U UNIVERSITY OF CINCINNATI Date: I, , hereby submit this original work as part of the requirements for the degree of: in It is entitled: Student Signature: This work and its defense approved by: Committee Chair: Approval of the electronic document: I have reviewed the Thesis/Dissertation in its final electronic format and certify that it is an accurate copy of the document reviewed and approved by the committee. Committee Chair signature: Torsional Stiffness Measuring Machine (TSMM) & Automated Frame Design Tools William Thomas Steed March. 6, 2010 Bachelor of Science in Mechanical Engineering Masters of Science in Mechanical Engineering College of Engineering Committee Chair: Randall Allemang Abstract Designing an automotive chassis is not an intuitive process. It, at times, can be very difficult depending on the geometry of the structure. Research was conducted at the University of Cincinnati to alleviate the burden of this task. Software tools were developed to help speed the design process. A new technique of measuring the torsional stiffness of a Formula SAE chassis design was created. Finally, a recommended process is presented to perform the design and validation of a Formula SAE chassis. As engineers we turn to different tools that we have access to in order to understand and iterate a design. In the area of space frames, design tools can be limited. To get an understanding of a chassis design, engineers turn to Finite Element Analysis (FEA) to gain a better understanding of these types of structures. Ultimately, manual iterations are not enough to completely optimize a structure to a desired goal. Software tools need to be developed in order to have a deep understanding of how the structure performs at each iteration. Two tools, a sensitivity and optimization tool, were written and the out come of each is discussed. Until 2007, the UC Formula SAE team has validated only the current year’s frame design and not the entire chassis design. In the world of Formula One racing it is essential to have knowledge not only of frame stiffness but also hub to hub chassis stiffness. Various ways to test chassis stiffness were investigated and designed. A static test was developed and performed. A finite element model and its correlation to this static test is discussed. ii COPYRIGHT NOTICE iii Acknowledgement This thesis has been the greatest culmination to an engineer-in-training process. I have great admiration for the following people because of their eagerness to help, their ambition to learn and their patience to listen and mature my ideas. Thank you: • To the “man upstairs” for giving me all the wonderful blessings of this life and sharing with me in all these years. • To my family for always believing in me, providing for me and giving me inspiration to be the best engineer I know how to be. • To the University of Cincinnati for providing a faculty of the best engineering professors and learning facilities to chase a student’s dream. • To Doctor Randall Allemang, for giving me the freedom to explore my ideas and for being a superb engineering role model. • To Doctor Allyn Phillips for aiding in the development of my Matlab skills and for your patience while I shared the lab’s equipment. • To my thesis committee. Thank you for your thoughts and time. • To Douglas Hurd and David Breheim. Thank you for expert advice and patience. • To the 2005 - 2007 University of Cincinnati FSAE teams for sharing your ideas, your talents and your passion for building race cars and believing that this research can provide a deeper understanding of each design. • To my colleague Benjamin Stoney; without your help this would not have been possible. Thanks brother, for working as hard on these cars as you do and for all the great welds. • To my colleague Fredrick Jabs for conversing with me to mature my ideas and pushing the limits of engineering design. • To my colleague Ryan Lake for setting great examples for future teams and engineering students. Thanks for your thoughts and time. It has been fun! • To my colleague David Moster for all the long loud years of learning how to become great engineers. Thanks for keeping us fast! • To my colleagues Ben Rawe, Abbey Yee, Ravi Mantrala and Bill Wise for the extra thoughts and hands they provided during testing. • To my colleague Dan Alford for your support and dedication to getting the University of Cincinnati FSAE back to top 5. • To Carroll Smith for creating a collegiate activity that challenges engineers to be better than ever could have thought they could be. Preparing for and competing in this series has been the one of the greatest accomplishment of my life. This thesis is dedicated to my family and friends: Margaret and Ray Winialski, William, Brian, Kathleen, Edward & Jean Steed, Robert Boehm, Sara, Grant, & William Leto, Mary Ann & Norman Noe, Josh Kullis, Sindney Tippet & Paul Tinetti. iv Table of Contents Chapter 1: Development of the Race Car Frame ................................................................ 1 The Ladder Frame ........................................................................................................... 2 The Space Frame............................................................................................................. 3 The Composite Monocoque ............................................................................................ 4 Chapter 2: Background ....................................................................................................... 7 Chapter 3: Frame Model ................................................................................................... 11 Geometry Construction ................................................................................................. 12 Element Types .............................................................................................................. 14 Material & Section Properties ....................................................................................... 16 Meshing......................................................................................................................... 18 Frame Model Design Iterations & Constraints ............................................................. 19 Chapter 4: Chassis Model ................................................................................................. 24 Why Model the Chassis? .............................................................................................. 25 Revolute Joint ............................................................................................................... 30 Model Constraints ......................................................................................................... 33 Chapter 5: Sensitivity Analysis & Optimization Tools .................................................... 36 Chapter 6: Torsional Stiffness Measuring Machine (TSMM) .......................................... 44 Fixture ........................................................................................................................... 46 Mechanical Fuse ........................................................................................................... 49 Strain Gauge Setup ....................................................................................................... 52 Strain Gage Installation................................................................................................. 53 Strain Gage Wiring ....................................................................................................... 53 LVDT Calibration ......................................................................................................... 55 Testing........................................................................................................................... 56 Chapter 7: Conclusion / Future Recommendations .......................................................... 61 Conclusion .................................................................................................................... 61 Design Tools ................................................................................................................. 63 Torsional Stiffness Measuring Machine ....................................................................... 65 Appendix A FEA Checklist .............................................................................................. 70 Appendix B Scripts ........................................................................................................... 71 Torsional Stiffness Script .............................................................................................. 71 Sensitivity/Eigen Value Analysis Script ....................................................................... 72 Create Combo Script ..................................................................................................... 74 TSMM Post-Processing Script (ctorsion.m) ................................................................. 77 Appendix C: ITER06 Sensitivity Analysis ....................................................................... 78 Appendix D: ITER07 Sensitivity Analysis ....................................................................... 85 Appendix E: LVDT Calibration Curves ........................................................................... 93 Appendix F: Load Cylinder Calibration Curves ............................................................... 94 Appendix G: Torsional Stiffness