@inproceedings{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 = {Proceedings of ISABE 2017, ISABE-2017-22568, Manchester, September 3.-8., 2017}, booktitle = {Proceedings of ISABE 2017, ISABE-2017-22568, Manchester, September 3.-8., 2017}, publisher = {ISABE}, pages = {14}, language = {en} } @inproceedings{BeirowFigaschewskyKuehhornetal., author = {Beirow, Bernd and Figaschewsky, Felix and K{\"u}hhorn, Arnold and Bornholm, Alfons}, title = {Vibration Analysis of an Axial Turbine Blisk with Optimized Intentional Mistuning Pattern}, series = {Proceedings of ISROMAC 2017, Maui, Hawaii, December 16-21, 2017}, booktitle = {Proceedings of ISROMAC 2017, Maui, Hawaii, December 16-21, 2017}, pages = {9}, abstract = {Aiming to limit 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. 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 mistuning being really manufactured 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.}, language = {en} } @misc{BeirowFigaschewskyKuehhornetal., author = {Beirow, Bernd and Figaschewsky, Felix and K{\"u}hhorn, Arnold and Bornholm, Alfons}, title = {Modal Analyses of an Axial Turbine Blisk With Intentional Mistuning}, series = {Journal of Engineering for Gas Turbines and Power}, volume = {140}, journal = {Journal of Engineering for Gas Turbines and Power}, number = {1}, issn = {0742-4795}, doi = {10.1115/1.4037588}, pages = {012503-1 -- 012503-11}, abstract = {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.}, language = {en} } @misc{BeirowKuehhornFigaschewskyetal., author = {Beirow, Bernd and K{\"u}hhorn, Arnold and Figaschewsky, Felix and Bornholm, Alfons and Repetckii, Oleg V.}, title = {Forced Response Reduction of a Blisk by Means of Intentional Mistuning}, series = {Journal of Engineering for Gas Turbines and Power}, volume = {141}, journal = {Journal of Engineering for Gas Turbines and Power}, number = {1}, issn = {1528-8919}, doi = {10.1115/1.4040715}, pages = {011008-1 -- 011008-8}, abstract = {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.}, language = {en} } @inproceedings{BeirowFigaschewskyKuehhorn, author = {Beirow, Bernd and Figaschewsky, Felix and K{\"u}hhorn, Arnold}, title = {An Inverse Approach to Identify Tuned Aerodynamic Damping, System Frequencies, and Mistuning, Part 2: Application to Blisks at Rest}, series = {Proceedings of the 15th International Symposium on Unsteady Aerodynamics, Aeroacoustics \& Aeroelasticity of Turbomachines, ISUAAAT15, 24-27 September 2018, University of Oxford, UK}, booktitle = {Proceedings of the 15th International Symposium on Unsteady Aerodynamics, Aeroacoustics \& Aeroelasticity of Turbomachines, ISUAAAT15, 24-27 September 2018, University of Oxford, UK}, publisher = {ISUAAAT Scientific Committee}, pages = {2}, language = {en} } @misc{BeirowFigaschewskyKuehhornetal., author = {Beirow, Bernd and Figaschewsky, Felix and K{\"u}hhorn, Arnold and Bornholm, Alfons}, title = {Vibration Analysis of an Axial Turbine Blisk with Optimized Intentional Mistuning Pattern}, series = {Journal of Sound and Vibration}, volume = {442}, journal = {Journal of Sound and Vibration}, issn = {0022-460X}, doi = {10.1016/j.jsv.2018.10.064}, pages = {11 -- 27}, abstract = {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.}, language = {en} } @inproceedings{KochBeirowFilippatosetal., author = {Koch, Ilja and Beirow, Bernd and Filippatos, Angelos and K{\"u}hhorn, Arnold and Gude, Maik}, title = {Methodical Approach for Simulation the Vibration of Damaged Fibre Reinforced Composite Rotors Under Consideration of Aerodynamic Influences}, series = {18th European Conference on Composite Materials (ECCM18), Athen (Griechenland), 25.-28. Juni 2018}, booktitle = {18th European Conference on Composite Materials (ECCM18), Athen (Griechenland), 25.-28. Juni 2018}, pages = {8}, language = {en} } @inproceedings{BeirowKuehhornFigaschewskyetal., author = {Beirow, Bernd and K{\"u}hhorn, Arnold and Figaschewsky, Felix and Bornholm, Alfons and Repetckii, Oleg V.}, title = {Forced Response Reduction of a Blisk by Means of Intentional Mistuning}, series = {ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, Volume 7C: Structures and Dynamics, Oslo, Norway, June 11-15, 2018}, booktitle = {ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, Volume 7C: Structures and Dynamics, Oslo, Norway, June 11-15, 2018}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-5115-9}, doi = {10.1115/GT2018-76584}, pages = {10}, abstract = {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.