Mössbauer spectra of iron oxides in the bulk and nanocrystalline states

Magnetic nanoparticles are very important in modern industry. These particles are used in many different spheres of life. Nanoparticles have unusual physical and chemical properties connected both with quantum dimensional effects and with the increased role of the surface atoms. Most clearly the difference between the properties of bulk materials and nanoparticles can be seen in the magnetic properties of these materials. The most typical magnetic properties of nanomaterials are superparamagnetism with the size of the cluster from 1 to 10 nm; single-domain magnetic state of nanoclusters and nanostructures up to 20 nm; magnetization processes connected with magnetic cluster ordering and with its forms and sizes; quantum magnetic tunneling effects when magnetization changes by jumps and giant magnetoresistance effects. For research of the magnetic properties of iron-containing nanostructures, it is convenient to apply Mӧssbauer spectroscopy. In this work a number of nano-sized samples of iron oxides were examined by Mössbauer spectroscopy. The Mössbauer spectra of nanoparticles with various sizes were obtained. Mössbauer spectra of iron oxide nanoparticles were compared with the spectra of bulk samples. It was shown how the spectra of iron oxide nanoparticles change depending on the particle sizes.

Multifrequency VLBI Observations of Selected Active Galactic Nuclei

In this dissertation, active galactic nuclei (AGN) are discussed, as they are seen with the high-resolution radio-astronomical technique called Very Long Baseline Interferometry (VLBI). This observational technique provides very high angular resolution (_ 10−300 = 1 milliarcsecond). VLBI observations, performed at different radio frequencies (multi-frequency VLBI), allow to penetrate deep into the core of an AGN to reveal an otherwise obscured inner part of the jet and the vicinity of the AGN’s central engine. Multi-frequency VLBI data are used to scrutinize the structure and evolution of the jet, as well as the distribution of the polarized emission. These data can help to derive the properties of the plasma and the magnetic field, and to provide constraints to the jet composition and the parameters of emission mechanisms. Also VLBI data can be used for testing the possible physical processes in the jet by comparing observational results with results of numerical simulations. The work presented in this thesis contributes to different aspects of AGN physics studies, as well as to the methodology of VLBI data reduction. In particular, Paper I reports evidence of optical and radio emission of AGN coming from the same region in the inner jet. This result was obtained via simultaneous observations of linear polarization in the optical and in radio using VLBI technique of a sample of AGN. Papers II and III describe, in detail, the jet kinematics of the blazar 0716+714, based on multi-frequency data, and reveal a peculiar kinematic pattern: plasma in the inner jet appears to move substantially faster that that in the large-scale jet. This peculiarity is explained by the jet bending, in Paper III. Also, Paper III presents a test of the new imaging technique for VLBI data, the Generalized Maximum Entropy Method (GMEM), with the observed (not simulated) data and compares its results with the conventional imaging. Papers IV and V report the results of observations of the circularly polarized (CP) emission in AGN at small spatial scales. In particular, Paper IV presents values of the core CP for 41 AGN at 15, 22 and 43 GHz, obtained with the help of the standard Gain transfer (GT) method, which was previously developed by D. Homan and J.Wardle for the calibration of multi-source VLBI observations. This method was developed for long multi-source observations, when many AGN are observed in a single VLBI run. In contrast, in Paper V, an attempt is made to apply the GT method to single-source VLBI observations. In such observations, the object list would include only a few sources: a target source and two or three calibrators, and it lasts much shorter than the multi-source experiment. For the CP calibration of a single-source observation, it is necessary to have a source with zero or known CP as one of the calibrators. If the archival observations included such a source to the list of calibrators, the GT could also be used for the archival data, increasing a list of known AGN with the CP at small spatial scale. Paper V contains also calculation of contributions of different sourced of errors to the uncertainty of the final result, and presents the first results for the blazar 0716+714.

