RIDE AND DIRECTIONAL DYNAMIC ANALYSIS OF ARTICULATED FRAME STEER VEHICLES Alireza Pazooki A Thesis in The Department of Mechanical and Industrial Engineering Presented in Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy (Mechanical Engineering) at Concordia University Montreal, Quebec, Canada December 2012 © Alireza Pazooki, 2012 i CONCORDIA UNIVERSITY SCHOOL OF GRADUATE STUDIES This is to certify that the thesis prepared By: Alireza Pazooki Entitled: Ride and Directional Dynamic Analysis of Articulated Steer Vehicles and submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY (Mechanical Engineering) complies with the regulations of the University and meets the accepted standards with respect to originality and quality. Signed by the final examining committee: Chair Dr. Amir G. Aghdam External Examiner Dr. Corina Sandu External to Program Dr. S. Samuel Li Examiner Dr. A. K. Waizuddin Ahmed Examiner Dr. Ramin Sedaghati Thesis Supervisor Dr. Subhash Rakheja, Dr. Dongpu Cao Approved by Dr. Ali Dolatabadi, Graduate Program Director December 5, 2012 Dr. Robin A.L. Drew, Dean Faculty of Engineering & Computer Science ii ABSTRACT Pazooki Alireza, Ph.D. Concordia University, 2012 Articulated frame steer vehicles (ASVs), widely employed in different off-road sectors, are generally unsuspended vehicles. Owning to their complex operating environment, high mass center, relatively soft and large diameter tires, wide load variations and load distribution, and kineto-dynamics of the frame steering mechanism, these vehicles transmit higher magnitudes of low frequency whole-body vibration (WBV) to the operators and also exhibit lower roll and directional stability limits. While the superior performance potentials of axle suspension in limiting the WBV exposure have been clearly demonstrated, the implementations in ASVs have been limited due to the complex design challenges associated with conflicting requirements posed by the ride and roll/directional stability requirements. Growing concerns on human driver comfort and safety, and increasing demands for higher speed ASVs such as articulated dump trucks, however, call for alternate suspension designs for realizing an improved compromise between the ride and stability performance. This dissertation research is aimed at analysis of a torsio-elastic axle suspension concept for achieving improve ride, while preserving the directional stability limits of the ASV. For this purpose a comprehensive three- dimensional model of the articulated frame steer vehicles is developed for design and analysis of the proposed axle suspension concept. The model is formulated considering a three-dimensional tire model, tire lag, coherent right- and left-terrain track roughness, and kinematics and dynamics of the steering struts. Field measurements were performed to characterize the ride properties of a conventional forestry skidder and that of a skidder retrofitted with the rear-axle torsio- iii elastic suspension under different load conditions. The measured data were analyzed to assess the ride performance potential of the suspension and to examine validity of the simulation model. Both the field measured and simulation results revealed that the proposed suspension could yield significant reductions in the magnitudes of vibration transmitted to the operator location, irrespective of the load and speed conditions. A simple yaw-plane model of the vehicle is also formulated to study the role of steering system design including the steering valve flows, kineto-dynamics of the steering struts and leakage flows on the snaking stability limits of the ASV. The results showed that the critical speeds are strongly dependent upon the kineto-dynamics of the articulated steering system. The comprehensive three-dimensional model subsequently used for analysis of integrated ride and roll/directional stability limits of the vehicle and the axle suspension designs. The stability performance measures are defined to assess the vehicle stability limits under steady as well as transient directional maneuvers. The results show that the proposed rear-axle suspension deteriorates the stability performance only slightly, irrespective of the load condition. It is concluded that the proposed suspension concept could yield a very good compromise in ride and stability performance. The proposed model could serve as an effective and efficient tool for integrated ride and handling analysis and to seek primary suspension designs for an improved compromise between the ride and stability performance of ASVs. iv ACKNOWLEDGMENTS The author wishes to express his sincere appreciation to his thesis supervisors, Dr. Subhash Rakheja and Dr. Dangpu Cao, for initiating the study topic and for their great supports and continued guidance and efforts through the thesis work. The author also wishes to acknowledge Quebec Government, Concordia University, Hydro Quebec and CONCAVE center for their financial support: International Tuition Fee Remission, Concordia Merit Award, Concordia Accelerator Award, Hydro Quebec Award, and Research Assistantship, respectively. The author also thanks colleagues, faculty and staff at the department of Mechanical and Industrial Engineering, and CONCAVE center, for their contributions to this thesis work. The author also wishes to acknowledge Dr. Thomas Heegaard Langer and Hydrema Company for their great corporations. Finally, the author would like to express his special thanks to his family and friends, specially, Mr. Reza Ahani and Mr. Kordestani for their support and encouragement. The author would like to dedicate this thesis to the memory of his father who passed away in 2004 to keep his spirit alive and to his mother for her great support. v LIST OF CONTENTS LIST OF FIGURES .................................................................................................... iXVI LIST OF TABLES ........................................................................................................ XVI NOMENCLATURE ..................................................................................................... XVI CHAPTER 1 LITERATURE REVIEW AND SCOPE OF THE DISSERTATION ........................... 1 1.1 Introduction ............................................................................................................. 1 1.2 Review of Relevant Literature ................................................................................ 5 1.2.1 Characterization of vibration and vibration assessment of off-road vehicles .... 6 1.2.2 Ride dynamic analyses and vibration control ................................................... 