Studies of rotor dynamics using a multibody simulation approach

The non-idealities in a rotor-bearing system may cause undesirable subcritical superharmonic resonances that occur when the rotating speed of the rotor is a fraction of the natural frequency of the system. These resonances arise partly from the non-idealities of the bearings. This study introduces a novel simulation approach that can be used to study the superharmonic vibrations of rotor-bearing systems. The superharmonic vibrations of complex rotor-bearing systems can be studied in an accurate manner by combining a detailed rotor and bearing model in a multibody simulation approach. The research looks at the theoretical background of multibody formulations that can be used in the dynamic analysis of flexible rotors. The multibody formulations currently in use are suitable for linear deformation analysis only. However, nonlinear formulation may arise in high-speed rotor dynamics applications due to the cenrrifugal stiffening effect. For this reason, finite element formulations that can describe nonlinear deformation are also introduced in this work. The description of the elastic forces in the absolute nodal coordinate formulation is studied and improved. A ball bearing model that includes localized and distributed defects is developed in this study. This bearing model could be used in rotor dynamics or multibody code as an interface elements between the rotor and the supporting structure. The model includes descriptions of the nonlinear Hertzian contact deformation and the elastohydrodynamic fluid film. The simulation approaches and models developed here are applied in the analysis of two example rotor-bearing systems. The first example is an electric motor supported by two ball bearings and the second is a roller test rig that consists of the tube roll of a paper machine supported by a hard-bearing-type balanceing machine. The simulation results are compared to the results available in literature as well as to those obtained by measuring the existing structure. In both practical examples, the comparison shows that the simulation model is capable of predicting the realistic responses of a rotor system. The simulation approaches developed in this work can be used in the analysis of the superharmonic vibrations of general rotor-bearing systems.

Sellumassan varastosäiliön rakenneanalyysi

Tämä työ käsittelee valkaistun ja valkaisemattoman sellumassan varastosäiliön tärinää ja värähtelyä. Värähtelyn seurauksena säiliön seinämän jäykisterenkaan hitsausliitokseen on syntynyt särö. Työn tavoitteena on selvittää, mikä johtaa särön syntyyn ja miten kestäväm-piä varastosäiliöitä voidaan rakentaa materiaali-, valmistus- tai rakennemuutoksien avulla. Työ alkoi tutkimalla rakennemateriaalina olevan duplex-teräksen mikrorakenteen ominai-suuksia, sekä sen hitsattavuutta ja seostamista kirjallisuustutkimuksena. Kirjallisuustutki-musta jatkettiin selvittämällä mahdollisia vaurion syntymekanismeja seinämän särölle. Työssä analysoitiin myös tehtaalla mitattuja värähtelyarvoja. Lopuksi laskettiin FE-analyysillä tyhjän varastosäiliön ominaismuodot ja -taajuudet moodianalyysillä, sekä selvi-tettiin harmonisella analyysillä pinnankorkeuden vaihtelun vaikutus siirtymävasteeseen ja kriittisiin värähtelytaajuuksiin. Varastosäiliöön kohdistuvaa värähtelyä ei ole mahdollista poistaa kokonaan, mutta väräh-telyn aiheuttamia seurauksia kyetään rajaamaan useilla keinoilla. Toimenpiteinä voivat olla ainakin seinämän materiaalin paksuuden lisääminen, jäykisteripojen lisääminen ja kriittisten sellun pinnankorkeuksien välttäminen. Kriittiseksi pinnankorkeudeksi havaittiin 40–45 %:n täyttöaste ja turvalliseksi korkeudeksi 35–38 %:n täyttöaste. Varastosäiliölle kriittisen ominaistaajuuden katsotaan syntyvän taajuuksilla 3,3–3,8 Hz ja 5,8–6,4 Hz. Sellumassa putoaa varastosäiliöön noin 2 Hz taajuudella.

Multibody models for examination of touchdown bearing systems

Increased rotational speed brings many advantages to an electric motor. One of the benefits is that when the desired power is generated at increased rotational speed, the torque demanded from the rotor decreases linearly, and as a consequence, a motor of smaller size can be used. Using a rotor with high rotational speed in a system with mechanical bearings can, however, create undesirable vibrations, and therefore active magnetic bearings (AMBs) are often considered a good option for the main bearings, as the rotor then has no mechanical contact with other parts of the system but levitates on the magnetic forces. On the other hand, such systems can experience overloading or a sudden shutdown of the electrical system, whereupon the magnetic field becomes extinct, and as a result of rotor delevitation, mechanical contact occurs. To manage such nonstandard operations, AMB-systems require mechanical touchdown bearings with an oversized bore diameter. The need for touchdown bearings seems to be one of the barriers preventing greater adoption of AMB technology, because in the event of an uncontrolled touchdown, failure may occur, for example, in the bearing’s cage or balls, or in the rotor. This dissertation consists of two parts: First, touchdown bearing misalignment in the contact event is studied. It is found that misalignment increases the likelihood of a potentially damaging whirling motion of the rotor. A model for analysis of the stresses occurring in the rotor is proposed. In the studies of misalignment and stresses, a flexible rotor using a finite element approach is applied. Simplified models of cageless and caged bearings are used for the description of touchdown bearings. The results indicate that an increase in misalignment can have a direct influence on the bending and shear stresses occurring in the rotor during the contact event. Thus, it was concluded that analysis of stresses arising in the contact event is essential to guarantee appropriate system dimensioning for possible contact events with misaligned touchdown bearings. One of the conclusions drawn from the first part of the study is that knowledge of the forces affecting the balls and cage of the touchdown bearings can enable a more reliable estimation of the service life of the bearing. Therefore, the second part of the dissertation investigates the forces occurring in the cage and balls of touchdown bearings and introduces two detailed models of touchdown bearings in which all bearing parts are modelled as independent bodies. Two multibody-based two-dimensional models of touchdown bearings are introduced for dynamic analysis of the contact event. All parts of the bearings are modelled with geometrical surfaces, and the bodies interact with each other through elastic contact forces. To assist in identification of the forces affecting the balls and cage in the contact event, the first model describes a touchdown bearing without a cage, and the second model describes a touchdown bearing with a cage. The introduced models are compared with the simplified models used in the first part of the dissertation through parametric study. Damages to the rotor, cage and balls are some of the main reasons for failures of AMB-systems. The stresses in the rotor in the contact event are defined in this work. Furthermore, the forces affecting key bodies of the bearings, cage and balls can be studied using the models of touchdown bearings introduced in this dissertation. Knowledge obtained from the introduced models is valuable since it can enable an optimum structure for a rotor and touchdown bearings to be designed.