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The Benefits of Four-Wheel Drive for a High-Performance FSAE Electric Racecar Elliot Douglas Owen

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The Benefits of Four-Wheel Drive for a High-Performance FSAE Electric Racecar Elliot Douglas Owen The Benefits of Four-Wheel Drive for a High-Performance FSAE Electric Racecar by Elliot Douglas Owen Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Bachelor of Science in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2018 c Elliot Douglas Owen, MMXVIII. All rights reserved. The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created. Author.................................................................... Department of Mechanical Engineering May 18, 2018 Certified by . David L. Trumper Professor Thesis Supervisor Accepted by . Rohit Karnik Associate Professor of Mechanical Engineering Undergraduate Officer 2 The Benefits of Four-Wheel Drive for a High-Performance FSAE Electric Racecar by Elliot Douglas Owen Submitted to the Department of Mechanical Engineering on May 18, 2018, in partial fulfillment of the requirements for the degree of Bachelor of Science in Mechanical Engineering Abstract This thesis explores the performance of Rear-Wheel Drive (RWD) and Four-Wheel Drive (4WD) FSAE Electric racecars with regards to acceleration and regenerative braking. The benefits of a 4WD architecture are presented along with the tools for further optimization and understanding. The goal is to provide real, actionable information to teams deciding to pursue 4WD vehicles and quantify the results of difficult engineering tradeoffs. Analytical bicycle models are used to discuss the effect of the Center of Gravity location on vehicle performance, and Acceleration-Velocity Phase Space (AVPS) is introduced as a useful tool for optimization. Lap-time Simulation is used to determine the regenerative braking energy available for recovery during a race for RWD and 4WD vehicles. Thesis Supervisor: David L. Trumper Title: Professor 3 4 Acknowledgments This thesis is dedicated to MIT Motorsports, because racecar. I have many people to thank for my current state in life. My family has enabled me to attend MIT and apply myself whole-heartedly to mechanical engineering. My parents have always been extremely supportive of my projects even when it means they cannot walk into my room due to unorganized piles of hardware on the floor. It is a small miracle no one ever impaled their foot on a 6-32 tap. My brother has always served as an example of academic discipline and I have learned much from him. MIT, the mechanical engineering department, its professors, the GEL program, and the Edgerton Center have all provided incredible opportunities to learn why things break, make yo-yos, lead projects, and turn big pieces of metal into smaller pieces of metal. My teammates and peers have created the amazing environment that allows FSAE to flourish, and allowed me to push myself on large projects like the MY2017 battery pack. No one person can build a racecar alone, and I feel very fortunate to have seen the early years of the team's struggle to get a vehicle to turn on. We have come so far since the dark days of MY2014 and MY2015 and still have very far to go. Special thanks to Orlando Ward, Kevin Chan, Brian Sennett, Nelson Brock, Andrew Carlson, Roberto Melendez, Sammi Bray, Luis Mora, Cheyenne Hua, Henry Merrow, and Ethan Perrin for teaching me and helping me with the battery. A final shoutout to a chance encounter with Adam from the CTU Prague Team at the 2016 competition who destroyed all the American teams. Your advice has proved very helpful. \I will share another, maybe the most important experience: The only thing that can stop you from achieving your goal is you. Literally." - Adam Podhrazsky Thanks to all my friends at MIT and around the country for their surprising acceptance of \that racecar thing" I do. Thanks to Susan Nitta, Kayla Rajsky, Katherine Paseman, and Becky Steinmeyer for all their mentorship. Finally, thanks to my amazing girlfriend, Ka-Yen Yau, for her unending kindness, support, and impeccable comma usage. Roll Tech! 5 Story of this Thesis This thesis was born from the desire to make MIT Motorsport's MY2019 vehicle better than MY2018. During December of 2017, I thought about improving car performance in quantifiable terms such as power, mass, drag, and efficiency. I determined that the Power to Mass Ratio (PTMR) of a vehicle was critically important, but I still knew very little about vehicle design. I tried analyzing a simple bicycle model of a rear-wheel drive racecar and realized that something as trivial as Center of Mass location played an enormous