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Im Rahmen dieser Arbeit werden Biegeeigenfrequenzen erster Ordnung von stillstehenden und rotierenden Turbinenschaufeln analysiert. Die Turbinenschaufel wird durch einen geraden Balken gleichbleibenden Querschnitts ersetzt. Die Anwendungsf��lle sind auf einseitig eingespannte Turbinenschaufeln beschr��nkt. Die Verschiebungen und Verformungen des Balkens unterliegen dabei der Bernoullischen Hypothese. Bei der rotierenden Turbinenschaufel wird zus��tzlich der Anstellwinkel des Balkens ber��cksichtigt. Dieser beschreibt in welcher Lage die Schwingung stattfindet. Sowohl flapping als auch lead-lag werden ber��cksichtigt. Die Rotationsebene ist normal zum Winkelgeschwindigkeitsvektor welcher in der Turbinenwellenachse liegt. Die Winkelgeschwindigkeit ist konstant. In dieser Arbeit werden zur Berechnung der Biegeeigenschwingungen vier unterschiedliche Verfahren betrachtet: das Punktmassenmodell, die N��herungsverfahren von Galerkin und Rayleigh sowie die Finite Elemente Methode. Diese werden analytisch, quasi-numerisch und numerisch gel��st. F��r die Auswertung wird das Programm MATLAB R2020b von Mathworks verwendet. Die Ergebnisse werden anschlie��end mit den experimentellen Werten verglichen.Die N��herungsverfahren von Galerkin und Rayleigh stellen, abh��ngig von de rgew��hlten Ansatzfunktion, eine gute ��bereinstimmung mit den gemessenen Werten dar. Das Verfahren von Rayleigh weist aufgrund des zweigliedrigen Ansatzes eine etwas bessere Genauigkeit bei der stillstehenden Turbinenschaufel auf. Die Methode der Finiten zylindrischen Balkenelemente weist ��hnlich der N��herungsverfahren von Galerkin und Rayleigh eine gute ��bereinstimmung mit den experimentellen Messungen auf. Damit eignen sich die bisher genannten Verfahren gut f��r Berechnungen der Biegeeigenschwingungen. Im Gegensatz dazu zeigt das Punktmassenmodell, aufgrund der getroffenen Vereinfachungen, erhebliche Schw��chen gegen��ber den anderen Verfahren. Trotz der hohen Ungenauigkeit wird der physikalische Zusammenhang jedoch auch hier gut dargestellt. Alle Verfahren zeigen, dass sich bei Ber��cksichtigung der Rotation die Eigenkreisfrequenzen erh��hen., This master ��s thesis analyses first-order bending frequencies of stationary and rotating turbine blades. The turbine blade is represented by a cantilever beam of constant cross-section. The displacements and deformations of the beam are subject to the Bernoulli hypothesis.For the rotating turbine blade, the setting angle of the beam is also taken into account. It describes in which position the oscillation takes place. Both, flapping and lead-lag are considered as well. The plane of rotation is normal to the angularvelocity vector which lies in the turbine shaft axis. The angular velocity is constant.As part of this master ��s thesis, four different methods for calculating the natural frequencies are being studied: the point mass model, the approximation methods of Galerkin and Rayleigh, and the finite element method. These are solved analytically, quasi-numerically and numerically. The MATLAB R2020b program from Mathworks is used for the evaluation. The results are then compared with experimental values. The approximation methods of Galerkin and Rayleigh correspond well with the measured values, depending on the shape function chosen. Rayleigh���s method exhibits slightly better accuracy for the stationary turbine blade due to the two part approach. Similar to the approximate methods of Galerkin and Rayleigh, the finite cylindrical beam element method matches well with the experimental measurements. Thus, the methods mentioned so far are well suited for calculations of the natural bending vibrations. In contrast, the point mass model, due to the simplifications made, shows considerable weaknesses compared to the other methods. Despite the high inaccuracy, the physical context is also well represented here. All methods show that the natural frequencies increase when the rotation is taken into account.

