@misc{SasakarosBeckerWirsumetal., author = {Sasakaros, Marios and Becker, Jonte and Wirsum, Manfred and Beirow, Bernd}, title = {On the determination of nodal diameter spectrum and mistuning quantification of synchronous blade vbrations through blade-tip-timing measurements}, series = {Proceedings of the ASME Turbo Expo 2025, Memphis, June 16-20, 2025}, journal = {Proceedings of the ASME Turbo Expo 2025, Memphis, June 16-20, 2025}, publisher = {The American Society of Mechanical Engineers}, address = {New York, NY}, isbn = {978-0-7918-8885-8}, doi = {10.1115/GT2025-151774}, pages = {15}, abstract = {Synchronous vibrations can severely impact the service life of impellers. Previous studies have demonstrated that mistuning significantly influences the nodal diameter of these vibrations. Specifically, mistuned impellers exhibit forced vibration responses comprising multiple nodal diameters, leading to asymmetric vibration expression among the impeller sectors and substantial amplitude overshoots. Blade-Tip-Timing (BTT) is a promising technique for monitoring synchronous vibrations due to its non-intrusive nature and capability to monitor all blades simultaneously. This paper presents a novel method for calculating the Nodal Diameter Spectrum (NDS) of synchronous blade vibrations through BTT measurements. The method utilizes the vibration properties, which are estimated via BTT through the Circumferential Fourier Fit method, to reconstruct the blade vibrations. Since the vibration properties of the blades are not determined at the same time, the vibrations are synchronized to acquire the impeller Operational Deflection Shape (ODS), which can be associated with the mistuned impeller modes at the resonance crossings. Subsequently, the NDS is determined by performing Discrete Fourier Transform (DFT) analysis on the impeller ODS. Simulated data are used to assess the effect of the vibration sample point on the DFT results and the impact of noise. Based on these results a strategy for the determination of the NDS in a revolution is derived. Next, the method is applied to experimental data acquired from a turbocharger test bench. To investigate the consistency of the proposed method, the results of multiple datasets of the same vibration are presented. In addition, the method is validated by comparing the experimental results with those acquired by forced response simulations. Finally, by employing the experimentally determined impeller ODS and the NDS, mistuning quantification factors are calculated.}, language = {en} } @misc{NakosBeirow, author = {Nakos, Alex and Beirow, Bernd}, title = {Comparative experimental determination of mistuning of a bladed turbine wheel using different evaluation approaches}, series = {Proceedings of the ASME Turbo Expo 2025, Memphis, June 16-20, 2025}, journal = {Proceedings of the ASME Turbo Expo 2025, Memphis, June 16-20, 2025}, publisher = {The American Society of Mechanical Engineers}, address = {New York, NY}, isbn = {978-0-7918-8885-8}, doi = {10.1115/GT2025-151778}, pages = {11}, abstract = {Random mistuning of integrally manufactured turbine and compressor wheels can lead to severely high magnitudes in blade vibration. This is caused by unavoidable imperfections due to manufacturing processes or material inhomogeneities and the resulting deviation in geometry and structure between the individual blades. In order to be able to calculate the vibration response of bladed wheels correctly the actual mistuning should be quantified most accurately and taken into account e.g. in simulation models. Since mistuning is usually described as a frequency deviation of the nominal value measuring procedures have been developed in order to measure existing wheel hardware. An industry-suited procedure has been introduced by K{\"u}hhorn and Beirow [1] which modifies a conventional experimental modal analysis by isolating the blade that is excited and measured from all remaining ones. Therefore, additional masses are applied in order to cause a detuning and thus an isolated vibration of the blade under consideration. This enables the often coupled frequency response function peaks to decouple and obtain only one single peak which marks the actual frequency mistuning of the blade. Indeed, the procedure has proved to be accurate if isolated blade mode families are considered. In other cases, blade-disk-coupling can still be a problem and falsify the evaluation. The reason for this is an unfavourable application of the additional masses which most often cannot be avoided and may lead to an inaccurate or even erroneous mistuning value. However, Zhou et al. [2] have developed a novel approach to calculate an error term in order to correct the measured frequency mistuning. In this paper a radial turbine wheel is subjected to the blade frequency tests. The evaluation is carried out by using both, the conventional evaluation of the frequency response function and the novel approach. The error term is calculated and the mistuning distributions were corrected. Finally, the impact and measurement falsification of additional masses when testing a radial turbine wheel is discussed.}, language = {en} } @misc{BeirowNakosStecklinaetal., author = {Beirow, Bernd and Nakos, Alex and Stecklina, Caroline and Noack, Martin and Firl, Matthias and Sasakaros, Marios}, title = {Implementation of intentional mistuning by means of finite element based shape optimization}, series = {Proceedings of the ASME Turbo Expo 2025, Memphis, June 16-20, 2025}, journal = {Proceedings of the ASME Turbo Expo 2025, Memphis, June 16-20, 2025}, publisher = {The American Society of Mechanical Engineers}, address = {New York, NY}, isbn = {978-0-7918-8885-8}, doi = {10.1115/GT2025-151617}, pages = {11}, abstract = {Intentional Mistuning has turned out to be an effective measure to alleviate the maximum forced response of bladed wheels in the framework of numerous studies in the past. In particular solutions based on two different blade designs, following e.g. alternating or AABB patterns, have proved to be promising in this regard and moreover robust against the impact of unavoidable random mistuning. Thus, for example, a 40 percent reduction of the first blade bending maximum forced response has been proved experimentally for a turbine impeller of a turbo charger application. Despite this success, the technical implementation of the frequency based mistuning pattern followed an academic solution based on locally removing material at the leading edge tip, which is not suited for the use in serial wheels since it may disturb the flow channel. In addition, the forced response of other blade modes may be affected in a negative manner. In order to overcome these problems, an alternative way of implementing Intentional Mistuning is suggested by applying a marginal geometric modification of the blade thickness distribution to adjust the natural frequency of the first bending mode. Finite element based shape optimization is utilized to this end. Secondary conditions are ensuring that only the target frequency of the first bending mode is adjusted whereas natural frequencies of other modes are kept almost unchanged.