University of Southern Queensland Faculty of Health, Engineering & Sciences Optimisation of the Spoked Bicycle Wheel Submitted by Jason Keller In fulfilment of the requirements of the ENG4112 Research Project towards the degree of Bachelor of Engineering (Mechanical, in full) Submitted: October, 2013 {Page left intentionally blank} Optimisation of the Spoked Bicycle Wheel ABSTRACT Despite the long history of bicycle wheels, there has been very few design changes because the current design is known to work. This study aimed to develop a method to provide optimised spoking geometries for rear bicycle wheels. MATLAB® was used to optimise the spoke geometries based on the best combination of torsional and lateral stiffness. The developed script can be easily adapted to calculate the optimised geometry for any wheel with tensioned spokes. The load responses of the optimised wheels were then compared with conventional 2X and 3X spoke patterns and three commercially available wheels using ANSYS® FEA software. When the optimised geometries were simulated in ANSYS® under torsional, radial and lateral loads, their performance was better than the conventionally spoked and commercial wheels that had similar specifications. These results confirmed that wheel design can be improved. The recommended guidelines produced in this study only apply to the wheel geometries contain herein, as certain limits were imposed on the hub flange radius and the spoke diameters. Limitations on the use of existing theoretical models have also been identified. Keywords: Bicycle wheel, rear wheel, dished wheel, ANSYS, MATLAB, torsional stiffness, lateral stiffness, design, optimisation. [i] University of Southern Queensland Faculty of Health, Engineering and Sciences ENG4111 & ENG4112 Research Project Limitations of Use The Council of the University of Southern Queensland, its Faculty of Health, Engineering & Sciences, and the staff of the University of Southern Queensland, do not accept any responsibility for the truth, accuracy or completeness of material contained within or associated with this dissertation. Persons using all or any part of this material do so at their own risk, and not at the risk of the Council of the University of Southern Queensland, the Faculty of Health, Engineering & Sciences or the staff of the University of Southern Queensland. The dissertation reports an educational exercise and has no purpose or validity beyond this exercise. The sole purpose of the course pair entitled “Research Project” is to contribute to the overall education within the student’s chosen degree program. This document, the associated hardware, software, drawings, and other material set out in the associated appendices should not be used for any other purpose: if they are so used, it is entirely at the risk of the user. Dean Faculty of Health, Engineering & Sciences [ii] Optimisation of the Spoked Bicycle Wheel CERTIFICATION I certify that the ideas, designs and experimental work, results, analyses and conclusions set out in this dissertation are entirely my own effort, except where otherwise indicated and acknowledged. I further certify that the work is original and has not been previously submitted for assessment in any other course or institution, except where specifically stated. Jason Peter Keller Student Number: 0050093222 __________________________________ Signature __________________________________ Date [iii] Optimisation of the Spoked Bicycle Wheel ACKNOWLEDGEMENTS This research was carried out under the principal supervision of Dr. Ray Malpress. His help and guidance has been welcomed throughout and I would like to thank him for always being available when I needed him. I would also like to thank all of the USQ library staff for their dedication and success in gaining access to many out of publication texts. Without this help the work contained within this document would not have been possible. Finally, thanks go to my family, for providing an ear to listen, a shoulder to cry on and providing secretarial relief during the development of my spread sheets. Even though only a small contribution, the time away from the computer screen was much appreciated. [iv] Optimisation of the Spoked Bicycle Wheel TABLE OF CONTENTS ABSTRACT .............................................................................................................. i CERTIFICATION ......................................................................................................... iii ACKNOWLEDGEMENTS ........................................................................................... iv LIST OF FIGURES ..................................................................................................... viii LIST OF TABLES .......................................................................................................... x NOMENCLATURE ..................................................................................................... xiii GLOSSARY OF TERMS ............................................................................................ xiv CHAPTER 1 - BACKGROUND ................................................................................ 1 1.1 Outline of the Study ........................................................................................... 1 1.2 Introduction ........................................................................................................ 2 1.3 The Problem ....................................................................................................... 3 1.4 Spoked Wheel Design Variables ........................................................................ 3 1.5 Project Objectives ............................................................................................... 4 1.6 Wheel Buckling .................................................................................................. 6 1.7 Conclusion .......................................................................................................... 7 CHAPTER 2 - LITERATURE REVIEW ................................................................. 8 2.1 Introduction ........................................................................................................ 8 2.1.1 A note on A.J.S Pippard and his work on the theory of the spoked wheel . 8 2.2 The Spoked Bicycle Wheel ................................................................................ 9 2.2.1 History of the Spoked Wheel .................................................................... 10 2.2.2 Theoretical Analysis of the Spoked Wheel ............................................... 13 2.2.3 Finite Element Analysis of the Spoked Wheel ......................................... 18 2.2.4 Experimental Studies of the behaviour of a Spoked Bicycle Wheel ........ 22 2.2.5 Identified areas where further study is required ........................................ 29 2.3 Conclusions from literature .............................................................................. 31 CHAPTER 3 - METHODOLOGY .......................................................................... 32 [v] Optimisation of the Spoked Bicycle Wheel 3.1 Introduction ...................................................................................................... 32 3.2 The Optimisation Method................................................................................. 33 3.2.1 How Version 1.0 of the code works .......................................................... 34 3.3 The CAD models .............................................................................................. 38 3.4 Simulation of the optimised wheel geometries and commercial wheels .......... 40 3.4.1 Simulation Pre-processing ........................................................................ 42 3.4.2 Simulation Post-Processing ....................................................................... 46 3.5 Laboratory Test Procedure ............................................................................... 48 CHAPTER 4 - RESULTS AND VALIDATION .................................................... 51 4.1 The MATLAB® Optimisation Results ............................................................ 51 4.1.1 20 Spoke Wheels Optimisation Results and Discussion ........................... 52 4.1.2 24 Spoke Wheels Optimisation Results and Discussion ........................... 53 4.1.3 28 Spoke Wheels Optimisation Results and Discussion ........................... 53 4.1.4 32 Spoke Wheels Optimisation Results and Discussion ........................... 55 4.1.5 36 Spoke Wheels Optimisation Results and Discussion ........................... 55 4.1.6 48 Spoke Wheels Optimisation Results and Discussion ........................... 56 4.1.7 Conclusions from MATLAB® ................................................................. 57 4.2 The CAD Models of the optimised geometries ................................................ 60 4.3 The Finite Element Analysis Results ............................................................... 63 4.3.1 Validation of the FE Analysis ................................................................... 64 4.4 Radial, Lateral and Torsional Stiffness values calculated from the FE Analysis .......................................................................................................................... 72 4.4.1 Acceptance of the calculated radial stiffness values ................................. 74 4.4.2 Acceptance of the calculated lateral stiffness values ...............................