An investigation of the samco primas buss ride comfort by using the quarter car model with linear asymmetric damper

VIETNAM NATIONAL UNIVERSITY HO CHI MINH CITY HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY - DINH DUY LE AN INVESTIGATION OF THE SAMCO PRIMAS BUS’S RIDE COMFORT BY USING THE QUARTER CAR MODEL WITH LINEAR ASYMMETRIC DAMPER Discipline: Vehicle Engineering Major code: 8520116 MASTER’S THESIS HO CHI MINH CITY, July, 2022 THIS RESEARCH IS COMPLETED AT UNIVERSITY OF TECHNOLOGY – VNU – HCM CITY Instructor: Trần Hữu Nhân, Ph.D Examiner 1: Hồng Đức Thông, Ph.D Examiner 2: Nguyễn Văn Trạng, Ph.D Master’s thesis was defended at Ho Chi Minh City University of Technology, VNU-HCM on July 26th, 2022 The board of the Master’s Thesis Defense Council includes: Chairman: Lê Đình Tuân, Assoc.Prof.Ph.D Member: Võ Tấn Châu, Ph.D Secretary: Lê Tất Hiển, Assoc.Prof.Ph.D Reviewer 1: Hồng Đức Thông, Ph.D Reviewer 2: Nguyễn Văn Trạng, Ph.D Verification of the Chairman of the Master’s Thesis Defense Council and the Dean of Faculty of Transportation Engineering after the thesis being corrected (If any) CHAIRMAN DEAN - FACULTY OF OF THE COUNCIL TRANSPORTATION ENGINEERING VIETNAM NATIONAL UNIVERSITY HO CHI MINH CITY HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY SOCIALIST REPUBLIC OF VIETNAM Independence – Freedom - Happiness THE TASK SHEET OF MASTER’S THESIS Full name: Lê Đình Duy Studen code: 1870435 Date of Birth: 07/07/1996 Place of birth: Tiền Giang Major: Vehicle Engineering Major code: 8520116 I THESIS TOPIC: An investigation of the samco primas bus’s ride comfort by using the quarter car model with linear asymmetric damper ĐỀ TÀI LUẬN VĂN : Phân tích, đánh giá độ êm dịu xe khách Samco Primas mơ hình động lực học ¼ xe với giảm chấn thay đổi II TASKS AND CONTENTS: Research on theoretical basis of the dynamic model with the asymmetric damper Calculate for both cases of random road profile and single bump road profile Conduct simulation, analysis accordance with the suspension system's ride comfort and safety standards Get full understanding of the effect of asymmetric damper on the ride comfort, safety and hanlding control of the suspension system III TASKS STARTING DATE: September 06th, 2021 IV TASKS ENDING DATE: July 14th 2022 VIII INSTRUCTOR: Trần Hữu Nhân, Ph.D Ho Chi Minh City, July 14th 2022 INSTRUCTOR (Full name & Signature) HEAD OF DEPARTMENT (Full name & Signature) DEAN - FACULTY OF TRANSPORTATION ENGINEERING (Full name & Signature) i ACKNOWLEDGMENTS I would like to thank my mentor Dr Huu Nhan TRAN who instructed me throughout my work His motivation, patience, direct involvement in the research topic and, above all, friendly nature helped me to complete this work His vibration expertise in the automotive engineering field helped me at solving a large number of points throughtout this research I appreciate the guidance he offered me attain a higher level of maturity in my research work Futhermore, his valuable suggestions regarding different aspects of life will be helpful, and his insightful advice on several aspects of life will benefit me throughout my career path Next, I would like to thank all Faculty of Transportation Engineering members for supporting me in procedures and carrying out experiments during my Research-based Master’s Program I am also indebted to my family, without