This Master thesis describes the design of methodology for calculating the critical speed of rotating electric machines. The aim is to build finite element model of rotor system model, determine the natural frequencies to plot Campbell diagram and use this diagram to obtain the critical speeds. The Matlab software is used for this purpose and the Ansys software is used for verify the calculation.

The presented master's thesis deals with the safety assessment of several variants of the impeller with different blades length. The motivation for creating this thesis is to find the solution of the problem situation which is characterized by the breakdown of the steam turbine impeller with blades length of 30mm. As confirmed in this thesis, the impeller with blades length of 30mm is operated in the resonance. Likewise, according to the technical standard ČSN EN ISO 10437 its operation is not safe. As the correction action for the problem situation solving is proposed the prolongation of the impeller's blades. The safety is detected for six variants of impeller with dierent blades length. For each variant, there is executed a modal analysis and its results are drawn up into the Campbell diagram. On the basis of this diagram, the safety of individual components is evaluated. The last part of the masters thesis concerns with the examination of the influence of blades length on the modal properties of the impeller.

The master thesis deals with modal analysis of the blade of the steam turbine impeller. This analysis is made to find the frequency response of the blade in order to predict the dangerous speeds of the steam turbine. At first the problem situation is described. Than follows the research study which is focused on steam turbines and especially on the rotor dynamic systems and the way to ascertain the modal parameters of the dynamic system by experiment. After that the solution of the problem is performed by computational modelling. The results of the computation are analyzed in detail for different variations of the blade length by Campbell diagram. A graph showing dependency between dangerous speeds of the turbine and the blade length is made out of the results. Then the results are verified by experiment and the coefficients of proportional damping are specified. In conclusion the optimal variation of the blade length for the given operational state is determined.

Because blades in jet engine compressors are subject to dynamic loads based on the engine's speed, it is essential that the blades are properly "tuned" to avoid resonance at those frequencies to ensure safe operation of the engine. The tuning process can be time consuming for designers because there are many parameters controlling the geometry of the blade and, therefore, its resonance frequencies. Humans cannot easily optimize design spaces consisting of multiple variables, but optimization algorithms can effectively optimize a design space with any number of design variables. Automated blade tuning can reduce design time while increasing the fidelity and robustness of the design. Using surrogate modeling techniques and gradient-free optimization algorithms, this thesis presents a method for automating the tuning process of an airfoil. Surrogate models are generated to relate airfoil geometry to the modal frequencies of the airfoil. These surrogates enable rapid exploration of the entire design space. The optimization algorithm uses a novel objective function that accounts for the contribution of every mode's value at a specific operating speed on a Campbell diagram. When the optimization converges on a solution, the new blade parameters are output to the designer for review. This optimization guarantees a feasible solution for tuning of a blade. With 21 geometric parameters controlling the shape of the blade, the geometry for an optimally tuned blade can be determined within 20 minutes.

The master thesis deals with modal analysis of turbine wheel of aircraft engine. The first part is concerned with the modal analysis of the computational model of turbine wheel and separated turbine blade using the cyclic symmetry of the ANSYS software. This part of the thesis set the task of determining the natural frequency depending on the operating parameters of the motor. The second part of the thesis occupies with the experimental simulation of the task. The results of experimental simulation are verified and compared with the results from the computational modal analysis. The goal is to create a Campbell diagram and to determine the intervals of the critical revolution of the turbine wheel.

[pt] Neste trabalho um modelo dinâmico para um rotor vertical em balanço, considerando o fenômeno de contato com a sua guarda, é analisado. A conjunto é modelado como um sistema eixo-rotor-estator com contato. A análise do contato é particularmente complexa pela não linearidade nas equações de movimento. O impacto com o estator é levado em conta através do modelo de contato tipo Kelvin-Vôigt, e, as equações de movimento, do rotor, são deduzidas através da formulação Lagrangeana; estas equações podem capturar os fenômenos devido à vibração lateral, como: precessão direta, precessão retrograda, rolamento e escorregamento. Pela existência de diferentes parâmetros combinados e devido à não linearidade da equação de movimento, a resposta dinâmica não é simples de ser obtida apriori. Portanto, métodos numéricos são empregados para a solução, especificamente emprega-se o método de Runge-Kutta Fehlberg de passo variável. Os resultados da simulação mostram que para certas condições, o rotor pode mudar de orbita devido aos impactos com o estator, podendo chegar a realizar precessão retrograda. Este tipo de fenômeno é considerado como o mais violento e perigoso nas maquinas rotativas. Com o fim de estudar a dinâmica lateral do sistema, um rotor vertical em balanço com guarda anular é investigado. A passagem dela através de sua velocidade critica, quando conduzida por um motor elétrico, é analisada (e também quando o sistema opera em velocidades constantes). Além disso, neste trabalho, os resultados experimentais obtidos da bancada de experimentação são usados para estudar o fenômeno da precessão. / [en] In this work a dynamic model for the overhung rotor, considering the contact phenomenon between the rotor and the stator is analyzed. It is modeled as a shaft-rotor- stator system with contact. The analysis of contact is particularly complex, due to the high nonlinearity of motion equations. Impact with the stator is accounted by a consistent contact model, as Kelvin-Vôigt model, and, rotor`s motion equation is encountered employing Lagrangean`s method; this equations are capable of capturing the phenomenon due to lateral vibration, as: forward whirl, backward whirl, rolling or sliding along the stator. Due to the combined parameters and the effect of nonlinearity in motion equations, the dynamical response is not simple or easily predictable. Numerical simulation is the preferred method of analysis, exactly is used the Runge-Kutta Fehlberg method with variable step. Simulation results show that under certain conditions, a rotor changes its orbit due the impacts with the stator and after that, it executes backward whirl motion. It is a kind of phenomenon, which is considered as the most violent and dangerous in rotating machines. To this end, the analysis of a vertical overhung shaft-disc system with annular guard is investigated. The passing through its critical speed is analyzed when driven by an electric motor (also when the system operates under a constant rotational velocity). In addition, in this work the results obtained with an experimental test rig are used to investigate the whirl phenomenon.

This master’s thesis deals with the dynamic behaviour of vertical Francis turbine, which is atypical its shaft length. In the first part of thesis, there is theoretic research of water turbine, which is followed by derivation of equations for the Stodola rotor. The second part deals with the creation of the turbine shaft in 1D and 3D. A modal analysis was performed in the ANSYS Workbench software, based on which the Campbell diagram is created and it was determined the critical speed. And the harmonic analysis from which was determined the forces response in radial bearings, amplitude of deviation in radial direction in the turbine impeller and the generator and the axial displacement located in turbine impeller and axial bearing. 1D and 3D solutions were compared between themselves.