The additional interpolation information for the Euler-step is provided by the previous Newmark step. This integration procedure has been implemented and successfully applied to the FEM simulation of fast rotating structures, which will be also demonstrated during the presentation.
Using the example of a compressor test blisk with 29 blades different sources of mistuning and their consequences for the forced response are analysed under consideration of aeroelastic effects. In particular the impact of superimposing intentional structural mistuning by both random structural mistuning and aerodynamic mistuning is studied. For this purpose reduced order models of the blisk are adjusted for different mistuning distributions. The mistuning itself is characterized by assigning individual stiffness parameters to each blade. The aeroelastic coupling is included employing aerodynamic influence coefficients. By means of genetic algorithm optimizations, structural mistuning patterns are found which yield a mitigation of the forced response below that of the tuned design reference. Ideally a nearly 50 % reduction of maximum response magnitudes is computed for the fundamental bending mode and large mistuning. The solutions found have been proven to be robust with respect to additional random and aerodynamic mistuning in case of large intentional structural mistuning.
Reduced Order Analyses of Multi-stage Coupled Structures with Main Focus on Disk-Dominated Modes
(2016)
Rotors manufactured as blisk (Blade Integrated Disk) has become state-of-the-art in turbomachinery. This integral design saves a lot of mass and enables higher rotational speeds allowing for higher pressure ratios and hence an increased efficiency. The advantage comes along with the drawback that the structural damping level is extremely low. Nowadays, the dynamics of single-stage rotors is well-investigated, as dynamical analysis of cyclic structures is one of the most important subjects in applied research in turbomachinery. However, the stage-to-stage coupling effect is neglected in most cases. The importance of proper interstage treatment is obvious for adequate multi-stage analyses. Hence the structural dynamics of a multi-stage assembly has recently become an important area of research. In this paper, some multi-stage effects are discussed and three different reduced order techniques are summarized and demonstrated on a multi-stage assembly of academic blisks. The findings are compared to a FE-solution. Particular attention must be paid to disk-dominated modes, which are highly affected by multi-stage behavior. Mistuning modeling is not considered, because it mainly influences blade-dominated vibrations.
Rotors manufactured as blisk (Blade Integrated Disk) are manifoldly used in state-of-the-art turbomachinery.
Commonly, the endurance is evaluated by a numerical analysis of as designed rotor. Since small deviations due to the manufacturing cause slightly different blades, mistuning in turbomachinery is unavoidable. Mistuning causes increased vibration amplitudes - higher than those to be expected in case of the ideal design intention. Nowadays, there are various model updating procedures to ensure a more realistic modelling of blisks. Within Monte Carlo simulations, one obtains a well-approximated maximum vibration amplitude at
tolerable costs, the effect of fractional alterations of eigenmodes due to geometric imperfections is normally
neglected. Value and location of maximum stress are sensitive to geometric deviations but also decisive for an adequate calculation of the High Cycle Fatigue, which itself is one of the main causes of blisk failure.
The potential of intentional mistuning to reduce the maximum forced response is analyzed within the development of an axial turbine blisk for ship diesel engine turbocharger applications. The basic idea of the approach is to provide an increased aerodynamic damping level for particular engine order excitations and mode shapes without any significant distortions of the aerodynamic performance. The mistuning pattern intended to yield a mitigation of the forced response is derived from an optimization study applying genetic algorithms. Two blisk prototypes have been manufactured a first one with and another one without employing intentional mistuning. Hence, the differences regarding the real mistuning and other modal properties can be experimentally determined and evaluated as well. In addition, the experimental data basis allows for updating structural models which are well suited to compute the forced response under operational conditions. In this way, the real benefit achieved with the application of intentional mistuning is demonstrated.
Instabilities occurring during the implicit time-integration are still handicapping a time-efficient solution of large FEM systems of equations. Especially the simulation of flexible rotating structures is barely mastered by implicit FEM codes. For this, the Newmark algorithm and related algorithms are used for many years. Here, we derive the reasons for the mentioned inevitable numerical issues and present concepts that lead to an efficient and stable solution.
