FG Strukturmechanik und Fahrzeugschwingungen
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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.
The manufacturing geometrical variability in axial compressors is a stochastic source of uncertainty, implying that the real geometry differs from the nominal design. This causes the real geometry to lose the ideal axial symmetry. Considering the aerofoils of a stator vane, the geometrical variability affects the flow traversing it. This impacts the downstream rotor, especially when considering the aeroelastic excitation forces. Optical surface scans coupled with a parametrisation method allow for acquiring the information relative to the real aerofoils geometries. The measured data are included in a multi-passage and multi-stage CFD setup to represent the mistuned flow. In particular, low excitation harmonics on the rotor vane are introduced due to the geometrical deviations of the upstream stator. The introduced low engine orders, as well as their amplitude, depend on the stator geometries and their order. A method is proposed to represent the phenomena in a reduced CFD domain, limiting the size and number of solutions required to probabilistically describe the rotor excitation forces. The resulting rotor excitation forces are reconstructed as a superposition of disturbances due to individual stator aerofoils geometries. This indicates that the problem is linear in the combination of disturbances from single passages.
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.
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.
The manufacturing geometrical variability in axial compressors is a stochastic source of uncertainty, implying that the real geometry differs from the nominal design. This causes the real geometry to lose the ideal axial symmetry. Considering the aerofoils of a stator vane, the geometrical variability affects the flow traversing it. This impacts the downstream rotor, especially when considering the aeroelastic excitation forces. Optical surface scans coupled with a parametrization method allow for acquiring the information relative to the real aerofoils geometries. The measured data are included in a multi-passage and multi-stage CFD setup to represent the mistuned flow. In particular, low excitation harmonics on the rotor vane are introduced due to the geometrical deviations of the upstream stator. The introduced low engine orders as well as their amplitude depend on the stator geometries and their order. A method is proposed to represent the phenomena in a reduced CFD domain, limiting the size and number of solutions required to probabilistically describe the rotor excitation forces. The resulting rotor excitation forces are reconstructed as a superposition of disturbances due to individual stator aerofoils geometries. This indicates that the problem is linear in in the combination of disturbances from single passages.
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.
Creating very detailed finite element models of aero-engines is a very time-consuming process especially if structured meshes have to be generated for thousands of parts. Isogeometric analysis offers the possibility of an accelerated model creation process while achieving higher accuracy by using the non-uniform rational B-spline functions used for the geometry description also as basis functions for the finite element analysis. In this case, no meshing is necessary anymore. Here, we demonstrate this process by applying a self-developed tool which creates a geometry description and a computational model of a part at the same time. By the help of this tool we build up a simplified mechanical aero-engine model, which is used for transient implicit computations simulating the acceleration process of the rotor. We discuss the results as well as the computational time of isogeometric models in comparison to classical finite element models.
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.
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.
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.
The 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. Independently, the presence of aerodynamic damping is significant with respect to limit the forced response since structural damping ratios of integrally bladed rotors typically take extremely low values. Hence, detailed knowledge of respective damping ratios would be desirable while developing a robust rotor design. For this, far-reaching experimental investigations are carried out to determine the damping of a comparative wheel within a wide pressure range by simulating operation conditions in a pressure tank. Reduced-order models are built up for designing suitable intentional mistuning patterns by using the subset of nominal system modes approach introduced by Yang and Griffin (2001, “A Reduced-Order Model of Mistuning Using a Subset of Nominal System Modes,” J. Eng. Gas Turbines Power, 123(4), pp. 893–900), which conveniently allows for accounting both differing mistuning patterns and the impact of aeroelastic interaction by means of aerodynamic influence coefficients. Further, finite element analyses are carried out in order to identify appropriate measures of how 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. The first part of this three-part paper is focused on designing the IM pattern. The second and third part following, later on, will address the topics (i) experimental validation after implementation of the IM pattern at rest and under rotation, and (ii) the development of an approach for fast estimating damping ratios in the design phase.
Surrogate Models for the Prediction of Damping Ratios in Coupled Acoustoelastic Rotor-Cavity Systems
(2022)
Centrifugal compressors are versatile machines that many industries employ for a wide range of different applications, including the production of highly compressed gases. During the last decades, comprehensive research was conducted on the impact of high-pressure operating conditions on the vibrational behavior of radial compressors. In various studies, acoustic modes building up in the side cavities were found to be a potential source of high cycle fatigue. 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. In a recently published paper, the authors presented a generalized model which can predict this behavior. As it is not always possible to avoid operating close to or accelerating through a resonance, it is crucial to know the damping present within the system. Currently, only a few publications concentrate on the damping of radial impellers. Therefore, the authors present measurement data acquired from a test rig at the University of Duisburg-Essen, which reveals the damping behavior of a disk under varying operating conditions. Two surrogate models are proposed to predict the identified damping behavior. The first one is based solely on a one-dimensional piston model and the second approach uses an enhanced version of the generalized method. Finally, the measurement data is used to validate both surrogate systems.
The effect of different intentional mistuning (IM) patterns is investigated with respect to the forced response of an academic axial blisk. It could be shown in numerical analyses that a preliminary use of sensitivity algorithms helps to understand the feasibility and efficiency of introducing geometric changes of the blades. The implementation of IM patterns requires conducting intensive sensitivity studies based on FE simulations in order to identify the consequences of slight geometrical blade modifications on natural frequencies. Typical changes might be a modification of fillet radii or partial modifications of blade thickness, which are most suitable to adjust a target natural frequency without a severe loss of aerodynamic performance. A software tool developed at Irkutsk SAU is employed to evaluate the impact of mass and stiffness contributions, and with that, geometric deviations on blade natural frequencies.
