Design of a Low-Mass High-Torque Brushless Motor for Application in Quadruped Robotics
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Design of a Low-Mass High-Torque Brushless Motor for Application in Quadruped Robotics by Niaja Nichole Farve B.S., Electrical Engineering, Morgan State University, 2010 Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science MASSACHUSETTS IN at the OF TECHNOLO( MASSACHUSETTS INSTITUTE OF TECHNOLOGY JUL 0 1 201 June 2012 LIBRARIE @ Massachusetts Institute of Technology 2012. All rights reserved. ARCHIVES Author ( .... ... ......................................... Depar en Uoofiectrical Engineering and Computer Science May 23, 2012 /1 ///i / Certified by ....................... .. ... ... .' I Jeff rey H. Lan Professor of Electrical Engineering and omputer Science Thesis Supervisor A ccepted by ................. .............. C r Dmeei A. Kolodziejski Chairman, Department Committee on Graduate Students 2 Design of a Low-Mass High-Torque Brushless Motor for Application in Quadruped Robotics by Niaja Nichole Farve Submitted to the Department of Electrical Engineering and Computer Science on May 23, 2012, in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science Abstract The Biomimetic Robotics Group is attempting to build the fastest quadruped robot powered by electromagnetic means. The limitations in achieving this goal are the torque produced from motors used to power the robot, as well as the mass and power dissipation of these motors. These limitations formulate the need for a low- mass high-torque low-loss motor. This thesis outlines the process of designing a permanent-magnet synchronous motor that meet the goals of the robot while mini- mizing the total mass. The motor designed from this thesis is compared to motors currently used by the Group when quantifying improvements made. In the process of achieving the goal, a design was formulated using fundamental electromagnetic prin- ciples. This design was then tested using finite element analysis. The final design was fabricated in house and wired by hand. The fabricated motor was tested to quantify key performance parameters such as peak cogging torque, peak motor torque, and thermal time constant under robot conditions. The motor designed by this thesis was able to produce more torque than the current motor being used by the Biomimetic Robotics Group, by a factor of 1.6, while decreasing the mass by 23%. A lower than desired packing factor was achieved since the motor was wired by hand resulting in a higher power dissipation and lower than expected motor torque. This design will be used in the quadroped robot after improvements are made to the cogging torque and packing factor. Thesis Supervisor: Jeffrey H. Lang Title: Professor of Electrical Engineering and Computer Science 3 4 Acknowledgments "Gratitude is a quality similar to electricity: it must be produced and discharged and used up in order to exist at all" ~William Faulkner I am beyond grateful for the never ending number of friends and family present in my life that encourage and inspire me everyday. Without which every mountain climbed would have been unfathomably higher. I wish I could name every person, but I think the list would exceed this thesis. I am especially grateful for my mother, role model, and best friend. You have pushed me to try even when success seemed impossible. You have always been there to help fix my problems and see the rainbow in the storm. I hope to one day become half the mother you have been to me. MIT would not have been as enjoyable without the man in my life that has been unbelievably understanding and encouraging, Omar. The friends I left at Morgan have also sporadicly brightened my weekends at MIT with their visits, reminding me of what great life long friends I have made. Likewise, new friends made here at MIT have helped to put things in perspective and gave my a small group where I feel like "I belong". Thank you for always being there to give me a reality check and helping me enjoy life. I don't think I could have possibly found a better adviser. Thank you Jeff for being beyond patient and spending so much of your precious time with my endless questions. I am also grateful to this institution as well as the RLE lab for giving my the chance to succeed in such a rigorous and challenging environment. I have grown in ways unimaginable due to my experience here. This work was funded by a Brookhaven National Laboratory Masters GEM Fel- lowship, and the DARPA grant 019719-001. The Biomemtic Robotics Group also provided funding and a tremendous amount of support. I am grateful for each of these resources and would not have been able to complete this thesis without this 5 support. 