Meng Mechanical Engineering the Spherical Revolution
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MEng Mechanical Engineering The Spherical Revolution: Development and Promotion of an Open-source & Arduino-based Spherical Drive System in the Maker Community Alex DUNNETT May, 2020 Supervisor: David Polson Thesis submitted to the University of Sheffield in partial fulfilment of the requirements for the degree of Master of Engineering 1 PROJECT SUMMARY To promote consideration of omnidirectional actuators in a more diverse number of ap- plications; an open-source omnidirectional actuator was conceptualized, designed, con- structed and tested. Upon selection of a spherical motor configuration for the actuator, further research was conducted to determine which technology would could be adapted to power it. The research concluded with a selection of brushless DC motor technology as a means to actuate the spherical motor drive, with an emphasis on linear induction technology. To promote the development of omnidirectional drive systems within the open-source com- munity a set of generalised performance metrics was developed. Initially work was undertaken to better understand the principles behind linear induction and permanent magnet motor technology. Maxwell’s equations as well as insight from aca- demic literature on the subject were then used to construct an analytical model in MATLAB. The model was validated through both numerical and experimental means. Optimum design parameters, based on the recommendations of the design tool, were used to propose a design foundation from which a number of design concepts were generated. The designs were generated with consideration to the manufacturing capabilities of the IForge and the cost of materials. In parallel to the physical design, and working within the constraints of accessibility and Arduino-based hardware, a three phase open-source motor controller was developed. On account of Covid-19, the decision was taken to continue manufacture as accessibility was a design consideration. Third party suppliers were sourced in order to help build the components. In order to achieve this within an expanded, but still small, budget significant redesign was undertaken. The motor was then switched on and and an attempt to characterise performance was made. The findings were uploaded to the Project’s hackaday page in addition to a video which explained how any viewer could go about constructing their own device, starting with the motor controller and power supply. i CONTENTS 1 Project Summary i 2 Introduction 1 2.1 Omni-Directional Drives ................................ 1 2.2 Limitations of Omnidirectional Drives ........................ 2 2.3 The Maker Community ................................. 3 3 Literature Review 4 3.1 Methods of Omnidirectional Drive .......................... 4 3.1.1 Mecanum Wheels ................................ 4 3.1.2 Swerve Drive ................................... 4 3.1.3 Ball Drive ..................................... 4 3.2 Omnidirectional Drive Selection ............................ 5 3.3 Overview of the Arduino Platform ........................... 5 3.4 Omnidirectional Drive Systems ............................ 6 3.4.1 Ultrasonic Motors ................................ 7 3.4.2 Single-Stator Ultrasonic Motors (SSUM) .................. 7 3.4.3 Multi-stator Ultrasonic Motors (MSUM) .................. 8 3.4.4 Inverse Mouse Drives (IMD) .......................... 9 3.4.5 Stepper Motor .................................. 10 3.4.6 Linear Induction Motor (LIM) ......................... 12 3.4.7 Permanent Magnet Synchronous Motor (PMSM) ............. 14 3.5 Technology Selection .................................. 15 3.6 Conclusion from Literature Review .......................... 15 3.7 Aims & Objectives .................................... 16 4 Theory 17 4.1 The Maxwell Equations ................................. 17 4.1.1 Faraday’s Law .................................. 17 4.1.2 Lenz’s Law .................................... 17 4.1.3 Biot-Savart Law ................................. 18 4.1.4 Lorentz Equation ................................ 18 4.2 Linear Induction Motor ................................. 18 4.2.1 Operating Principles of the Induction Motor ................ 19 ii 4.2.2 LIM Topologies: Single-sided LIM ....................... 21 5 Modelling 22 5.1 Analytical Design Tool .................................. 22 5.1.1 Key Design Parameters ............................. 22 5.1.2 Analytical Methodology ............................ 23 5.2 Validation ......................................... 24 5.2.1 Analytical ..................................... 25 5.2.2 Experimental ................................... 25 5.2.3 Numerical .................................... 26 5.2.4 Conclusion .................................... 