10 1.2.3 Tire modeling .................................................................................................... 12 1.2.4 Terrain roughness ............................................................................................. 18 1.2.5 Vehicle Suspensions .......................................................................................... 20 1.2.6 Directional/roll stability dynamics ................................................................... 24 1.3 Scope and Objective of the Dissertation .............................................................. 32 1.3.1 Objectives of the dissertation research ............................................................. 33 1.3.2 Organization of the dissertation-manuscript based format .............................. 35 CHAPTER 2 RIDE DYNAMIC EVALUATIONS AND DESIGN OPTIMIZATION OF A TORSIO-ELASTIC OFF-ROAD VEHICLE SUSPENSION .................................... 40 2.1 Introduction ........................................................................................................... 40 2.2 Ride Dynamic Modeling of an Off-Road Skidder .............................................. 43 2.3 Torsio-Elastic Suspension Concept ...................................................................... 45 2.4 Development of a Ride Dynamic Vehicle Model with Rear-Axle Suspension .. 46 2.5 Field Measurements of Vehicle Ride Vibration Responses ................................ 49 2.6 Measurement Methods and Data Analyses ......................................................... 50 2.7 Response Analyses of the Vehicle Model .............................................................. 52 2.8 Estimation of an Equivalent Terrain Profile ....................................................... 54 2.9 Results and Discussions ......................................................................................... 58 2.9.1 Vehicle model validation ................................................................................. 60 2.9.2 Sensitivity analysis and optimization of the torsio-elastic suspension design .. 64 2.9.3 Optimization variables and objective functions ................................................ 66 2.10 Conclusions........................................................................................................... 69 APPENDIX 2-A: TIRE AND SUSPENSION FORCES AND MOMENTS ............ 72 CHAPTER 3 vi COMPREHENSIVE MODELING AND VALIDATION OF OFF-ROAD VEHICLE RIDE DYNAMICS ......................................................................................................... 74 3.1 Introduction ........................................................................................................... 74 3.2 Modeling of Tire-Terrain Interactions ................................................................. 78 3.2.1 Adaptive footprint tire model in the pitch-plane ............................................... 78 3.2.2 Lateral tire force ............................................................................................... 81 3.3 Ride Dynamics Modeling of Off-Road Vehicles .................................................. 82 3.3.1 Unsuspended off-road vehicles ......................................................................... 82 3.3.2 Suspended off-road vehicles with rear-axle torsio-elastic suspension ............. 84 3.3.3 Estimation of the terrain roughness profiles ..................................................... 86 3.4 Method of Analysis ................................................................................................ 93 3.5 Results Discussions and Model Validation .......................................................... 94 3.6 Parameter Sensitivity Analysis ............................................................................. 99 3.7 Conclusions........................................................................................................... 103 CHAPTER 4 KINETO-DYNAMIC DIRECTIONAL RESPONSE ANALYSIS OF AN ARTICULATED FRAME STEER VEHICLE .......................................................... 105 4.1 Introduction ......................................................................................................... 105 4.2 Kineto-Dynamic Modeling of the Steering System ........................................... 109 4.2.1 Steering system kinematics ..............................................................................110 4.2.2 Steering system dynamics ................................................................................ 111 4.3 Formulations of the 3-DOF Yaw Plane Vehicle Model ......................................117 4.3.1 Tire lateral forces ............................................................................................ 120 4.4 Method of Analysis .............................................................................................. 121 4.5 Results and Discussions...................................................................................121 4.5.1 Model validation ............................................................................................. 123 4.5.2 Steady-state response characteristics of the steering system .......................... 125 4.5.3 Yaw stability analysis ...................................................................................... 137 4.6 Conclusions and Design Guidance ..................................................................... 143 CHAPTER 5 A THREE-DIMENSIONAL MODEL OF AN ARTICULATED FRAME-STEER VEHICLE FOR COUPLED RIDE AND HANDLING DYNAMIC ANALYSES .. 146 5.1 Introduction ......................................................................................................... 146 5.2 Development of the 3-Dimentional Vehicle Dynamic Model: .......................... 150 5.2.1 External forces and moments: ......................................................................... 156 5.3 Method of Analysis .............................................................................................. 163 5.4 Results and Discussions ....................................................................................... 169 5.4.1 Model validations............................................................................................ 169 5.4.2 Ride dynamics responses of the articulated dump truck ................................. 172 vii 5.4.3 Roll and yaw stability analysis of articulated steer vehicle ............................ 175 5.4.4 Effect of terrain roughness on roll and yaw directional stability ................... 179 5.4.5 Effect of vehicle load on ride and yaw/roll responses .................................... 