ANALYSIS OF AN ARCHERY BOW USING FINITE ELEMENT METHOD AND THE DEVELOPMENT OF AN ARCERY BOW SHARVEENESH A/L VATHIVELLU Report submitted in partial fulfillment of the requirements for the awards of Bachelor of Mechanical Engineering Faculty of Mechanical Engineering UNIVERSITI MALAYSIA PAHANG JULY 2013 vii ABSTRACT In terms of Archer, it has been a well known sport worldwide. Basically, a bow consists of 3 main parts which is the riser, limb and the string. In improving the performance of the bow, it is crucial to research each and every part of the bow. There are many mathematical modelling has been done to improve the performance of the bow but only few analysis and experiments are done. Therefore, the objective of the study is to analyse the Archery Bow using Finite Element Method and to develop the Archery Bow. Two different methods were used before fabricating the bow which is to analyse the stress and strain of the bow drawn in CAD software using FEM software and to test experimentally using the strain gauge method. Validation between the results was used as a reference for fabrication. The best material was chosen by doing a simulation analysis on the composite materials which shows that E fibreglass have the best properties compared to the other fibreglass. Therefore, as for the results, E fibreglass is used to fabricate the limb of the bow so that it will be highly in strength and also in elasticity which is up to 72.4 GPa. The results shows that the fabricated bow have a lower strain which are 0.00244 compared to the current bow which is 0.004694. This shows that the fabricated bow have a higher potential to withstand much higher force compared to the current bow which makes the new bow to have a better quality. As for the error analysis, it shows that the higher force applied to the bows makes the error to increase to the increase in vibration and the damping force. viii ABSTRAK Dari segi sukan memanah, ia telah menjadi salah satu sukan yang terkenal di seluruh dunia. Pada asasnya, sebuah anak panah terdiri daripada 3 bahagian utama iaitu riser, limb dan tali. Dalam meningkatkan prestasi pada sesebuah busur, ia adalah penting untuk mengkaji untuk mengkajinya dengan keseluruhan. Terdapat banyak kajian telah dijalankan dalam bentuk kiraan matematik tetapi hanya beberapa analisis dan eksperimen telah dijalankan untuk menbuktikanya. Oleh itu, objektif kajian ini adalah untuk menganalisa anak panah dengan menggunakan kaedah simulasi dan untuk membuat sebuah anak panah. Dua kaedah yang berbeza telah digunakan sebelum membuat panah tersebut yang terdiri daripada kaedah menganalisis tekanan pada anak panah tesebut yang dilukis di perisian lukisan dan simulasinya menggunakan perisian FEM dan untuk menguji kaji menggunakan kaedah tolok ketegangan. Pengesahan antara keputusan yang telah digunakan sebagai rujukan untuk fabrikasi. Bahan yang terbaik telah dipilih dengan melakukan analisis simulasi bahan-bahan komposit yang menunjukkan bahawa gentian kaca E mempunyai ciri-ciri terbaik berbanding dengan gentian kaca yang lain. Oleh itu, sebagai untuk keputusan, kaca gentian E digunakan untuk membina anggota badan bagi anak panah tersebut supaya ia mempunyai kekuatan dan juga keanjalan yang baik sehingga 72.4 GPa. Keputusan menunjukkan bahawa busur direka mempunyai tekanan yang lebih rendah iaitu 0.00244 berbanding busur semasa yang 0.004694. Ini menunjukkan bahawa busur yang baru direka mempunyai potensi yang tinggi untuk menahan kuasa yang lebih tinggi berbanding dengan anak panah semasa yang membuat anak panah baru untuk mempunyai kualiti yang lebih baik. Bagi analisis ralat, ia menunjukkan bahawa kuasa yang lebih tinggi memjadikan nilai ralat semakin meningkat kerana peningkatan dalam getaran dan daya ketegangan. ix TABLE OF CONTENTS Page EXAMINAR’S DECLARATION ii SUPERVISOR'S DECLARATION iii STUDENT'S DECLARATION iv DEDICATION v ACKNOWLEDGEMENTS vi ABSTRACT vii ABSTRAK viii TABLE OF CONTENTS ix LIST OF TABLES xiii LIST OF FIGURES xiv LIST OF SYMBOLS xvi LIST OF ABBREVATIONS xvii CHAPTER 1 INTRODUCTION 1.1 Project Background 1 1.2 Problem Statement 2 1.3 Objective 3 1.4 Scopes of Project 3 1.5 Organisation of the Thesis 3 CHAPTER 2 LITERATURE REVIEW 2.1 Characteristics of a Bow 4 2.2 Types of Bow 5 2.2.1 Longbow 6 2.2.2 Recurve bows 6 2.2.2.1 Non-recurve bow 7 2.2.2.2 Static-recurve bow 8 2.2.2.3 Working-recurve bow 9 x 2.2.3 Compound bows 10 2.3 Composite Materials 11 2.3.1 Composites 11 2.3.2 Characteristics of composite materials 11 2.3.3 Reinforcements 12 2.3.3.1 Fibreglass 12 2.3.3.1 Aluminium 14 2.4 Fundamental Theory and Equations 14 2.4.1 Engineering stress and strain 14 2.4.2 Modulus