UNIVERSITY OF SOUTHAMPTON FACULTY OF ENGINEERING AND PHYSICAL SCIENCES Mechatronics Research Group A Linear to Rotary Magnetic Gear By Thang Van Lang Thesis for the degree of Doctor of Philosophy November 2020 UNIVERSITY OF SOUTHAMPTON ABSTRACT FACULTY OF ENGINEERING AND PHYSICAL SCIENCES Mechatronics Research Group Doctor of Philosophy A Linear to Rotary Magnetic Gear By Thang Van Lang Although magnetic gears are more expensive and larger than mechanical gears for a given power rating, they are more efficient They also offer the advantage of physical separation between the driving and driven shafts which can be in different environments, e.g., in water and in air Recent research has focused on rotary magnetic gears, with limited work on linear to rotary and vice versa motion conversions, which is desirable in many applications such as wave energy harvesting This thesis focuses on the development of the theory and design optimisation of a novel linear-rotary magnetic gear derived from a variable reluctance permanent magnet (transverse-flux) rotational machine topology The configuration of a linear to rotary magnetic gear is developed and discussed A design optimisation methodology is implemented based on finite element analysis Using this methodology, optimal proportions and dimensions of a linear to rotary magnetic gear demonstrator are determined It is shown that increasing the magnet thickness results in the increase transmitted torque, but with diminishing returns The optimal results showed that the maximum torque density obtained about 11.3 kNm/m3 The proposed design methodology is successfully applied to the design of a two-pole (on the rotor) magnetic gear A demonstrator is built and successfully tested, and theoretical predictions are validated Based on the demonstrator in this study, the use of a linear-rotary magnetic gear for applications such as wave energy harvesting looks promising i ii Table of Contents ABSTRACT i Table of Contents iii List of Figures vii List of Tables xiii Declaration of authorship xv Acknowledgements xvii Symbols xix Chapter Introduction 1.1 Motivation and problem statement 1.2 Magnetic gears 1.2.1 State of the art of magnetic gears 1.2.2 Overview of magnetic gear topologies 1.2.3 Converted magnetic gears 1.2.4 Field modulated magnetic gears 1.2.5 Associated linear topologies of MGs 13 1.3 A linear to rotary magnetic gear based on transverse-flux machine 16 1.4 Aims and objectives 22 Chapter Magnetic Field Theory 25 2.1 Introduction 25 2.2 Basic magnetic field theory 25 2.2.1 Biot-Savart law 25 2.2.2 Ampere’s circuital law 26 2.2.3 The magnetic circuits 27 2.2.4 Leakage and fringing effect 30 2.3 Magnetic field analysis 31 2.3.1 Reluctance network 31 2.3.2 Finite element analysis 32 2.3.3 Calculation of the torque with FEA 34 2.4 Magnetic materials 37 2.5 Summary 39 iii Chapter A linear to rotary magnetic gear 41 3.1 Structure of a magnetic gear 41 3.1.1 Topology development 41 3.1.2 Gear ratio 47 3.1.3 Force and torque characteristics 48 3.2 Topology modification 56 3.3 Comparative design 61 3.4 Varying pole pitch topology 64 3.5 Summary 69 Chapter Design optimisation of the magnetic gear 71 4.1 Introduction 71 4.2 Two-dimensional finite element analysis (2D-FEA) 72 4.3 Three-dimensional finite element analysis (3D-FEA) 79 4.4 Scaling 88 4.5 Design analysis 91 4.6 Summary 95 Chapter Prototype of the linear to rotary magnetic gear 99 5.1 Introduction 99 5.2 Prototype fabrication 100 5.3 Experiment set up 103 5.4 Experimental results 105 5.5 Summary 108 Chapter Conclusion 109 Chapter Future work 113 7.1 Overview 113 7.2 Dynamic modelling of the magnetic gear 114 7.2.1 Analytical model 114 7.2.2 Oscillating prediction 118 7.2.3 Modelling of the proposed magnetic gear with an external excitation train 120 7.3 Dynamic model of the rotational harvester 122 Appendix A 129 MATLAB-Simulink model 129 iv Appendix B 132 References 154 v ... SOUTHAMPTON ABSTRACT FACULTY OF ENGINEERING AND PHYSICAL SCIENCES Mechatronics Research Group Doctor of Philosophy A Linear to Rotary Magnetic Gear By Thang Van Lang Although magnetic gears are... 1.2.4 Field modulated magnetic gears 1.2.5 Associated linear topologies of MGs 13 1.3 A linear to rotary magnetic gear based on transverse-flux machine 16 1.4 Aims and objectives... 2.3.3 Calculation of the torque with FEA 34 2.4 Magnetic materials 37 2.5 Summary 39 iii Chapter A linear to rotary magnetic gear 41 3.1 Structure of a magnetic