3-D dynamic modeling and simulation of a multidegree of freedom 3-axle rigid truck with trailing arm bogie suspension

Transcription

1 University of Wollongong Research Online University of Wollongong Thesis Collection University of Wollongong Thesis Collections D dynamic modeling and simlation of a mltidegree of freedom 3-axle rigid trck ith trailing arm bogie sspension Bohao Li University of Wollongong Recommended Citation Li, Bohao, 3-D dynamic modeling and simlation of a mlti-degree of freedom 3-axle rigid trck ith trailing arm bogie sspension, M. Eng. thesis, School of Mechanical, Materials and Mechatronic Engineering, University of Wollongong, theses/583 Research Online is the open access instittional repository for the University of Wollongong. For frther information contact the UOW Library: research-pbs@o.ed.a

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3 3-D Dynamic Modeling and Simlation of a Mlti-degree of Freedom 3-axle Rigid Trck ith Trailing Arm Bogie Sspension A thesis sbmitted in (partial) flfillment of the reqirements for the aard of the degree of MASTER OF ENGINEERING RESEARCH (Mechanical Engineering) from UNIVERSITY OF WOLLONGONG by Bohao Li, ME Prac Faclty of Engineering Jne 006

4 CERTIFICATION I, Bohao Li, declare that this thesis, sbmitted in partial flfillment of the reqirements for the aard of Master of Engineering Research, in the School of Mechanical, Material & Mechatronic Engineering, University of Wollongong, is holly my on ork nless otherise referenced or acknoledged. The docment has not been sbmitted for qalifications at any other academic instittion. Bohao Li 5 April 006 I

5 Acknoledgements Development and completion of this thesis has been aided by the kind assistance of many people, ho have devoted their knoledge and time. Dr Arnold McLean, contribted mch to this thesis. His knoledge and experience in the area of pnematic systems and heavy vehicle air sspensions gave me great assistance. He alays encoraged me and provided many opportnities to contact the indstry inclding attendance at several conferences at hich I presented several papers. He also provided me ith nmeros research articles and trade brochres from his collection and even assisted ith financial assistance. Withot his gidance, it old have been impossible to complete this thesis. Professor Michael West kindly took over my spervision after Dr Arnold McLean as granted leave. His knoledge in dynamics and mathematics proved invalable in solving nmeros problems incrred dring the modeling process. He continosly gided me and inspired me to employ varios methods in the modeling process hich sccessflly transferred the physical vehicle into a mathematical model, eventally. Special thanks shold be given to Mr. Bill Haire, ho kindly provided me financial spport to continosly stdy in Astralia and provided me nmeros opportnities to contact the indstry. I old like to thank Dr Zho Zho, Mr Wang Xiaogang and Mr Zho Jianen, ho are my colleages of the CAE Department of Changan Atomobile Engineering Institte, for their sstained help and spport. I old also like to thank Mr Li Kai from MSC Softare Beijing Representative Office and Mr Chen Song from MSC Softare Chengd Representative Office for their II

6 assistance and qestion-ansering in sing MSC ADAMS. Finally, I shold thank my family in China and my friends all over Astralia, ho spported me continosly in the last 4 years. III

7 Abstract This thesis concentrates on the modeling and simlation of a mlti-degree of freedom 3- axle rigid trck. The linear model featres cab and seat sspensions, rigid live axles, and sspension geometries. The Lagrange s eqation as sed to obtain the motion eqations and system matrices, and the nmerical central difference method as adopted to obtain the system responses sbject to sinsoidal road excitations, programmed in MATLAB. Frthermore, the eigenvectors, the seat bonce acceleration, the maximm dynamic tyre loads and the maximm sspension dynamic deflections ere stdied. ADAMS/Vie as then sed to conveniently reexamine the model in the virtal environment as validation. Some advanced simlations sch as seep sine and trianglar bmp excitation ere also condcted in ADAMS. As a reslt, some very important characteristics of this particlar trck ere revealed hich can be sed either to better nderstand the vehicle dynamic performance or to improve the original design specifications. IV

