Generalizing sample tree information with semiparametric and parametric models

Summary

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.

Long-term fertilizer field trials: comparison of three mathematical response models

Selostus: Lannoituksen pitkäaikaiset kenttäkokeet: kolmen matemaattisen mallin vertailu

Predicting the growth response to thinning for Scots pine stands using individual-tree growth models

Summary

The application of agricultural land rating and crop models to CO2 and climate change issues in Northern regions : the Mackenzie Basin case study

Selostus: Viljelyvyöhykkeiden ja kasvumallien soveltaminen ilmastonmuutoksen tutkimisessa: Mackenzien jokialue, Kanada

Individual-tree basal area growth models for scots pine, pubescent birch and Norway spruce on drained peatlands in Finland

Summary