Intensive blade vibration due to aerodynamic excitation of blisks is known as major source of high cycle fatigue, which may cause severe failures of turbine and compressor wheels during operation. The problem is relevant for several sectors of industry such as power generation, aviation or vehicle manufacturing. In consequence, there is a broad request of preventing any inadmissible vibration at any time. The application of IM can be regarded as powerful tool to avoid both, large forced responses and self-excited vibration. However, there is a lack of knowledge about how to implement mistuning without strong distortions of the flow passage. The main objective of this work is to close this gap based on comprehensive numerical analyses with regard to the effects of intended geometric modifications of blades on modal quantities.
Using FE models, the effectiveness of the proposed block models of mistuning is analyzed with and without taking into account the operational speed of the axial impeller. In conclusion, the consequences of different IM implementations on the forced response of an academic blisk are discussed. In particular, the most promising IM patterns are identified yielding the least forced response.
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.
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.
Im Vordergrund des Forschungsprojekts steht die Reduktion der Schwingungsantwort einer Radialtur-bine. Die in den Vorgängervorhaben [1], [2] und [3] gewonnen Erkenntnisse und Methoden hinsichtlich des auftretenden Mistunings sollen auf die betrachtete Radialturbine übertragen und angewendet wer-den, sodass die zu erwartenden Schwingungsüberhöhungen dargestellt werden können. Aufbauend auf die drei Vorgängervorhaben soll zusätzlich erstmalig die erfolgreiche Umsetzung von Intentional Mistuning (IM) untersucht werden, welches das Potential besitzt die Schwingungsantwort drastisch re-duzieren zu können.
Auf Basis von numerischen Modalanalysen unter Verwendung der finiten Element-Methode werden Be-rechnungsmodelle erstellt, mit denen das Schwingungsverhalten beschrieben und ebenfalls ein geeig-netes Bearbeitungsmuster zur Umsetzung von IM erzielt werden kann. Diese stellen die Basis zur Er-arbeitung einer geometrischen Anpassung eines Versuchsträgers dar.
Da die Strukturdämpfung bei Radiallaufrädern im Hinblick auf Schaufelschwingungen verschwindend gering ausfällt, ist die aerodynamische Dämpfung von großer Bedeutung und liefert einen entscheiden-den Beitrag zur entsprechenden Schwingungsüberhöhung bzw. -reduktion. Mit Hilfe numerischer Strö-mungssimulationen werden aerodynamische Dämpfungskurven unter Betriebsbedingungen berechnet, welche im Rahmen der numerischen Simulationen zur Entwicklung geeigneter IM-Modifikationen mit-berücksichtigt werden.
Bei den Versuchsträgern handelt es sich um zwei baugleiche Radialturbinen eines Abgasturboladers gleicher Serie, welche im Rahmen von Schwingungsuntersuchungen im Stillstand sowie unter Betriebs-bedingungen untersucht werden sollen. Dabei dient ein Laufrad als unbearbeitete „getunte“ Referenz, an der die Schwingungsantwort des zweiten bearbeiteten Laufrades validiert werden soll. Im Rahmen von Schwingungsuntersuchungen bei Stillstand unter Laborbedingungen werden erste Analysen hin-sichtlich der erfolgreichen Umsetzung des IM vorgenommen, welche im späteren Verlauf des Projektes durch Messungen auf einem Prüfstand ergänzt werden. Dabei soll die Wirksamkeit der Anwendung von IM unter Betriebsbedingungen untersucht und nachgewiesen werden. Hierfür wird ein am IKDG der RWTH Aachen betriebener Abgasturboladerprüfstand an die spezifischen Anforderungen des aktuellen Turboladers angepasst und mit erforderlicher Messtechnik ausgerüstet.
Da die aerodynamische Dämpfung maßgeblich ist für das Schwingungsverhalten von Radiallaufrädern in Integralbauweise, werden experimentelle Modalanalysen unter veränderlichem Umgebungsdruck durchgeführt und auf der Basis hieraus abgeleiteter modaler Parameter eine Formel weiterentwickelt, welche eine Abschätzung des Dämpfungsniveaus während der Entwicklungsphase ermöglichen soll. Ziel hierbei ist die Möglichkeit zur Bewertung des zu erwartenden Schwingungsniveaus in frühen Sta-dien der Laufradentwicklung.
Simulation and Investigation of an Intentionally Mistuned Blisk Rotor in a High Pressure Compressor
(2022)
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.
Application of Intentional Mistuning to Reduce the Vibration Susceptibility of a Steam Turbine Wheel
(2022)
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.
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.
The manufacturing geometrical variability is a source of uncertainty, which cannot be avoided in the realization of machinery components. Deviations of a part 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. In particular, the amplitude of the forces acting as a source of excitation on the vibrating blades is studied. The geometrical variability of the upstream stator is investigated as input uncertainty. The variability is modeled starting from a series of optical surface scans. A stochastic model is created to represent the measured manufacturing geometrical deviations from the nominal model. A data reduction methodology is proposed in order to represent the uncertainty with a minimal set of variables. The manufacturing geometrical variability model allows to represent the input uncertainty and probabilistically evaluate its impact on the aeroelastic problem. An uncertainty quantification is performed in order to evaluate the resulting variability on the modal forcing acting on the vibrating rotor blades. Of particular interest is the possible rise of low engine orders due to the mistuned flow field along the annulus. A reconstruction algorithm allows the representation of the variability during one rotor revolution. The uncertainty on low harmonics of the modal rotor forcing can be therefore identified and quantified.