8 List of Symbols Amp, Amplitde, m A r Road roghness amplitde, m C System damping matrix of the 13 DoF trck model C 19 System damping matrix of the 19 DoF trck-poster system model F The reaction force vector of the 19 DoF trck-poster system model F dmax Maximm dynamic tyre force, N F s Static tyre force, N F Tyre contact force, N F max Maximm load applied on road, N G The gravity vector of the 19 DoF trck-poster system model G q ( f ) - Poer spectrm density in the time domain G q (n) - Poer spectrm density in the spatial domain I 1x Inertia of the front axle nsprng mass (roll), 80kgm I x Inertia of the centre axle nsprng mass (roll), 510kgm I 3x Inertia of the rear axle nsprng mass (roll), 510kgm I bx Inertia of the spring mass exclding the cab, arond the X axis (roll), 7800kgm I by Inertia of the sprng mass exclding the cab, arond the Y axis (pitch), 78000kgm I cx Inertia of the cab arond the X axis (roll), 150kgm I cy Inertia of the cab arond the Y axis (pitch), 100kgm I y Vehicle inertia arond the pitch axle, kgm K System stiffness matrix of the 13 DoF trck model K 19 System stiffness matrix of the 19 DoF trck-poster system model L Road srface ave length, m L f Distance from the leading axle to CG, m L r Distance from the trailing axle to CG, m V

9 M System mass matrix of the 13 DoF trck model M 1 Front axle nsprng mass, 450kg M Centre axle nsprng mass, 105kg M 3 Rear axle nsprng mass, 105kg M 19 System mass matrix of the 19 DoF trck-poster system model M b Sprng mass exclding the cab, 19000kg M c Mass of the cab, 500kg M cg The connection mass at the position of CG, kg M f The concentrated mass at font axle, kg M r The concentrated mass at rear axle, kg M s Mass of the seat and the driver, 10kg M t Total vehicle mass, kg P System potential energy R System dissipation energy T System kinematics energy T min The minimal period possessed in all modes V 0 Critical speed at hich the tyre begins to lose contact ith the road, km/h V 30% Critical Speed at hich the tyre contact force begins to be less than 30% of the static tyre load, km/h W Displacement vector of the 13 DoF trck model W & Velocity vector of the 13 DoF trck model W & Acceleration vector of the 13 DoF trck model W 19 Motion vector or displacement vector of the 19 DoF trck-poster system model W & 19 Velocity vector of the 19 DoF trck-poster system model W & 19 Acceleration vector of the 19 DoF trck-poster system model W s The static deflection vector of the 19 DoF trck-poster system model VI

10 a 1, a, b 1 ~b 5, e 1, e, l 1 ~l 3 Critical geometric dimensions, m a max Maximm relative seat acceleration, g c 1, c Front sspension damping coefficients, 708.5Ns/m c 3, c 4, c 5, c 6 Drive sspension coefficients, Ns/m c c1, c c, c c3, c c4 Cab sspension damping coefficients, 0.75e3 Ns/m ce, ce Drive axle sspension effective damping coefficients, Ns/m 3 ce4, ce5, 6 c s Seat damping coefficient, 0.e3Ns/m f(t) Road excitation vector h The distance beteen CG and the roll centre, m h ( t τ ) the system nit implse response hen t τ k 1, k Front axle sspension spring stiffnesses, 10.e4N/m k 3, k 4, k 5, k 6 Drive axle sspension spring stiffnesses, 0.9e4N/m k c1, k c, k c3, k c4 Cab sspension spring stiffnesses, 100e3N/m ke, ke Drive axle sspension effective stiffnesses, N/m, 3 ke4, ke5, 6 k 1, k Front tire stiffnesses, 0.69e6N/m k 3, k 4, k 5, k 6 Drive tyre stiffnesses, 1.38e6N/m k s Seat spring stiffness, 0e3N/m n - Spatial freqency, m -1 1 Steer axle left sspension static deflection, m Steer axle right sspension static deflection, m 3 Centre axle left sspension static deflection, m 4 Centre axle right sspension static deflection, m 5 Rear axle left sspension static deflection, m 6 Rear axle right sspension static deflection, m VII