Automation concept for an electrically excited synchronous motor: Setup and requirements specification

This bachelor’s thesis is a part of the research project realized in the summer 2011 in Lappeenranta University of Technology. The goal of the project was to create an automation concept for controlling an electrically excited synchronous motor. This thesis concentrates on the setup and requirements specification part of the concept. The setup consists of ABB AC500 as the PLC master device, DCS800 as an exciter and ACS800 as a frequency converter. The ACS800 frequency converter uses permanent magnet synchronous machine software to control the stator’s magnetic field, the DC drive handles the excitation and the AC500 PLC master controls the communication and functionality of the system. The requirements specification briefly explains the general over-view of the concept, the use and functionality of the PLC program and the requirements needed for the whole concept and the PLC program to work as intended.

Spin-Dynamics in Cold Gases of 87Rb and Atomic Hydrogen. The spins they are a-changin’

In this thesis the dynamics of cold gaseous atoms is studied. Two different atomic species and two different experimental techniques have been used. In the first part of the thesis experiments with Bose-Einstein condensates of Rb-87 are presented. In these experiments the methods of laser cooling and magnetic trapping of atoms were utilized. An atom chip was used as the experimental technique for implementation of magnetic trapping. The atom chip is a small integrated instrument allowing accurate and detailed manipulation of the atoms. The experiments with Rb-87 probed the behaviour of a falling beam of atoms outcoupled from the Bose-Einstein condensate by electromagnetic field induced spin flips. In the experiments a correspondence between the phases of the outcoupling radio frequency field and the falling beam of atoms was found. In the second part of the thesis experiments of spin dynamics in cold atomic hydrogen gas are discussed. The experiments with atomic hydrogen are conducted in a cryostat using a dilution refrigerator as the cooling method. These experiments concentrated on explaining and quantifying modulations in the electron spin resonance spectra of doubly polarized atomic hydrogen. The modifications to the previous experimental setup are described and the observation of electron spin waves is presented. The observed spin wave modes were caused by the identical spin rotation effect. These modes have a strong dependence on the spatial profile of the polarizing magnetic field. We also demonstrated confinement of these modes in regions of strong magnetic field and manipulated their spatial distribution by changing the position of the field maximum.

Side peaks in Nb and NbTi point-contact spectra

Superconductor – normal metal point contacts were investigated, using different combinations of Cu, brass, Nb and NbTi. The resulting spectra contained side peaks. The currents at which these side peaks appeared, depended on the radii of the contacts. For contacts with Nb this dependence was quadratic, while for contacts with NbTi it was linear. Based on this, we argue that the side peaks in the case of the Nb contacts are due to the critical current density being exceeded. In contrast, side peaks of the NbTi contacts are caused by the self-magnetic field exceeding the lower critical field of NbTi. The NbTi contacts did not show the expected contribution from the vanishing Maxwell resistance of the superconductor, a question which remained open.

Studies of Solar Activity with Emphasis on Quasi-Periodic Oscillations

In this thesis mainly long quasi-periodic solar oscillations in various solar atmospheric structures are discussed, based on data obtained at several wavelengths, focussing, however, mainly on radio frequencies. Sunspot (Articles II and III) and quiet Sun area (QSA) (Article I) oscillations are investigated along with quasi-periodic pulsations (QPP) in a flaring event with wide-range radio spectra (Article IV). Various oscillation periods are detected; 3–15, 35–70 and 90 minutes (QSA), 10-60 and 80-130 minutes (in sunspots at various radio frequencies), 3-5, 10-23, 220-240, 340 and 470 minutes (in sunspots at photosphere) and 8-12 and 15-17 seconds (in a solar flare at radio frequencies). Some of the oscillation periods are detected for the first time, while some of them have been confirmed earlier by other research groups. Solar oscillations can provide more information on the nature of various solar structures. This thesis presents the physical mechanisms of some solar structure oscillations. Two different theoretical approaches are chosen; magnetohydrodynamics (MHD) and the shallow sunspot model. These two theories can explain a wide range of solar oscillations from a few seconds up to some hours. Various wave modes in loop structures cause solar oscillations (<45 minutes) both in sunspots and quiet Sun areas. Periods lasting more than 45 minutes in the sunspots (and a fraction of the shorter periods) are related to sunspot oscillations as a whole. Sometimes similar oscillation periods are detected both in sunspot area variations and respectively in magnetic field strength changes. This result supports a concept that these oscillations are related to sunspot oscillations as a whole. In addition, a theory behind QPPs at radio frequencies in solar flares is presented. The thesis also covers solar instrumentation and data sources. Additionally, the data processing methods are presented. As the majority of the investigations in this thesis focus on radio frequencies, also the most typical radio emission mechanisms are presented. The main structures of the Sun, which are related to solar oscillations, are also presented. Two separate projects are included in this thesis. Solar cyclicity is studied using the extensively large solar radio map archieve from Metsähovi Radio Observatory (MRO) at 37 GHz, between 1978 and 2011 (Article V) covering two full solar cycles. Also, some new solar instrumentation (Article VI) was developed during this thesis.

