Electromagnetic analysis of hydropower generators is commonpractice but there is little emphasis on studying the effect ofrotor whirling in the analysis. This paper demonstrates the use ofthe unbalanced magnetic pull (UMP) curves based on purely dynamiceccentricity motion for a wide range of whirling frequencies in theprediction of the steady state UMP in the case of mixed eccentricitiesmotion. The latter motion type is more realistic in practice. Actualelectromagnetic (EM) simulations are also carried out for these mixedeccentricities motion cases in order to verify the proposed method. Goodagreement between the UMP from the actual EM simulations and theUMP predictions are made when low eccentricities exist. The proposedmethod is thus very useful since firstly, very few EM software packagescan handle mixed eccentricities motion and secondly, since actual EMsimulations of intricate rotor centre motion are time-consuming, theproposed method is a big time saver. A modified feature selective validation(FSV) method, the FSV-UPC, is also applied to assess the similarities andthe differences in the force computations.

Electromagnetic (EM) analysis of hydropower generators iscommon practice but there is little emphasis on studying the effect of rotorwhirling in the analysis. This paper explores the effect on electromagneticanalysis as the rotor is allowed to whirl both in forward and inbackward directions under no-load conditions. As a hydropower generatorrotor shaft can experience whirling when under eccentric operation,the objective is to examine how whirling can affect the unbalancedmagnetic pull (UMP), flux densities, damper currents, and ohmic lossesin a synchronous hydropower generator. These results are obtained ina commercial FEM-based EM field modelling software package thatallows various degrees of freedom in motion types and multiple motioncomponents to be set. It is seen that backward whirling tends to inducehigher eddy currents than forward whirling does.

Misalignment between the rotor geometrical axis and the geometrical stator axis in a hydropower generator is usually present at standstill and when the machine is under operation. Now, rotor-stator eccentricity in a rotating electrical machine is a harbinger to abnormal operating conditions of the machine. This rotor-stator eccentricity gives rise to a phenomenon called the unbalanced magnetic pull (UMP). Though the topic of UMP has been studied for more than a century, little attention has been paid to another phenomenon which is whirling and more specifically to non-synchronous whirling. Whereas the rotor-stator standstill misalignment can be cured to an acceptable level, a rotor when under operation normally entails whirling as well. Whirling is a reality in hydropower generators which are vertical machines and the latter are studied in this thesis work. It turns out that studying the effects of whirling in conjunction with the UMP can lift off pre-conceived ideas and hence provide a more qualitative and quantitative assessment of the effects of the nature and consequences of having a hydropower generator operating with UMP present. This thesis work provides simple theoretical conceptualisations that capture the phenomena of whirling and of the UMP, and purports to provide mechanical and electrical engineers with information on the necessity of studying these two phenomena simultaneously. With only the rotor eccentricity type considered in this work, the contributions are limited to mechanical dynamic simulations in the first part of the research work in addition to electromagnetic (EM) simulations in the second part of the research work. The validity of these EM simulations has been verified with an actual reported measurement. As for the mechanical dynamic analyses that cover the first part of the research work and which concern in essence one case of rotor eccentricity, valuable information such as the maximum rotor centre displacements inside the stator of the generator together with stability characteristics of the rotor motion are arrived at. These analyses indicate how stable the hydropower generator is under operation when UMP is present due to rotor eccentricity. It shows that one needs to consider both components of the UMP which are the radial UMP and the tangential UMP. Leaving out the tangential UMP component and/or considering a simplified whirling-independent model of the radial UMP lead(s) to a false representation of the dynamics of the generator when treated as a mechanical system. The analyses are new as a model that is used cares for both components of the UMP. In the second part of the research work, an electromechanics approach is preferred and emphasis is put on showing that important EM parameters such as force or the UMP, currents and ohmic losses are affected when non-synchronous whirling exists. The consideration of whirling as intimately linked to the UMP leads in the last stages of the research work to a robust and reliable method to compute the steady state UMP magnitude(s) up to sufficiently large eccentricities when two primary types of eccentricities, which are a purely static eccentricity and a purely dynamic eccentricity, co-exist. This novel computation method is of utmost importance and is a breakthrough in this area for four reasons: Firstly, there is no other work in the literature that has looked at mixed eccentricities motion of the geometric centre of the rotor in conjunction with simultaneous consideration of the UMP and the whirling phenomena. Secondly, it is fast as it is a semi-analytical method that rests on some previously done EM simulations which can be obtained with certain commercial EM field modelling software packages. Thirdly, it dispenses the analyst to have one of the rare contemporary commercial EM software products that can handle such intricate rotor centre motion since the proposed method rests upon less complicated EM simulations. And fourthly, it enables an analyst to obtain very good estimates of the UMP for a rotor centre motion that better mimics the true motion occurring in practice inside the stator of a hydropower generator. Altogether, the contributions in this thesis work can profoundly shape the strategies for better machine designs and analysis of the UMP without discounting previous knowledge that has been amassed since the end of the nineteenth century in this field. It is hoped that the research work carried out will help in the long interdisciplinary pursuit and allegiance to honing hydropower technology through creating an awareness of the need to study non-synchronous whirling effects as opposed to only looking at the usual synchronous whirling motion.

