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Influence of Frame Stiffness and Rider Position on Bicycle Dynamics: an Analytical Study Trevor Alan Williams University of Wisconsin-Milwaukee

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Influence of Frame Stiffness and Rider Position on Bicycle Dynamics: an Analytical Study Trevor Alan Williams University of Wisconsin-Milwaukee University of Wisconsin Milwaukee UWM Digital Commons Theses and Dissertations August 2015 Influence of Frame Stiffness and Rider Position on Bicycle Dynamics: An Analytical Study Trevor Alan Williams University of Wisconsin-Milwaukee Follow this and additional works at: https://dc.uwm.edu/etd Part of the Engineering Commons Recommended Citation Williams, Trevor Alan, "Influence of Frame Stiffness and Rider Position on Bicycle Dynamics: An Analytical Study" (2015). Theses and Dissertations. 985. https://dc.uwm.edu/etd/985 This Thesis is brought to you for free and open access by UWM Digital Commons. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of UWM Digital Commons. For more information, please contact [email protected]. INFLUENCE OF FRAME STIFFNESS AND RIDER POSITION ON BICYCLE DYNAMICS: AN ANALYTICAL STUDY by Trevor Williams A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in Engineering at The University of Wisconsin-Milwaukee August 2015 ABSTRACT INFLUENCE OF FRAME STIFFNESS AND RIDER POSITION ON BICYCLE DYNAMICS: AN ANALYTICAL STUDY by Trevor Williams The University of Wisconsin-Milwaukee, 2015 Under the Supervision of Professors Anoop Dhingra and Sudhir Kaul Advanced analytical and computational capabilities are allowing researchers to enhance the model complexity of bicycles and motorcycles in order to understand handling, stability and dynamic behavior. These models allow designers to investigate new frame layouts, alternative materials and different architectures. The structural stiffness of a frame plays a critical role in the handling behavior of a bike. However, the influence of structural stiffness has received limited attention in the existing literature. This study attempts to fill the gap by presenting analytical results that investigate the influence of structural stiffness in conjunction with rider positions on three distinct bicycle layouts. The analytical model consists of four rigid bodies: rear frame, front frame (front fork and handle bar assembly), front wheel and rear wheel. The overall model exhibits three degrees-of-freedom: the roll angle of the frame, the steering of the front frame and the rotation of the rear wheel with respect to the frame. The rear frame is divided into two parts, the rider and the bicycle frame, that are assumed to be rigidly connected. This is done in order to allow the model to account for varying rider positions. The influence of frame flexibility is studied by coupling the structural stiffness of the frame to the governing equations of motion. The governing equations of motion from a benchmark bike in the existing literature have been used, and then modified to accommodate rider positions and frame stiffness. Layouts from the benchmark bicycle, a commercially manufactured bicycle, and a cargo bicycle are used ii for this study in conjunction with rider positions ranging from a no hands position to a small aero tuck. The results are analyzed and compared with some proven analytical and experimental results in the existing literature. Results indicate that some of the rider positions can play a significant role in influencing the dynamic characteristics of a bike. Structural stiffness is seen to significantly affect the weave mode when the stiffness is reduced substantially. It is observed that the forward and lower rider positions are generally associated with a faster speed for onset of self-stability, that additionally last for a longer range of speeds. Furthermore, addition of a large luggage load to the cargo bike is seen to have a stabilizing effect as well as increase instability sensitivity to stiffness. Overall, it is observed that the inclusion of frame stiffness and an assessment of the distribution of a rider’s mass are important factors that govern the dynamic behavior of a bike, and should therefore be carefully evaluated. iii © Copyright by Trevor Williams, 2015 All Rights Reserved iv TABLE OF CONTENTS Chapter 1: Introduction ................................................................................................................... 1 1.1 Scope of Thesis ....................................................................................................................... 2 1.2 Overview of Thesis ................................................................................................................. 3 Chapter 2: Literature Review ........................................................................................................... 5 2.1 Rider and Frame Permutations .............................................................................................. 6 2.2 Frame Stiffness....................................................................................................................... 8 2.3 Conclusions .......................................................................................................................... 10 Chapter 3: Theoretical Background ............................................................................................... 12 3.1 Mathematical Modeling ....................................................................................................... 12 3.2 Geometric Modeling ............................................................................................................ 20 3.2.1 Rider Modeling .............................................................................................................. 20 3.2.2 Frame Modeling ............................................................................................................ 25 3.3 Finite Element Model ........................................................................................................... 32 3.4 Numerical Simulation ........................................................................................................... 37 Chapter 4: Frame Geometry and Rider Positions .......................................................................... 39 4.1 The Eigenvalue Problem ...................................................................................................... 39 4.2 Benchmark Bicycle ............................................................................................................... 42 4.3 Jamis Bicycle ......................................................................................................................... 44 4.4 Cargo Bicycle ........................................................................................................................ 49 Chapter 5: Frame Flexibility ........................................................................................................... 56 5.1 Jamis Bicycle ......................................................................................................................... 56 5.2 Cargo Bicycle ........................................................................................................................ 61 5.3 Modal Analysis ..................................................................................................................... 70 Chapter 6: Conclusion and Future Scope ....................................................................................... 74 6.1 Conclusions .......................................................................................................................... 74 6.2 Future Research ................................................................................................................... 77 REFERENCES ................................................................................................................................... 79 v LIST OF FIGURES Figure 3-1: Bicycle model with coordinate system ........................................................................ 13 Figure 3-2: Rider positions from left to right: No Hands, Relaxed, On Hoods ............................... 23 Figure 3-3: Rider positions from left to right: Aerobars and Aero Tuck ........................................ 24 Figure 3-4: Jamis Satellite bicycle .................................................................................................. 25 Figure 3-5: Cargo bicycle by Third Coast Bike Works ..................................................................... 26 Figure 3-6: Example of butted tubing ............................................................................................ 26 Figure 3-7: Parametric model of the Cargo bicycle ....................................................................... 28 Figure 3-8: Parametric model of the Jamis Satellite ...................................................................... 29 Figure 3-9: Wheel height effect on trail and steering tilt .............................................................. 31 Figure 3-10: Simplified ANSYS Jamis model ................................................................................... 33 Figure 3-11: Simplified ANSYS Cargo model .................................................................................. 33 Figure 4-1: Eigenvalues of Weave modes of a loaded Cargo bicycle with no rider ....................... 40 Figure 4-2: Real Weave eigenvectors of loaded Cargo bicycle with no rider ................................ 41 Figure 4-3: Imaginary Weave eigenvectors of loaded Cargo bicycle with no rider ....................... 41 Figure 4-4: Benchmark bicycle eigenvalues, natural frequency, and damping ratio .................... 44 Figure 4-5: Jamis
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