Microcracks and Vortices in Superconducting Thin Films

In this work, superconducting YBa₂ Cu₃O_6+x (YBCO) thin films have been studied with the experimental focus on the anisotropy of BaZrO₃ (BZO) doped YBCOthin films and the theoretical focus on modelling flux pinning by numerically solving Ginzburg- Landau equations. Also, the structural properties of undoped YBCO thin films grown on NdGaO₃ (NGO) and MgO substrates were investigated. The thin film samples were made by pulsed laser ablation on single crystal substrates. The structural properties of the thin films were characterized by X-ray diffraction and atomic force microscope measurements. The superconducting properties were investigated with a magnetometer and also with transport measurements in pulsed magnetic field up to 30 T. Flux pinning was modelled by restricting the value of the order parameter inside the columnar pinning sites and then solving the Ginzburg-Landau equations numerically with the restrictions in place. The computations were done with a parallel code on a supercomputer. The YBCO thin films were seen to develop microcracks when grown on NGO or MgO substrates. The microcrack formation was connected to the structure of the YBCO thin films in both cases. Additionally, the microcracks can be avoided by careful optimization of the deposition parameters and the film thickness. The BZO doping of the YBCO thin films was seen to decrease the effective electron mass anisotropy, which was seen by fitting the Blatter scaling to the angle dependence of the upper critical field. The Ginzburg-Landau simulations were able to reproduce the measured magnetic field dependence of the critical current density for BZO doped and undoped YBCO. The simulations showed that in addition to the large density also the large size of the BZO nanorods is a key factor behind the change in the power law behaviour between BZO doped and undoped YBCO. Additionally, the Ginzburg-Landau equations were solved for type I thin films where giant vortices were seen to appear depending on the film thickness. The simulations predicted that singly quantized vortices are stable in type I films up to quite large thicknesses and that the size of the vortices increases with decreasing film thickness, in a way that is similar to the behaviour of the interaction length of Pearl vortices.

Wind Turbine Direct-Drive Permanent-Magnet Generator with Direct Liquid Cooling for Mass Reduction