26 6 Arduino Motor Controller 27 6.1 Motor Controller Design Specification ........................ 27 6.2 Code Development ................................... 28 6.2.1 SPWM Signal ................................... 28 6.2.2 Polarity Switching ................................ 29 6.2.3 Adaption for Three Phase Inversion ..................... 30 6.2.4 Testing ...................................... 31 7 System Analysis 32 7.1 Generic Metrics ..................................... 32 7.1.1 Inertia ....................................... 33 7.1.2 Torque ...................................... 33 7.1.3 Driving Frequency ................................ 33 7.1.4 Efficiency ..................................... 33 7.1.5 Uniformity .................................... 34 7.2 Specific Metrics ..................................... 34 7.2.1 Goodness Factor ................................ 34 7.2.2 Magnetic Flux Linkage ............................. 35 8 Optimised Design 36 8.1 Independent Design Parameters ........................... 36 8.2 Dependent Design Parameters ............................ 36 8.3 Optimisation of Key Parameters ............................ 36 8.3.1 Scale Factor and Rotor Material ....................... 37 8.3.2 AWG ........................................ 38 iii 8.3.3 Permanent Magnet Grade ........................... 38 9 Design for Manufacture 39 9.1 Concept Generation and Design Selection ..................... 39 9.2 Covid 19 .......................................... 40 9.3 Stator ........................................... 40 9.3.1 Windings ..................................... 41 9.4 Rotor ............................................ 41 9.4.1 Rotor Core .................................... 42 9.4.2 Support Structure ............................... 42 9.4.3 Prototype ..................................... 43 9.5 Permanent Magnet Synchronous Motor ....................... 43 9.5.1 Permanent Magnet Synchronous Rotor ................... 43 10 Testing Methodology 45 10.1 Sense Rig ......................................... 45 10.1.1 Peak Current .................................. 45 10.1.2 Peak Voltage ................................... 46 10.1.3 Flux Density ................................... 46 10.1.4 Angular Acceleration .............................. 46 11 Results 47 11.1 Characterisation of a Dysfunctional Omnidirectional Drive System ....... 47 12 Engagement with Open-Source Community 49 12.1 Hackaday ......................................... 49 12.2 YouTube .......................................... 49 13 Discussion 50 13.1 Future Work ....................................... 50 14 Appendix A ix 14.1 Motor Controller Theory ................................ ix 14.1.1 SPWM Production ............................... ix 15 Microcontroller theory x 15.0.1 Lower Frequency Limit ............................. x 15.0.2 Upper Frequency Limit ............................. xi iv 15.0.3 Interrupts .................................... xi 15.0.4 Component Selection ............................. xi 16 Appendix B xiii 17 Appendix C xix 17.1 Fritzing Diagram of 3 Phase Motor Controller .................... xxiii 18 Appendix D xxiv v NOMENCLATURE The next list... Physical Constants −12 −3 −1 ϵ0 Permittivity of Free Space 8:8542 × 10 m kg µS Relative Permeability of Mild Steel 1000 −3 ρCu1 Density of Copper 8; 940 kg:m −8 ρCu2 Resistivity of Copper 1:71 × 10 Ω:m −3 ρCu1 Density of Steel 7; 750 kg:m −7 ρCu2 Resistivity of Steel 1:18 × 10 Ω:m −3 ρCu1 Density of Aluminium 2; 700 kg:m −7 ρCu2 Resistivity of Aluminium 2:65 × 10 Ω:m −3 ρCu1 Density of ABS 1; 040 kg:m 16 ρCu2 Resistivity of ABS 1:50 × 10 Ω:m −3 ρCu1 Density of Air 1:225 kg:m 16 ρCu2 Resistivity of Air 1:30 × 10 Ω:m Design Parameters (Default Values) l Stator Width 0:06 m Rin Stator Inner Radius 0:05 m ϕ Phases 3 p Number of Poles 4 −3 δairgap Airgap 2 × 10 m Fbf Bearing Friction 0 N R Rotor Diameter 0:1 m δShell Shell Thickness 0:03 m ! Frequency 1 Hz Ipeak Current Limit 4 A Vpeak DC Source Voltage 12 V R0 DC Internal Resistance 1:5 Ω Rload Additional Circuit Resistance 0 Ω Slotw Slot Width 0:005m vi Sloth Slot Height 0:01m N45 Neodymium Magnet Rating −3 XPM Permanent Magnet Cube Length 5 × 10 m Key Design Parameter MShell Rotor Shell Material MCore Rotor Core Material SF Linear Size Scale Factor ACoil American Wire Gauge of Coil AW G Physical Quantities E Electric Flux Density C:m−2 B Magnetic Flux Density T Φ Magnetic Flux Linkage T G Goodness Factor qenc Enclosed Charge C Ienc Enclosed Current A S Slip J Current Density Am−2 XL Reactance Ω XR Resistance Ω Z Impedance Ω Mathematical Notation −! B Denotes Vector Field × Denotes Cross Product ◦ Denotes Dot Product n^ Denotes Normal Vector H Denotes Surface Integral vii ACKNOWLEDGEMENTS I would like to take this opportunity to thank the following