@inproceedings{KoberKuehhornKeskin, author = {Kober, Markus and K{\"u}hhorn, Arnold and Keskin, Akin}, title = {Instability problems in implicit transient FEM simulations of fast rotating elastic structures - Description of the phenomenon and possible solutions}, series = {Proceedings of NAFEMS DACH Conference 2018, Bamberg, May 14-16, 2018}, booktitle = {Proceedings of NAFEMS DACH Conference 2018, Bamberg, May 14-16, 2018}, publisher = {NAFEMS Deutschland, {\"O}sterreich, Schweiz GmbH}, address = {Grafing}, isbn = {978-1-910643-14-3}, pages = {48 -- 52}, language = {en} } @misc{WeberKuehhorn, author = {Weber, Robby and K{\"u}hhorn, Arnold}, title = {Mistuning Identification Approach With Focus on High-Speed Centrifugal Compressors}, series = {Journal of Engineering for Gas Turbines and Power}, volume = {14}, journal = {Journal of Engineering for Gas Turbines and Power}, number = {3}, issn = {1528-8919}, doi = {10.1115/1.4040999}, pages = {7}, language = {en} } @misc{KoberKuehhornKeskin, author = {Kober, Markus and K{\"u}hhorn, Arnold and Keskin, Akin}, title = {Instabilit{\"a}tsprobleme bei der impliziten transienten FEM-Simulation schnell rotierender elastischer Strukturen - Beschreibung des Ph{\"a}nomens und L{\"o}sungsm{\"o}glichkeiten}, series = {NAFEMS-Online-Magazin}, volume = {48}, journal = {NAFEMS-Online-Magazin}, number = {4}, issn = {2311-522X}, pages = {36 -- 49}, language = {en} } @misc{HenkeNoackGeyeretal., author = {Henke, Anna-Sophia and Noack, Martin and Geyer, Thomas and Heinrich, Christoph Rocky and Beirow, Bernd and Sarradj, Ennes and K{\"u}hhorn, Arnold}, title = {Calculation of the Modal Behavior of Structured Sheet Metal}, series = {International Journal of Lightweight Materials and Manufacture}, journal = {International Journal of Lightweight Materials and Manufacture}, issn = {2588-8404}, doi = {10.1016/j.ijlmm.2019.01.004}, pages = {13}, language = {en} } @misc{BeirowKuehhornFigaschewskyetal., author = {Beirow, Bernd and K{\"u}hhorn, Arnold and Figaschewsky, Felix and H{\"o}nisch, Peter and Giersch, Thomas and Schrape, Sven}, title = {Model update and validation of a mistuned high-pressure compressor blisk}, series = {The Aeronautical Journal}, volume = {123}, journal = {The Aeronautical Journal}, number = {1260}, issn = {2059-6464}, doi = {10.1017/aer.2018.149}, pages = {230 -- 247}, abstract = {In order to prepare an advanced 4-stage high-pressure compressor rig test campaign, details regarding both accomplishment and analysis of preliminary experiments are provided in this paper. The superior objective of the research project is to contribute to a reliable but simultaneously less conservative design of future high pressure blade integrated disks (blisk). It is planned to achieve trend-setting advances based on a close combination of both numerical and experimental analyses. The analyses are focused on the second rotor of this research compressor, which is the only one being manufactured as blisk. The comprehensive test program is addressing both surge and forced response analyses e.g. caused by low engine order excitation. Among others the interaction of aeroelastics and blade mistuning is demanding attention in this regard. That is why structural models are needed, allowing for an accurate forced response prediction close to reality. Furthermore, these models are required to support the assessment of blade tip timing (BTT) data gathered in the rig tests and strain gauge (s/g) data as well. To gain the maximum information regarding the correlation between BTT data, s/g-data and pressure gauge data, every blade of the second stage rotor (28 blades) is applied with s/g. However, it is well known that s/g on blades can contribute additional mistuning that had to be considered upon updating structural models. Due to the relevance of mistuning, efforts are made for its accurate experimental determination. Blade-by-blade impact tests according to a patented approach are used for this purpose. From the research point of view, it is most interesting to determine both the effect s/g-instrumentation and assembling the compressor stages on blade frequency mistuning. That is why experimental mistuning tests carried out immediately after manufacturing the blisk are repeated twice, namely, after s/g instrumentation and after assembling. To complete the pre-test program, the pure mechanical damping and modal damping ratios dependent on the ambient pressure are experimentally determined inside a pressure vessel. Subsequently the mistuning data gained before is used for updating subset of nominal system mode (SNM) models. Aerodynamic influence coefficients (AICs) are implemented to take aeroelastic interaction into account for forced response analyses. Within a comparison of different models, it is shown for the fundamental flap mode (1F) that the s/g instrumentation significantly affects the forced response, whereas the impact of assembling the compressor plays a minor role.