If the rotor of an induction motor is not concentric with the stator then an electromagnetic force is generated in a direction that will increase the eccentricity. This is called unbalanced magnetic pull (UMP). The first part of the work presented in this dissertation develops theoretical models which allow the calculation of the UMP in cage induction motors due to static rotor eccentricity. These account for any winding configuration including parallel stator winding connection. The second part of the work verifies the models experimentally using two different cage induction motors. The agreement between predicted and measured values of UMP and line current is found to be good. The investigation leads to several new aspects of the damping effects of parallel stator windings and the cage rotor being highlighted.

Wind energy has been the fastest emerging renewable energy source over the last decade. The overriding provisos to minimise greenhouse emissions and increasing concerns regarding energy security have been the major inducements for many countries to make a resolute transition to new and non-conventional power sources. Direct-drive systems for wind turbines are potentially a more reliable alternative to gearbox driven systems. Gearboxes are liable to significant accumulated fatigue torque loading with relatively high maintenance costs. It is with this in mind that the primary focus of this research is on direct-drive wind turbines. Generators in direct-drive wind turbines tend to be of large diameter and heavier due to the support structure required to maintain as small air-gap as possible between the stationary and rotating parts of the generator. Permanent magnet generators (PMGs) are the most common type to be used within direct-drive wind turbines nowadays. Generators and other drive-train components in wind turbines experience significant varying loads, which may lead to a bearing failure. These varying loads can lead to misalignment within the drivetrain producing eccentricity between the generator rotor and stator. Rotor eccentricity generates a magnetic force referred to as Unbalanced Magnetic Pull (UMP). The induced UMP for the same rotor eccentricity is much higher in PMGs than induction generators because of the higher permanent magnet magnetic field. UMP is an important issue requiring further research. A part of this study provides a more detailed treatment of UMP under varying rotor eccentricity regimes for various permanent magnet machine topologies. The effect of UMP in direct-drive PMGs on the lifetime of the main bearing is a topic that requires more research aimed at proposing design improvements and solutions. The hope being that the availability of such solutions can be applied to practical reductions in operating costs. In brief, identification of the root causes of failure and impacts on component lifetime remain a subject of research. Establishing analytical tools for studying the impact of UMP on component lifetime in direct drive wind turbines and identifying the prospects for air gap winding machines using single bearing configuration are the two key areas for further research. Firstly, this research aims to establish the relationship between bearing forces and different types of eccentricities and UMP in direct drive machines. It is intended to use such models for predicting bearing wear and fatigue. Secondly, this research aims to establish the analytical tools for studying static, dynamic and tilting eccentricity in air-gap winding direct drive generators. Such tools are used to increase the understanding of the dynamics of direct drive PM generators. The final step of this study is using a multi-body simulation software (SIMPACK) to initiate investigations and comparison by providing assessments of electromagnetic interaction and internal drive-train loading for four possible designs for a proposed 5MW direct-drive wind turbine in response to the loads normally seen by a wind turbine. The four designs include: (a) iron-cored PM direct-drive generator supported by two main bearings, (b) airgap winding PM direct-drive generator supported by two main bearings, (c) iron-cored PM direct-drive generator supported by a single main bearing, (d) airgap winding PM direct-drive generator supported by a single main bearing. An aero-elastic simulation code (HAWC2) is used to extract the hub loads for different wind speeds corresponding to the normal operation of the wind turbine. The dynamic eccentricity and its influence on the electromagnetic interaction and consequential effects on bearing loading for all four designs is examined to determine the most optimal support structural configuration for a direct-drive system. In summary, the main aim of this thesis is studying the effect of different types of rotor eccentricities in different types of direct drive PMGs on the main bearing arrangements. The results show that static rotor eccentricity has the maximum impact compared to the other types of eccentricities. The main result of an eccentricity is the induced UMP which applies directly as an extra force on the bearings. The influence of UMP on bearing wear is studied. This influence is found to be significant in PM machines and should be considered when designing the bearing stiffness. A 20% static rotor eccentricity in a PM machine is found to induce an UMP that roughly equals third the total weight of the machine. A single bearing design for a direct-drive wind turbine is proposed and compared with a conventional two-bearing design. The results show that the Iron-cored PM direct-drive generator supported by two main bearings design and airgap winding PM direct-drive generator supported by a single main bearing design have advantages over the other two designs in this study.