The effect of intentional mistuning has been analyzed for an axial turbocharger blisk with the objective of limiting the forced response due to low engine order excitation (LEO). The idea behind the approach was to increase the aerodynamic damping for the most critical fundamental mode in a way that a safe operation is ensured without severely losing aerodynamic performance. Apart from alternate mistuning a more effective mistuning pattern is investigated, which has been derived by means of optimization employing genetic algorithms. In order to keep the manufacturing effort as small as possible only two blade different geometries have been allowed which means that an integer optimization problem has been formulated. Two blisk prototypes have been manufactured for the purpose of demonstrating the benefit of the intentional mistuning pattern identified in this way: A first one with and a second one without employing intentional mistuning. The real mistuning of the prototypes has been experimentally identified. It is shown that the benefit regarding the forced response reduction is retained in spite of the negative impact of unavoidable additional mistuning due to the manufacturing process. Independently, further analyzes have been focused on the robustness of the solution by considering increasing random structural mistuning and aerodynamic mistuning as well. The latter one has been modeled by means of varying aerodynamic influence coefficients (AIC) as part of Monte Carlo simulations. Reduced order models have been employed for these purposes.
As-manufactured impellers behave significantly different from nominal impellers. There are no identical blades due to geometric and material deviations. In this paper three model updating procedures are discussed with the objective to achieve realistic models of as-manufactured impellers. The techniques are applied to radial inflow turbine wheel of an exhaust gas turbocharger. The first approach creates a model through optical measurement and mesh morphing. The second approach is based on a contactless measurement of blade individual vibration responses. An iterative update process gains the corresponding mistuning pattern and thus the associated model. Third, a model is found by an optimisation, that identified a mistuning pattern, that fits modal characteristics, which are evaluated during experimental modal analysis at vacuum. In-depth analyses of these models are realised to determine advantages and drawbacks of the procedures.
Blade vibrations are one of the main cost drivers in turbo-machinery. Computational blade vibration analysis facilitates an enormous potential to increase the productivity in the design of bladed components. Increasing computing power as well as improved modeling and simulation methods lead to comprehensive calculation results. This allows for a more precise prediction and assessment of experimental data.
Usually, in the field of turbomachinery, identical blades are assumed to lower the required computational resources. However, mistuning is unavoidable, since small deviations due to the manufacturing process will lead to slightly different blade behavior. Potential effects such as mode localization and amplification can be treated statistically and have been thoroughly studied in the past. Since then, several reduced order models (ROMs) have been invented in order to calculate the maximum vibration amplitude of a fleet of mistuned blisks. Most commonly, mistuning is thereby modeled by small material deviations from blade to blade, e.g. Young’s modulus or density.
Nowadays, it is common knowledge that the level of manufacturing imperfection (referred as level of mistuning) significantly influence mode localization as well as vibration amplification effects. Optical measurements of the geometric deviations of manufactured blades and converting to a high-fidelity finite element model make huge progress. However, to the knowledge of the authors, there is no reliable method, that derives a characteristic quantity from the geometric mistuning, that fits into the mentioned statistically approaches.
Therefore, experimental data is needed to quantify the level of mistuning. Several approaches, which isolate blade individual parameters, are used to identify the dynamic behavior of axial compressors and turbines. These methods can be applied to medium-speed centrifugal turbine wheels but tend to fail to evaluate high-speed compressor with splitter blades. This paper briefly presents the original approach and discusses the reasons for failure. Thereafter, a new approach is proposed. Finally the level of mistuning and important quantities to perform a statistical evaluation of a high-speed compressor is shown.
Copyright © 2018 by ASME
Due to the increasing turbine inlet temperature and in order to improve the overall efficiency it is necessary to optimize the cooling design of the hot gas components of an aero engine.
The current paper discusses the strategy of optimizing a rotor blade cooling configuration of a small civil aero engine, comprising of films and internal turbulators (ribs). An insight into the parametrization is given including the location of the films and ribs as well as the number of the films and ribs. The parameter reduction results in 18 input parameters for the optimizations to limit the number of parameters to an acceptable level.