Today’s electrical machine technology allows increasing the wind turbine output power by an order of magnitude from the technology that existed only ten years ago. However, it is sometimes argued that high-power direct-drive wind turbine generators will prove to be of limited practical importance because of their relatively large size and weight. The limited space for the generator in a wind turbine application together with the growing use of wind energy pose a challenge for the design engineers who are trying to increase torque without making the generator larger. When it comes to high torque density, the limiting factor in every electrical machine is heat, and if the electrical machine parts exceed their maximum allowable continuous operating temperature, even for a short time, they can suffer permanent damage. Therefore, highly efficient thermal design or cooling methods is needed. One of the promising solutions to enhance heat transfer performances of high-power, low-speed electrical machines is the direct cooling of the windings. This doctoral dissertation proposes a rotor-surface-magnet synchronous generator with a fractional slot nonoverlapping stator winding made of hollow conductors, through which liquid coolant can be passed directly during the application of current in order to increase the convective heat transfer capabilities and reduce the generator mass. This doctoral dissertation focuses on the electromagnetic design of a liquid-cooled direct-drive permanent-magnet synchronous generator (LC DD-PMSG) for a directdrive wind turbine application. The analytical calculation of the magnetic field distribution is carried out with the ambition of fast and accurate predicting of the main dimensions of the machine and especially the thickness of the permanent magnets; the generator electromagnetic parameters as well as the design optimization. The focus is on the generator design with a fractional slot non-overlapping winding placed into open stator slots. This is an a priori selection to guarantee easy manufacturing of the LC winding. A thermal analysis of the LC DD-PMSG based on a lumped parameter thermal model takes place with the ambition of evaluating the generator thermal performance. The thermal model was adapted to take into account the uneven copper loss distribution resulting from the skin effect as well as the effect of temperature on the copper winding resistance and the thermophysical properties of the coolant. The developed lumpedparameter thermal model and the analytical calculation of the magnetic field distribution can both be integrated with the presented algorithm to optimize an LC DD-PMSG design. Based on an instrumented small prototype with liquid-cooled tooth-coils, the following targets have been achieved: experimental determination of the performance of the direct liquid cooling of the stator winding and validating the temperatures predicted by an analytical thermal model; proving the feasibility of manufacturing the liquid-cooled tooth-coil winding; moreover, demonstration of the objectives of the project to potential customers.

Kestomagnetoidun roottorin mekaniikkasuunnittelu ja -analysointi

Työssä kehitettiin suurnopeuskäyttöön soveltuva kestomagnetoitu roottori olemassa olevan induktiokoneen staattorirunkoon. Kehitystyön tarkoituksena oli selvittää roottorin mekaaniset raja-arvot, kuten maksimi kehänopeus. Samalla otettiin kantaa myös tarvittaviin analysointi- ja mitoitusmenetelmiin. Maksimi kehänopeuden, laakeroinnin ja roottorin skaalattavuuden selvittäminen edellytti myös tarkkaa materiaaliselvitystä ja optimointia. Tästä syystä työn aikana tehtiin tiivistä yhteistyötä materiaalitoimittajien kanssa. Työn tuloksena syntyi uusi menetelmä toteuttaa radiaalisen magneettivuon luova kestomagneettiroottori 200 m/s kehänopeudelle. Suunniteltua roottoriratkaisua käytetään testausroottorina, jolla selvitetään valmistuksen, kokoonpanon ja sähkötehon rajoitteet käytännössä. Suunnittelutyö edellyttikin jatkuvaa iterointia sähkösuunnittelun ja roottorin osien valmistajien kanssa, jotta löydettiin paras kompromissiratkaisu roottorin prototyyppiin. Tämän seurauksena saatiin luotua varsin tarkat suunnittelu- ja analysointiraja-arvot kestomagneettiroottorin tuotteistettavia versioita varten.

Analytic evaluation of three-phase short circuit demagnetization and hysteresis loss risk in rotor-surface-magnet Permanent-Magnet Synchronous Machines

Permanent magnet synchronous machines (PMSM) have become widely used in applications because of high efficiency compared to synchronous machines with exciting winding or to induction motors. This feature of PMSM is achieved through the using the permanent magnets (PM) as the main excitation source. The magnetic properties of the PM have significant influence on all the PMSM characteristics. Recent observations of the PM material properties when used in rotating machines revealed that in all PMSMs the magnets do not necessarily operate in the second quadrant of the demagnetization curve which makes the magnets prone to hysteresis losses. Moreover, still no good analytical approach has not been derived for the magnetic flux density distribution along the PM during the different short circuits faults. The main task of this thesis is to derive simple analytical tool which can predict magnetic flux density distribution along the rotor-surface mounted PM in two cases: during normal operating mode and in the worst moment of time from the PM’s point of view of the three phase symmetrical short circuit. The surface mounted PMSMs were selected because of their prevalence and relatively simple construction. The proposed model is based on the combination of two theories: the theory of the magnetic circuit and space vector theory. The comparison of the results in case of the normal operating mode obtained from finite element software with the results calculated with the proposed model shows good accuracy of model in the parts of the PM which are most of all prone to hysteresis losses. The comparison of the results for three phase symmetrical short circuit revealed significant inaccuracy of the proposed model compared with results from finite element software. The analysis of the inaccuracy reasons was provided. The impact on the model of the Carter factor theory and assumption that air have permeability of the PM were analyzed. The propositions for the further model development are presented.