This thesis involves the development and study of a finite element model of a hermetic, single-vane compressor and a single-phase alternating current induction motor assembled in a common housing. The manufacturer of this unit is experiencing a high scrap rate due to interference during operation between the stator and rotor of the motor. The rotor shaft of the motor is non-typical because of its cantilever design. The finite element model was first subjected to eigenvalue analysis. This revealed that the interference producing displacements were not the result of torque application to the rotor at a frequency close to an eigenvalue of the mechanical system. After a review of the literature and discussions with Electrical Engineering Department faculty possessing extensive motor experience, it was surmised that the physical phenomenon causing the rotor displacement was unbalanced magnetic pull. This phenomenon occurs in the air gap of rotating electric machines due to eccentricity in the air gap. The model was then subjected to simultaneous harmonic force inputs with magnitudes of unity on the rotor and stator surfaces to simulate the presence of unbalanced magnetic pull. It was found that the rotor shaft acts as a cantilever beam while the stator and housing are essentially rigid. The displacements due to these forces were examined and then scaled to develop the motor parameters necessary to produce the radial forces required for stator/rotor interference. Several recommendations were then made regarding possible solutions to the interference problem. / Master of Science

Induction machines are the most widely used type of electrical machines because of their robustness, simplicity, and relatively low cost. However, the small airgap in the induction machine makes them more susceptible to Unbalanced Magnetic Pull (UMP). This is because the magnitude of the UMP is a function of the degree of eccentricity, which is the ratio between the length of misalignment and the mean airgap length. The bearing-related failure accounts for approximately 41% of the total failures of induction machines; the percentages of bearing-related failure would be higher for applications in a harsher environment. In this thesis, the UMP caused by rotor eccentricity is investigated, because a small degree of rotor eccentricity is unavoidable due to the manufacturing tolerance and 80% of the mechanical faults could cause rotor eccentricity in electrical machines. When the rotor is not at the centre of the stator, the eccentric rotor causes an uneven airgap around the rotor, in which the magnetic permeance with the higher harmonics content will be created. The magnetomotive force (MMF) produces additional pole-pair ±1 magnetic flux around the airgap. The interaction between each magnetic flux with its pole pair ±1 magnetic flux produces UMP. As only the magnetic flux that crosses the airgap causes UMP, the magnetic flux is categorised into magnetising flux and airgap leakage flux, because both types of flux possess different characteristics at a different rotor slip. As the airgap leakage flux is difficult to calculate analytically, an empirical method is proposed to estimate the UMP caused by the airgap leakage flux. Then, the UMP caused by the magnetising flux can also be estimated by using the empirical method. The parameters for the empirical method can be found by using either the FEA or the experimental results. The damping effect of the magnetising flux in a parallel connected rotor bar is discussed and a damping coefficient is introduced to explain this scenario. The damping coefficient can also be used to calculate the UMP in a steady state analysis. UMP comparisons between the cage rotor and wound rotor induction machines are made. The wound rotor has a much higher UMP because the pole-specific wound rotor could not damp the additional pole pair ±1 magnetic flux. Therefore, a damper winding at the stator slot is also proposed in order to damp the UMP by producing a counteracting flux. In addition, analytical equations have also been derived for different scenarios, such as static eccentricity, dynamic eccentricity, axial-varying eccentricity, and skew rotor bars. Finite Element Analysis (FEA) and experimental work are used to demonstrate the derived analytical equation. Furthermore, the power losses caused by the rotor eccentricity are investigated. Iron losses, copper losses, and frictional loss are discussed and compared with both the analytical equation and the FEA results. In order to reduce the UMP in the induction machines, the two proposed methods are the slip control method and damper windings topology. The slip control method utilises the non-linearity characteristic of the UMP at different rotor slip. To find the optimum operating slip with the lowest UMP, the UMP/Torque ratio is introduced. The characteristics of the UMP/Torque ratio varies with the type and design of the induction machines. However, this method is only applicable when the machine is lightly loaded, because the magnetising flux is limited by the capped terminal voltage and the core saturation of the machine. For the damper winding topology, a circulating current flowing in the damper winding could produce a counteracting flux to damp the UMP. The proposed damper windings configuration is only suitable for the induction machine with an even pole pair number. Finally, comparisons between both UMP reduction methods are made.

This dissertation thesis deals with the computational modelling of the dynamic response of the rotating electrical machine structure on the application of the magnetic forces. Apart from the dynamic response of the ideal symmetrical machine, the influence of the air gap eccentricity on the dynamics response is studied in this work. A basic type of the air gap eccentricity, which is caused by eccentric mounting of the rotor pack on the shaft of the rotor, is considered. The calculations the dependence of the magnetic forces on the time and a misalignment of the rotor pack are performed as first. The computational model of the magnetic field of the rotating electrical machine, which is based on solution of the electromagnetic coupled field analysis by finite element method, is used for this purpose. An analysis of the influence of the unbalanced magnetic pull and the stiffness of some parts of the machine on the modal properties of the machine is performed in the second part of this thesis. A third part of this thesis is focused on the calculation of the dynamic response of the machine during the steady state operation of the machine and the influence of the rotor pack misalignment on the dynamic response is studied. The obtained results showed that the tangential components of the magnetic forces, which act on the stator pack, excite significant torsional vibration of the stator. Besides the vibration of the stator of the machine, the influence of the rotor pack misalignment on the sound power of the machine, vibration of the rotor, loads of rotor bearings and air gap eccentricity is studied in this thesis.