}, language = {en} } @misc{GambittaBeirowKlauke, author = {Gambitta, Marco and Beirow, Bernd and Klauke, Thomas}, title = {Structural dynamics of an axial compressor's rear blisk drum and multi-stage coupling}, series = {ASME Turbo Expo 2024: Turbomachinery Technical Conference and Exposition, June 24-28, 2024, London, United Kingdom}, journal = {ASME Turbo Expo 2024: Turbomachinery Technical Conference and Exposition, June 24-28, 2024, London, United Kingdom}, isbn = {978-0-7918-8803-2}, doi = {10.1115/GT2024-128647}, language = {en} } @misc{NakosBeirow, author = {Nakos, Alex and Beirow, Bernd}, title = {On the Influence of Installation on the Forced Response of Radial Turbine Wheels}, series = {Proceedings of Global Power and Propulsion Society, GPPS Hongkong, October 16 - 19, 2023}, journal = {Proceedings of Global Power and Propulsion Society, GPPS Hongkong, October 16 - 19, 2023}, issn = {2504-4400}, doi = {10.33737/gpps23-tc-138}, pages = {10}, abstract = {Radial turbine wheels are commonly designed as integrally bladed rotors featuring extremely low structural damping in comparison to separate designs of blades and disk. Consequently, they are more prone to vibration. Moreover, random blade mistuning due to unavoidable inaccuracies in manufacture or material inhomogeneities can severely increase the maximum forced blade vibration amplitude compared to the tuned counterpart. Unfortunately, this response magnification may worsen in case of small damping. Since modes exhibiting blade dominated vibration are usually considered vulnerable in this regard, the influence of disk and shaft and its mounting conditions seems to be negligible. In this paper, reduced order models are employed in order to simulate the forced response of a radial turbine wheel. Experimental modal analyses have been carried out to provide realistic damping ratios considering both the single turbine wheel hardware as well as the full rotor mounted in a turbocharger test rig. Test runs are conducted and non-intrusive blade-tip-timing technology provides measurement data to validate the simulation models. Contrary to the original presumption, it is shown that additional structural damping contributed by assembling can significantly influence the forced response even though the focus is on blade dominated vibration.}, language = {en} } @misc{SasakarosSchafferusWirsumetal., author = {Sasakaros, Marios and Schafferus, Markus and Wirsum, Manfred and Zobel, Arthur and Vogt, Damian and Nakos, Alex and Beirow, Bernd}, title = {Experimental Investigation of Synchronous Flow Induced Blade Vibrations on a Radial Turbine - Part 2: Influence of Different Inlet Guide Vane Configurations}, series = {Proceedings of ASME Turbo Expo 2023, Boston, Massachusetts, June 26-30, 2023, Volume 11, A. Aerodynamics excitation and damping, bearing and seal dynamics}, journal = {Proceedings of ASME Turbo Expo 2023, Boston, Massachusetts, June 26-30, 2023, Volume 11, A. Aerodynamics excitation and damping, bearing and seal dynamics}, publisher = {ASME}, address = {New York}, isbn = {978-0-7918-8705-9}, doi = {10.1115/GT2023-102243}, pages = {15}, abstract = {The occurrence of blade vibrations in radial turbines leads to limit cycle oscillations, which in time increase the risk of component failure due to high cycle fatigue. In this context, the precise determination of the resonance operating points and the estimation of the vibration magnitudes are essential for an accurate assessment of the service life of the turbocharger components. In radial turbines forced blade vibrations are primarily flow induced. These vibrations are produced by the non-uniform flow field in the circumferential direction which acts on the blades as a cyclic pressure fluctuation. Previous studies have identified the inlet guide vane (IGV) and the spiral turbine housing as the primary sources of the non-uniform flow field. In the present study a thorough experimental investigation of the synchronous blade vibrations of a radial turbine is performed. First, the blade vibration modes were measured experimentally and calculated numerically for the determination of the speed ranges that need to be examined. Subsequently, the vibrations were captured with two redundant measurement systems during real turbocharger operation. Strain gauges were applied on certain blades while eight optical sensors were distributed on the circumference of the turbine shroud for the measurement of the blades tips deflection through a commercial tip-timing system. In the first part, the blade vibrations caused by the "nominal" IGV are presented. Part 2 analyses the changes of the blade vibrations due to the application of two different IGVs. The first IGV has the same number of vanes as the "nominal" IGV. Nevertheless, it generates additional low engine order excitations by intentionally varying the distance between the vanes. Next, an IGV with a higher number of vanes is employed for the excitation at higher frequencies and thus of higher blade modes. Contrary to expectations, certain synchronous vibrations can be measured in the experiments of all IGVs. These cannot be attributed to the spiral turbine casing.}, language = {en} } @misc{SchafferusSasakarosWirsumetal., author = {Schafferus, Markus and Sasakaros, Marios and Wirsum, Manfred and Zobel, Arthur and Vogt, Damian and Nakos, Alex and Beirow, Bernd}, title = {Experimental Investigation of Synchronous Flow Induced Blade Vibrations on a Radial Turbine - Part 1: Nominal Inlet Guide Vane}, series = {Proceedings of ASME Turbo Expo 2023, Boston, Massachusetts, June 26-30, 2023, Volume 11, A. Aerodynamics excitation and damping, bearing and seal dynamics}, journal = {Proceedings of ASME Turbo Expo 2023, Boston, Massachusetts, June 26-30, 2023, Volume 11, A. Aerodynamics excitation and damping, bearing and seal dynamics}, publisher = {ASME}, address = {New York}, isbn = {978-0-7918-8705-9}, doi = {10.1115/GT2023-103037}, pages = {13}, abstract = {The service life of today's turbochargers is limited among other things by the mechanical load caused by blade vibrations. In this context, the precise determination of the resonance operating points and the estimation of the vibration magnitudes are essential for an accurate assessment of the service life of the turbocharger components. Forced blade vibrations in radial turbines are primarily flow induced. Flow induced blade vibrations are caused by the nonuniform flow field in the circumferential direction which acts on the blades as a cyclic pressure fluctuation. Previous studies identified the inlet guide vane (IGV) as well as the spiral turbine housing as the primary sources of the non-uniform flow field. In the present study a thorough experimental investigation of the synchronous blade vibrations of a radial turbine is performed. A detailed description of the experimental setup is given. In this setup the vibrations are captured with two redundant measurement systems during real turbocharger operation. Strain gauges, applied on certain blades, as well as optical tip-timing sensors distributed on the circumference of the turbine shroud are used. The advantages of the combined usage of these two measuring systems are shown in the paper. Initially, the blade vibration modes are determined experimentally in stand still tests and numerically calculated through FEM models. This served for the creation of a Campbell diagram, which determined the speed ranges that are examined. The mistuning, which is not taken into account in the numerics, is therefore determined via the experiment. In addition, the experimental results are compared with those of numerics and the frequencies from standstill test. The first part of this two-part paper is focused on the vibrations caused by the "nominal" IGV. This "nominal" IGV has twice the number of blades compared to the rotor. Part 2 will analyze the changes of the blade vibrations due to the application of two different IGVs.}, language = {en} } @misc{ZobelFuhrerVogtetal., author = {Zobel, Arthur and Fuhrer, Christopher and Vogt, Damian and Nakos, Alex and Beirow, Bernd and Blessing, Alexander and Zippack, Carolin}, title = {On the Influence of Bearing Modeling Details on the Dynamical System Effects of a Mid-Size Turbocharger Rotor}, series = {Proceedings of ASME Turbo Expo 2023, Boston, Massachusetts, June 26-30, 2023, Volume 11, A. Aerodynamics excitation and damping, bearing and seal dynamics}, journal = {Proceedings of ASME Turbo Expo 2023, Boston, Massachusetts, June 26-30, 2023, Volume 11, A. Aerodynamics excitation and damping, bearing and seal dynamics}, publisher = {ASME}, address = {New York}, isbn = {978-0-7918-8705-9}, doi = {10.1115/GT2023-102098}, pages = {11}, abstract = {The investigation of the excitation of turbocharger rotors to quantify the High-Cycle-Fatigue (HCF) risk is still a demanding task nowadays. The common way to investigate such phenomena is to look either at the turbine or the compressor rotor in an isolated manner. This approach gives mostly reliable results, if the investigated excitation pattern is stemming from the up- or downstream parts in the machine. However, there is a lack of studies on the