View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Repository@USM A STUDY ON THE EFFECT OF OUT-OF-ROUNDNESS OF DRUM BRAKE ROTOR ON THE BRAKING FORCE USING THE FINITE ELEMENT METHOD by MUHAMMAD NAJIB BIN ABDUL HAMID Thesis submitted in fulfilment of the requirements for the degree of Master of Science JUNE 2007 ACKNOWLEDGEMENTS I would like to express my truly gratitude and highest appreciation to my supervisor Assoc. Prof. Dr Zaidi Mohd Ripin for his precious guidance, support, training, advice and encouragement throughout my Master of Science study. My special acknowledgement is also dedicated to Universiti Sains Malaysia for providing me with the scholarship through the Graduate Assistant scheme during my study. I also would like to thank all the technicians for their valuable support and help. I would like to express my gratefulness to my beloved family for their support especially to my parents who have done most excellent in providing me with education. I would also acknowledge my entire friends at School of Mechanical Engineering for their great and favorable support. A truly thankfulness are dedicated to all who involve in this project directly and indirectly. Thank you very much. ii TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ii TABLE OF CONTENTS iii LIST OF TABLES v LIST OF FIGURES vi LIST OF NOMENCLATURES viii LIST OF PUBLICATIONS & SEMINARS x ABSTRAK xi ABSTRACT xii CHAPTER ONE : INTRODUCTION 1.0 Background 1 1.1 Problem statement 2 1.2 Research scope and objective 2 1.3 Thesis outline 3 CHAPTER TWO : LITERATURE REVIEW 2.0 General overview 4 2.1 Friction material 5 2.2 Drum brake construction 6 2.3 Brake effectiveness 11 2.4 Contact analysis 21 2.5 Other studies on drum brake analysis 25 2.6 Discussion 25 2.8 Summary 27 CHAPTER THREE : METHODOLOGY 3.0 Introduction 28 3.1 Braking force experiment 30 3.2 Finite element analysis 35 3.3 Lining compression test 38 iii 3.4 Roundness measurement 39 3.5 Summary 40 CHAPTER FOUR : RESULTS AND DISCUSSION 4.0 Introduction 41 4.1 Roundness measurement 41 4.2 Lining compression test 44 4.3 Braking force experiment results 45 4.4 Finite element analysis 51 4.5 Discussion 56 4.6 Summary 59 CHAPTER FIVE : CONCLUSIONS AND RECOMMENDATIONS 5.0 Conclusions 61 5.1 Recommendations 62 REFERENCES 63 LIST OF PUBLICATIONS & SEMINARS 66 iv LIST OF TABLES Page 2.1 Total brake factors for different designs of simplex drum brake 20 4.1 The brake force and brake factor for various load level. 48 4.2 Parameter value for the motorcycle drum brake analyzed 49 4.3 Brake factor values calculated from Hohmann and Mahmoud 49 equation 4.4 Contact pressure distribution along trailing and leading lining at 52 the certain angle rotation 4.5 The Pearson’s coefficient of correlations 59 v LIST OF FIGURES Page 2.1 Coefficient of friction variations against the number of brakes 6 with the drum brake. 2.2 A design of simplex or leading-trailing drum brake 8 2.3 Duplex drum brake with two single-piston wheel 9 2.4 Duo-servo drum brake operation. The primary shoe on the left 10 exerts a force on the secondary shoe on the right 2.5 Schematic of an internally expanding shoe brake 12 2.6 Two shoes on simplex drum brake 15 2.7 A brake with two leading shoes 16 2.8 Brake factor C* as a function of the coefficient of friction 17 2.9 Schematic of simplex S-cam drum brake used by Hohmann et 18 al (1999) in analysis to formulate brake parameter 2.10 Simplified Free Body Diagram for simplex drum brake 19 2.11 Drum brake pressure distributions 22 3.1 The drum brake used for the analysis 28 3.2 Flowchart for the overall methodology of the study 29 3.3 Drum brake mounted on the bracket for testing 31 3.4 Experimental setup for measuring brake force for a drum brake 32 using Universal Testing Machine (UTM). 3.5 Force diagram on the drum brake experiment 33 3.6 The drawing of drum brake used in this analysis 35 3.7 The dimension of brake shoe 36 3.8 Brake shoe modeled in ABAQUS 6.5 37 3.9 Drum brake system modeled in ABAQUS 38 3.10 Brake shoe compression test modeling to validate the value 39 of lining modulus of elasticity 3.11 The brake drum in place for roundness test 40 4.1 Roundness profile with a marking sign using 250 µm scale 42 range 4.2 Roundness profile using scale range of 50 µm 42 4.3 Roundness profile of the drum brake rotor inside surface using 43 a scale range of 25 µm 4.4 Result for lining shoe compression for experiment and 44 modeling vi 4.5 Variation of braking torque with the angle of rotation for 46 repeated measurement of 50N applied load 4.6 Variation of measured braking torque to the rotation angle for 4 different pedal load 4.7 Variation of brake factor for different load experimentally and 