}, 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{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{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{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{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} } @misc{HeinrichUnglaubeBeirowetal., author = {Heinrich, Christoph Rocky and Unglaube, Tina and Beirow, Bernd and Brillert, Dieter and Steff, Klaus and Petry, Nico}, title = {Surrogate Models for the Prediction of Damping Ratios in Coupled Acoustoelastic Rotor-Cavity Systems}, series = {Proceedings of ASME Turbo Expo 2021, ASME Paper Number: GT2021-58835}, journal = {Proceedings of ASME Turbo Expo 2021, ASME Paper Number: GT2021-58835}, 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. In other fields of application, like gas injection for enhanced oil recovery, discharge pressures over 600 bar and gas densities over 300 kg/m^3 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. In multiple studies, acoustic modes building up in the side cavities were found to be a potential source of high cycle fatigue in radial compressors. Nowadays, it is well-known that an increase in gas pressure levels leads to a more pronounced fluid-structure interaction between the side cavities and the impeller resulting 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. In a recently published paper, the authors presented a generalized model to predict the natural frequencies and mode shapes of acoustoelastic rotor-cavity systems. This approach reduces the computational cost significantly while retaining the accuracy of a finite element simulation. So far, the model was only validated using measurement data of an impeller at standstill under varying cavity pressures. In this study, the authors show that the generalized model can predict the natural frequencies of rotating systems with sufficient accuracy by using measurement data of a disk spinning at multiple rotational speeds in a cylindrical cavity. As it is not always possible to avoid operating close to or accelerate through a resonance of the compressor, it is crucial to know the damping present within the system that limits the amplitudes for a given excitation force. While many studies focus on the identification of damping ratios in axial turbomachines, only a few publications concentrate on the damping of radial impellers. Therefore, the authors present measurement data acquired from the test rig at University Duisburg-Essen, Chair of Turbomachinery, which reveals the damping behavior of a spinning disk under varying operating conditions. Three surrogate models are proposed to predict the identified damping behavior. The first one is based solely on a one-dimensional piston model. The second approach uses an enhanced version of the generalized method, while the third one is a combination of both. After deriving these three models, the measurement data is used to validate the surrogate systems. The paper concludes with a discussion of the measurement results and the benefits and limitations of the proposed models.}, language = {en} } @misc{GambittaKuehhornBeirowetal., author = {Gambitta, Marco and K{\"u}hhorn, Arnold and Beirow, Bernd and Schrape, Sven}, title = {Stator Blades Manufacturing Geometrical Variability in Axial Compressors and Impact on the Aeroelastic Excitation Forces}, series = {Proceedings of ASME Turbo Expo 2021, ASME Paper Number: GT2021-59642}, journal = {Proceedings of ASME Turbo Expo 2021, ASME Paper Number: GT2021-59642}, abstract = {The manufacturing geometrical variability is a source of uncertainty, which cannot be avoided in the realization of a machinery. Deviations of a component geometry from its nominal design are inevitably present due to the manufacturing process. In the case of the aeroelastic forced response problem within axial compressors, these uncertainties may affect the vibration characteristics. For this reason, the impact of geometrical uncertainties due to the manufacturing process onto the modal forcing of axial compressor blades is investigated in this study. The research focuses on the vibrational behavior of an axial compressor rotor blisk (blade-integrated disk) and in particular the amplitude of the forces acting as source of excitation on the vibrating blades (modal forcing). Within this context, the geometry of the upstream stator plays an important role as in general the main harmonics of the rotor excitation forces are produced by its wake. Therefore, small variations of the upstream stators geometries, such as the ones caused by the manufacturing process, may affect the resulting forcing. In particular, the geometrical variability of the upstream stator implies that the hypothesis of a cyclic-symmetrical flow is no longer valid. This may cause the introduction of lower harmonic components in the modal forces, generally referred to as Low Engine Orders (LEO). The geometrical variability is modelled starting from a series of optical surface scans. A set of optical measurements of manufactured stator blades originating from the same nominal design constitutes the baseline dataset on which the geometrical model is built. The measured blades as well as the relative nominal geometry are parametrized to describe the individual blades surfaces. The parameterization is accomplished by slicing the surfaces in radial sections and describing each of these with a set of NACA-like parameters [1]. The measured geometrical deviations from the nominal model can therefore be described as an offset of such parameters. A reduced representation of the variables representing the input uncertainty (noise variables) is obtained via Principal Components Analysis. Afterwards a sampling on the reduced noise variables domain can be done to represent the modelled uncertainty and perform