Cost Reduction of Permanent Magnet Synchronous Machines

Electrical machine drives are the most electrical energy-consuming systems worldwide. The largest proportion of drives is found in industrial applications. There are, however many other applications that are also based on the use of electrical machines, because they have a relatively high efficiency, a low noise level, and do not produce local pollution. Electrical machines can be classified into several categories. One of the most commonly used electrical machine types (especially in the industry) is induction motors, also known as asynchronous machines. They have a mature production process and a robust rotor construction. However, in the world pursuing higher energy efficiency with reasonable investments not every application receives the advantage of using this type of motor drives. The main drawback of induction motors is the fact that they need slipcaused and thus loss-generating current in the rotor, and additional stator current for magnetic field production along with the torque-producing current. This can reduce the electric motor drive efficiency, especially in low-speed, low-power applications. Often, when high torque density is required together with low losses, it is desirable to apply permanent magnet technology, because in this case there is no need to use current to produce the basic excitation of the machine. This promotes the effectiveness of copper use in the stator, and further, there is no rotor current in these machines. Again, if permanent magnets with a high remanent flux density are used, the air gap flux density can be higher than in conventional induction motors. These advantages have raised the popularity of PMSMs in some challenging applications, such as hybrid electric vehicles (HEV), wind turbines, and home appliances. Usually, a correctly designed PMSM has a higher efficiency and consequently lower losses than its induction machine counterparts. Therefore, the use of these electrical machines reduces the energy consumption of the whole system to some extent, which can provide good motivation to apply permanent magnet technology to electrical machines. However, the cost of high performance rare earth permanent magnets in these machines may not be affordable in many industrial applications, because the tight competition between the manufacturers dictates the rules of low-cost and highly robust solutions, where asynchronous machines seem to be more feasible at the moment. Two main electromagnetic components of an electrical machine are the stator and the rotor. In the case of a conventional radial flux PMSM, the stator contains magnetic circuit lamination and stator winding, and the rotor consists of rotor steel (laminated or solid) and permanent magnets. The lamination itself does not significantly influence the total cost of the machine, even though it can considerably increase the construction complexity, as it requires a special assembly arrangement. However, thin metal sheet processing methods are very effective and economically feasible. Therefore, the cost of the machine is mainly affected by the stator winding and the permanent magnets. The work proposed in this doctoral dissertation comprises a description and analysis of two approaches of PMSM cost reduction: one on the rotor side and the other on the stator side. The first approach on the rotor side includes the use of low-cost and abundant ferrite magnets together with a tooth-coil winding topology and an outer rotor construction. The second approach on the stator side exploits the use of a modular stator structure instead of a monolithic one. PMSMs with the proposed structures were thoroughly analysed by finite element method based tools (FEM). It was found out that by implementing the described principles, some favourable characteristics of the machine (mainly concerning the machine size) will inevitable be compromised. However, the main target of the proposed approaches is not to compete with conventional rare earth PMSMs, but to reduce the price at which they can be implemented in industrial applications, keeping their dimensions at the same level or lower than those of a typical electrical machine used in the industry at the moment. The measurement results of the prototypes show that the main performance characteristics of these machines are at an acceptable level. It is shown that with certain specific actions it is possible to achieve a desirable efficiency level of the machine with the proposed cost reduction methods.