Two optimizations are carried out with the primary objectives of non-dimensional mass flow and overall cooling effectiveness. Different optimization algorithms are used, namely AMGA and NSGA-II, and compared afterwards. A further optimization is carried out with direct objectives of mass flow and mean surface temperature using the AMGA algorithm.
The outputs from the optimizations are presented as a pareto-front. These plots are used for a comparison of the optimization algorithms and formulations respectively. Finally, the differences are discussed and the advantages and disadvantages of the algorithms used are highlighted.
Copyright © 2018 by Rolls-Royce Deutschland Ltd & Co KG
With the objective of attenuating the forced response of an axial turbine blisk for ship Diesel engine applications efforts have been made to increase the aerodynamic damping contribution for the most critical modes. In this regard the potential of intentional mistuning is investigated since it offers the opportunity to ensure a safe operation without a severe loss of aerodynamic performance. Genetic algorithms have been chosen to derive an optimized mistuning pattern resulting in a forced response clearly below that of the tuned counterpart. In order to keep the manufacturing effort within a limit only two possible blade geometries are allowed, which means that an integer optimization problem has been formulated. For the purpose of demonstrating the benefit of the intentional mistuning pattern found, two blisk prototypes have been manufactured: One with and another one without employing intentional mistuning for purposes of comparison. Furthermore, this offers the opportunity for an experimental determination of actually manufactured mistuning and other modal properties as well. The experimental data basis is employed to update structural models, which are well suited to demonstrate the forced response reduction under operational conditions. Finally, the robustness of the gain achieved with intentional mistuning could be proved towards both additional but unavoidable random structural and aerodynamic mistuning.
In modern compressors the assessment of blade vibration levels as well as health monitoring of the components are fundamental tasks. Traditionally, this assessment is done by the application of strain gauges to some blades of the assembly. In contrast to strain gauges, blade tip timing (BTT) offers a contactless monitoring of all blades of a rotor and there is no need of a telemetry system. A major issue in the interpretation of BTT data is the heavily undersampled nature of the signal. Usually, newly developed BTT algorithms are tested with sample data created by simplified structural models neglecting many of the uncertainties and disturbing influences of real applications. This work focuses on the creation of simulated BTT datasets as close as possible to real case measurements. For this purpose a subset of nominal system modes (SNM) representation of a compressor rotor is utilized. This model is able to include a large number of features present in real measurements, such as mistuning, static blade deflections due to centrifugal loads, aerodynamic damping and multiple mode resonances. Additionally, manufacturing deviations of the blade geometry, probe positioning errors in the BTT system and noise in the time of arrivals (TOAs) are captured by the BTT simulation environment. The main advantage of the created data is the possibility to steadily increase the signal complexity. Starting with a “perfect” signal the simulation environment is able to add different uncertainties one after the other. This allows the assessment of the influence of different features occurring in real measurements on the performance and accuracy of the analysis algorithms. Finally, a comparison of simulated BTT data and real data acquired from a rig test is shown to validate the presented approach of BTT data generation.
Copyright © 2018 by Rolls-Royce Deutschland Ltd & Co KG
Turbolader tragen erheblich zur Steigerung des Motorenwirkungsgrads bei. Rotierende Komponenten sind infolge der Fliehkraft, der zur Aufladung notwendigen Strömungsumlenkungen, der instationären Druckschwankungen der Strömung sowie von Temperaturgradienten als hochbelastete Laufräder einzustufen, die unter erheblicher Schwingungsanfälligkeit leiden. Am Lehrstuhl Strukturmechanik und Fahrzeugschwingungen der BTU Cottbus-Senftenberg wurde im Rahmen eines FVV-Forschungsvorhabens der Einfluss der fertigungsbedingten Toleranzen auf eben jenes Schwingungsverhalten untersucht. Es wird nachgewiesen, dass Intentional Mistuning zu signifikant niedrigeren Belastungen führen kann.