role in the maximum acceleration of a vehicle. I tried to separately analyze improved power to mass ratio and improved traction, but was looking for a single way to characterize the entire performance of the vehicle. In late December, I stumbled upon a way to visualize all the limits of the vehicle simultaneously and started my exploration of Acceleration-Velocity Phase Space (AVPS)-which will be discussed thoroughly. In the beginning of January, I traveled through Europe to visit six of the top FSAE Electric and Combustion teams. The trip was eye-opening. I left convinced that the Euro- pean teams did everything better than their counterparts in the States. They had lighter and more powerful batteries, Four Wheel Drive (4WD), carbon fiber monocoque frames and custom made everything. After that trip, my focus turned to 4WD. How important was it? Could MIt even do it? I started looking for motors, but realized I didn't even know what to look for. This pushed me to develop more complicated analytical bicycle models to estimate vehicle acceleration. From there, I started to integrate aerodynamic effects, tire models and bicycle models into AVPS. With an analytical framework to estimate vehicle performance, I then set to learn as much as I could about the benefits of 4WD. I realized that a vehicle doesn't need a very powerful front powertrain to achieve high acceleration. However, my experience in Europe showed that many teams used high power motors on the front. To figure out what sort of power was really necessary, I started to analyze regenerative braking. My investigation led me to lap-time simulation and to the realization of a strong and weak 4WD architecture. Taking this knowledge back to the AVPS models, I realized that the power-limited region offered even more opportunities for vehicle-level optimization. 6 Contents 1 FSAE Background . 15 1.1 FSAE Electric Competition . 15 1.2 MIT Motorsports Recent History . 15 1.3 State of the Art in Formula Student Electric . 17 2 Four-Wheel Drive Background . 18 2.1 Preliminary Appeal of 4WD . 18 2.2 Scope of this Thesis . 19 2.3 Common Models: Point Mass, Bicycle, and Two-Track . 19 3 Acceleration Analysis . 21 3.1 Summary of Benefits and Approaches . 21 3.2 Bicycle Models . 22 3.3 Tire Load Sensitivity . 28 3.4 Load Sensitive Rear-Wheel Drive (LSRWD) . 29 3.5 Load Sensitive Four-Wheel Drive (LS4WD) . 32 3.6 Aerodynamic Forces . 36 3.7 Preliminary Front-Rear Power Split . 40 3.8 Practical Limits to Acceleration Curves . 42 3.9 Acceleration-Velocity Phase Space . 43 3.10 Fine Tuning AVPS Models . 50 3.11 Preliminary Acceleration Takeaways . 55 3.12 Power Split in the Power Limited Region . 55 3.13 Weak and Strong 4WD . 56 3.14 Acceleration Takeaways . 64 7 3.15 Sensitivities and Final Comments . 64 4 Endurance Analysis . 65 4.1 Limitations of the Point Mass Model . 66 4.2 The Importance of Regenerative Braking . 67 4.3 Outputs of OptimumLap . 69 4.4 Preliminary Endurance Takeaways . 72 4.5 Power Split During Braking . 73 4.6 Braking Power Distributions . 76 4.7 Final Comments . 79 5 Next Steps . 80 8 List of Figures 1.1 MIT Motorsports MY2017 Vehicle . 16 1.2 AMZ Racing's Pilatus Vehicle . 17 2.1 Point Mass Model . 20 2.2 Bicycle Model Sketch . 20 2.3 Two Track Model . 21 3.1 Bicycle Model FBD . 23 3.2 RWD G's by CG Location . 25 3.3 RWD G's with Reasonable CG . 26 3.4 Bicycle Model FBD . 27 3.5 Load Sensitivity Plot . 28 3.6 LSRWD G's by CG . 31 3.7 LSRWD G's with Reasonable CG . 32 3.8 LS4WD G's by CG Location . 34 3.9 LS4WD G's with Reasonable CG Location . 35 3.10 Comparison Between Models by CGx . 36 3.11 Aerodynamic Forces . 37 3.12 Aerodynamic FBD . 38 3.13 Model Acceleration with Aero . 39 3.14 4WD Acceleration by Front and Rear . 41 3.15 LS4WD Power Split . 42 3.16 AVPS Acceleration Limited . 44 3.17 AVPS Acceleration Limited Simulation . 45 3.18 AVPS Acceleration and Speed Limited . 46 9 3.19 AVPS Acceleration and Speed Limited Simulation . 47 3.20 AVPS Acceleration, Speed and Power Limited . 48 3.21 AVPS Acceleration, Speed, and Power Limited Simulation . 49 3.22 AVPS Model for LS4WD Standard Car . 51 3.23 AVPS LS4WD Simulation . 52 3.24 AVPS Model for LSRWD Standard Car . 53 3.25 AVPS LSRWD Simulation . 54 3.26 LS4WD AB Plot V = 0 . 58 3.27 LS4WD AB Plot V = 20 . 59 3.28 Constant Force Contour at V = 20 . 60 3.29 Strong and Weak Power Split . 61 3.30 Strong and Weak Force Split . 62 3.31 Strong and Weak Torque Split . 63 4.1 OptimumLap Simulation . 66 4.2 MY2017 Battery Discharge Curve . 68 4.3 Longitudinal Braking Forces . 70 4.4 Normalized Braking Power . 71 4.5 Braking Energy . 72 4.6 Vehicle Normal Forces . 74 4.7 Vehicle Traction Forces .
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