}, language = {en} } @misc{FigaschewskyKuehhornBeirowetal., author = {Figaschewsky, Felix and K{\"u}hhorn, Arnold and Beirow, Bernd and Giersch, Thomas and Schrape, Sven}, title = {Analysis of mistuned forced response in an axial high-pressure compressor rig with focus on Tyler-Sofrin modes}, series = {The Aeronautical Journal}, journal = {The Aeronautical Journal}, number = {123}, issn = {2059-6464}, doi = {10.1017/aer.2018.163}, pages = {356 -- 377}, abstract = {This paper aims at contributing to a better understanding of the effect of Tyler-Sofrin Modes (TSMs) on forced vibration responses by analysing a 4.5-stage research axial compressor rig. The first part starts with a brief review of the involved physical mechanisms and necessary prerequisites for the generation of TSMs in multistage engines. This review is supported by unsteady CFD simulations of a quasi 2D section of the studied engine. It is shown that the amplitude increasing effect due to mistuning can be further amplified by the presence of TSMs. Furthermore, the sensitivity with respect to the structural coupling of the blades and the damping as well as the shape of the expected envelope is analysed. The second part deals with the Rotor 2 blisk of the research compressor rig. The resonance of a higher blade mode with the engine order of the upstream stator is studied in two different flow conditions realised by different variable stator vane (VSV) schedules which allows to separate the influence of TSMs from the impact of mistuning. A subset of nominal system modes representation of the rotor is used to describe its mistuned vibration behaviour, and unsteady CFD simulations are used to characterise the present strength of the TSMs in the particular operating conditions. Measured maximum amplitude vs blade pattern and frequency response functions are compared against the predictions of the aeromechanical models in order to assess the strength of the TSMs as well as its influence on vibration levels.}, language = {en} } @misc{WeberKuehhorn, author = {Weber, Robby and K{\"u}hhorn, Arnold}, title = {Mistuning und D{\"a}mpfung radialer Turbinen- und Verdichterlaufr{\"a}der}, series = {Abschluss- und Zwischenberichte der Forschungsstellen Turbomaschinen : Fr{\"u}hjahrstagung 2019 : Tagungsband : 2019 - W{\"u}rzburg}, journal = {Abschluss- und Zwischenberichte der Forschungsstellen Turbomaschinen : Fr{\"u}hjahrstagung 2019 : Tagungsband : 2019 - W{\"u}rzburg}, publisher = {Forschungsvereinigung Verbrennungskraftmaschinen e.V.}, address = {Frankfurt am Main}, pages = {75 -- 109}, abstract = {Abschlussbericht zum FVV-Projekt Mistuning und D{\"a}mpfung III}, language = {de} } @misc{NaveedKuehhornKober, author = {Naveed, Zishan and K{\"u}hhorn, Arnold and Kober, Markus}, title = {Comparative Evaluation of Isogeometric Analysis and Classical FEM with Regard to Contact Anaylsis}, series = {12th European LS-DYNA Conference 2019, 14-16 May 2019, Koblenz}, journal = {12th European LS-DYNA Conference 2019, 14-16 May 2019, Koblenz}, pages = {10}, abstract = {Isogeometric analysis represents a newly developed technique that offers the application of Computer Aided Designs (CAD) concept of Non-uniform Rational B-Splines (NURBS) tool to describe the geometry of the computational domain. The simplified transition of CAD models into the computational domain eliminates the problems arising from the geometrical discontinuities induced by the faceted approximation of the mesh. Moreover, numerical analysis directly on NURBS objects significantly reduces the design-to-analysis time compared to traditional FEA approach. In the field of contact mechanics, when finite elements are applied to geometry with curved surfaces, the result is a non-smooth geometrical representation of interface surfaces which may lead to mesh interlocking, high jumps and spurious oscillations in contact forces. To eliminate these issues, various surface smoothening strategies are to be employed in case of FEM. Isogeometric based analysis alleviates these issues without employing any additional smoothening strategy due to inherent higher order continuity of NURBS basis functions and much more accurate results are obtained compared to conventional FE approach. In the current study, LS-DYNA is used to demonstrate the capabilities and advantage of an isogeometric analysis though an example of pendulum under gravitational load. The numerical simulation results are analytically validated and the comparison of NURBS surfaces with faceted surfaces is carried out to investigate the accuracy.