of elasticity 15 2.4.3 Poisson's ratio 15 2.4.4 Equation of elastic curve 15 2.4.5 Deflection at the limb tip 15 2.5 Mathematical Formulas Used For Bow Fabrication 16 2.6 Literature Review Summary 19 CHAPTER 3 METHODOLOGY 3.1 Cad Modelling 21 3.1.1 Overview 21 3.1.2 SolidWorks modelling steps 22 3.1.3 Archery bow riser modelling 23 3.1.4 Archery bow limb modelling 24 3.1.4.1 Fibreglass limb 24 3.1.4.2 Wood limb 26 3.2 Finite Element Method Analysis 27 3.2.1 Overview 27 3.2.2 Model meshing 28 3.2.3 Setting up the boundary conditions and parameters 31 3.3 Experimental Setup 32 3.3.1 Overview 32 3.3.2 Strain gauge set up 32 3.3.3 National Instrument - Data Acquisition set up 34 3.3.4 DASYlab software setup 35 3.4 Fabrication of the Archery Bow 38 3.4.1 Fabrication of Archery Riser 38 3.4.2 Fabrication of Archery Limb 40 3.5 Numerical Analysis 43 3.5.1 Calculation for archery limb 43 xi 3.5.2 Calculation for strain gauge 44 3.5.3 Galerkin method analysis 45 3.6 The Process Flow of the Study 53 CHAPTER 4 RESULTS AND DISCUSSION 4.1 Simulation result 55 4.1.1 Simulation result for Fibreglass limbs 55 4.1.2 Simulation result for Wood limbs 59 4.2 Experimental result 60 4.3 Comparison btween experimental and simulation result 64 4.4 Numerical calculation 67 4.4.1 Numerical validation using Galerkin analysis 67 4.4.2 Numerical Validation using Error Analysis 68 CHAPTER 5 CONCLUSION AND RECOMMENDATIONS 5.1 Conclusion 70 5.2 Recommendation 72 REFERENCES 73 APPENDICES 75 A Solidworks Drawings and Simulation 76 B Fabrication Flow 82 C Gantt Chart for Final Year Project 1 & 2 87 xii LIST OF TABLES Table No. Title Page 2.1 Fiberglass and its properties 13 2.2 Terms and description of formula used 18 2.3 Literature review summary table 19 3.1 Mechanical properties of fiberglass 32 3.2 Strain gauge details 33 4.1 Data used for calculation of validation 68 4.2 Amount of error for current and fabricated limb for 50 N 69 4.3 Percentage error analysis for current and fabricated limb 69 xiii LIST OF FIGURES Figure No. Title Page 2.1 Main parts in an Archery bow 5 2.2 Non-recurve bow in three different situations 7 2.3 Static recurve bow in three different situations 8 2.4 Working recurve bow in three different situations 9 2.5 Compound bow 10 2.6 Free body diagram of a drawn bow 16 2.7 Free body diagram of a drawn bow limb 17 2.8 Free body diagram of a riser 17 2.9 Literature review summary in percentage 20 3.1 Modelling CAD geometry 22 3.2 2-Dimensional drawing of riser 23 3.3 3-Dimensional drawing of riser 24 3.4 Sketching of limb 25 3.5 2-Dimensional drawing of limb 25 3.6 3-Dimensional drawing of riser 25 3.7 3-Dimensional drawing of wood limb 26 3.8 Analysis in FEM 27 3.9 The effect of mesh size towards time of analysis and number of 29 errors 3.10 The different size and ways of meshing 29 3.11 Limb meshed model 30 3.12 Riser meshed model 31 xiv 3.13 Strain gauge wire placed on the limb 33 3.14 Location of strain gauge on the bow 33 3.15 Connecting strain gauge wires to NI-DAQmx 34 3.16 Ni-DAQmx 35 3.17 NI-DAQmx and DASYLab setup 36 3.18 Fabrication of Bow riser 38 3.19 Bow riser before surface finishing 39 3.20 Bow riser after surface finishing and varnishing 39 3.21 Chopped Strand Mat (CSM) fiberglass 40 3.22 Woven fiberglass 40 3.23 Layers of fiberglass pasted 41 3.24 The limb which is grinded to the desired size 41 3.25 Fabrication of Bow limb 42 3.26 The process flow of the study 53 4.1 Maximum strain versus force applied for fiberglass limb 55 4.2 Maximum stress versus force applied 56 4.3 Maximum deflection versus force applied 57 4.4 Maximum strain versus force applied for wood limb 59 4.5 Strain versus time for fiberglass limb 60 4.6 Strain versus time for wood limb 62 4.7 Strain versus time for fabricated E glass limb 63 4.8 Comparison graph of strain versus time for simulation result and 64 fiberglass limb 4.9 Comparison graph of strain versus time for simulation result and 65 fabricated limb 4.10 Percentage error graph for current and fabricated limb 69 xv LIST OF SYMBOLS A Cross sectional area P Pressure E Modulus of Elasticity a Acceleration m Mass t 3-Dimensional drawing of riser Engineering stress Engineering strain Change in length v Poisson's ratio b Width h Height N Newton R Difference in resistance Ohm ( Unit for current ) Sg Gauge factor xvi LIST OF ABBREVATIONS 2D 2-Dimensional 3D 3-Dimensional CAD Computer Aided Design FEM Finite Element Method FEA Finite Element Analysis CSM Chopped Strand Mat CHAPTER 1 INTRODUCTION 1.1 PROJECT BACKGROUND In the early days, the invention of bow plays an important role in the history of mankind where it is mainly used for the purpose of war and hunting.