their cooperation and financial support, pursuing a Master’s degree would have been impossible Apart from these people, I am grateful to other departments at Ho Chi Minh City University of Technology for helping me with some computational problem that I faced in my research Finally, I acknowledge Ho Chi Minh City University of Technology (HCMUT), VNU-HCM for supporting this study I thank them all Ho Chi Minh City, July, 2022 Researcher, Lê Đình Duy Instructor: Trần Hữu Nhân, Ph.D ii ABSTRACT This thesis investigates the Samco Primas bus’s ride comfort by using a quarter car model with both linear symmetric damper and linear asymmetric one The linear asymmetric damper’s effects on the ride comfort, safety, and handling were investigated to get a deeper understanding of the suspension system design processes of an inner city Samco Primas bus The dynamic responses were analyzed for both two cases of linear symmetric and linear asymmetric dampers using the quarter car model with two degrees of freedom (2 DOFs) subjected to random road profiles and single bump cases of triangular and sine-squared bumps In conclusion, the obtained results show that the linear symmetric damper performs the same as that of the linear asymmetric one in terms of comprehensive performance when the vehicle is subjected to a random road profile The ride comfort, the working space have been significantly improved in specific range of velocity in case of the linear asymmetric damper However, in general, slightly better performance has been obtained in case of the linear symmetric damper case Instructor: Trần Hữu Nhân, Ph.D iii TÓM TẮT LUẬN VĂN THẠC SĨ Luận văn nghiên cứu độ êm dịu xe Samco Primas mơ hình động lực dạng ¼ xe với hai loại giảm chấn đối xứng giảm chấn bất đối xứng Ảnh hưởng giảm chấn bất đối xứng đến độ êm dịu, an toàn khả vận hành nghiên cứu để hiểu rõ trước thực trình thiết kế hệ thống treo xe Samco Primas Đáp ứng động lực học xe buýt với hai trường hợp giảm chấn đối xứng bất đối xứng phân tích dựa mơ hình xe hai bậc tự tác dụng mặt đường ngẫu nhiên, hai loại đường tác dụng đột ngột dạng tam giác bán bình phương hàm sin Tóm lại, kết thu cho thấy giảm chấn đối xứng cho khả vận hành tương tự giảm chấn bất đối xứng mặt đường ngẫu Độ êm dịu, không gian làm việc cải thiện cách đáng kể số vùng vận tốc cụ thể trường hợp sử dụng giảm chấn bất đối xứng Tuy nhiên, nhìn chung, giảm chấn đối xứng đem lại khả vận hành tốt Instructor: Trần Hữu Nhân, Ph.D iv ASSURANCE I am Dinh Duy LE, Master’s student of Department of Vehicle Engineering, Faculty of Transportation, class 2018, at Ho Chi Minh City University of Technology I guarantee that the information below is accurate: (i) I conducted all of the work for this research study by myself (ii) This thesis uses actual, reliable, and highly precise sources for its references and citations (iii) The information and findings of this study were produced independently by me and honesty Ho Chi Minh City, 07th July, 2022 Researcher, Lê Đình Duy Instructor: Trần Hữu Nhân, Ph.D v TABLE OF CONTENTS ACKNOWLEDGMENTS i ABSTRACT ii TÓM TẮT LUẬN VĂN THẠC SĨ iii ASSURANCE iv LIST OF FIGURES vii LIST OF TABLES ix LIST OF ABBREVIATIONS .x CHAPTER 1: OUTLINE 1.1 Introduction 1.2 Literature Review 1.3 Scope 1.4 Research methodology .4 1.5 Research findings and contributions CHAPTER 2: THEORY