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A finite element program for rotordynamical applications
2004 (English)Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Today, hydropower is a very important energy source since we tend to consume more and more electricity. The hydropower produces about half of the total electricity in Sweden. The basic principle of hydro power plants is that it transforms the kinetic energy of the flowing water in the turbine into electric energy via the generator. The turbine and generator is connected through a rotor, which is a shaft made of steel and can in some plants be up to several tens of meters long. It is being held in position by very stiff axial and radial bearings. There are often large forces (both static and dynamic) acting on the rotor and in some cases this can lead to failure. These failures could perhaps be avoided if the dynamics of these rotors were better understood. The outcome of this thesis is a software developed in Matlab for calculating and simulating the dynamical behaviour of rotors in hydropower plants. With this software it is possible to calculate natural frequencies and mode shapes for both torsion and bending vibration, and to predict critical speeds (Campbell diagrams). Special consideration has been taken in order to make the software as general and versatile as possible. The software is based on modules, so there is room to expand the software if one wishes to add other features. Since the geometry is read from a user-specified excel spreadsheet, the software is well suited for almost any kind of rotors, not only for rotors in hydropower plants. Further it is also possible to perform transient response simulations of the complete model using different kinds of ODE solvers in Matlab. The transient response simulation results in displacements and forces in bearings for bending vibration, and the stress in each element for torsion vibration. For the transient response simulation it is possible to define general forces that acts on the system, for instance constant forces, oscillating forces, impulse forces and so on. It is also possible to add non-linear stiffness and damping to the bearings, with respect to the spin speed. This could be very useful in start-up simulations of rotors, since the spin speed has a significant influence on the bearing stiffness. Today many rotors in hydro power plants have tilting pad bearings, which means that the bearing stiffness at standstill is very small and full stiffness is reached only at the operating speed. The effect of electro magnetic pull due to the generator has also been considered, and calculations show that this has a weakening effect of the structure, and hence decreasing the natural frequencies. The subdivision of the model into finite elements in the software is based on FEM theory, and we have used two kinds of beam elements, Euler-Bernoulli and Timoshenko. These have a very similar behaviour for most geometries, but in some cases the results differ a bit. To be certain that the software is accurate, we have done some calculations of natural frequencies for both bending and torsion vibration with different geometries, boundary conditions and number of elements. We have then compared it with both elementary cases as well as results from I-DEAS. Euler-Bernoulli formulation tended to be more accurate when compared with elementary cases, and Timoshenko formulation more accurate compared with I- DEAS. This could be explained by the fact that the elementary cases and Euler-Bernoulli formulation does not take shear deformation into account, while I-DEAS and Timoshenko formulation does. We have also compared the software with other commercial software. The calculations have been done on two different 70MW Kaplan rotors. The results are very similar with the one obtained with commercial software, both for bending and torsion vibrations. Timoshenko formulation was a little more accurate, for both torsion and bending vibration, and this is probably because of the shear deformation mentioned earlier.

Place, publisher, year, edition, pages
Keyword [en]
Technology, Rotordynamic, Finite element method, critical speed, Campbell, diagram
Keyword [sv]
URN: urn:nbn:se:ltu:diva-48304ISRN: LTU-EX--04/050--SELocal ID: 5c30f093-c507-49bb-9eb1-ae2727e37367OAI: diva2:1021645
Subject / course
Student thesis, at least 30 credits
Educational program
Mechanical Engineering, master's level
Validerat; 20101217 (root)Available from: 2016-10-04 Created: 2016-10-04Bibliographically approved

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