Electromagnetic (EM) analysis of hydropower generators is common practice but rotor whirling is little studied. This paper suggests a novel semi-analytical method for estimating the steady state unbalanced magnetic pull (UMP) when the rotor centre is undergoing mixed eccentricities motion. The ability to estimate the UMP for mixed eccentricities motion in finite element method (FEM)-based modelling software packages is rare. The proposed methodology in its formulation takes advantage of the fact that a purely dynamic eccentricity motion including non-synchronous whirling and a purely static eccentricity motion can be more amenable to implement in existing FEM-based EM modelling software products for UMP estimation. After these initial separate UMP results are obtained, the proposed method can be applied for virtually any mixed eccentricities motion cases up to sufficiently large eccentricities for quick analysis instead of running the mixed eccentricities simulations directly in a FEM-based software package. Good agreement between the UMP from the actual EM mixed eccentricities motion simulations in a commercial FEM-based software package and the UMP estimations by the novel method is made for a wide range of eccentricities that may commonly occur in practice. A modified feature selective validation (FSV) method, the FSV-UPC, is applied to assess the similarities and the differences in the UMP computations

Eccentricity leading to unbalanced magnetic pull (UMP) in electrical machines is a significant concern in industry. The UMP is known to be composed of two components: a radial component and a tangential one. Models that are used in industry tend to include the radial component alone. In this article, a Jeffcott rotor model together with a new UMP model that incorporates both radial and tangential UMP constituents is studied for an industrial hydropower generator. Characterizing the UMP as springs permits the model to inherit UMP stiffness contribution. Interesting dynamics are observed with the new model for a wide range of external forcing frequencies. It is shown firstly that the new UMP model is sensitive to forcing frequency in the rotor movements. Secondly, it is found that this sensitivity to forcing frequency increases with decreasing rotor system stiffness. Moreover, quasi-periodic motion in the rotor displacements is observed and it is noted that the rotor does not need to be forced by frequencies above its critical speed for this less desirable motion to occur. Thus, it becomes interesting to be able to account for the UMP stiffness contribution in order to curb machine malfunction which might result from these UMP forces

Eccentricity leading to unbalanced magnetic pull (UMP) in electrical machines is a significant concern in industry. The UMP is known to be composed of two components: A radial component and a tangential one. Models that are used in industry currently tend to include the radial component alone. In this paper, a Jeffcott rotor model together with a new UMP model that incorporates both radial and tangential UMP constituents is studied for an industrial hydropower generator. Characterising the UMP as springs permits the model to inherit UMP stiffness contribution. Interesting dynamics are observed with the new model for a wide range of external forcing frequencies. It is shown firstly that the new UMP model is sensitive to forcing frequency in the rotor movements. Moreover, complex dynamics in the displacements of the rotor are observed for some forcing frequencies and it is noted that the rotor does not need to be forced by frequencies above its critical speed for this less desirable motion to occur. Eigenvalue-based stability analysis is performed and shows that damping of the rotor and of the bearings are important when non-synchronous whirling of the rotor is considered. Accounting for both components of UMP is an important cornerstone in the generation of better rotor design parameters which can help to curb rotor-stator malfunction and can contribute in the design of long lasting rotors to the betterment of hydropower technology.

Eccentricity leading to unbalanced magnetic pull (UMP) in electrical machines is a significant concern in industry. The UMP is known to be composed of two components: A radial component and a tangential one. Models that are used in industry currently tend to include the radial component alone. In this paper, a Jeffcott rotor model together with a new UMP model that incorporates both radial and tangential UMP constituents is studied for an industrial hydropower generator. Characterising the UMP as springs permits the model to inherit UMP stiffness contribution. Interesting dynamics are observed with the new model for a wide range of external forcing frequencies. It is shown firstly that the new UMP model is sensitive to forcing frequency in the rotor movements. Moreover, complex dynamics in the displacements of the rotor are observed for some forcing frequencies and it is noted that the rotor does not need to be forced by frequencies above its critical speed for this less desirable motion to occur. Eigenvalue-based stability analysis is performed and shows that damping of the rotor and of the bearings are important when non-synchronous whirling of the rotor is considered. Accounting for both components of UMP is an important cornerstone in the generation of better rotor design parameters which can help to curb rotor-stator malfunction and can contribute in the design of long lasting rotors to the betterment of hydropower technology.