Hydropower research is often perceived to be an old and exhausted field of study but with ageing equipment and the need for more intermittent operation caused by an increased share of other renewable energy sources new challenges lie ahead. The main focus of this dissertation are the electromagnetic forces resulting from nonuniform air gap flux, whether it be caused by rotor eccentricity or a faulty field winding. Results are predominantly obtained from measurements on an experimental generator and numerical simulations. With the computational capacity available today it is possible to numerically analyse physical phenomena that previously could only be studied with analytical tools. Numerical models can also be expanded to encompass more than one aspect of generator operation in coupled field-circuit models without model complexity surpassing computer capability. Three studies of unbalanced magnetic pull, UMP, in synchronous salient pole generators constitute the main part of this thesis. The first is a study of how parallel stator circuits affect the unbalanced magnetic pull caused by rotor eccentricity. Depending on the relationship between the geometry of the separate circuits and the direction of the eccentricity it was found that parallel circuits could reduce the UMP substantially. Secondly, an investigation of the effect of damper winding configuration on UMP was performed. The results showed that damper winding resistivity and the distance between the damper bars in a pole determine the effectiveness of the damper winding in reducing the UMP. Simulations of a production machine indicate that the reduction can be substantial from damper windings with low resistivity. The third study analyses the consequences of field winding interturn short circuits. Apart from a resulting rotating unbalanced magnetic pull it is found that the unaffected poles with the same polarity as the affected pole experience an increase in flux density. In a fourth article a new stand still frequency response, SSFR, test method including measurements of damper winding voltage and current is presented. It is found that the identified models are capable of predicting the stator to damper transfer function both with and without the damper winding measurements included.

This dissertation thesis deals with the computational modelling of the dynamic response of the rotating electrical machine structure on the application of the magnetic forces. Apart from the dynamic response of the ideal symmetrical machine, the influence of the air gap eccentricity on the dynamics response is studied in this work. A basic type of the air gap eccentricity, which is caused by eccentric mounting of the rotor pack on the shaft of the rotor, is considered. The calculations the dependence of the magnetic forces on the time and a misalignment of the rotor pack are performed as first. The computational model of the magnetic field of the rotating electrical machine, which is based on solution of the electromagnetic coupled field analysis by finite element method, is used for this purpose. An analysis of the influence of the unbalanced magnetic pull and the stiffness of some parts of the machine on the modal properties of the machine is performed in the second part of this thesis. A third part of this thesis is focused on the calculation of the dynamic response of the machine during the steady state operation of the machine and the influence of the rotor pack misalignment on the dynamic response is studied. The obtained results showed that the tangential components of the magnetic forces, which act on the stator pack, excite significant torsional vibration of the stator. Besides the vibration of the stator of the machine, the influence of the rotor pack misalignment on the sound power of the machine, vibration of the rotor, loads of rotor bearings and air gap eccentricity is studied in this thesis.

In a synchronous machine, radial, tangential, and axial forces are generated. In this thesis, three different technologies to control them are proposed. The first one, involves the utilization of the radial forces that arise between the rotor and the stator. This is achieved by segmenting the rotor field winding into groups of poles and controlling their corresponding magnetization individually. This technology is particularly useful to achieve magnetic balance and to create controllable radial forces. The second technology, involves the control of the rotor field in order to influence the tangential forces that produce torque. This is achieved by inverting the rotor field winding polarity with respect to the stator field. With this technique, breaking and accelerating torques can be created. It is particularly useful to start a synchronous machine. Finally, the application of axial forces with a magnetic thrust bearing is discussed. The main benefits of this technology are higher efficiency and increased reliability. The work presented in this thesis was carried out within the Division of Electricity in the Department of Engineering Sciences at Uppsala University. It is based on original research supported by analytical calculations, computational simulations and extensive experimental work.

The Master's thesis deals with the mechanical design of electric machine rotor. Within the first two chapters of the practical part of the thesis two simplified computational models of the rotor (level 1 models) are compiled. Specifically, the model of flexible rotor mounted on rigid supports and model of rigid rotor mounted on flexible supports. The essence of these computational models lies in solvability using simple equations. Using these models can save time when constructing a pre-design of the rotor geometry. The following chapter is devoted to comparing different approaches to computational modeling of rotor using FEM. A predetermined preliminary design of a high-speed massive rotor is investigated. Computational models of different levels at stress-strain analysis and modal analysis are presented. It also includes a suggestion on how to proceed effectively in a given analysis.