On the dynamics of an hydropower generator subjected to unbalanced magnetic pull : characterisation and analysis
Abstract: 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.
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