Magnetization studies of polystyrene/multiwall carbon nanotube composite films

Lappeenranta University of Technology School of Technology Technical Physics Evgenii Zhukov MAGNETIZATION STUDIES OF POLYSTYRENE/MULTIWALL CARBON NANOTUBE COMPOSITE FILMS Master’s thesis 2015 55 pages, 41 pictures, 9 Tables. Examiners: Professor Erkki Lähderanta D.Sc. Ivan Zakharchuk Keywords: polystyrene, multi-walled carbon nanotubes, MWCNT, composite, magnetization, SQUID. In this thesis magnetic properties of polystyrene/multiwall carbon nanotube (MWCNT) composites are investigated with Quantum Design SQUID magnetometer (MPMS XL). The surface of the composite films is studied via BRUKER Multimode 8 Atomic Force Microscope, as well. The polystyrene/MWCNT composites have been prepared by the group of professor Okotrub (Physics Chemistry of Nanomaterials laboratory, Nikolaev Institute of Inorganic Chemistry, Russia). The composite films have been prepared by solution processing and stretching method. The approximate length and inner diameter of the MWCNTs used in fabrication are 260 μm and 10 nm, respectively. The content of MWCNTs is 1 and 2.5 contents percent (wt%) for studied samples. The stretching of the samples is 30% for samples with 1 and 2.5 wt% content, and one sample with 1 wt% loading of MWCNTs is 100% stretched. MWCNTs aligned perpendicular to a silicon substrate are used as a reference sample. The magnetization field dependencies of the samples exhibit hysteresis behavior. The values of saturation magnetization of composite films are much less compared to that of the reference sample. The saturation magnetization coercitivity field value drops with decrease of MWCNT content. At high magnetic fields strong presence of diamagnetism is observed. Measurements in magnetic field parallel and perpendicular to the composite plate display anisotropy with respect to the direction of stretching. Temperature dependences of magnetization for all samples display difference between zero-field cooled and field-cooled curves of magnetization. This divergence confirms the presence of magnetic interactions in the material. The atomic force microscopy study of the composites’ surfaces revealed that they are relatively smooth and the nanotubes are aligned with the axis of stretching to some extent. 

New methods for controlling twin configurations and characterizing twin boundaries in 5M Ni-Mn-Ga for the development of applications

Traditional methods for studying the magnetic shape memory (MSM) alloys Ni-Mn-Ga include subjecting the entire sample to a uniform magnetic field or completely actuating the sample mechanically. These methods have produced significant results in characterizing the MSM effect, the properties of Ni-Mn-Ga and have pioneered the development of applications from this material. Twin boundaries and their configuration within a Ni-Mn-Ga sample are a key component in the magnetic shape memory effect. Applications that are developed require an understanding of twin boundary characteristics and, more importantly, the ability to predictably control them. Twins have such a critical role that the twinning stress of a Ni-Mn-Ga crystal is the defining characteristic that indicates its quality and significant research has been conducted to minimize this property. This dissertation reports a decrease in the twinning stress, predictably controlling the twin configuration and characterizing the dynamics of twin boundaries. A reduction of the twinning stress is demonstrated by the discovery of Type II twins within Ni-Mn-Ga which have as little as 10% of the twinning stress of traditional Type I twins. Furthermore, new methods of actuating a Ni-Mn-Ga element using localized unidirectional or bidirectional magnetic fields were developed that can predictably control the twin configuration in a localized area of a Ni-Mn-Ga element. This method of controlling the local twin configuration was used in the characterization of twin boundary dynamics. Using a localized magnetic pulse, the velocity and acceleration of a single twin boundary were measured to be 82.5 m/s and 2.9 × 107 m/s2, and the time needed for the twin boundary to nucleate and begin moving was less than 2.8 μs. Using a bidirectional magnetic field from a diametrically magnetized cylindrical magnet, a highly reproducible and controllable local twin configuration was created in a Ni-Mn-Ga element which is the fundamental pumping mechanism in the MSM micropump that has been co-invented and extensively characterized by the author.

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.