11 c1 Cab front left sspension static deflection, m c Cab front right sspension static deflection, m c3 Cab rear left sspension static deflection, m c4 Cab rear right sspension static deflection, m s Seat sspension static deflection, m 1 Left steer tyre static deflection, m Right steer tyre static deflection, m 3 Left centre tyre static deflection, m 4 Right centre tyre static deflection, m 5 Left rear tyre static deflection, m 6 Right rear tyre static deflection, m v Vehicle forard speed, m/s 1 Bonce of the left steer heel poster type excitation rig, m Bonce of the right steer heel poster type excitation rig, m 3 Bonce of the left centre heel poster type excitation rig, m 4 Bonce of the right centre heel poster type excitation rig, m 5 Bonce of the left rear heel poster type excitation rig, m 6 Bonce of the right rear heel poster type excitation rig, m 100 Chassis bonce, m 101 Steer axle bonce, m 10 Centre axle bonce, m 103 Rear axle bonce, m VIII

12 104 Cab bonce, m 106 Driver seat bonce, m & t max Maximm absolte seat acceleration, m/s f - Freqency bandidth in the time domain, Hz n - Freqency bandidth in the spatial domain, Hz t Simlation time interval, s Λ A n n matrix comprised of the eigenvales λ ( i 1,,, n) Λ A n n matrix comprised of the eigenvales λ i ( i 1,,, n) α The dynamic tyre force coefficient, dimensionless δ, Phase angle, rad ε Sspended mass distribtion coefficient θ 100 Chassis roll, radian θ 101 Steer axle roll, radian θ 10 Centre axle roll, radian θ 103 Rear axle roll, radian θ 104 Cab roll, radian ρ y Vehicle gyration radis arond the pitch axle, m i σ - The poer of the road nevenness in the bandidth of n q~ n A n n matrix comprised of the eigenvector ( i 1,, Λ, n) A n n matrix comprised of the eigenvector ( i 1,, Λ, n) 100 Chassis pitch, radian 104 Cab pitch, radian i i IX

13 n The phase angle of the nth heel, rad φ An n n matrix comprised by φ ( i 1,, Λ, n) φ An n n matrix comprised by φ ( i 1,, Λ, n) ω, System natral freqency, rad/s ω Drive freqency, rad/s; ω v L dr i dr / i X

14 List of Figres and Tables Figre (-1): 3-axle rigid trck chassis layot Figre (-): Trck chassis layot simplified 3-D vie Figre (-3): Adopted vehicle axis system Figre (-4): 3-axle rigid trck general model Figre (-5): 3-axle rigid trck model 3-D vie Figre (-6): Eqivalent stiffness and damping of a trailing arm sspension Figre (-7): 3-D rigid trck model sing eqivalent sspension stiffness and damping Figre (3-1): Road Profile Figre (3-): Road excitations of high and lo freqency cases Figre (3-3): Excitation phase angle beteen the left and the right steering heel Figre (3-4a): System time response, 1 st 7 th DoF, high drive freqency, 1 0 Figre (3-4b): System time response, 8 th 13 th DoF, high drive freqency, 1 0 Figre (3-5a): System time response, 1 st 7 th DoF, high drive freqency, 1 Figre (3-5b): System time response, 8 th 13 th DoF, high drive freqency, 1 Figre (3-6a): System time response, 1 st 7 th DoF, lo drive freqency, 1 0 Figre (3-6b): System time response, 8 th 13 th DoF, lo drive freqency, 1 0 Figre (3-7a): System time response, 1 st 7 th DoF, lo drive freqency, 1 Figre (3-7b): System time response, 8 th 13 th DoF, lo drive freqency, 1 Figre (3-8a): Seat to cab floor relative bonce time response, high drive freqency, 0 1 Figre (3-8b): Cab to chassis relative bonce time response, high drive freqency, 0 1 Figre (3-9a): Seat to cab floor relative bonce time response, high drive freqency, XI

