Mathematical Models for the Design of Electrical Machines

This book is a comprehensive set of articles reflecting the latest advances and developments in mathematical modeling and the design of electrical machines for different applications. The main models discussed are based on the: i) Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series in 2-D or 3-D with a quasi-Cartesian or polar coordinate system); ii) electrical, thermal and magnetic equivalent circuit; iii) hybrid model. In these different papers, the numerical method and the experimental tests have been used as comparisons or validations

Determination of an Optimum Fictitious Air Gap and Rotor Disk Thickness for a Coreless AFPMM

This article presents the research on the optimum distance (fictitious air gap) between permanent magnets of the coreless axial flux permanent magnet machine with a double rotor and single stator. Magnetic flux density of the permanent magnets follows the mean flux path between the opposite magnets. The size of the leakage flux depends on the axial distance between the magnets, the distance between adjacent magnets and the back iron of the rotor disks. If the fictitious air gap (clearance between opposite permanent magnets) is too large, the flux path will close through the adjacent magnet and not the opposite one. The article presents the finite element analysis of the magnetic flux density between the permanent magnets mounted on the rotor disks where the fictitious air gap thickness was set as a variable to determine the maximum clearance. Connection between bending (pull) forces of rotor disks and fictitious air gap thickness is also presented with the mechanical stress analysis of rotor disks

In-wheel motors for electric vehicles

PhD ThesisThe in-wheel motor technology as the source of traction for electric vehicles has been researched recently because it is compact and ease-to-integrate. The motor is housed in the wheel. Since the room for the motor is tightly defined by the size of the wheel and there is no gearing system, the motor must have a high torque density to drive the vehicle directly and a high efficiency to keep cool. The existing motor uses a surface-mounted magnet topology. To make it more cost-competitive, the magnet material needs to be reduced while maintaining the torque performance at the rated operating condition. It is the motive of this Ph.D. research. The thesis starts with a brief introduction on the background of the electric vehicle. Then the major challenges of the in-wheel motor technology are summarised. With the derived specifications, an induction machine and a switched reluctance machine are then simulated and analysed. Still, the permanent magnet synchronous machine is proved to have the highest torque density. Change from surface-mounted to interior topology, six new magnet topologies are investigated. The V-shaped interior magnet topology shows superior torque-to-magnet-mass ratio and is easy-to-manufacture. It gives 96% torque while using 56% of the magnet mass compared to the existing motor due to the assist from the additional reluctance torque and the lower magnetic circuit reluctance. The key to use less magnet mass while avoiding the demagnetisation is the front iron shielding effect. The analytical explanation on the better resistance to demagnetisation in the V-shaped motor is provided. The magnet loss mechanism is discussed for proper segmentation. Detailed design adjustments are made to compromise between the torque-to-magnet-mass ratio and the manufactural practicality. Issues regarding to lower mechanical rigidity occurred in initial assembly of the prototype and solutions are proposed. Followed by successful assembly, experimental tests were conducted and results show good agreement with the simulation. A specific form of torque ripple is found in the V-shaped motor and occurs generally in all fractional-slot concentrated-winding machines with saliency. It is explained by an analytical model. This model is also extended to explain the generally lower reluctance torque in vi fractional-slot concentrated-winding machines. Potential design improvements are suggested and simulated for future versions.Protean Electri

Axial flux permanent magnet machines for direct drive applications

This thesis explores aspects of the design, analysis, and experimental test of permanent magnet axial flux machines for use in diesel engine generator sets, vertical axis wind turbines, and wheel motors for solar cars. The characteristic geometry of axial flux machines is naturally more suitable than that of conventional topologies in certain applications. However, convenient and accurate methods of electromagnetic design and analysis are less well established for such machines. The purpose of the research described herein is to benchmark a range of methods of analysis which can be extended to novel designs. There is a particular focus on the use of Finite Element Analysis to facilitate greater understanding of these machines through the illustration and quantification of the electromagnetic aspects of their operation, and the verification of a selection of analytical approaches. Prototype TORUS machines are first considered; the various analyses are then extended to iron-cored axial flux machines having slotted conductors and finally to a selection of novel machines having concentrated coils and an ironless stator. The analyses are successfully extended to a range of machines, and the particular suitability of axial flux permanent magnet machines in certain direct drive applications is demonstrated