50 theoretically 4.8 The location of the centre of pressure for leading and trailing 53 shoes 4.9 The variation of brake factor for 50N applied load 54 4.10 The comparison between experimental result and finite 55 element analysis result for applied load of 50N 4.11 The part where the wear is affected the most in the test 57 4.12 Variation of the braking force and the roundness profile with 58 the angular rotation of the drum brake, the diagram above it shows the orientation of the drum when rotated 4.13 The relationship of roundness effect 60 vii NOMENCLATURES a : distance between drum centre point and pivot point b1 : distance between drum centre point and cam contact point for leading shoe b2 : distance between drum centre point and cam contact point for trailing shoe c : distance between drum centre point and tangential force C* : brake factor C1 : brake shoe factor (leading shoe) C2 : brake shoe factor (trailing shoe) F : applied load force Ff : friction force Fb : braking force h : distance between cam centre point and pivot point K : Spring stiffness Ma : applied moment Mf : friction force moment Mn : normal force moment Mt : total moment N : normal reaction force Pi : pressure at node Pmax : maximum pressure (leading shoe) P’max : maximum pressure (trailing shoe) Pn : normal pressure on small element Pr : radial pressure on small element R1 : reaction force by friction (leading shoe) R2 : reaction force by friction (trailing shoe) r : radius of brake lining viii ri : inner radius of drum rotor rl : length of the arm lever ro : outer radius of drum S1 : reaction force at cam or rolls point (leading shoe) S2 : reaction force at cam or rolls point (trailing shoe) T : torque T2L : torque for double leading brake w : width of brake lining W : applied load xcp : centre of pressure μ : friction coefficient α : angle of brake lining φ : angle of element on brake lining measured from pivot point θ1 : angle between pivot point and starting point of lining. θ2 : angle between pivot point and ending point of lining ix LIST OF PUBLICATIONS & SEMINARS Page 1 Analysis of contact pressure distribution effect on drum brake 66 squeal noise using the finite element method 2 Analysis of brake shoe vibration using multi body dynamics 66 approach x KAJIAN KESAN KETIDAK-BULATAN PEMUTAR GELENDONG BREK TERHADAP DAYA BREK DENGAN MENGGUNAKAN KAEDAH UNSUR TERHINGGA ABSTRAK Rekabentuk kasut depan-kasut mengekor digunakan dengan meluas sebagai brek belakang untuk kereta penumpang dan lori ringan. Gelendong brek biasanya dianggap bulat sepenuhnya dan ini dilaporkan dalam mana-mana hasil kerja yang telah dilakukan oleh penyelidik. Sebelum ini, kesan sebenar terhadap kebulatan gelendong dengan daya brek belum lagi dikaji. Dalam kajian ini, gelendong brek motosikal diuji kebulatannya dan dijalankan ujian daya brek serta ujian mampatan bahan pelapiknya. Ujian kebulatan dilakukan dengan menggunakan alat ujian kebulatan Mitutoyo RA-100 untuk mendapatkan profil kebulatan. Manakala ujian daya brek dijalankan dengan menggunakan mesin ujian semesta. Ujian mampatan bahan pelapik juga dijalankan dengan menggunakan mesin ujian semesta untuk menentu-sahkan nilai modulus keanjalan Young. Analisis kaedah unsur juga digunakan dalam kajian ini. Hasil keputusan menunjukkan gelendong brek adalah tidak bulat sepenuhnya manakala keputusan ujian brek pula menunjukkan daya brek yang berubah-ubah. Hubungan antara hasil experimen dan kaedah unsur terhingga menunjukkan hubungan yang baik dengan nilai pekali Pearson 0.828. Hasil keputusan menunjukkan bahawa bentuk gelendong memberi kesan kepada taburan tekanan sentuhan, daya brek dan juga faktor brek. Daya brek dan faktor brek meningkat dengan daya yang dikenakan. Nilai brek faktor dikira dalam julat 0.5 ke 2.0 yang mana hampir kepada nilai teori faktor brek 2.0 bagi pekali geseran 0.3. Dengan ini boleh disimpulkan bahawa kebulatan mempengaruhi daya geseran brek yang terhasil yang mana akan mempengaruhi nilai pekali brek. xi A STUDY ON THE EFFECT OF OUT OF ROUNDNESS OF DRUM BRAKE ROTOR ON THE BRAKING FORCE USING THE FINITE ELEMENT METHOD ABSTRACT The leading-trailing shoe design is used extensively as rear brake on passenger cars and light weight pickup trucks. In the drum brake, the drum is assumed to be perfectly round and this is the case as reported by simulation work done elsewhere. The true effect of roundness of the drum on the brake force has not been investigated. In this study, a brake drum of a motorcycle was subjected to the roundness test, the brake force test and the lining compression test. Firstly, the roundness test was carried out using the Mitutoyo Roundtest RA-100 to determine the roundness profile of drum.