Eccentricity leading to unbalanced magnetic pull (UMP) in electrical machines is a significant concern in industry. The UMP is known to be composed of two components: A radial component and a tangential one. Models that are used in industry currently tend to include the radial component alone. In this study, a Jeffcott rotor model together with a new UMP model that incorporates both the radial and tangential UMP constituents is studied for an industrial hydropower generator. Characterising the UMP as springs permits the proposed model to inherit UMP stiffness contribution. It is shown firstly that the new UMP model is sensitive to forcing frequency in the rotor movements and secondly, that this sensitivity to forcing frequency increases with decreasing rotor system stiffness. Moreover, quasi-periodic motion in the rotor displacements is observed for some forcing frequencies and system stiffnesses. Eigenvalue-based stability analysis is performed and shows that damping and stiffness of the rotor and of the bearings are important when non-synchronous whirling of the rotor comes into play. Accounting for both UMP components is an important cornerstone in the generation of better rotor designs which can help to curb rotor-stator malfunction and can contribute in the design of long lasting rotors.

Eccentricity leading to unbalanced magnetic pull (UMP) in rotating electrical machines is a significant concern in industry. The UMP arises due to magnetic flux crossing the air-gap between the rotor and stator, and can be more intense than the useful peripheral force that the machine develops. Electric machines are the workhorses of any modern society and for over a century, the UMP phenomenon has been studied and this mainly by electrical engineers. Though, several refinements have been made in the equations describing this electromagnetic force to account for the effects such as saturation of iron parts and parallel circuits in the machine armature, the treatment of UMP is scarce in literature, and its characterisation and analysis remains a conundrum, and stays a subject of current research in electrical machinery design. Until a few years back, the UMP was thought to consist only of one component which acts in the radial direction. Though theoretical and mathematical developments have advanced to a very high level and are still forthcoming, there is generally no agreed model. The UMP model that tends to be utilised in industry only assumes the existence of the radial UMP and further simplifies the analysis by considering the maximum radial UMP stiffness to be applicable at all whirling angular velocities of the rotor. The present work comes in as furnishing two original contributions with emphasis on the understanding of the dynamics in lieu of considering both mechanical and electrical parameters that would create hard-to-analyse abstractions. First, it is shown that the simple model currently being used in industry may be fraught with risks. A new corrected model that accounts for both UMP components is thereby proposed in this work. This model is cast into stiffness terms and the separate effects of the radial UMP and that of the tangential UMP as well as their combined effects are explored quantitatively. So as to have tangible results that can be explained and the dynamics understood, a symmetrical Jeffcott rotor is used to simulate the newly proposed UMP model. Other pertinent simplifications include the use of a combined damping value for the rotor and bearings, the exclusion of unbalance force on the rotor due to mass eccentricity effect, the omission of the effects of saturation in the magnetic circuits together with assumption of linear behaviour of the UMP curves with eccentricity for low eccentricity values. Several important results surface from the analysis. It is found that the new UMP model is sensitive to forcing frequency in the rotor movements and that this sensitivity to forcing frequency increases with decreasing rotor system stiffness. Moreover, quasi-periodic motion in the rotor displacements is observed and it is noted that the rotor does not need to be forced by frequencies above its critical speed for this less desirable motion to occur.The second contribution in this thesis lays ground for stability consideration which is a cornerstone in the sound understanding of the design and operation of any machinery. Stability analysis is indispensable as disturbances do exist in real-life that can drive machines away from an equilibrium operating point. For the system at hand, it becomes essential to investigate the effect(s) of non-synchronous whirling on the stability of the system. Eigenvaluebased stability analysis is performed on the simple Jeffcott model and results show that damping, and stiffness of the rotor and of the bearings are important when non-synchronous whirling of the rotor comes into play. The original contributions in this work as depicted above comes primarily from the formulation and use of an UMP model that accounts for both the radial and the tangential UMP components. This allows unprecedented results to be arrived at that can be expected to be part of a crucial milestone in the generation of better rotor design parameters which can help to curb rotor-stator malfunction and can contribute in the design of long lasting rotors. This influential contribution will help in the long interdisciplinary pursuit and allegiance to honing hydropower technology.