15 1 Figre (3-9b): Cab to chassis relative bonce time response, high drive freqency, 1 Figre (3-10a): Seat to cab floor relative bonce time response, lo drive freqency, 0 1 Figre (3-10b): Cab to chassis relative bonce time response, lo drive freqency, 0 1 Figre (3-11a): Seat to cab floor relative bonce time response, lo drive freqency, 1 Figre (3-11b): Cab to chassis relative bonce time response, lo drive freqency, 1 Figre (4-1): Dynamic tyre load time response, V7.78m/s, 1 0 Figre (4-): Dynamic tyre load time response, V7.78m/s, 1 Figre (4-3): Dynamic tyre load time response, V4.17m/s, 1 0 Figre (4-4): Dynamic tyre load time response, V4.17m/s, 1 Figre (4-5): Left steer tyre maximm dynamic tyre load verss speed Figre (4-6): Right steer tyre maximm dynamic tyre load verss speed Figre (4-7): Left centre tyre maximm dynamic tyre load verss speed Figre (4-8): Right centre tyre maximm dynamic tyre load verss speed Figre (4-9): Left rear tyre maximm dynamic tyre load verss speed Figre (4-10): Right rear tyre maximm dynamic tyre load verss speed Figre (4-11): Main sspension dynamic deflection time response, V7.78m/s, 0 1 Figre (4-1): Main sspension dynamic deflection time response, V7.78m/s, 1 XII

16 Figre (4-13): Main sspension dynamic deflection time response, V4.17m/s, 1 0 Figre (4-14): Main sspension dynamic deflection time response, V4.17m/s, 1 Figre (4-15): Seat bonce acceleration time response, V7.78m/s, 1 0 Figre (4-16): Seat bonce acceleration time response, V7.78m/s, 1 Figre (4-17): Seat bonce acceleration time response, V4.17m/s, 1 0 Figre (4-18): Seat bonce acceleration time response, V4.17m/s, 1 Figre (4-19): Relationships beteen G q (f), G q (n) and v Figre (5-1a): The ADAMS/Vie model of the 3-axle trck in ireframe mode Figre (5-1b): The ADAMS/Vie model of the 3-axle trck in rendered mode Figre (5-): Seat acceleration for the 0.4g acceleration condition Figre (5-3): Seat acceleration for the0.6g deceleration condition Figre (5-4): Seat acceleration for the 0.5g left cornering condition Figre (5-5): Seat acceleration for the 0.5g right cornering condition Figre (5-6): Seat acceleration for the 5g bonce condition Figre (5-7): Comparison of the seat acceleration PSD for the seep sine simlation Figre (5-8): Comparison of the seat, cab and chassis vertical acceleration PSD for the seep sine simlation Figre (5-9): Comparison of the vertical acceleration PSD transferability for the seep sine simlation Figre (5-10): Chinese standard trianglar bmp plse excitation for heavy trcks Figre (5-11): Trianglar bmp plse excitation seat vertical acceleration magnitde freqency response Figre (5-1): Seat vertical vibration factor contribtion chart Figre (6-1): Position of the roll centre and the CG Figre (6-): Location of the roll axis XIII