The accurate prediction of blade vibrations is a key factor for the development of reliable turbomachines. This paper focusses on forced vibrations. The excitation frequency is an integer multiple of the rotor revolution frequency, which is commonly called engine order. Aerodynamic excitation of blades is created by stator wakes or the potential fields of downstream obstacles, which usually leads to high engine orders correlating to the number of vanes. Resonance crossings appear at higher frequencies corresponding to higher modes. Besides high engine orders, low engine orders not related to the number of vanes may exist. They can be caused by a disturbance of the perfect cyclic symmetry of the flow pattern due to geometry variations or inlet distortions. Inlet distortions result from installation effects, maneuvers or crosswind. Low engine orders affect fundamental modes at high engine speeds. High static loads due to centrifugal forces combined with dynamic excitation and low damping may lead to unacceptable high stresses.
This paper aims at getting a better understanding of the simulative prediction of low engine order excitation with special focus on inlet distortions. Under investigation is a 4.5 stage research compressor rig, for which an extensive amount of test data is available. A three dimensional CFD-model of the compressor is used to compute the forcings generated by different distortion patterns. The first two stages are modeled as a full-annulus, which allows to fully resolve the spatial content of the inlet distortion patterns. The rotor 2 blisk is of special interest in this investigation. The propagation of the distortion after stage 2 with rotor 2 is not of interest, therefore the downstream stages are modeled as single passages in order to save computational time. The distortion patterns are the outcome of traversals of different screens with total pressure probes. During distortion measurements, the screens located in the inlet duct were rotated relative to the fixed instrumentation. The traversals in resonance of the first bending mode of rotor 2 with a low engine order four showed a dependency of the screen angle on the vibration amplitude. Acceleration and deceleration maneuvers through this resonance were conducted with screen angles set to those of smallest and highest response. Vibration amplitudes of the blisk rotor are measured by strain gauges and a blade tip timing system. Simulation results are compared against vibration measurements. Aerodynamic damping is calculated with the influence coefficient method. The effects of mistuning are included in the calculation of vibration amplitudes via a subset of nominal system modes model to give a meaningful comparison against real engine hardware. The mistuning distribution of the blisk was identified at rest for the fundamental bending mode. The presence of a 2nd excitation mechanism of unknown source explains the observed test data. This unknown source is not included in the CFD model. A direct comparison of simulation and measurement is still possible by leveraging the observed superposition effects of both excitation sources. The consequent approach is to identify and substract the forcing due to the unknown source, leaving only the delta forcing due to inlet distortions.
The manufacturing process always produces onto the components a certain amount of geometrical uncertainty. This results inevitably in the introduction of a certain amount of variability within the manufactured parts. Even if the differences are small, all the resulting geometries will differ from each other. The present work focuses on the effect of the manufacturing geometrical variability on the high pressure compressor of a turbofan engine for civil aviation. The deviations of the geometry over the axial compressor blades are studied and modelled for the representation in the computational models. Such variability is of particular interest for the forced response problem, where small deviations of the geometry from the ideal nominal model can imply significant differences in the vibrational responses.
The information regarding the geometrical mistuning is extracted from a set of manufactured components surface scans of a blade integrated disk (blisk) rotor. The measured geometries are analyzed over a large amount of set radial sections, defining a set of opportune parameters to represent the deviations from the nominal design. A spline fit of the parameters over the radial sections allows the creation of a set of variables describing the geometry. The dimension of the variables domain is reduced using the principal component analysis approach, this allows to obtain an optimal subset of geometrical modes as linear combination of the above mentioned parameters. The reconstruction of the modelled geometries is performed for the implementation in complex CFD and FEM solvers. This is done via the application of the modelled delta nominal-to-measure geometrical offset to the hot geometry of the desired test case. The generated model allows a stochastic representation of the variability, providing an optimal set of variables to represent it. Moreover the approach as defined allows to apply the modelled variability to different blades, e.g. different stators or rotors, utilizing the nominal geometry as input. The aeroelastic analyses considering geometry based mistuning is carried on a test-rig case, focusing on how such variability can affect the modal forcing generated on the blades.