existence of responses, which may exist due to the coupling between compressor and turbine. With the increase of computational capabilities and the improvement of FE tools, it is possible to create a full rotor model featuring the compressor and the turbine wheel as well as the bearings to investigate the dynamical behavior of the full rotor at different resonances. To carry out such an investigation, both wheels and the shaft are modeled. The axial, as well as the radial bearings, are modelled realistically by suitable elements and values. Due to the asymmetry of damping and stiffness properties, the resulting system matrices are asymmetrical as well. The eigenfrequencies and mode shapes of such a system can be obtained in a reasonable time by carrying out a modal analysis using the QR damp eigensolver in Ansys APDL. The present paper will show the differences in dynamical system effects of a mid-size turbocharger with different shaft support conditions. For this purpose, the FE simulation with the full rotor and fixed support at the radial bearing position, which is comparable to the isolated rotor consideration, will be compared to the model featuring the detailed bearing modeling with stiffness and damping values originating from the OEM. Besides the detailed process of modeling the bearings, the mutual influence of both rotor wheels at certain eigenfrequencies is analyzed. This allows to conclude on the level of detailing needed to ensure that dynamical system effects are properly accounted.}, language = {en} } @misc{GambittaBeirowKlauke, author = {Gambitta, Marco and Beirow, Bernd and Klauke, Thomas}, title = {Investigation of Rear Blisk Drum Dynamics Under Consideration of Multi-Stage Coupling}, series = {Proceedings of ASME Turbo Expo 2023, Boston, Massachusetts, June 26-30, 2023}, journal = {Proceedings of ASME Turbo Expo 2023, Boston, Massachusetts, June 26-30, 2023}, isbn = {978-0-7918-8705-9}, doi = {10.1115/GT2023-103756}, abstract = {The analysis of the structural dynamics of multistage cyclic structures as linked components is required to model the interstage coupling. In turbomachinery, this can result in a collaboration between different compressor or turbine stages. This paper investigates the coupling between two rear drum blade integrated disk stages of an axial compressor to support the mechanical design process. Considering the vibration modeshapes of a multistage system, different components may co-participate in the dynamics. For this reason, a criteria to identify the modes affected by the coupling and to quantify this coupling is defined. This allows to distinguish between modes with inter-stage coupling, requiring the multistage system for their description, and uncoupled modes, involving a single stage. In addition, it is of interest to research methods to reduce the impact of the coupling on the vibrating system without drastically altering the geometry of the components. The vibration analyses of a two-stage compressor generalized geometry, representative of a compressor rear drum blisk, is presented as a study case. The use of a reducing method allows to describe the behavior of the nominal multistage system with a computationally efficient technique, enabling a parametric analysis of the stages' coupling. The investigation considers the effect of a set of geometrical and mechanical parameters on the dynamics, identifying the driving parameters of the coupled vibration characteristics.}, language = {en} } @misc{GambittaBeirowKlauke, author = {Gambitta, Marco and Beirow, Bernd and Klauke, Thomas}, title = {Investigation of Rear Blisk Drum Dynamics Under Consideration of Multi-Stage Coupling}, series = {ASME Journal of Engineering for Gas Turbines and Power}, volume = {146}, journal = {ASME Journal of Engineering for Gas Turbines and Power}, number = {2}, doi = {10.1115/1.4063633}, pages = {8}, abstract = {The analysis of the structural dynamics of multistage cyclic structures as linked components is required to model the interstage coupling. In turbomachinery, this can result in a collaboration between different compressor or turbine stages. This paper investigates the coupling between two rear drum blade integrated disk stages of an axial compressor to support the mechanical design process. Considering the vibration modeshapes of a multistage system, different components may coparticipate in the dynamics. For this reason, criteria to identify the modes affected by the coupling and to quantify this coupling are defined. This allows to distinguish between modes with interstage coupling, requiring the multistage system for their description, and uncoupled modes, involving a single stage. In addition, it is of interest to research methods to reduce the impact of the coupling on the vibrating system without drastically altering the geometry of the components. The vibration analyses of a two-stage compressor generalized geometry, representative of a compressor rear drum blisk, are presented as a study case. The use of a reducing method allows to describe the behavior of the nominal multistage system with a computationally efficient technique, enabling a parametric analysis of the stages' coupling. The investigation considers the effect of a set of geometrical and mechanical parameters on the dynamics, identifying the driving parameters of the coupled vibration characteristics.}, language = {en} } @misc{NakosBeirowWirsumetal., author = {Nakos, Alex and Beirow, Bernd and Wirsum, Manfred and Schafferus, Markus and Sasakaros, Marios and Vogt, Damian and Zobel, Arthur}, title = {Mistuning and Damping of a Radial Turbine Wheel. Part 3: Validation of Intentional Mistuning During Machine Operation}, series = {Proceedings of ASME Turbo Expo 2023, Boston, Massachusetts, June 26-30, 2023}, journal = {Proceedings of ASME Turbo Expo 2023, Boston, Massachusetts, June 26-30, 2023}, isbn = {978-0-7918-8706-6}, doi = {10.1115/GT2023-101993}, abstract = {This contribution investigates the implementation and verification of intentional mistuning (IM) to a radial turbine wheel of an exhaust turbocharger. In principle, inaccuracies in manufacture or material inhomogeneities may lead to random blade mistuning and thus localized modes with severely magnified blade vibrations can occur. With regard to axial compressors and turbines, IM has proved to be an efficient measure to mitigate the forced response. For radial turbine wheels, on the other hand, a successful implementation of IM into a wheel hardware has not yet been presented. This work aims at the design, implementation, and verification of successful IM considering both measurements at standstill and test runs on a turbocharger test rig. The fundamental analyses have been carried out in part one [1] of this three-part paper in order to find a suitable IM-pattern featuring only two different blade designs. The AABB sequence was identified to be the most promising one in terms of mitigating the maximum forced response of the fundamental bending mode at the considered operating point. In concrete terms, a 40\% attenuation of the maximum forced response was predicted by employing reduced order models. The second part [2] discussed the detailed geometric adaption of the turbine wheel hardware focussing on the implementation and validation of the IM pattern under laboratory conditions (standstill). Part three is about validating the efficacy of IM under operating conditions. In that sense, the successful implementation of IM and thus the machining of the wheel hardware are investigated within the framework of test runs on a turbocharger test rig. Test runs are conducted for both a wheel with and a wheel without IM. Non-intrusive blade-tip-timing (BTT) technology is employed to record forced response data. A well-known approach to evaluate the raw data namely times of arrival (TOA) without the availability of a once-per-revolution (OPR) signal is adapted, implemented, and applied for the evaluation. The results are compared to those received by using a commercial evaluation software for BTT measurement data. Finally, the actual gain achieved by means of IM is discussed in detail.