}, language = {en} } @misc{WeberKuehhornBeirow, author = {Weber, Robby and K{\"u}hhorn, Arnold and Beirow, Bernd}, title = {Mistuning und D{\"a}mpfung radialer Turbinen- und Verdichterlaufr{\"a}der}, series = {MTZ - Motortechnische Zeitschrift}, volume = {80}, journal = {MTZ - Motortechnische Zeitschrift}, number = {9}, issn = {0024-8525}, doi = {10.1007/s35146-019-0094-2}, pages = {74 -- 78}, abstract = {Turbolader tragen erheblich zur Steigerung des Motorenwirkungsgrads bei. Rotierende Komponenten sind infolge der Fliehkraft, der zur Aufladung notwendigen Str{\"o}mungsumlenkungen, der instation{\"a}ren Druckschwankungen der Str{\"o}mung sowie von Temperaturgradienten als hochbelastete Laufr{\"a}der einzustufen, die unter erheblicher Schwingungsanf{\"a}lligkeit 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 f{\"u}hren kann.}, language = {de} } @misc{WeberKuehhornBeirow, author = {Weber, Robby and K{\"u}hhorn, Arnold and Beirow, Bernd}, title = {Mistuning and Damping of Turbine and Compressor Impellers}, series = {MTZ worldwide}, volume = {80}, journal = {MTZ worldwide}, number = {9}, issn = {2192-9114}, doi = {10.1007/s38313-019-0090-4}, pages = {72 -- 77}, abstract = {Turbocharging is known to be a well-established technology for an engine's efficiency and power output by forcing extra compressed air into the combustion chamber. The centrifugal loads, necessary flow deflections, unsteady pressure fluctuations, and structural temperature gradients put a high strain on rotating components. Additionally, those components are prone to high-cycle fatigue. The Chair of Structural Mechanics and Vehicle Vibrational Technology at the BTU Cottbus-Senftenberg investigated the impact of manufacturing tolerances on the vibrational behavior of several turbine and compressor impellers. Finally, it is shown that intentional mistuning can lead to significantly lower stresses.}, language = {en} } @misc{HardenbergKuehhornFanter, author = {Hardenberg, Alexander and K{\"u}hhorn, Arnold and Fanter, Maren}, title = {Bewertung der Auswirkungen von Strukturmodifikationen und Modellvereinfachungen unter Einsatz der FEA-FEA Korrelation auf das Modalverhalten einer Triebwerksgeh{\"a}usestruktur}, series = {2. VDI-Fachtagung Schwingungen 2019 : W{\"u}rzburg, 05. und 06. November 2019}, journal = {2. VDI-Fachtagung Schwingungen 2019 : W{\"u}rzburg, 05. und 06. November 2019}, publisher = {VDI-Verlag}, address = {D{\"u}sseldorf}, isbn = {978-3-18-092366-6}, language = {de} } @misc{BeirowKuehhornFigaschewskyetal., author = {Beirow, Bernd and K{\"u}hhorn, Arnold and Figaschewsky, Felix and Bornholm, Alfons}, title = {Vibration analysis of a mistuned axial turbine blisk}, series = {ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition, June 17-21, 2019, Phoenix, Arizona, USA}, journal = {ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition, June 17-21, 2019, Phoenix, Arizona, USA}, isbn = {978-0-7918-5869-1}, doi = {10.1115/GT2019-92047}, pages = {12}, abstract = {An axial turbine blisk for turbocharger applications is analyzed with respect to the effect of intentional mistuning on the forced response. Originally, the intentional mistuning pattern has been designed by employing a genetic algorithm optimization in order to reduce the forced response caused by low engine order excitation (LEO) of the fundamental flap mode. The solution found has been implemented in a prototype of that blisk. For the purpose of comparison, a second reference blisk has been manufactured without intentional mistuning. The actual mistuning distributions of the blisks have been identified by employing blade-by-blade impact testing. Alternatively, a new inverse approach has been employed, which is based on a least squares formulation and benefits from less experimental effort. Based on the information gained by the aforementioned testing procedures, subset of nominal systems (SNM)-models have been updated, which allow for considering the aeroelastic coupling by means of aerodynamic influence coefficients (AIC). Despite of small but unavoidable deviations from the design intention it could be proved within numerical simulations that the intended 70 per cent reduction of the maximum forced response is nevertheless achieved. In addition, the paper is addressing the effect of the aforementioned intentional mistuning pattern on a higher mode, which is relevant for the durability as well. Hence, new SNM-models have to be updated in order to calculate the forced response due to EO-excitation caused by the nozzle guide vane. Although the original mistuning pattern has been optimized solely for reducing the forced response of the fundamental flap mode, it hardly affects the higher mode forced response in a negative manner.