Synchronous reluctance motors with fractional slot-concentrated windings

PhD ThesisToday, high efficiency and high torque density electrical machines are a growing research interest and machines that contain no permanent magnet material are increasingly sought. Despite the lack of interest over the last twenty years, the permanent magnet-free synchronous reluctance machine is undergoing a revival and has become a research focus due to its magnet-free construction, high efficiency and robustness. They are now considered a potential future technology for future industrial variable speed drive applications and even electric vehicles. This thesis presents for the first time a synchronous reluctance motor with fractional slot-concentrated windings, utilizing non-overlapping single tooth wound coils, for high efficiency and high torque density permanent magnet-free electric drives. It presents all stages of the design and validation process from the initial concept stage through the design of such a machine, to the test and validation of a constructed prototype motor. The prototype machine utilizes a segmented stator core back iron arrangement for ease of winding and facilitating high slot fill factors. The conventional synchronous reluctance motor topology utilizes distributed winding systems with a large number of stator slots, presenting some limitations and challenges when considering high efficiency, high torque density electrical machines with low cost. This thesis aims to present an advancement in synchronous reluctance technology by identifying limitations and improving the design of synchronous reluctance motors through development of a novel machine topology. With the presented novel fractional slot concentrated winding machine design, additional challenges such as high torque ripple and low power factor arise, they are explored and analysed - the design modified to minimise any unwanted parasitic effects. The electrical and electromagnetic characteristics of the developed machine are also explored and compared with that of a conventional machine. A novel FEA post-processing technique is developed to analyse individual air-gap field harmonic torque contributions and the machines dq theory also modified in order to account for additional effects. The developed machine is found to be lower cost, lower mass and higher efficiency than an equivalent induction or conventional synchronous reluctance motor, but does suffer higher torque ripples and lower power factor. The prototype is validated using static and dynamic testing with the results showing a good match with finite element predictions. The work contained within this thesis can be considered as a first step to developing commercial technology based on the concept for variable speed drive applications.Financial assistance was provided by was provided by the UK Engineering and Physical Sciences Research Council (EPSRC) in the form of a Doctoral Training Award and additional financial assistance was kindly provided by Cummins Generator Technologies, Stamford, UK, through industrial sponsorship of this wor

Towards Fully Additively-Manufactured Permanent Magnet Synchronous Machines: Opportunities and Challenges

With the growing interest in electrification and as hybrid and pure electric powertrains are adopted in more applications, electrical machine design is facing challenges in terms of meeting very demanding performance metrics for example high specific power, harsh environments, etc. This provides clear motivation to explore the impact of advanced materials and manufacturing on the performance of electrical machines. This paper provides an overview of additive manufacturing (AM) approaches that can be used for constructing permanent magnet (PM) machines, with a specific focus on additively-manufactured iron core, winding, insulation, PM as well as cooling systems. Since there has only been a few attempts so far to explore AM in electrical machines (especially when it comes to fully additively-manufactured machines), the benefits and challenges of AM have not been comprehensively understood. In this regard, this paper offers a detailed comparison of multiple multi-material AM methods, showing not only the possibility of fully additively-manufactured PM machines but also the potential significant improvements in their mechanical, electromagnetic and thermal properties. The paper will provide a comprehensive discussion of opportunities and challenges of AM in the context of electrical machines

Design Synthesis and Optimization of Permanent Magnet Synchronous Machines Based on Computationally-Efficient Finite Element Analysis

In this dissertation, a model-based multi-objective optimal design of permanent magnet ac machines, supplied by sine-wave current regulated drives, is developed and implemented. The design procedure uses an efficient electromagnetic finite element-based solver to accurately model nonlinear material properties and complex geometric shapes associated with magnetic circuit design. Application of an electromagnetic finite element-based solver allows for accurate computation in intricate performance parameters and characteristics. The first contribution of this dissertation is the development of a rapid computational method that allows accurate and efficient exploration of large multi-dimensional design spaces in search of optimum design(s). The computationally efficient finite element-based approach developed in this work provides a framework of tools that allow rapid analysis of synchronous electric machines operating under steady-state conditions. In the developed modeling approach, major steady-state performance parameters such as, winding flux linkages and voltages, average, cogging and ripple torques, stator core flux densities, core losses, efficiencies and saturated machine winding inductances, are calculated with minimum computational effort. In addition, the method includes means for rapid estimation of distributed stator forces and three-dimensional effects of stator and/or rotor skew on the performance of the machine. The second contribution of this dissertation is the development of the design synthesis and optimization method based on a differential evolution algorithm. The approach relies on the developed finite element-based modeling method for electromagnetic analysis and is able to tackle large-scale multi-objective design problems using modest computational resources. Overall, computational time savings of up to two orders of magnitude are achievable, when compared to current and prevalent state-of-the-art methods. These computational savings allow one to expand the optimization problem to achieve more complex and comprehensive design objectives. The method is used in the design process of several interior permanent magnet industrial motors. The presented case studies demonstrate that the developed finite element-based approach practically eliminates the need for using less accurate analytical and lumped parameter equivalent circuit models for electric machine design optimization. The design process and experimental validation of the case-study machines are detailed in the dissertation