}, language = {en} } @misc{NakosBeirowZobel, author = {Nakos, Alex and Beirow, Bernd and Zobel, Arthur}, title = {Vibration Analyses of Radial Turbine Wheels Considering Structural and Aerodynamic Mistuning}, series = {Proceedings of Global Power and Propulsion Society}, journal = {Proceedings of Global Power and Propulsion Society}, issn = {2504-4400}, doi = {10.33737/gpps22-tc-61}, pages = {9}, abstract = {Radial turbine wheels of exhaust gas turbochargers are permanently exposed to centrifugal, thermal, and aerodynamic loading. However, since these wheels are commonly designed as integral structures featuring relatively little mechanical damping, they are prone to the impact of unavoidable structural random mistuning, which may evoke severe magnifications of the forced response. Nonetheless, the safe operation of turbochargers has to be ensured at any time so that the contribution of aerodynamic damping is of particular importance. Moreover, the application of intentional mistuning is known to be a suitable measure to limit or even reduce the forced response by means of increasing the resulting aerodynamic damping. In this paper, two turbine wheels of the same type are considered, one manufactured with and another one without intentional mistuning. Experimental determinations of the mistuning patterns actually reveal deviations from the design intentions, which are considered in updated numerical models. Forced response simulations demonstrate that the targeted response reduction affected by intentional mistuning is achieved anyhow. Furthermore, the general robustness of the solution is proved with respect to the maximum forced response by means of comprehensive probabilistic numerical analyses addressing the impact of additional random structural mistuning, the magnitude of intentional mistuning, and aerodynamic mistuning.}, language = {en} } @misc{NakosBeirowZobel, author = {Nakos, Alex and Beirow, Bernd and Zobel, Arthur}, title = {Mistuning and Damping of a Radial Turbine Wheel. Part 2: Implementation and Validation of Intentional Mistuning}, series = {ASME 2022 Turbomachinery Technical Conference \& Exposition (GT2022)}, journal = {ASME 2022 Turbomachinery Technical Conference \& Exposition (GT2022)}, abstract = {A radial turbine impeller of an exhaust turbocharger is analyzed in view of both free vibration and forced response. 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. Contrary, the use of intentional mistuning (IM) has proved to be an efficient measure to mitigate the forced response. In part one of this three-part paper fundamental analyses have been carried out to find a suitable intentional mistuning pattern which is featuring only two different blade designs [1]. This part is focused on the implementation and validation of the intentional mistuning pattern and discusses the detailed geometric adaption of the turbine wheel hardware. The final design of the geometric adaption is developed in terms of manufacturability and efficiency so that a reliable and robust solution is presented. Its machined adaption is validated by both vibration testing at rest and optical measurements so that manufacturing deviations are detected and their impacts discussed and evaluated. Reduced order models are built up for checking the effect of the implemented intentional mistuning pattern on the forced response by using the subset of nominal system modes (SNM) approach introduced by Yang and Griffin [2], which conveniently allows for accounting both the design intention of the mistuning pattern and the actually machined implementation due to manufacturing deviations.}, language = {en} } @misc{BeirowGolzePopig, author = {Beirow, Bernd and Golze, Mark and Popig, Frederik}, title = {Application of Intentional Mistuning to Reduce the Vibration Susceptibility of a Steam Turbine Wheel}, series = {ASME 2022 Turbomachinery Technical Conference \& Exposition (GT2022)}, journal = {ASME 2022 Turbomachinery Technical Conference \& Exposition (GT2022)}, abstract = {Intentional mistuning (IM) is employed on a last stage turbine wheel to alleviate both the flutter susceptibility and maximum forced response. Primarily, operations at nominal speed under part-load conditions may cause unfavorable flow conditions facilitating flow separation. As a consequence, the original design intention with identical blades features negative aerodynamic damping ratios with respect to the first bending mode family. In order to prevent any self-excited vibration phenomena, intentional alternate mistuning is utilized to increase the least aerodynamic damping ratio as far as it takes a positive value and hence, to contribute to a stabilization of the rotor. For the purpose of numerically analyzing the vibration behavior, reduced order models are built up, which are based on modal reduction techniques, namely the subset of nominal system modes (SNM) [1] and the fundamental mistuning model (FMM) [2]. These types of models conveniently allow for considering both, different mistuning distributions in terms of probabilistic analyses and the aeroelastic interaction by means of prescribing aerodynamic damping ratios and aeroelastic natural frequencies of the tuned counterpart or aerodynamic influence coefficients, respectively. A detailed study is presented regarding the correction of frequency mistuning magnitudes in terms of considering the impact of centrifugal stiffening, which plays a significant role in case of long low pressure turbine blades featuring high aspect ratios. Since alternate IM cannot be implemented perfectly, every bladed wheel as manufactured will exhibit small but unavoidable structural deviations from the design intention, which are known as random mistuning. To ensure the robustness of the IM solution in terms of positive aerodynamic damping ratios at any time, comprehensive probabilistic analyses are conducted with respect to superimposing random structural mistuning at first. Secondly, the impact of varying mistuning magnitude is analyzed. Thirdly, the robustness towards aerodynamic mistuning is investigated by means of small variations of aeroelastic influence coefficients and consequently, the inter blade phase angle dependent aerodynamic damping curves. Moreover, it becomes apparent that alternate IM superimposed with both, random structural and aerodynamic mistuning also mitigates the maximum forced response at part-speed conditions.}, language = {en} } @misc{YangBeirowGiersch, author = {Yang, Jingjie and Beirow, Bernd and Giersch, Thomas}, title = {Simulation and Investigation of an Intentionally Mistuned Blisk Rotor in a High Pressure Compressor}, series = {ASME 2022 Turbomachinery Technical Conference \& Exposition (GT2022)}, journal = {ASME 2022 Turbomachinery Technical Conference \& Exposition (GT2022)}, abstract = {In modern aircraft engines, blade integrated disk (blisk) is widely implemented. While blisk rotor design brings numerous advantages including weight reduction, aerodynamic efficiency improvement, and manufacturing simplification, its low mechanical damping due to the absence of friction between disk and blades makes the rotor more susceptible to vibration. Given that damage to blisk rotor sometimes requires the whole assembly to be replaced, effort has been made to alleviate the unexpected vibration amplitude within operating range, among which intentional mistuning is regarded as one of the commonly used technique. Mistuning refers to blade-to-blade deviation of mechanical properties, which is inevitable in practice due to manufacturing tolerances or wear. Through the application of intentional mistuning, it is expected that the amplitude of synchronous or nonsynchronous vibration (NSV) will be reduced without severely losing aerodynamic performance. In this paper, the effect of intentional mistuning has been investigated for the blisk rotor of a 1.5-stage transonic research compressor at Technical University of Darmstadt. According to the previous test campaign, the baseline rotor has shown its susceptibility to NSV due to first torsion mode in the near stall region. The rotor was then intentionally mistuned. Subsequent tests have proven a successful suppression of flutter problem. In order to have a comprehensive understanding of the effect of the applied mistuning pattern, simulations are performed using a FVM based CFD solver to produce comparable results as shown in the test campaign. In the simulation, mistuned systems are modelled in comparison with the nominal tuned reference. Geometrical disturbance and frequency disturbance are introduced to the tuned model first separately and then simultaneously. In this way, contribution of aerodynamic and structural mistuning to the suppression of NSV is identified based on the CFD results. Later, system eigenvalues of the mistuned aeromechanical model are determined by making use of the blade individual response in time domain. The obtained results are compared with mistuned eigenvalues calculated by a reduced order model (ROM), which utilizes the idea of subset of nominal modes (SNM). This makes it possible to demonstrate the feasibility of using SNM to carry out stability analysis when designing mistuning pattern for vibration of NSV type. It also allows a compare between the linear structural model of the SNM and the non-linear aeromechanic model of the CFD solver on capturing the non-linear nature of the flow, especially in the context of NSV.