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Institute
An advanced design of sandwichstructures does not only require the knowledge of the global stress- and deformation behavior, but also the knowledge of the local effects, such as load singularities and the loss of stability caused by the short wave wrinkling of one (bending) or both (pressure) sandwich skins.Based on the nonlinear theory for sandwich shells with seven kinematic degrees of freedom, introduced from Kühhorn and Schoop an improved theory for plane sandwich shells with eight degrees of freedom will be presented, enabling a much better representation of the sandwich core behavior.Due to consideration of quadratic core thickness and linear core shear strain as well as longitudinal core deformation an improved prediction of the wrinkling behavior is succeeded even for thick cores and thin skins.The kinematic quantities as well as the nonlinear-differential equations and the simplified equations of first order theory resulting from them are given.Finally applying the well known classical problems of stability loaded by pressure and bending, the efficiency of this 8 DOF-theory ist demonstrated. A comparison with a detailed finite element (plain strain) calculation shows the high quality of these results.The presented sandwich theory characterized by eight degrees of freedom enables the calculation of nearly all essential sandwich phenomena even for thick cores.
An advanced design of sandwichstructures does not only require the knowledge of the global stress- and deformation behavior, but also the knowledge of the local effects, such as load singularities and the loss of stability caused by the short wave wrinkling of one (bending) or both (pressure) sandwich skins.Based on the nonlinear theory for sandwich shells with seven kinematic degrees of freedom, introduced from Kühhorn and Schoop an improved theory for plane sandwich shells with eight degrees of freedom (position vector r, director d, and intensity factors az1, az2 for including core flexibility) will be presented, enabling a much better representation of the sandwich core behavior.Due to consideration of quadratic core thickness and linear core shear strain as well as longitudinal core deformation an improved prediction of the wrinkling behavior is succeeded even for thick cores and thin skins.The kinematic quantities as well as the nonlinear-differential equations achieved from the principle of virtual work and the simplified equations of first order theory resulting from them are given.Finally applying the well known classical problems of stability loaded by pressure and bending, the efficiency of this 8 DOF-theory is demonstrated. A comparison with a detailed finite element (plain strain) calculation shows the high quality of these results.The presented sandwich theory characterized by eight kinematic degrees of freedom is valid for arbitrary displacements, rotations and moderat strains enables the calculation of nearly all essential sandwich phenomena even for thick cores.
Ökonomische und ökologische Bedürfnisse verlangen von modernen Konstruktionen sowohl eine hochintegrative Bauweise als auch eine massive Gewichtseinsparung. Dies führt zu neuen Leichtbaukonstruktionen mit einem stetig zunehmenden Anteil an Faserverbundlösungen. Die hierbei eröffnete Möglichkeit, kraftfluß- und beanspruchungsgerecht auszulegen, erschließt sich erst vollständig durch die sichere Anwendung moderner FE-Programme wie beispielsweise ABAQUS. Nutzt man darüber hinaus die Möglichkeit der flexiblen Script-Programmierung, so lassen sich wirkungsvolle Effizienzsteigerungen durch die gezielte Erstellung spezifischer Eingabemenüs und Ausgaberoutinen erreichen. Dieser Beitrag veranschaulicht an Hand eines ausgeführten und getesteten CFK-Modellflügels unter Biegebeanspruchung, die Vorgehensweise bei Verwendung von ABAQUS und der Script-Sprache Python.
Simulation fluidgedämpfter Strukturschwingungen mittels partitionierter Fluid-Struktur-Kopplung
(2005)
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.
Die Verbesserung von Kalibriermethoden für Hochdruckverdichterstufen in ausgeführter Integralbauweise verlangt von den Ingenieuren ein detaillierteres Verständnis der strukturdynamischen Zusammenhänge dieses komplexen Bauteils. Als Ausgangsbasis werden zunächst für das perfekte Normdesign bei Ausnutzung der vorliegenden zyklischen Rotationssymmetrie numerische Ergebnisse vorgestellt. Dabei stehen bezüglich des Schwingverhaltens die Kopplungseffekte zwischen Scheibe und Schaufeln im Mittelpunkt, wobei experimentelle Untersu-chungen am realen Bauteil ergänzend hinzugezogen werden. Zukünftig wird in einem weiteren Schritt im Rahmen erheblich aufwendigerer Berechnungen mit der Berücksichtigung von Imperfektionen hinsichtlich der filigranen Schaufeln die Rotationssymmetrie aufgegeben und somit die Basis für eine gezielte Beeinflussung des Schwingverhaltens infolge von Mistuning - Effekten geschaffen.
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.
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.