STUDY ON THE QUASI-ZERO STIFFNESS VIBRATION ISOLATION SYSTEM

MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION VO NGOC YEN PHUONG “STUDY ON THE QUASI-ZERO STIFFNESS VIBRATION ISOLATION SYSTEM” MAJOR: MECHANICAL ENGINEERING MAJOR CODES: 9520103 THE DOCTORAL THESIS Ho Chi Minh City, Oct./ 2022 TIEU LUAN MOI download : skknchat123@gmail.com moi nhat MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION VO NGOC YEN PHUONG “STUDY ON THE QUASI-ZERO STIFFNESS VIBRATION ISOLATION SYSTEM” MAJOR: MECHANICAL ENGINEERING MAJOR CODES: 9520103 SCIENTIFIC SUPERVISORS: Assoc Prof Dr Le Thanh Danh Dr Nguyen Minh Ky Reviewer 1: Reviewer 2: Reviewer 3: Ho Chi Minh City, Oct./ 2022 TIEU LUAN MOI download : skknchat123@gmail.com moi nhat TIEU LUAN MOI download : skknchat123@gmail.com moi nhat TIEU LUAN MOI download : skknchat123@gmail.com moi nhat ORIGINALITY STATEMENT “I hereby declare that this submission is my own work, done under the supervision of Assoc Prof Dr Le Thanh Danh and Dr Nguyen Minh Ky and all the best of my knowledge, it contains no illegal materials previously published or written by another person.” Ho Chi Minh City, Oct 10 th 2022 Vo Ngoc Yen Phuong i TIEU LUAN MOI download : skknchat123@gmail.com moi nhat ACKNOWLEDGEMENT This dissertation was put down in writing from 2018 to 2021 during my time as a Doctor of Philosophy Candidate at the Mechanical Engineering Faculty at Ho Chi Minh City University of Technology and Education I would like to express my deep gratitude to Assoc Prof Dr Le Thanh Danh for bestowing me the opportunity to take part in his research group as well as for his conscientious instruction as my principal doctoral mentor Simultaneously, he let me experience my independent study and he always supervised carefully during my research schedule Besides, I also want to thank Dr Nguyen Minh Ky from the Faculty of Mechanical Engineering of HCMC University of Technology and Education for his devotion as a cosupervisor for my PhD thesis I would like also to acknowledge the National Foundation for Science and Technology Development (NAFOSTED, Vietnam) and Ho Chi Minh City University of Technology and Education for their financial assistance throughout my research project Thanks to their interest, this thesis has been accomplished on time I am really grateful to my colleagues at Mechanical Engineering Faculty at Industrial University of Ho Chi Minh City for their friendly supports In addition, I would like to appreciate the lecturers at Mechanical Engineering Faculty at University of Technology and Education for their meaningful assistance Finally, I express my thanks to my family, especially my mother, my husband and my two daughters for their emotional encouragement throughout my study Ho Chi Minh City, Oct / 2022 Vo Ngoc Yen Phuong ii TIEU LUAN MOI download : skknchat123@gmail.com moi nhat ABSTRACT The thesis of “Study on the quasi-zero stiffness vibration isolation system” is presented in six chapters The thesis introduces an innovation quasi -zero stiffness adaptive vibration isolation model (QSAVIM) composed by semicircular CAM-wedge-pneumatic spring mechanism One with the positive stiffness including the wedges, the rollers and the two rubber air springs, is used to support the load The other comprising the semi-circular cams, the rollers and other air springs, whose stiffness is negative, is employed to adjust the system stiffness In this model, a component which is non-steel elastic element is the pneumatic spring including rubber air spring and pneumatic cylinder are employed respectively in the proposal model The restoring model of a commercial rubber air spring is analyzed and developed, which is contributed by three factors including compressed air, friction and viscoelasticity of the rubber bellow Herein, the nonlinear hysteresis model of the rubber tube is also considered Then, an experimental rig is set up to identify and verify the parameters of the rubber air spring model In addition, the friction force of the pneumatic cylinder is also investigated through using virtual prototyping technology The complex nonlinear dynamic response of the quasi-zero stiffness adaptive vibration isolation model which is a parallel connection between a load bearing mechanism and a stiffness corrected one is realized The important feature of the proposed model is that it is easy not only to adjust the stiffness to adapt according to the change of the isolated mass but to improve the isolation effectiveness in low frequency region that is useful in practical application The studied results show that the effectiveness of the proposed model is much better than the equivalent traditional model iviii TIEU LUAN MOI download : skknchat123@gmail.com moi nhat CONTENTS OF THESIS Cover page Page Originality statement .i Acknownledgement ii Abstract iii Contents iv Nomenclature .v List of figures vi List of tables .vii Abbreviation .viii CHAPTER 1: INTRODUCTION……………………………………………………… 10 1.1 The necessity of vibration isolation……………………………….