Durch Schwingungen ausgel��ste Br��che von Turbinenschaufeln verursachen in thermischen Turbomaschinen erhebliche Sch��den. Besonders im Resonanzfall, wenn eine Erregerfrequenz mit einer Eigenfrequenz der schwingenden Struktur zusammenf��llt, ist mit einer ��berschreitung der Festigkeitsgrenze zu rechnen. Diese Arbeit widmet sich daher der Ermittlung der Eigenfrequenzen einer zylindrischen Einzelschaufel. Dabei werden mit f��nf Modellen unterschiedliche Einfl��sse ber��cksichtigt und deren qualitative wie quantitative Auswirkungen analysiert. Des Weiteren erfolgt eine Gegen��berstellung der analytisch ermittelten und der mittels Finite-Elemente-Methode gewonnenen Ergebnisse. Es wird gezeigt, worauf bei der Anwendung der numerischen Methode zu achten ist und welche Genauigkeit bei der analytischen Berechnung zu erwarten ist., Fractures of turbine blades due to vibrations cause considerable damage in thermal turbomachines. Especially in the case of resonance where an excitation frequency equals a natural frequency of the vibrating structure, the strength limit is expected to exceed. This work is therefore devoted to the determination of the natural frequencies of a single cylindrical blade. With five models different influences are taken into account and their qualitative and quantitative effects are identified. Furthermore, there is a comparison of the analytically determined results and the results obtained by means of finite element method. It is shown what is important when using the numerical method and which accuracy can be expected from the analytical calculation.

Global air traffic is predicted to rise long-term (2012-2031) at an annual rate of almost 5%, signifying a 100% increase in passenger and freight volumes over the next 15-20 years. In view of the environmental consequences, 2011 saw the release by the EU of Vision Flightpath 2050, which sets ambitious goals for pollution and noise reduction (including a 75% reduction in CO2, taking the year 2000 as benchmark). A potential CO2 emission saving in the order of 15-20% is achievable simply by stepping up the efficiency and optimizing the weight of aircraft jet en-gines. One promising option for achieving these targets is the substitution of the very heavy iron and nickel-based super alloys currently in use for high temperature applications by new, lighter materials. Alongside the general weight-saving achievable, this development will also enable an increase in the response times for movable components by up to 50%. The current work focuses on titanium aluminide alloys based on gamma-TiAl and alpha2-Ti3Al, which combine the attributes „light, corrosion-protected and extremely tough“. The application potential of this material at moderate to high temperatures (500°C-800°C) makes it a particularly attractive option for manufacturing rotating turbine blades and wheels. The main barrier to the general introduction of TiAl components is the nature of this material: very hard and brittle, and, in a melt, extremely reactive. Cost-effective manufacture of TiAl low pressure turbine blades on the industrial scale is achievable by the near-net shape casting approach. The manufacture of single near net shape prototypes using centrifugal casting has already been successfully demonstrated. However, transferring this approach to industrial standard has not hitherto been possible. Starting from the current technological platform already achieved, this work aims to develop a stable and reproducible manufacturing process chain, thus laying the foundation for future series casting of near-net shape TiAl low pressure turbine blades (up to approx. 300 mm in length) for jet engines. This will enable the transfer of the huge potential of this difficult-to-process intermetallic material to a broad field of application within the aerospace industry. This calls for close investigation of component, material and the various process steps as a complex, rather than in isolation. Alongside the fundamental definition of a casting concept and corresponding process parameters, and the subsequent technology transfer to production plant specifically developed for the production of TiAl components, an essential focus of the technology development within the scope of this paper is an all-round optimization of the casting process. Not only the melt flow up to the shell mould but also mould-filling of the cavities is covered in this research. It is demonstrated that modelling a complex, thin-walled blade geometry is only achievable by goal-oriented adaptation of the crucible tilt process and the gating and feeder technology. Verification of the suitability of both the ceramic material and furnace used in being able to meet the dimensional tolerances demanded then provides the basis for the production of a small series of 600 turbine blades, the setting up of which is based on bringing together knowledge previously obtained. Verification of a stable and reproducible process chain is executed by evaluating process stability and component quality.

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