180 5.4.6 Effect of suspension parameters on ride and yaw/roll responses ................... 181 5.5 Conclusions........................................................................................................... 185 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS ...................................................... 187 6.1 Highlights and major contributions of the dissertation research.................... 187 6.2 Conclusion ............................................................................................................ 188 6.3 Recommendations for Future Studies ............................................................... 190 REFERENCES .............................................................................................................. 192 viii LIST OF FIGURES Figure 1.1: A pictorial view and a schematic of an articulated frame steer vehicle. ……...5 Figure 1.2: (a) Three-dimensional tractor model and the related forces and torques acting on the body, axle, and wheel [100]; and (b) virtual multi-body model of a wheel loader [21]……………..…………………………….…………..………………12 Figure 1.3: Tire models used for ride dynamic analysis [117]………………………….14 Figure 1.4: Adaptive footprint tire model………………………………………………..15 Figure 1.4: Adaptive footprint tire model. ........................................................................ 15 Figure 1.5: (a) tire model consisting of spring and damper in parallel [100]; (b) tire model consisting of spring and damper in series [101]; and (c) visco-plastic model [110, 119]. ...................................................................................................................... 15 Figure 1.6: Roughness characteristics of different surfaces. ............................................ 19 Figure 1.7: Full-vehicle interconnected suspension arrangements: (a) hydraulic; (b) pneumatic; and (c) hybrid [154]. .......................................................................... 24 Figure 1.8: A three-DOF linear yaw-plane model of the articulated steer vehicle [159]. . 28 Figure 1.9: (a) Planar models of a forestry skidder [29]; and (b) a multibody model of an ASV for stability analysis [21]. ............................................................................ 29 Figure 2.1: Schematic of a wheeled forestry skidder. ....................................................... 43 Figure 2.2: Pitch- and roll-plane representations of a conventional skidder: (a) Pitch- plane; (b) Roll-plane, (front axle; front view); and (c) Roll-plane, (rear axle; rear view). .................................................................................................................... 44 Figure 2.3: The prototype rear-axle torsio-elastic suspension: (a) isometric schematic; (b) pictorial view; (c) roll-plane illustration of the suspension. ................................. 45 Figure 2.4: Schematic representation of the 13-DOF suspended vehicle model: (a) roll plane; (b) pitch plane; and (c) torsio-elastic suspension linkage mechanism. ...... 47 Figure 2.5: Locations of accelerometers on the cabin floor: “1”, “2”and “3”, oriented along the x, y and z -axes at the rear-left, respectively; “4” at the seat base along z -axes; “5” front-left along z -axes; and “6” front-right along z -axes. ............ 51 Figure 2.6: Spatial spectral density of terrain elevation identified from measured data at various discrete frequencies and the power regression curve (r2=0.6425). .......... 56 Figure 2.7: Comparisons of roughness profiles of some of the off-road terrains with that ix estimated for the forestry terrain. .......................................................................... 57 Figure 2.8: Comparisons of measured acceleration PSD responses at the cab floor of the suspended and unsuspended vehicles: (a) fore-aft; (b) lateral; (c) vertical; (d) pitch; and (e) roll. .................................................................................................. 62 Figure 2.9: Comparisons of acceleration PSD responses of the suspended vehicle model with those of the measured data: (a) vertical; (b) pitch; and (c) roll. .................... 63 Figure 2.10: Pareto optimal solutions for weighted accelerations responses: (a) roll vs vertical acceleration; (b) pitch vs vertical acceleration; (c) pitch vs roll acceleration. .......................................................................................................... 68 Figure 3.1: Adaptive foot-print radial tire model. ............................................................. 79 Figure 3.2: (a) Wheel-terrain contact patch; and (b) Circle-line interaction representation. ............................................................................................................................... 80 Figure 3.3 Tire lateral ride dynamic model consisting of linear spring and damper in series. .................................................................................................................... 82 Figure 3.4: Pitch- and roll-plane representations of an unsuspended skidder: (a) Pitch- plane; and (b) Roll-plane, (front view) ................................................................. 83 Figure 3.5: Schematic representation of the 14-DOF suspended vehicle model: (a) roll plane; (b) pitch plane; and (c) torsio-elastic suspension linkage mechanism. ...... 85 Figure 3.6: Comparison of the roughness profile with that estimated from model proposed by Hac [133]. ......................................................................................... 88 Figure 3.7: Comparison of the coherence values obtained from Eq. (3.16) with that approximated by fractional system function. ........................................................ 90 Figure 3.8 Flowchart of the proposed method to find the time series of two tracks profiles. ................................................................................................................. 91 Figure 3.9: Time histories of roughness of the (a) left track; and (b) right track (U=5km/h). ........................................................................................................... 91 Figure 3.10: Coherence of the two track profiles compared with the target coherence. .. 92 Figure 3.11: Roll displacement (a) time-history; and (b) PSD spectrum. ......................... 92 Figure 3.12: Comparisons of acceleration PSD responses of the conventional vehicle model with those of the measured data. ................................................................ 95 Figure 3.13: Comparisons of acceleration PSD responses of the suspended vehicle model x