}, language = {en} } @misc{GambittaBeirowSchrape, author = {Gambitta, Marco and Beirow, Bernd and Schrape, Sven}, title = {A Digital Twin of Compressor Blisk Manufacturing Geometrical Variability for the Aeroelastic Uncertainty Quantification of the Aerodynamic Damping}, series = {Turbo Expo 2022 : Rotterdam Ahoy Convention Centre, Rotterdam, The Netherlands, Conference and Exhibition: June 13 - 17, 2022}, journal = {Turbo Expo 2022 : Rotterdam Ahoy Convention Centre, Rotterdam, The Netherlands, Conference and Exhibition: June 13 - 17, 2022}, abstract = {This study is centered on the aeroelastic problem for axial compressors blisk airfoils in presence of geometrical uncertainties. The combined problem of structural dynamics and unsteady aerodynamics is of interest for these machines due to the stress induced by the blades vibration. In this field, deviations from the nominal cyclic symmetry (in geometry, material or fluid properties) are generally referred to as mistuning. In particular, the geometrical mistuning is addressed resulting from the manufacturing process of blisk airfoils. The impact of these uncertainties on the aeroelastic problem is evaluated, focusing on the aerodynamic damping. The analysis of the manufacturing geometrical variability is approached in a probabilistic manner. A model representing the uncertainty is created starting from a dataset of optical surface scans. The measured geometries are parameterized in order to numerically describe the differences from the nominal geometry with a set of variables. The creation of a mean geometry of the measured blades allows to simplify the description of the uncertainty, which can be then modelled describing the distributions of geometrical deviations over the blade height. In order to create a stochastic model for the geometrical uncertainty, a data reduction method is implemented in the model. This aims to describe the variability within a minimum required accuracy while using a minimal set of variables. For this purpose, an Autoencoder is used to define a compressed representation of the dataset of interest. The method is based on the training of a Neural-Network, which tries to represent the identity function for the given data while forcing a variables reduction in the intermediate layers. A regularization method for the reduced variables is also introduced in order to avoid correlations and normalize the distributions. The computation of the aerodynamic damping is performed using a CFD solver. A steady-state representation of the investigated axial compressor rig is validated using available experimental data. The unsteady computations are done for one configuration at one shaft speed, which is representative of two relevant crossings in the Campbell diagram for the studied blisk. This indicates resonance conditions for two vibrational mode shapes of the component. The Aerodynamic Influence Coefficients (AIC) method is used to calculate the aerodynamic damping curve for the two vibrational mode shapes of interest. This allows to obtain the damping values over the different inter-blade phase angles with one single solution per mode shape, while reducing the domain to a sub-assembly of the investigated blisk. The Uncertainty Quantification (UQ) uses the implemented geometrical variability model and the defined solution method for the calculation of the aerodynamic damping. To describe the input uncertainty (manufacturing geometrical variability) the space of the variables resulting from the Autoencoder data reduction is used. A sampling is generated, representing with each sample a set of three mistuned blades. For each sample, the three resulting blade surfaces are inserted in the AIC setup, representing the vibrating blade as well as the relative direct upstream and downstream blades. This allows to evaluate the uncertainty on the amplitude and phase of the influence coefficients relative to the three blades and finally on the aerodynamic damping curve. The data reduction provided by the Autoencoder proved to be very efficient, especially if compared to linear methods as the principal components analysis. This allowed to include in the UQ multi-passage variations for a better representation of a real geometry. The output uncertainty on the aerodynamic damping could therefore be evaluated taking these effects in consideration. The results can be combined in an aeroelastic reduced order model with the mistuning of the mechanical properties of the component to represent the mistuned blades vibrations.}, language = {en} } @misc{BeirowGolzePopig, author = {Beirow, Bernd and Golze, Mark and Popig, Frederik}, title = {Vibration Reduction of a Steam Turbine Wheel by Means of Intentional Mistuning}, series = {Advances in Mechanism Design III : Proceedings of TMM 2020}, journal = {Advances in Mechanism Design III : Proceedings of TMM 2020}, publisher = {Springer}, address = {Cham}, isbn = {978-3-030-83593-4}, issn = {2211-0984}, doi = {10.1007/978-3-030-83594-1_8}, pages = {73 -- 82}, abstract = {A last stage steam turbine wheel is analyzed with the objective to alleviate the flutter susceptibility by employing intentional mistuning (IM). In particular, the operation at nominal speed under part-load conditions may cause unfavorable flow conditions facilitating flow separation. In consequence, negative aerodynamic damping ratios occur for the first bending mode family in some circumstances. Employing intended alternate mistuning of adequate magnitude has proved to be a promising measure to stabilize rotors in terms of avoiding self-excited vibration phenomena. From the manufacturing point of view, this two-blade design is advantageous as well and hence, chosen here as a first measure to attenuate flutter susceptibility. Two prototypes of bladed disks series have been made, which are exhibiting small but unavoidable deviations from the design intention due to manufacturing. The real blade alone frequencies have been identified within foregoing experimental investigations. Numerical modal analyses carried out for the prototypes as manufactured finally reveal that there is an additional positive contribution of random mistuning in terms of further enhancing the least aerodynamic damping ratio. Another promising and robust IM pattern is found by using generic algorithms to optimize the least aerodynamic damping ratio yielding stable conditions at any time as well. Moreover, it shows that IM combined with random mistuning also mitigates the maximum forced response at part-speed conditions.