}, language = {en} } @misc{FigaschewskyKuehhornBeirowetal., author = {Figaschewsky, Felix and K{\"u}hhorn, Arnold and Beirow, Bernd and Giersch, Thomas and Schrape, Sven and Nipkau, Jens}, title = {An inverse approach to identify tuned aerodynamic damping, system frequencies and mistuning - Part 3: Application to engine data}, series = {ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition, June 17-21, 2019, Phoenix, Arizona, USA}, journal = {ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition, June 17-21, 2019, Phoenix, Arizona, USA}, isbn = {978-0-7918-5868-4}, doi = {10.1115/GT2019-91337}, pages = {13}, abstract = {A novel approach for the identification of tuned aerodynamic damping, system frequencies, forcing and mistuning has been introduced in the first part of this paper. It is based on the forced response equations of motion for a blade dominated mode family. A least squares formulation allows to identify the system's parameters directly from measured frequency response functions (FRFs) of all blades recorded during a sweep through a resonance. The second part has dealt with its modification and application to experimental modal analyses of blisks at rest. This 3rd part aims at presenting the application of the approach to blade tip timing (BTT) data acquired in rig tests. Therefore, blisk rotors of two different engines are studied: a single stage fan rig and a 4.5 stage high pressure compressor (HPC) rig. The rig test campaign of the fan blisk included also an intentional mistuning experiment that allows to study the performance of the identification approach for a similar rotor with two different mistuning levels. It is demonstrated that the approach can identify aerodynamic damping curves, system frequencies, mistuning pattern and forced travelling wave modes (TWMs) from state of the art BTT data monitored during rig or engine tests. All derived mistuning patterns could be verified with reference measurements at standstill. The derived aerodynamic damping curves and system frequencies show a reasonable agreement with simulations. For the HPC case a multitude of excited TWMs could be identified which also lines up with previous simulations.}, language = {en} } @misc{MaywaldHeinrichKuehhornetal., author = {Maywald, Thomas and Heinrich, Christoph Rocky and K{\"u}hhorn, Arnold and Schrape, Sven and Backhaus, Thomas}, title = {Prediction of Geometrically Induced Localization Effects Using a Subset of Nominal System Modes}, series = {ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition June 17-21, 2019 Phoenix, Arizona, USA}, journal = {ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition June 17-21, 2019 Phoenix, Arizona, USA}, isbn = {978-0-7918-5869-1}, doi = {10.1115/GT2019-90884}, pages = {9}, abstract = {It is widely known that the vibration characteristics of blade integrated discs can dramatically change in the presence of manufacturing tolerances and wear. In this context, an increasing number of publications discuss the influence of the geometrical variability of blades on phenomena like frequency splitting and mode localization. This contribution is investigating the validity of a stiffness modified reduced order model for predicting the modal parameters of a geometrically mistuned compressor stage. In detail, the natural frequencies and mode shapes, as well as the corresponding mistuning patterns, are experimentally determined for an exemplary rotor. Furthermore, a blue light fringe projector is used to identify the geometrical differences between the actual rotor and the nominal blisk design. With the help of these digitization results, a realistic finite element model of the whole compressor stage is generated. Beyond that, a reduced order model is implemented based on the nominal design intention. Finally, the numerical predictions of the geometrically updated finite element model and the stiffness modified reduced order model are compared to the vibration measurement results. The investigation is completed by pointing out the benefits and limitations of the SNM-approach in the context of geometrically induced mistuning effects.