6 Contents 1 Introduction 11 1.1 Project Description .. ... ... ... ... ... .... ... ... 11 1.2 Robot Description .. ... ... ... ... ... .... ... ... 12 1.3 Application .. .... .... ... .... ... .... ... .... 13 1.4 First-Pass Comparison .... .... .... .... .... .... 13 1.5 Approach . .... ... .... .... ... .... ... .... ... 15 1.6 Challenges . ... ... ... ... ... ... ... .... ... ... 20 2 Formulation 23 2.1 Simplified Model .... .... .... .... ..... .... .... 23 2.2 Magnet Model. .. .. ... ... ... .. ... ... ... .. ... 23 2.3 Current Model .. ... ... ... .... ... ... ... ... ... 28 2.4 Combining models .. .... ..... .... .... .... .... 30 2.5 Design Parameters ..... ..... ..... ..... ..... ... 32 2.6 Optimization .... ... .... ... .... ... .... ... ... 36 3 Design 39 3.1 Materials .. ... ... ... .. ... ... ... ... .. ... ... 39 3.2 Dimensions .. ... ... ... ... .. ... ... ... .. ... .. 39 3.3 Mass and Rotor Inertia Calculations ... ... ... ... ... ... 43 3.4 Resistance and Inductance Calculations .. .... .... ... .... 43 3.5 Finite Element Analysis .... .... ..... .... .... .... 45 7 4 Fabrication 49 4.1 Hardware ................................. 49 4.1.1 Laminations .. ..... ..... .... ..... ..... .. 49 4.1.2 M agnets ... .... ..... ..... .... ..... .... 54 4.1.3 W ire ...... ........ ........ ....... ... 54 4.2 Procedure ..... ..... ..... ..... ..... ..... ... 54 4.2.1 Winding Process ... ...... ..... ...... ..... 55 4.2.2 Magnet Alignment . ..... ..... .... ..... .... 55 4.2.3 Encasing Stator and Rotor ..... ...... ..... .... 58 5 Testing 61 5.1 Resistance ... ..... ..... ..... ..... ..... ..... 61 5.2 Inductance .... .. ... .... .... ..... .... .... 63 5.3 Back EMF. .... .. ..... ..... ..... ..... ... 64 5.4 Cogging Torque ... ..... .... .... .... .... .... .. 67 5.5 Thermal Performance. .. .... .... .... .... ..... ... 68 5.6 R esults ...... ...... ....... ...... ...... .... 71 6 Conclusion 75 6.0.1 Future Work. ..... ..... .... ..... ..... .. 76 A MATLAB Script 79 B FEA Settings 91 B.1 COMSOL Setup ..... ..... ..... ..... ..... ..... 91 B.2 COMSOL Settings ....... ...... ...... ...... ... 92 C Cogging Torque Experimental Data 95 C.1 Measured Data . ...... ....... ...... ...... .... 95 D Thermal Resistance Experimental Data 97 D.1 Measured Data . ... ... ... ... ... ... .... ... ... 97 8 List of Figures 1-1 MIT Cheetah Robot conceptual design. ... ..... ..... .... 12 1-2 Power dissipation versus mass trade off curve for doubly-wound motor near 2400 W. Each data point represents the performance of one motor design ... .... .... .... .... .... .... .... .... 16 1-3 Power dissipation versus mass trade-off curve for permanent-magnet motor at 40 Nm over a wide power range. Each data point represents the performance of one motor design. .... .... .... .... 16 1-4 Power dissipation versus mass trade-off curve for permanent magnet motor near 2400 W at 40 Nm. This figure is an expansion of Figure 1-3. ....... ... .................................... 17 1-5 Power dissipation versus mass trade-off curve for permanent magnet motor near 2400 W at 50 Nm. .. .... .... .... .... ... 17 1-6 Power dissipation versus mass trade-off curve for permanent-magnet motor at 50 Nm over a wide power range. Each data point represents the performance of one motor design. .. .... ..... ..... 18 1-7 Fundamental motor layout . .... ..... ..... ..... .... 18 1-8 Example of motor flux lines .... .... .... .... .... ... 19 1-9 Design approach flow chart. .... ...... ...... ....... 21 2-1 Magnet only model for the designed motor. ... ... ... .... .. 24 2-2 Current only model for the designed motor. ... .... ... .... 29 2-3 Complete model for the designed motor. ... ... ... ... ... 31 2-4 Resistance Calulation .. ... ... .... ... ... ... ... ... 35 9 2-5 Chart of all designed dimensions. ................. 37 3-1 Final motor design front view illustrated with MATLAB. .... 40 3-2 Final motor design side view illustrated with MATLAB..... 41 3-3 Hyperco 50 B-H curve used as a design input. .......... 42 3-4 Magnetic field lines for designed motor depicted with COMSOL. 46 3-5 Motor torque profile data collected from COMSOL. ...... 46 3-6 Cogging torque derived through FEA ......... ...... 47 4-1 Complete motor 2D image. ....... ... 50 4-2 Complete motor of 3D image...... 51 4-3 Drawing of designed stator ... .... .... 52 4-4 Drawing of stator zoomed in. ..... ... 53 4-5 Phase A beginnging the wiring process . .. 56 4-6 Phase B beginnging the wiring process . ... 56 4-7 Phase C beginnging the wiring process ... 56 4-8 Winding Process ............ .. .. 57 4-9 Magnet and Rotor ........... .. 58 4-10 Complete Motor ............. .. 59 5-1 Moment arm addition made to the motor ... ... 62 5-2 Measured back EMF from experiments ......