}, 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} } @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{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} } @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{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{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{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{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{WagnerKuehhornJanetzkeetal., author = {Wagner, Frank and K{\"u}hhorn, Arnold and Janetzke, Timm and Gerstberger, Ulf}, title = {Multi-Objective Optimization of the Cooling Configuration of a High Pressure Turbine Blade}, series = {ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, Volume 5C: Heat Transfer Oslo, Norway, June 11-15, 2018}, journal = {ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, Volume 5C: Heat Transfer Oslo, Norway, June 11-15, 2018}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-5110-4}, doi = {10.1115/GT2018-75616}, pages = {10}, abstract = {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}, language = {en} } @misc{FigaschewskyHanschkeKuehhorn, author = {Figaschewsky, Felix and Hanschke, Benjamin and K{\"u}hhorn, Arnold}, title = {Efficient Generation of Engine Representative Tip Timing Data Based on a Reduced Order Model for Bladed Rotors}, series = {ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, Volume 7C: Structures and Dynamics, Oslo, Norway, June 11-15, 2018}, journal = {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/GT2018-76342}, pages = {12}, abstract = {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}, language = {en} } @misc{WeberKuehhorn, author = {Weber, Robby and K{\"u}hhorn, Arnold}, title = {Mistuning Identification Approach With Focus on High-Speed Centrifugal Compressors}, series = {ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, Volume 7C: Structures and Dynamics, Oslo, Norway, June 11-15, 2018}, journal = {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/GT2018-75382}, pages = {10}, abstract = {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}, language = {en} } @misc{WeberKuehhornHeinrich, author = {Weber, Robby and K{\"u}hhorn, Arnold and Heinrich, Christoph Rocky}, title = {Modelling and analysis of a high-speed turbine impeller concerning mistuning}, series = {The 14th International Conference of machinery (VETOMAC XIV), Lissabon, 10-13 September 2018}, journal = {The 14th International Conference of machinery (VETOMAC XIV), Lissabon, 10-13 September 2018}, doi = {10.1051/matecconf/201821118002}, pages = {6}, abstract = {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.}, language = {en} } @misc{FigaschewskyBeirowKuehhornetal., author = {Figaschewsky, Felix and Beirow, Bernd and K{\"u}hhorn, Arnold and Nipkau, Jens and Giersch, Thomas and Powers, Bronwyn}, title = {Design and Analysis of an Intentional Mistuning Experiment Reducing Flutter Susceptibility and Minimizing Forced Response of a Jet Engine Fan}, series = {ASME Turbo Expo 2017, GT2017-64621, June 26-30, 2017, Charlotte, NC, USA, Volume 7B}, journal = {ASME Turbo Expo 2017, GT2017-64621, June 26-30, 2017, Charlotte, NC, USA, Volume 7B}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-5093-0}, doi = {10.1115/GT2017-64621}, pages = {13}, abstract = {Recent demands for a reduction of specific fuel consumption of jet engines have been opposed by increasing propulsive efficiency with higher bypass ratios and increased engine sizes. At the same time the challenge for the engine development is to design safe and efficient fan blades of high aspect ratios. Since the fan is the very first rotor stage, it experiences significant distortions in the incoming flow depending on the operating conditions. Flow distortions do not only lead to a performance and stall margin loss but also to remarkable low engine order (LEO) excitation responsible for forced vibrations of fundamental modes. Additionally, fans of jet engines typically suffer from stall flutter, which can be additionally amplified by reflections of acoustic pressure waves at the intake. Stall flutter appears before approaching the stall line on the fan's characteristic and limits its stable operating range. Despite the fact that this "flutter bite" usually affects only a very narrow speed range, it reduces the overall margin of safe operation significantly. With increasing aspect ratios of ultra-high bypass ratio jet engines the flutter susceptibility will probably increase further and emphasizes the importance of considering aeromechanical analyses early in the design phase of future fans. This paper aims at proving that intentional mistuning is able to remove the flutter bite of modern jet engine fans without raising issues due to heavily increased forced vibrations induced by LEO excitation. Whereas intentional mistuning is an established technology in mitigating flutter, it is also known to amplify the forced response. However, recent investigations considering aeroelastic coupling revealed that under specific circumstances mistuning can also reduce the forced response due to engine order excitation. In order to allow a direct comparison and to limit costs as well as effort at the same time, the intentional mistuning is introduced in a non-destructive way by applying heavy paint to the blades. Its impact on the blade's natural frequencies is estimated via finite element models with an additional paint layer. In parallel, this procedure is experimentally verified with painted fan blades in the laboratory. A validated SNM (subset of nominal system modes) representation of the fan is used as a computational model to characterize its mistuned vibration behavior. Its validation is done by comparing mistuned mode shape envelopes and frequencies of an experimental modal analysis at rest with those obtained by the updated computational model. In order to find a mistuning pattern minimizing the forced response of mode 1 and 2 at the same time and satisfying stability and imbalance constraints, a multi-objective optimization has been carried out. Finally, the beneficial properties of the optimized mistuning pattern are verified in a rig test of the painted rotor. Copyright © 2017 by Rolls-Royce Deutschland Ltd \& Co KG}, language = {en} } @misc{HanschkeKlaukeKuehhorn, author = {Hanschke, Benjamin and Klauke, Thomas and K{\"u}hhorn, Arnold}, title = {The Effect of Foreign Object Damage on Compressor Blade High Cycle Fatigue Strength}, series = {ASME Turbo Expo 2017, GT2017-63559, June 26-30, 2017, Charlotte, NC, USA, Volume 7A}, journal = {ASME Turbo Expo 2017, GT2017-63559, June 26-30, 2017, Charlotte, NC, USA, Volume 7A}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-5092-3}, doi = {10.1115/GT2017-63599}, pages = {9}, abstract = {For a considerable amount of time blade integrated disks (blisks) are established as a standard component of high pressure compressors (HPCs) in aero engines. Due to the steady requirement to increase the efficiency of modern HPCs, blade profiles get thinned out and aerodynamic stage loading increases. Ever since, aerofoil design has to balance structural and aerodynamic requirements. One particularity of aero engines is the possibility to ingest different kinds of debris during operation and some of those particles are hard enough to seriously damage the aerofoil. Lately, a growing number of blisk-equipped aero engines entered service and the question of foreign object damage (FOD) sensitivity relating to compressor blade high cycle fatigue (HCF) has emerged. Correct prediction of fatigue strength drop due to a FOD provides a huge chance for cost cutting in the service sector as on-wing repairs (e.g. borescope blending) are much more convenient than the replacement of whole blisks and corresponding engine strips. The aim of this paper is to identify critical FOD-areas of a modern HPC stage and to analyze the effects of stress concentrations — caused by FOD — on the fatigue strength. A process chain has been developed, that automatically creates damaged geometries, meshes the parts and analyses the fatigue strength. Amplitude frequency strength (af-strength) has been chosen as fatigue strength indicator owing to the fact, that amplitudes and frequencies of blade vibrations are commonly measured either by blade tip timing or strain gauges. Furthermore, static and dynamic stress concentrations in damaged geometries compared to the reference design were computed. A random variation of input parameters was performed, such as the radial damage position at blade leading edge and damage diameter. Based on