an Uncertainty Quantification (UQ) on the relative quantities of interest, in this case the modal forcing. The computation of the modal forcing is done through a CFD solver, computing the unsteady flow field around the rotor blades. The domain considered in this case is a 1.5 stage of the axial compressor, including the rotor and the up- and down-stream stators. The solutions are initialized from a validated steady state solution of the considered compressor rig. The time-dependent pressure field calculated on the rotor blades is projected onto the relative vibrational mode shapes of interests (from structural modal analyzes). The resulting forces are analyzed by means of their spectrum, evaluating the amplitudes for the present engine orders (higher harmonics of the shaft mechanical speed). The UQ uses Monte Carlo methods to evaluate the impact of the geometrical variability onto the modal forcing. The modelled uncertainty on the geometries is introduced into the CFD solver to compute the deviations on the quantities of interest. A reconstruction of the forces acting on the rotor during one revolution is obtained. This allows to evaluate the uncertainty on the present engine orders as well as the possible rise of LEO for the rotor blades in presence of a mistuned upstream stator. [1]: Lange A., Vogeler K., G{\"u}mmer V., Schrapp H. and Clemen C. (2009). "Introduction of a Parameter Based Compressor Blade Model for Considering Measured Geometry Uncertainties in Numerical Simulation." Proceedings of ASME Turbo Expo. GT2009-59937}, language = {en} } @misc{NakosBeirowZobel, author = {Nakos, Alex and Beirow, Bernd and Zobel, Arthur}, title = {Mistuning and Damping of a Radial Turbine Wheel. Part 1: Fundamental Analyses and Design of Intentional Mistuning Pattern}, series = {Proceedings of ASME Turbo Expo 2021, ASME Paper Number: GT2021-59283}, journal = {Proceedings of ASME Turbo Expo 2021, ASME Paper Number: GT2021-59283}, abstract = {The radial turbine impeller of an exhaust turbocharger is analyzed in view of both free vibration and forced response. Stator vane rings located upstream between engine and turbine wheel are applied to guide the exhaust gases in optimized flow directions. Hence, turbine wheels are subjected to aerodynamic excitations causing forced vibrations of blades and the whole turbine. Due to random blade mistuning resulting from unavoidable inaccuracies in manufacture or material inhomogeneities, localized modes of vibration may arise, which involve the risk of severely magnified blade displacements and inadmissibly high stress levels compared to the tuned counterpart. In consequence, damages may occur along with a dramatic decrease of efficiency or even a total failure during engine operation as worst-case scenarios. Contrary, the use of intentional mistuning has proved to be an efficient measure to mitigate the forced response. Independently, the presence of aerodynamic damping is significant with respect to limit the forced response since structural damping ratios of blade integrated disks (blisks) typically take extremely low values. Thus, a detailed knowledge of respective damping ratios would be desirable while developing a robust blisk design. For this, far-reaching experimental investigations are carried out to determine damping curves of a comparative wheel within a wide pressure range by simulating operation conditions in a pressure tank. They are the basis to develop empirical formulas for damping estimation which could be be taken into account during future design processes. In order to get an idea of the real structural behaviour, further measurements are conducted to determine the present mistuning of the turbine wheel, which facilitates to update structural models and finally allows to compute the forced response in an accurate manner. Reduced order models are built up for designing suitable intentional mistuning patterns by using the subset of nominal system mode (SNM) approach introduced by Yang and Griffin [1], which conveniently allows for accounting both differing mistuning patterns and the impact of aeroelastic interaction. For this, the aerodynamic damping curves are determined by means of computational flow simulations. The SNM approach finally provides appropriate mistuning patterns by conducting optimization studies based on genetic algorithms. The robustness of the found solutions is proved by additionally superimposing both random mistuning and experimentally determined mistuning of the original wheel. Finite element analyses are carried out in order to identify appropriate measures to implement intentional mistuning patterns, which are featuring only two different blade designs. In detail, the impact of specific geometric modifications on blade natural frequencies is investigated. After implementation of the intentional mistuning pattern, which will be described in Part 2 of this paper later on, the success of taken measures will be reviewed based on both, experimental testing at standstill conditions and in a test stand by running the wheel under realistic operational conditions. [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} }