AND SIMULATION MODEL 2.1 Damper Configuration 2.2 Characteristics of linear asymmetric damper .8 2.3 Linear asymmetric damper model .13 2.4 Quarter car model 15 2.5 Random road profiles 17 2.6 ISO 2631-1:1997 .24 2.6.1 Vibration evaluation .24 2.6.2 Frequency weighting .26 2.7 IIR filter design 27 2.8 Evaluation indexes 30 Instructor: Trần Hữu Nhân, Ph.D vi 2.9 Runge-Kutta Method .31 2.10 Calculation flowchart 32 2.11 MATLAB Program 33 CHAPTER 3: CALCULATED RESULTS AND DISCUSSION 35 3.1 Analysis of evaluation indexes 40 3.2 Extended results with a transient road profile 43 CHAPTER 4: CONCLUSION 50 DANH MỤC CÁC CƠNG TRÌNH KHOA HỌC 52 REFERENCES 55 APPENDIX 59 ❖ INPUT.m 59 ❖ fn2k.m 59 ❖ RANDOM_road_generate.m 60 ❖ RANDOM_Road_Profile.m 61 ❖ Main.m 63 PLAGIARISM CHECK .70 CURRICULUM VITAE .73 LÝ LỊCH TRÍCH NGANG 74 Instructor: Trần Hữu Nhân, Ph.D vii LIST OF FIGURES Fig 1 An intercity bus Samco Primas Fig A rebound phase of a shock absorber [11] Fig 2 Types of shock absorbers and basic structures [5] Fig Paramerers of Twin tube shock absorber [5] Fig Working principle of Mono-tube shock absorber [12] Fig The actual damping characteristic curve [12] Fig An experimental model to find the characteristics of shock absorbers [13] 10 Fig Displacement of harmonic excitation ( u0 = 10 (mm), f = 0.05 (Hz)) [13] 10 Fig Velocity of harmonic excitation ( u0 = 10 (mm), f = 0.05 (Hz)) [13] 11 Fig A relationship between FD (v) and different velocity values [13] 11 Fig 10 The damping characteristic curve obtained from the experiment [12] 12 Fig 11 The force-velocity characteristics 13 Fig 12 Quarter car models [16] .15 Fig 13 Quarter car model and force diagram 16 Fig 14 Classification of roads, classes A to H [9] 19 Fig 15 A typical example of C-Class random road at velocity of 60 (km/h) 20 Fig 16 Relationship between health and duration of acceleration value [10] 25 Fig 17 Frequency weighting curves [10] 27 Fig 18 ARMA Model 28 Fig 19 Calculation flowchart 33 Fig 20 Organization of MATLAB program files 33 Fig The sprung mass displacement in time domain at the vehicle’s velocity of 60 (km/h) 36 Fig The unsprung mass displacement in time domain at the vehicle’s velocity of 60 (km/h) .36 Fig 3 The suspension dynamic deflection in time domain at the vehicle’s velocity of 60 (km/h) 37 Instructor: Trần Hữu Nhân, Ph.D 60 kt=1000000; clear k_s syms k_s M = [mu 0;0 ms]; K = [k_s+kt -k_s; -k_s k_s]; A = M\K; [~,D] = eig(A); wns = (D(1,1)); fns = wns/(4*pi^2); k = double(solve(fns-a^2,k_s)); end ❖ RANDOM_road_generate.m function [y dy] = RANDOM_road_generate (v_V, dist, Phi0, Psi) global rr_w rr_freq_min rr_freq_max rr_n Omin = 2*pi*rr_freq_min; Omax = 2*pi*rr_freq_max; dO = (Omax-Omin)/(rr_n-1); O = Omin:dO:Omax; O0 = 1; Phi = Phi0.*(O./O0).^(-rr_w); Amp = sqrt(2*Phi*dO); t_end_vel = dist/v_V; time = 0:0.001:t_end_vel; Instructor: Trần Hữu Nhân, Ph.D 61 s_V=v_V*time; y = zeros(1,length(time)); % for ii=1:length(time) y_temp(ii) = 0; dy_temp(ii) = 0; for jj = 1:rr_n y_temp(jj) = Amp(jj)*sin(Om(jj)*v_V*time(ii)+Psi(jj)); dy_temp(jj)= Amp(jj)*Om(jj)*v_V*cos(Om(jj)*s_V(ii)+Psi(jj)); end y(ii)=sum(y_temp); dy(ii)=sum(dy_temp); end end ❖ RANDOM_Road_Profile.m clc; global rr_w rr_freq_min rr_freq_max rr_n RRPA dRRPA RRPB dRRPB RRPC dRRPC RRPD dRRPD TEND RRPClass dRRPClass vo v_step v_end rr_w = 2.0; rr_freq_min = 0.5; rr_freq_max = 50; rr_n = 512; % Omin = 2*pi*rr_freq_min; Omax = 2*pi*rr_freq_max; dO = (Omax-Omin)/(rr_n-1); Instructor: Trần Hữu Nhân, Ph.D 62 O = Omin:dO:Omax; Psi_random = 2*pi*rand(size(O)); % vo=5; v_step=5; v_end=120; vel = (vo:v_step:v_end)/3.6; Phi0_A = 1*10e-6; Phi0_B = 2*10e-6; Phi0_C = 8*10e-6; Phi0_D = 32*10e-6; % -dist = 100; t_end_vel = dist/min(vel); time = 0:0.001:t_end_vel; n = length(time); m = length(vel); TEND = zeros(1,m); for jj=1:m [y0_A dy0_A] = RANDOM_road_generate (vel(ii), dist, Phi0_A, Psi_random); [y0_B dy0_B] = RANDOM_road_generate (vel(ii), dist, Phi0_B, Psi_random); [y0_C dy0_C] = RANDOM_road_generate (vel(ii), dist, Phi0_C, Psi_random); [y0_D dy0_D] = RANDOM_road_generate (vel(ii), dist, Phi0_D, Psi_random); nl_A = length(y0_A); nl_B = length(y0_B); nl_C = length(y0_C); nl_D = length(y0_D); RRPA (1:nl_A,ii) = y0_A; dRRPA (1:nl_A,ii) = dy0_A; RRPB (1:nl_B,ii) = y0_B; dRRPB (1:nl_B,ii) = dy0_B; Instructor: Trần Hữu Nhân, Ph.D 63 RRPC (1:nl_C,ii) = y0_C; dRRPC (1:nl_C,ii) = dy0_C; RRPD (1:nl_D,ii) = y0_D; dRRPD (1:nl_D,ii) = dy0_D; TEND (ii) = dist/vel(ii); RRPClass(1:nl_A,1,ii)=y0_A; dRRPClass(1:nl_A,1,ii)=dy0_A; RRPClass(1:nl_B,2,ii)=y0_B; dRRPClass(1:nl_B,2,ii)=dy0_B; RRPClass(1:nl_C,3,ii)=y0_C; dRRPClass(1:nl_C,3,ii)=dy0_C; RRPClass(1:nl_D,4,ii)=y0_D; dRRPClass(1:nl_D,4,ii)=dy0_D; end save 'RANDOM_Road_Profile' save ('RRPDist', 'RRPA','dRRPA', 'RRPB','dRRPB', 'RRPC','dRRPC', 'RRPD','dRRPD', 'TEND'); ❖ Main.m clc; close all; clear all; load 'input_random' load 'RANDOM_Road_Profile' global ms mu ks kt cs ct c1 c2 c12 c22 RRPClass dRRPClass TEND vo v_step v_end vel = vo:v_step:v_end; t_step=0.001; fs=1/t_step; N_v=length(vel); N_class=4; for n=1:N_v Instructor: Trần Hữu Nhân, Ph.D 64 int_vel=round(vel(n)/vo); t=0:t_step:TEND(int_vel); kk(n)=length(t); for jj=1:N_class x(1)=0; x_a(1)=0; x_a2(1)=0; y(1)=0; y_a(1)=0; y_a2(1)=0; z(1)=0; z_a(1)=0; z_a2(1)=0; q(1)=0; q_a(1)=0; q_a2(1)=0; g(1)=0; g_a(1)=0; g_a2(1)=0; s(1)=0; s_a(1)=0; s_a2(1)=0; fdamper(1)=0; fdamper_a(1)=0; fdamper_a2(1)=0; h=t_step; t(1)=0; u=zeros(1,kk(n)+1); u(1)=RRPClass(1,jj,n); Instructor: Trần Hữu Nhân, Ph.D 65 du(1)=dRRPClass(1,jj,n); for ii=1:kk(n) if ((q_a(ii)-z_a(ii))>0) c=c1; else c=c2; end if ((q_a2(ii)-z_a2(ii))>0) c_2=c12; else c_2=c22; end [k1,k2,k3,k4,l1,l2,l3,l4,m1,m2,m3,m4,n1,n2,n3,n4] = Myrungekutta(h,cs,u(ii),du(ii),x(ii),y(ii),z(ii),q(ii)); [k1_a,k2_a,k3_a,k4_a,l1_a,l2_a,l3_a,l4_a,m1_a,m2_a,m3_a,m4_a,n1_a,n2_a,n3_a, n4_a] = Myrungekutta(h,c,u(ii),du(ii),x_a(ii),y_a(ii),z_a(ii),q_a(ii)); [k1_a2,k2_a2,k3_a2,k4_a2,l1_a2,l2_a2,l3_a2,l4_a2,m1_a2,m2_a2,m3_a2,m4_a2,n 1_a2,n2_a2,n3_a2,n4_a2] = Myrungekutta(h,c_2,u(ii),du(ii),x_a2(ii),y_a2(ii),z_a2(ii),q_a2(ii)); x(ii+1)=x(ii)+(1/6)*(k1+2*(k2+k3)+k4)*h; x_a(ii+1)=x_a(ii)+(1/6)*(k1_a+2*(k2_a+k3_a)+k4_a)*h; x_a2(ii+1)=x_a2(ii)+(1/6)*(k1_a2+2*(k2_a2+k3_a2)+k4_a2)*h; y(ii+1)=y(ii)+(1/6)*(l1+2*(l2+l3)+l4)*h; y_a(ii+1)=y_a(ii)+(1/6)*(l1_a+2*(l2_a+l3_a)+l4_a)*h; y_a2(ii+1)=y_a2(ii)+(1/6)*(l1_a2+2*(l2_a2+l3_a2)+l4_a2)*h; z(ii+1)=z(ii)+(1/6)*(m1+2*(m2+m3)+m4)*h; z_a(ii+1)=z_a(ii)+(1/6)*(m1_a+2*(m2_a+m3_a)+m4_a)*h; z_a2(ii+1)=z_a2(ii)+(1/6)*(m1_a2+2*(m2_a2+m3_a2)+m4_a2)*h; q(ii+1)=q(ii)+(1/6)*(n1+2*(n2+n3)+n4)*h; q_a(ii+1)=q_a(ii)+(1/6)*(n1_a+2*(n2_a+n3_a)+n4_a)*h; Instructor: Trần Hữu Nhân, Ph.D 66 q_a2(ii+1)=q_a2(ii)+(1/6)*(n1_a2+2*(n2_a2+n3_a2)+n4_a2)*h; if (ii