results of the different samples, correlations of input parameters and the fatigue strength drop have been investigated. Evaluation shows a significant mode dependence of critical blade areas with a large scatter between drops in fatigue strength visible for mode to mode comparison. Keeping in mind the necessity of fast response times in the in-service sector, FOD sensitivity computations could be performed for all blade rows of the HPC — including the analysis of possible borescope blending geometries — in the design stage. Finally, the actual amplitude frequency levels (af-levels) of the modes excited during operation have to be appropriately taken into consideration. For example, a pronounced af-strength drop due to a FOD may not be critical for safe engine operations because the observed mode is excited by small af-levels during operation. Hence, the endurance ratio — a quotient of af-level and af-strength — is used as assessment criterion. Copyright © 2017 by ASME}, language = {en} } @misc{MaywaldBackhausSchrapeetal., author = {Maywald, Thomas and Backhaus, Thomas and Schrape, Sven and K{\"u}hhorn, Arnold}, title = {Geometric Model Update of Blisks and its Experimental Validation for a Wide Frequency Range}, series = {ASME Turbo Expo 2017, GT2017-63446, June 26-30, 2017, Charlotte, NC, USA, Volume 7A}, journal = {ASME Turbo Expo 2017, GT2017-63446, June 26-30, 2017, Charlotte, NC, USA, Volume 7A}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-5092-3}, doi = {10.1115/GT2017-63446}, pages = {9}, abstract = {The contribution discusses a model update procedure and its experimental validation in the context of blisk mistuning. Object of investigation is an industrial test blisk of an axial compressor which is milled from solid using a state of the art 5-axis milling machine. First, the blisk geometry is digitized by a blue light fringe projector. Digitization is largely automated using an industrial robot cell in order to guarantee high repeatability of the measurement results. Additionally, frequency mistuning patterns are identified based on vibration measurements. Here, the system excitation is realized by a modal impact hammer. The blade response is detected using a laser scanning vibrometer. Furthermore, all blades except the currently excited one are detuned with additional masses. Applying these masses allows to identify a blade dominated natural frequency for each blade and every mode of interest. Finally, these blade dominated frequencies are summarized to mode specific mistuning patterns. The key part of the contribution presents a model update approach which is focused on small geometric deviations between real engine parts and idealized simulation models. Within this update procedure the nodal coordinates of an initially tuned finite element blisk model were modified in order to match the geometry of the real part measured by blue light fringe projection. All essential pre- and post-processing steps of the mesh morphing procedure are described and illustrated. It could be proven that locally remaining geometric deviations between updated finite element model and the optical measurement results are below 5 μm. For the purpose of validation blade dominated natural frequencies of the updated finite element blisk model are calculated for each sector up to a frequency of 17 kHz. Finally, the numerically predicted mistuning patterns are compared against the experimentally identified counterparts. At this point a very good agreement between experimentally identified and numerically predicted mistuning patterns can be proven across several mode families. Even mistuning patterns of higher modes at about 17 kHz are well predicted by the geometrically mistuned finite element model. Within the last section of the paper, possible uncertainties of the presented model update procedure are analyzed. As a part of the study the digitization of the investigated blisk has been repeated for ten times. These measurement results serve as input for the model update procedure described before. In the context of this investigation ten independent geometrical mistuned simulation models are created and the corresponding mistuning patterns are calculated. Copyright © 2017 by Rolls-Royce Deutschland Ltd \& Co KG}, 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 = {ASME Turbo Expo 2017, GT2017-63193, June 26-30, 2017, Charlotte, NC, USA, Volume 7B}, journal = {ASME Turbo Expo 2017, GT2017-63193, June 26-30, 2017, Charlotte, NC, USA, Volume 7B}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-5093-0}, doi = {10.1115/GT2017-63193}, pages = {10}, 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. Copyright © 2017 by ASME}, language = {en} } @misc{BackhausMaywaldSchrapeetal., author = {Backhaus, Thomas and Maywald, Thomas and Schrape, Sven and Voigt, Matthias and Mailach, Roland}, title = {A Parametrization Describing Blisk Airfoil Variations Referring to Modal Analysis}, series = {ASME Turbo Expo 2017, GT2017-64243, June 26-30, 2017, Charlotte, NC, USA, Volume 7A}, journal = {ASME Turbo Expo 2017, GT2017-64243, June 26-30, 2017, Charlotte, NC, USA, Volume 7A}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-5092-3}, doi = {10.1115/GT2017-64243}, abstract = {This paper will present a way to capture the geometric blade by blade variations of a milled from solid blisk as well as the manufacturing scatter. Within this idea it is an essential task to digitize the relevant airfoil surface as good as possible to create a valid surface mesh as the base of the upcoming evaluation tasks. Since those huge surface meshes are not easy to handle and are even worse in getting quantified and easy interpretable results, it should be aimed for an easily accessible way of presenting the geometric variation. The presented idea uses a section based airfoil parametrization that is based on an extended NACA-airfoil structure to ensure the capturing of all occurring characteristic geometry variations. This Paper will show how this adapted parametrization method is suitable to outline all the geometric blade by blade variation and even more, refer those airfoil design parameters to modal analysis results such as the natural frequencies of the main mode shapes. This way, the dependencies between the modal and airfoil parameters will be proven.}, language = {en} } @misc{KrauseStelldingerHanschkeetal., author = {Krause, Christoph and Stelldinger, Marco and Hanschke, Benjamin and K{\"u}hhorn, Arnold and Giersch, Thomas}, title = {Asynchronous Response Analysis of Non-Contact Vibration Measurements on Compressor Rotor Blades}, series = {ASME Turbo Expo 2017, GT2017-63200, June 26-30, 2017, Charlotte, NC, USA, Volume 7B}, journal = {ASME Turbo Expo 2017, GT2017-63200, June 26-30, 2017, Charlotte, NC, USA, Volume 7B}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-5093-0}, doi = {10.1115/GT2017-63200}, abstract = {Although the research in non-intrusive techniques for the measurement of vibration have made major progress since the beginning in the 1960's, they are still mainly used as additional tool to the common strain gauges. Therefore, there is still a great deal of interest in the improvement of such non-contact vibration measurement techniques, to replace the intrusive ones with alternative techniques. One possibility to monitor all blades at once is blade tip-timing. The probes for a blade tip-timing measurement system are mounted circumferentially in the engine casing to log the passing times of the rotor blades. These logged time data will be compared with theoretically calculated passing times. The deviation between measured and calculated passing times can be transformed to blade displacement values. In recent years, several methods to analyse the acquired vibration data have been developed and improved. They are directed to evaluate synchronous and asynchronous blade vibration events. This paper focuses on the identification of asynchronous vibrations on rotor blades using blade tip-timing. Taking the data from all probes into account gives an opportunity to determine the vibration of each single blade. Due to the usage of a research test rig, all measurement data could be acquired