}, language = {en} } @misc{NaveedKuehhornKober, author = {Naveed, Zishan and K{\"u}hhorn, Arnold and Kober, Markus}, title = {Contact Behaviour of Isogeometric Analysis for Rotating Structures and its Industrial Application by Coupling to the Classical Finite Element Method}, series = {VII International Conference on Isogeometric Analysis, M{\"u}nchen, 18.-20. September 2019}, journal = {VII International Conference on Isogeometric Analysis, M{\"u}nchen, 18.-20. September 2019}, pages = {1}, abstract = {Especially for rotating structures like bearings non-smooth contact surfaces, as they appear in classical finite element modeling, lead to various problems during the analysis involving mesh interlocking and spurious oscillations in contact forces. In order to eliminate these issues, very fine meshes and additional smoothing strategies are employed in case of the finite element method (FEM). But also Non-Uniform Rational B-splines (NURBS) based isogeometric analysis (IGA) can be very useful for the contact analysis due to the inherent higher order continuity of NURBS basis functions. In this contribution, the contact behavior using classical FEA and IGA approaches is studied by means of an example of a pendulum under gravitational load. In addition, a more practical example of a coupled IGA-FEM problem with a cylindrical roller bearing is also reported in this paper. This research study of contact analysis has been carried out for the above mentioned examples using LS-DYNA and illustrates that contact surfaces of coarsely meshed geometry lock the rotation of the parts in case of classical FEM. On the contrary, when the contact surface is represented by NURBS elements it allows the rotation of the parts and effectively alleviates the contact force oscillation.}, language = {en} } @misc{FranzKuehhornGierschetal., author = {Franz, Falco and K{\"u}hhorn, Arnold and Giersch, Thomas and Schrape, Sven and Figaschewsky, Felix}, title = {Influence of Inlet Distortions on the Forced Vibration of a High Pressure Compressor Rig}, series = {ASME 2020 Turbo Expo - Virtual Conference, September 2020}, journal = {ASME 2020 Turbo Expo - Virtual Conference, September 2020}, abstract = {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.}, language = {en} } @misc{GambittaKuehhornSchrape, author = {Gambitta, Marco and K{\"u}hhorn, Arnold and Schrape, Sven}, title = {Geometrical Variability Modelling of Axial Compressor Blisk Aerofoils and Evaluation of Impact on the Forced Response Problem}, series = {ASME 2020 Turbo Expo - Virtual Conference, September 2020}, journal = {ASME 2020 Turbo Expo - Virtual Conference, September 2020}, abstract = {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.}, language = {en} } @misc{HeinrichKuehhornSteffetal., author = {Heinrich, Christoph Rocky and K{\"u}hhorn, Arnold and Steff, Klaus and Petry, Nico}, title = {Generalized Model for the Approximation of Coupled Acousto-Mechanical Natural Frequencies in High-Pressure Centrifugal Compressors}, series = {ASME 2020 Turbo Expo - Virtual Conference, Spetember 2020}, journal = {ASME 2020 Turbo Expo - Virtual Conference, Spetember 2020}, abstract = {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.}, language = {en} } @misc{ElMasryKuehhornFigaschewsky, author = {ElMasry, Seif and K{\"u}hhorn, Arnold and Figaschewsky, Felix}, title = {Investigation of Working Line Variation Onto Forced Response Vibrations of a Compressor Blisk}, series = {Turbo Expo 2021, Virtual Conference and Exhibition: September 21, 2020}, journal = {Turbo Expo 2021, Virtual Conference and Exhibition: September 21, 2020}, abstract = {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.}, language = {en} } @misc{WeberKuehhornKlaukeetal., author = {Weber, Robby and K{\"u}hhorn, Arnold and Klauke, Thomas and Schrape, Sven}, title = {The Effect of Sand Erosion on a Compressor Blade and its Modal Properties}, series = {Proceedings of ASME Turbo Expo 2020, Turbomachinery Technical Conference and Exposition, GT2020, September 21-25, 2020, Virtual, Online}, journal = {Proceedings of ASME Turbo Expo 2020, Turbomachinery Technical Conference and Exposition, GT2020, September 21-25, 2020, Virtual, Online}, pages = {9}, abstract = {The wear and damage of High-Pressure Compressor (HPC) blades due to erosion or Foreign Object Damage (FOD) have a significant influence on HPC aerodynamic performance, vibration resistance against High-Cycle Fatigue (HCF) and thus component lifetime. The changes in airfoil geometry reduce the overall engine efficiency. Furthermore extended off-wing engine maintenances due to blade failures are increasing the cost of ownership. The safe operation of every