Stem straightness and compression wood in a 22-year-old stand of container-grown Scots pine trees

Abstract

Vibrations in Rotating Machinery Arising from Minor Imperfections in Component Geometries

Vibrations in machines can cause noise, decrease the performance, or even damage the machine. Vibrations appear if there is a source of vibration that excites the system. In the worst case scenario, the excitation frequency coincides with the natural frequency of the machine causing resonance. Rotating machines are a machine type, where the excitation arises from the machine itself. The excitation originates from the mass imbalance in the rotating shaft, which always exists in machines that are manufactured using conventional methods. The excitation has a frequency that is dependent on the rotational speed of the machine. The rotating machines in industrial use are usually designed to rotate at a constant rotational speed, the case where the resonances can be easily avoided. However, the machines that have a varying operational speed are more problematic due to a wider range of frequencies that have to be avoided. Vibrations, which frequencies equal to rotational speed frequency of the machine are widely studied and considered in the typical machine design process. This study concentrates on vibrations, which arise from the excitations having frequencies that are multiples of the rotational speed frequency. These vibrations take place when there are two or more excitation components in a revolution of a rotating shaft. The dissertation introduces four studies where three kinds of machines are experiencing vibrations caused by different excitations. The first studied case is a directly driven permanent magnet generator used in a wind power plant. The electromagnetic properties of the generator cause harmonic excitations in the system. The dynamic responses of the generator are studied using the multibody dynamics formulation. In another study, the finite element method is used to study the vibrations of a magnetic gear due to excitations, which frequencies equal to the rotational speed frequency. The objective is to study the effects of manufacturing and assembling inaccuracies. Particularly, the eccentricity of the rotating part with respect to non-rotating part is studied since the eccentric operation causes a force component in the direction of the shortest air gap. The third machine type is a tube roll of a paper machine, which is studied while the tube roll is supported using two different structures. These cases are studied using different formulations. In the first case, the tube roll is supported by spherical roller bearings, which have some wavinesses on the rolling surfaces. Wavinesses cause excitations to the tube roll, which starts to resonate at the frequency that is a half of the first natural frequency. The frequency is in the range where the machine normally operates. The tube roll is modeled using the finite element method and the bearings are modeled as nonlinear forces between the tube roll and the pedestals. In the second case studied, the tube roll is supported by freely rotating discs, which wavinesses are also measured. The above described phenomenon is captured as well in this case, but the simulation methodology is based on the flexible multibody dynamics formulation. The simulation models that are used in both of the last two cases studied are verified by measuring the actual devices and comparing the simulated and measured results. The results show good agreement.

K-liitoksen epäkeskeisen tuennan aiheuttaman sekundäärisen momentin määritys

Työssä on tutkittu laboratoriokokeen ja elementtimenetelmän avulla eri geometrioiden vaikutusta sekundääriseen momentin syntymiseen K-liitoksella. Kokeen liitos on tehty S700-lujuusluokan Ruukin Optim 700 plus MH nelikulmaisista rakenneputkista (RHS). Elementtimalleissa on käytetty geometrista ja materiaalista epälineaarisuutta ennustamaan liitoksen muodonmuutoskykyä ja laskennallista kestävyyttä. Liitoksen elementtimalleissa muutettavia geometrioita ovat: vapaaväli, uumasauvan ja paarteen välinen kulma, paarteen seinämän paksuus, liitoksen eksentrisyys ja uumasauvan ja paarteen leveyden suhde. Laboratoriokokeen liitoksen vetouumasauvassa vaikuttava sekundäärisen momentin aiheuttama jännitys on noin 25 % vetouumasauvan myötörajasta. Suurin sekundäärinen momentti syntyy, kun vapaaväliä pienennetään ja uumasauvaa kavennetaan paarteeseen nähden. Eurocode 3:n mitoitusohjeita voidaan elementtimallien perusteella soveltaa tietyille geometrioille turvallisesti.