…….10 1.2 The aim of the research……………………………………………….…11 1.3 The problems are needed solutions…………………………………… 11 1.4 Research scope and object…………………………… …………… …11 1.5 Research approach………………………………………………… ….12 1.6 Contents of thesis ……………………………………………………… 12 1.7 Organization of thesis……………………………………………………14 1.8 The obtained results……………………………………………… ……14 1.9 The scientific and application contribution of the thesis…………… 15 SUMMARY OF CHAPTER 1………………………………………….…… 15 CHAPTER 2: LITERATURE REVIEWS ……………………………………………….… 17 2.1 Vibration Isolation……………………………………………… … …….17 2.2 Models of proposed vibration isolation………………………………… 19 iv TIEU LUAN MOI download : skknchat123@gmail.com moi nhat 2.2.1 Isolated model using Euler spring………………………………… 19 2.2.2 Isolated model featuring quasi-zero stiffness characteristic……… 21 SUMMARY OF CHAPTER 2……………………………………………….…38 CHAPTER 3: FUNDAMENTAL OF RELATIVE THEORIES…………………………… 39 3.1 Air spring……………………………………………………………… ….39 3.1.1 Introduction………………………………………………………….39 3.1.2 General structure of rubber bellow………………………………….40 3.2 Mathematical model of the compressed air……………………………….42 3.3 Frictional model of pneumatic cylinder and rubber material………… 43 3.3.1 Frictional model of pneumatic cylinder……………………………43 3.3.2 Frictional model of rubber material……………………………… 44 3.4 Viscoelastic model of the rubber material……………………………… 46 3.5 Normal form method……………………………………………………….46 3.6 Multi scale method…………………………………………………….……49 3.7 Runge-kutta method……………………………………………………… 50 3.8 Poincaré section…………………………………………………………… 52 3.9 Brief introduction of Genetic Algorithm………………………………… 53 SUMMARY OF CHAPTER 3………………………………………………….55 CHAPTER 4: QUASI-ZERO STIFFNESS VIBRATION ISOLATOR USING A RUBBER AIR SPRINGS…………………………………………………………………………….… 56 4.1 Mechanical model of isolator…………………………………………………… 57 4.2 Restoring model of a rubber air spring………………………………… 59 4.2.1 Compressed air force……………………………………………… 60 4.2.2 Frictional force…………………………………………………… 61 iv TIEU LUAN MOI download : skknchat123@gmail.com moi nhat 4.2.3 Viscoelastic force………………………………………………….62 4.2.4 Test rig …………………………………………………………….64 4.2.5 Model identification and verification results…………………… 65 4.3 Static analysis of the isolator ………………………………………… …68 4.3.1 Stiffness model …………………………………………………….70 4.3.2 Analysis of equilibrium position……………………………….… 74 4.4 Dynamic analysis……………………………………………………………78 4.4.1 Dynamic Equation…………………………………………… … 79 4.4.2 Equation of vibration transmissibility………………………… …80 4.5 Effects of configurative parameters on vibration transmissibility curve.88 4.5.1 Influence of pressure ratio on the shape of the amplitude-frequency response curve…………………………………………………………88 4.5.2 Influence of geometrical parameters on the resonant peak…….….92 4.5.3 Effects of damping on vibration transmissibility curve……………93 4.6 Complex dynamic analysis……………………………………………… ….94 4.6.1 Frequency jump phenomenon………………………………………95 4.6.2 Bifurcation phenomenon ………………………………………… 97 4.6.3 Dynamic response under random excitation……………….……….99 4.7 Design procedure for obtaining quasi-zero stiffness isolator………… 102 4.8 Experimental result and apparatus………………………………… … 105 SUMMARY OF CHAPTER 4………………………………………………… 112 CHAPTER 5: QUASI-ZERO STIFFNESS VIBRATION ISOLATOR USING A PNEUMATIC CYLINDERS……………………………………………………………… 114 5.1 Model of QSAVIM using a PC………………………………………… 114 iv TIEU LUAN MOI download : skknchat123@gmail.com moi nhat ... The thesis of ? ?Study on the quasi-zero stiffness vibration isolation system? ?? is presented in six chapters The thesis introduces an innovation quasi -zero stiffness adaptive vibration isolation. .. 17 Fig 2.2 The transmissibility curve of the conventional vibration isolation system 18 Fig 2.3 A model of low frequency vibration isolation [5] 19 Fig 2.4 A QZS vibration isolation model for...MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION VO NGOC YEN PHUONG ? ?STUDY ON THE QUASI-ZERO STIFFNESS VIBRATION ISOLATION SYSTEM? ?? MAJOR: MECHANICAL