engine within a reduced number of shop visits requires a reliable prediction of future deterioration. This enables the optimization of services and off-wing time. One contribution to this is a better understanding of the component's dynamics and based on this providing an improved wear modeling to reliably predict the remaining lifetime and the decreased efficiency. This contribution determines the material removal of HPC blades due to sand erosion. Originally, this stage was built as a blisk (Blade Integrated Disk). After sand erosion test completion, the blisk was cut into segments containing one airfoil only. First, the material removal is determined for ten blades of one exemplary rotor. A blue light fringe projector is employed to identify the geometrical differences between the eroded blades and the nominal design. Second, realistic finite element models are generated to enable comparable modal analyses of eroded blades. This procedure suffers from unavoidable and mostly random imperfections due to the manufacturing process, which significantly affects the blade surface before the erosion test can be conducted. Therefore, an already published approach is implemented in the third step to predict the blade surface after erosion based on nominal blade design. The investigation is completed by comparing measured and predicted surfaces. Finally, the aforementioned tool is employed to predict the locations and intensities of the material losses and the accompanying change in modal properties of this compressor blade concerning operational time.}, language = {de} } @misc{HeinrichKuehhornSteffetal., author = {Heinrich, Christoph Rocky and K{\"u}hhorn, Arnold and Steff, Klaus and Petry, Nico}, title = {Generalized Model for the Approximation of Coupled Acousto-Mechanical Natural Frequencies in High-Pressure Centrifugal Compressors}, series = {Journal of Engineering for Gas Turbines and Power}, journal = {Journal of Engineering for Gas Turbines and Power}, issn = {1528-8919}, doi = {10.1115/1.4049447}, pages = {27}, abstract = {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. During the last decades, comprehensive research was conducted on the impact of high pressure operating conditions on the vibrational behavior of centrifugal compressors. 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, it incurs high computational costs and is, therefore, time-consuming. The authors of the current paper propose a generalized model to overcome this challenge. It uses the uncoupled modes of the impeller and side cavities in a modal superposition to approximate the coupled system's natural frequencies. In this way, the intended design geometries are considered while reducing the computational effort significantly. In a numerical study, the generalized model is applied to different systems of increasing complexity, and the results are compared to a finite element analysis. Finally, the paper concludes with a discussion of the limitations and benefits of all employed numerical methods.}, language = {en} } @misc{BeirowKuehhornWeberetal., author = {Beirow, Bernd and K{\"u}hhorn, Arnold and Weber, Robby and Popig, Frederik}, title = {Vibration Analyses of an Axial Turbine Wheel with Intentional Mistuning}, series = {Journal of Engineering for Gas Turbines and Power}, volume = {143}, journal = {Journal of Engineering for Gas Turbines and Power}, number = {6}, issn = {1528-8919}, doi = {10.1115/1.4049449}, abstract = {The last stage bladed disk of a steam turbine is analyzed with respect to both flutter susceptibility and limitation of forced response. Due to the lack of variable stator vanes unfavorable flow conditions may occur which increases the risk of flutter at part load conditions. For this reason, intentional mistuning is employed with the objective to prevent any self-excited vibrations. A first step in this direction is done by choosing alternate mistuning, which keeps the manufactural efforts in limits. In this sense, two different series of blades have been made. However, small deviations from the design intention are unavoidable due to the manufacturing procedure, which could be proved by bonk tests carried out earlier. The influence of these additional deviations is considered in numerical simulations. Moreover, the strong dependence of blade frequencies on the speed is taken into account since centrifugal stiffening effects significantly attenuate the blade-to-blade frequency difference. Focusing on the first flap mode it could be shown that a mitigation of flutter susceptibility is achieved by prescribing alternate mistuning, which indeed evokes an increase of originally small aerodynamic damping ratios. Nevertheless, the occurrence of negative damping ratios could not be completely precluded at part load conditions. That is why optimization studies are conducted based on genetic algorithms with the objective function of maximizing the lowest aerodynamic damping ratios. Finally, mistuning patterns could be identified featuring a tremendous increase of aerodynamic damping ratios. The robustness of the solutions could be proved by superimposing additional random mistuning.