17 Table (-1): Critical Geometric Dimensions Table (-): Static deflections of some critical components Table (-3): Reaction forces on tyres Table (3-1): Some system characteristics of different modes Table (3-): Phase angles of the eigenvectors in degrees Table (4-1): The maximm dynamic tyre load and dynamic road load, V7.78m/s, 0 1 Table (4-): The maximm dynamic tyre load and dynamic road load, V7.78m/s, 1 Table (4-3): The maximm dynamic tyre load and dynamic road load, V4.17m/s, 0 1 Table (4-4): Maximm dynamic deflections of vehicle main sspensions, V4.17m/s, 1 Table (4-5): Speed at hich the tyres lose contact ith the road Table (4-6): Maximm dynamic deflections of vehicle main sspensions, V7.78m/s, 0 1 Table (4-7): Maximm dynamic deflections of vehicle main sspensions, V7.78m/s, Table (4-8): Maximm dynamic deflections of vehicle main sspensions, V4.17m/s, 0 1 Table (4-9): Maximm dynamic deflections of vehicle main sspensions, V4.17m/s, 1 Table (5-1) : Joints types, nmbers and fnctions Table (5-): ADAMS/Vie trck model predicted static tyre forces Table (5-3): ADAMS/Vie trck model predicted sspension static deflections Table (5-4): ADAMS/Vie trck model predicted maximm dynamic tyre forces XIV

18 Table (5-5): Adams/ Vie trck model predicted modal parameters Table (5-6): ADAMS/Vie trck model predicted mode principal motions Table (5-7): Predicted static tyre force comparison Table (5-8): Predicted maximm dynamic tyre force comparison Table (5-9): Predicted static sspension deflection comparison Table (5-10): Predicted damped natral freqencies comparison Table (5-11): Predicted seat accelerations for varios extreme operational conditions Table (5-1): Predicted maximm seat vertical accelerations at different speeds for the trianglar bmp plse excitation. Table (5-13): Candidate factor settings Table (5-14): Factor combination trail list XV

19 Table of Contents Table of Contents Table of Contents...1 Chapter 1: Introdction Backgrond Thesis Aims Literatre Revie Brief Development History of Vehicle Dynamics Ride Dynamics Dynamic modeling of the vehicle vibration system Previos research finding Heavy vehicle dynamics Featres of the Model Used in This Thesis Methodology...15 Chapter : Modeling of a 19 DoF 3-Axle Rigid Trck Poster Vibration System.16.1 The Trailing Arm Bogie Sspension Global Coordinate System Assmptions and Simplifications Limitations Some Special Considerations for Varios Components Modeling of the Unsprng Mass Motion of the Cab Sprng Mass Distribtion Derivation of the System Motion Eqation Using the Lagrange s Eqation Degrees of Freedom Draings of the Model Derivative of the Motion Eqations Calclation of the Sspension Static Deflection and the Reaction Force on Each Wheel...47 Chapter 3: Model Nmerical Simlation Redction of the 19 DoF trck-poster model to the 13 DoF trck model

20 Table of Contents 3. Calclation of eigenvales and eigenvectors in state-space Complex eigenvales, complex eigenvectors and the complex modal matrix Some system characteristics obtained by eigenvales and eigenvectors System Simlation The central difference method Road roghness excitation Time response predictions...67 Chapter 4: Case Stdies Dynamic tyre force Maximm dynamic sspension deflection Maximm seat bonce acceleration...96 Chapter 5: Simlation of the 13 DoF Trck Model Using ADAMS/Vie ADAMS Modeling Preprocessing of the ADAMS/Vie Model Adaptation of the 13 DoF Model to the ADAMS/Vie Model Modeling of the Sspension Force Joints of the ADAMS/Vie Model Motion Constraints Modeling of the Vibrating Actators Simlation of the ADAMS Model ADAMS Solver Settings Simlation Types Static Simlation Dynamic Simlation Modal Simlation Comparison of the ADAMS Simlation Reslts ith the Previos 13 DoF Model Extreme Operational Condition Simlation Seep Sine Simlation Standard Trianglar Bmp Excitation Simlation Contribtion Analysis...16 Chapter 6: Conclsions and Recommendations Conclsions...130

21 Table of Contents 6. Special Considerations for Vehicle Roll Mechanics Frther Research Recommendations References Appendix 1: Static Deflection and Reaction Force - MATLAB Programming Code...14 Appendix : MATLAB Programming Simlation Code Appendix 3: System Time Responses...16 Appendix 4: Trck Model Mode Shapes