in simulated real case operation scenarios. Analysis data were evaluated with a developed post processing routine based on a Fourier transformation algorithm coupled with a least square fitting procedure. Since compressor surge represents one of the most critical non synchronous events during compressor operation, in this paper a special interest is paid to the analysis of compressor surges. Vibration frequencies revealed during surge investigation will be compared with simultaneously measured strain gauge data to ensure the reliability of blade tip-timing measurement and analysis. To explain the results in more detail, the possibility of a blade damaged triggered shift of the blade characteristic frequency is shown. The most promising result of the analysis is the close correlation between the identified vibration frequencies of compressor surge events and the afterwards determined frequency mistuning and crack distributions. Blade damage becomes visible through increasing deviation between characteristic frequencies of different blades as result of multiple surge events. In addition, with the comparison of mean frequency records over each single surge among each other it is possible to restrict the blade damage time. Subsequently, the possibility to develop a process routine to predict blade damage during compressor test series could arise.}, language = {en} } @misc{FigaschewskyKuehhornBeirowetal., author = {Figaschewsky, Felix and K{\"u}hhorn, Arnold and Beirow, Bernd and Giersch, Thomas and Nipkau, Jens and Meinl, Ferdinand}, title = {Simplified Estimation of Aerodynamic Damping for Bladed Rotors, Part 2: Experimental Validation During operation}, series = {ASME Turbo Expo 2016, Turbomachinery Technical Conference and Exposition, Volume 7B, Structures and Dynamics, Seoul, South Korea, June 13-17, 2016}, journal = {ASME Turbo Expo 2016, Turbomachinery Technical Conference and Exposition, Volume 7B, Structures and Dynamics, Seoul, South Korea, June 13-17, 2016}, publisher = {ASME}, address = {New York, NY [u.a.]}, isbn = {978-0-7918-4984-2}, doi = {10.1115/GT2016-56458}, abstract = {Due to increasing requirements of future engine projects, much effort has been spent on the design of more efficient turbomachinery blades in the recent years. Besides aerodynamic efficiency constraints, these designs need to meet structural criteria ensuring that they are safe and robust with respect to High Cycle Fatigue (HCF). The estimation of the resonant vibration amplitude is done based on the aerodynamic force and the overall damping level. Since, for many applications the contribution of mechanical damping is often rather low compared to the aerodynamic counterpart, the determination of the aerodynamic damping is vital for the estimation of the forced vibration response. This second part is meant to contribute to a simplified computation of the aerodynamic damping during operation by making additional assumptions: The investigated mode family shall not suffer from flutter, has a high reduced frequency and the influence of adjacent blades is negligible. Under these circumstances a simplified approach can be introduced that allows for the computation of the mean value of the aerodynamic damping based on a steady state CFD solution of the regarded stage. It is well known, that the aerodynamic damping of a blade mode family depends on the inter blade phase angle (IBPA) and its direction of propagation, which is not covered by the simplified approach. For higher modes the difference between the minimum and maximum damping is often low and the mean value is a good approximation, whereas for fundamental modes there is often a significant difference. However, it is shown that considering a mistuned vibration response of the rotor, the expected value of the mistuned damping exhibits the mean value of IBPA-dependent aerodynamic damping. CFD simulations of an oscillating airfoil indicate a certain validity range of the simplified approach based on a modified reduced frequency and inlet Mach number, which allows to determine for which industrial applications the approach is most suitable. Finally, this range of validity is verified with experimentally determined overall damping values from strain gauge measurements during operation for 2 different industrial applications, an axial compressor stage of a jet engine and a radial turbine stage of a turbocharger. Copyright © 2016 by Rolls-Royce Deutschland Ltd \& Co KG}, language = {en} } @misc{BeirowMaywaldFigaschewskyetal., author = {Beirow, Bernd and Maywald, Thomas and Figaschewsky, Felix and K{\"u}hhorn, Arnold and Heinrich, Christoph Rocky and Giersch, Thomas}, title = {Simplified Determination of Aerodynamic Damping for Bladed Rotors, Part 1: Experimental Validation at Rest}, series = {ASME Turbo Expo 2016, Turbomachinery Technical Conference and Exposition, Volume 7B, Structures and Dynamics, Seoul, South Korea, June 13-17, 2016}, journal = {ASME Turbo Expo 2016, Turbomachinery Technical Conference and Exposition, Volume 7B, Structures and Dynamics, Seoul, South Korea, June 13-17, 2016}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-4984-2}, doi = {10.1115/GT2016-56535}, abstract = {Considering both a radial turbine rotor of a turbocharger and an axial compressor test blisk at rest, aerodynamic damping characteristics are experimentally and numerically analyzed. Linear dependencies of modal damping ratios on the ambient pressure or the acoustic impedance, respectively, could be shown within experiments carried out inside a pressure chamber. The impact of the ambient air clearly dominates the modal damping ratios compared to the minor contribution of the structure. Assuming that acoustic emission can be regarded as main source of aerodynamic damping a simplified approach for its determination is introduced which only depends on natural frequency, mode shape and acoustic impedance. It is shown that a satisfying match between experiment and computation is achieved for those cases which are dedicated to sufficiently small ratios between wave lengths of acoustic emissions and blade distances.}, language = {en} } @misc{WagnerKuehhornWeissetal., author = {Wagner, Frank and K{\"u}hhorn, Arnold and Weiss, Thomas and Otto, Dierk}, title = {Influence of different parametrizations on the optimum design of a high pressure turbine blade firtree}, series = {ASME Turbo Expo 2016, Turbomachinery Technical Conference and Exposition, Volume 7A, Structures and Dynamics, Seoul, South Korea, June 13-17, 2016}, journal = {ASME Turbo Expo 2016, Turbomachinery Technical Conference and Exposition, Volume 7A, Structures and Dynamics, Seoul, South Korea, June 13-17, 2016}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-4983-5}, doi = {10.1115/GT2016-56749}, pages = {11}, abstract = {Today the design processes in the aero industry face many challenges. Apart from automation itself, a suitable parametric geometry setup plays a significant role in making workflows usable for optimization. At the same time there are tough requirements against the parametric model. For the lowest number of possible parameters, which should be intuitively ascertainable, a high flexibility has to be ensured. Within the parameter range an acceptable stability is necessary. Under these constraints the creation of such parametric models is a challenge, which should not be underestimated especially for a complex geometry. In this work different kinds of parametrization with different levels of complexity will be introduced and compared. Thereby several geometry elements will be used to handle the critical regions of the geometry. In the simplest case a combination of lines and arcs will be applied. These will be replaced by superior elements like a double arc construct or different formulations of b-splines. There will be an additional focus on the variation of spline degree and control points. To guarantee consistency a set of general parameters will be used next to the specific ones at the critical regions. The different parameter boundaries have a influence on the possible geometries and should therefore be tested separately before an optimization run.}, language = {en} }