}, language = {en} } @misc{HardenbergKuehhornFanter, author = {Hardenberg, Alexander and K{\"u}hhorn, Arnold and Fanter, Maren}, title = {Correlating and Updating Finite Element Models of Different Fidelity Using an Energy-Based Approach}, series = {Turbo Expo 2020, Virtual Conference, Virtual Conference and Exhibition, Online, September 21 - 25, 2020}, journal = {Turbo Expo 2020, Virtual Conference, Virtual Conference and Exhibition, Online, September 21 - 25, 2020}, abstract = {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.}, language = {en} } @misc{BeirowKuehhornWeberetal., author = {Beirow, Bernd and K{\"u}hhorn, Arnold and Weber, Robby and Popig, Frederik}, title = {Vibration Analyses of an Axial Turbine Wheel With Intentional Mistuning}, series = {Turbo Expo 2020, Virtual Conference, Virtual Conference and Exhibition, Online, September 21 - 25, 2020}, journal = {Turbo Expo 2020, Virtual Conference, Virtual Conference and Exhibition, Online, September 21 - 25, 2020}, abstract = {The last stage bladed disk of a steam turbine is analyzed with respect to both flutter susceptibility and limitation of forced response. Due to the lack of variable stator vanes unfavorable flow conditions may occur which can lead to flow separation in some circumstances. Consequently, there is the risk of flutter in principle, particularly at nominal speed under part load conditions. For this reason, intentional mistuning is employed by the manufacturer with the objective to prevent any self-excited vibrations. A first step in this direction is done by choosing alternate mistuning, which keeps the manufactural efforts in limits since only two different blade designs are allowed. In this sense, two different series of blades have been made. However, it is well known that small deviations from the design intention are unavoidable due to the manufacturing procedure, which could be proved by bonk tests carried out earlier. The influence of these additional but unwanted deviations is considered in numerical simulations. Moreover, the strong dependence of blade frequencies on the speed is taken into account since it significantly attenuates the blade to blade frequency difference in this particular case. Within an academic study the turbine wheel is modelled as blade integrated disk in order to demonstrate fundamental effects of intentional mistuning on flutter susceptibility and forced response. For that purpose, reduced order models are built up by using the subset of nominal system mode approach introduced by Yang and Griffin [1], which conveniently allows for taking into account both differing mistuning patterns and the impact of aeroelastic interaction. Focusing on the first flap mode it could be shown that a mitigation of flutter susceptibility is achieved by prescribing alternate mistuning, which indeed affects an increase of originally small aerodynamic damping ratios. Nevertheless, the occurrence of negative damping ratios could not be completely precluded at part load conditions. That is why optimization studies are conducted based on genetic algorithms with the objective function of maximizing the lowest aerodynamic damping ratios. Again only two different blade designs are admitted. Finally, mistuning patterns could be identified causing a tremendous increase of aerodynamic damping ratios. The robustness of the solutions found could be proved by superimposing additional random mistuning. Another study is focused on the impact of mistuning strength. Further analyses are addressing the forced response at part speed conditions, where different resonance crossings are becoming apparent in the Campbell plot. An increase of the forced response compared to the tuned counterpart is partly unpreventable because of unfavorable aerodynamic damping curves. Independently, the maximum forced response has to be limited also in case of applying large intentional mistuning. [1] Yang, M. T., Griffin, J. H., „A Reduced-Order model of Mistuning Using a Subset of Nominal System Modes". J Eng Gas Turb Power, 123, pp. 893-900 (2001).}, language = {en} }