A validated CFD model is used to extract the force generated by the unsteady pressure field over the selected vibrational mode shapes of the rotor blades. The blade mode shapes are extracted form a FEM model of the whole blisk and the blades displacements are mapped over the CFD model nodes. The uncertainty quantification of the geometrical variability effect on the modal forcing is performed utilizing Monte Carlo methods. A reduced model for the CFD solution is employed, utilizing a single passage multi blade row which assumes a time-space periodicity solving the governing equations in the frequency domain. This allows for conducting an uncertainty quantification considering the large domain of the variables used to describe the geometries compared to the computational resources needed for the single solution. The unsteady modal forcing is studied as amplitude and phase shift for the different engine orders (frequencies arising from the engine working condition as higher harmonics of the shaft speed). In particular the scatter of the main engine orders forcing amplitudes for the manufactured blades can be compared with the nominal responses to predict the possible amplification due to the geometrical variability. Finally the results are compared to a larger computational model to assess the influence of multiple variable blades in the assembly.
The oil and gas, chemical, and process industries employ centrifugal compressors for a wide range of applications. Due to this, the conditions, under which centrifugal compressors have to operate, vary significantly from case to case. Gas pipeline compressors, for example, may feature discharge pressures well over 100 bar (1450 psi). In other fields of application, like gas injection, which is used to enhance oil recovery, this quantity can reach considerably higher values. Here, discharge pressures over 600 bar (8702 psi) and gas densities over 300 kg/m3 (18.7284 lb/ft3) are not uncommon. During the last decades, comprehensive research was conducted on the impact of high pressure operating conditions on the vibrational behavior of centrifugal compressor wheels. Nowadays, it is well-known that an increase in gas pressure levels leads to a more pronounced interaction between the side cavities and the impeller, which results in a frequency shift of the acoustic and structural modes.
For the safe operation of compressors, it is necessary to predict these coupled natural frequencies accurately. The state-of-the-art approach to achieve this objective is the finite element method. While this technique provides high-quality results, the simulation of acousto-mechanical systems is still a time-consuming process that incurs high computational costs. Therefore, finite element models are, in this case, not suitable for probabilistic studies, sensitivity analyses, and comprehensive simulations of the full operating range of the compressor. In 2013, Magara proposed a simplified model based on an annular plate between two cylindrical cavities to solve this problem. While this method reduces the required computational effort significantly, its use is limited to platelike impellers.
The authors of the current paper propose a more generalized method to overcome the challenges mentioned above. It uses the uncoupled structural and acoustic modes of the actual impeller and side cavities in a modal superposition to approximate the natural frequencies of the coupled acousto-mechanical system. In this way, the intended design geometries of the impeller and side cavities are considered while maintaining the advantages of Magara's model regarding the computational effort. In a numerical study, Magara's method and the generalized model are applied to different systems of increasing complexity. The investigation starts with a simple annular plate in a cylindrical cavity and ends with two actual compressor impellers. At every complexity level, the results of both approaches are compared to a finite element analysis. Moreover, measurement data of a simplified rotor in a cylindrical cavity is used to validate the numerical models. Finally, the paper concludes with a discussion of the limitations and benefits of all employed numerical methods.
Investigation of Working Line Variation Onto Forced Response Vibrations of a Compressor Blisk
(2020)
Avoidance of high vibration amplitudes of rotor blades on the conventional working line of the compressor is a design requirement. However, rotors of aircraft engine compressors could temporarily operate near choke and stall conditions, due to transient manoeuvers or deterioration. As a result, the vibration levels might change, which could lead to a premature high cycle fatigue of the blades. This paper aims at studying the effect of different throttle positions at five constant aerodynamic speed lines ranging from 60% to 100% of the maximum speed onto the resulting vibration amplitudes and aerodynamic damping values on an integrally bladed disk (blisk) of a transonic research compressor.
Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD) simulations are performed via an automated workflow, which reads aerodynamic data of the operating points of interest and runs all necessary aeromechanic computations along with their corresponding post-processing routines to calculate the resulting system response and amplitude frequency values.
Using this workflow, Eigenfrequencies and mode-shapes of the rotor blades are obtained through multiple FEA simulations that are automatically executed at all relevant shaft speeds. The time-averaged flow pressure field on the blades is extracted from steady CFD simulations of the whole compressor and mapped onto the structural mesh of the rotor. Through a Spokes diagram, operating points in close proximity to resonance spots are identified, as well as their corresponding excited vibration modes. To obtain the time-variable flow pressure fields on the blades, unsteady CFD simulations are performed using a single passage model of the rotor with its upstream and downstream stators, as space-time periodicity of the flow data across the annulus is assumed. Additionally, a CFD rotor model with only a quarter section of the full annulus is built, where a unidirectional coupling approach between the structure and the fluid is applied to calculate the aerodynamic damping values.
The calculated vibration amplitudes at engine orders of interest are then compared to strain gauge readings of a corresponding rig test. After validation of the simulation data, the sensitivity of the forced response due to working line variations is studied. Looking at the maximum aerodynamic speed line, it is clear that operating points near compressor stall are accompanied by high vibration response relative to the aerodynamic design point. A possible reason for this amplification is the change of flow incidence and the increase of pressure loss at the upstream blade-row. However, this effect becomes less articulated in the lower speed lines, where amplitudes of the forced vibrations change only slightly between different throttling positions. In this paper, the three-dimensional flow inside the passages is also carefully studied, which allows to better understand the relationship between flow characteristics and the resulting vibration response of compressor blades.
Correlating and Updating Finite Element Models of Different Fidelity Using an Energy-Based Approach
(2020)
Building finite element models of complex structures requires the engineer to make various simplifying assumptions. While there exists no unique way of modeling, the resulting model depends to a level on experience and engineering judgement. The inherent model uncertainties can be subdivided into three categories: idealization errors, discretization errors and parameter errors. Understanding the effect of different modeling assumptions and minimizing these uncertainties is key for creating efficient and physical meaningful finite element models. In this paper the effects of different modeling assumptions are analyzed by comparing finite element models of an aero engine turbine casing. Various models of different fidelity are created reaching from simple shell element representations neglecting geometric features like bosses, fixings and holes, to higher fidelity mixed dimensional models using coupled shell and three-dimensional elements. To quantify their impact on the stiffness and mass properties, the different models are correlated with a high-fidelity three-dimensional finite element model using numerical modal data. A novel method is proposed based on the strain and kinetic energy distribution to assess the effect of different modeling assumptions on the model structure. This is done by splitting the discretized model into multiple sections of interest and calculating the perturbation of energies within the related splits. The derived strain and kinetic energy perturbations are then used in addition to other correlation criteria like the modal assurance criteria or the relative difference in eigenfrequencies to analyze the impact of the different modeling assumptions. Having quantified the differences, the difficulties of error localization using modal data are discussed in the context of the correlation results. Finally, the effectiveness of the derived perturbation values are demonstrated by updating a finite element model of an aero engine turbine casing in the presence of structural simplifications using an evolutionary optimization algorithm and comparing the model updating strategy to the standard sensitivity-based updating approach. If the resulting updated model is used to predict structural modifications or untested loading conditions, the updated parameters might lose their physical meaning when altering regions of the model not in error. Therefore, it is important to examine the physical significance of the updated parameters. It is shown how the energy-based approach can help to address this problem. All in all, the proposed energy-based approach can be used to compare various modeling strategies in order to build efficient finite element models as well as assist in the choice of parameters for subsequent model updating to validate the numerical model against test data.
This paper presents a new FE-based stress-related topology optimization approach for finding bending governed flexible designs. Thereby, the knowledge about an output displacement or force as well as the detailed mounting position is not necessary for the application. The newly developed objective function makes use of the varying stress distribution in the cross section of flexible structures. Hence, each element of the design space must be evaluated with respect to its stress state. Therefore, the method prefers elements experiencing a bending or shear load over elements which are mainly subjected to membrane stresses. In order to determine the stress state of the elements, we use the principal stresses at the Gauss points. For demonstrating the feasibility of the new topology optimization approach, three academic examples are presented and discussed. As a result, the developed sensitivity-based algorithm is able to find usable flexible design concepts with a nearly discrete 0 − 1 density distribution for these examples.