Prediction of the Off-Road Rigid-Ring Model Parameters for Truck Tire and Soft Soil Interactions By Kristian Lee Lardner A Thesis Presented in Partial Fulfillment of the Requirements for the Degree of Master of Applied Science in Automotive Engineering Faculty of Engineering and Applied Science University of Ontario Institute of Technology Oshawa, Ontario, Canada July 2017 © 2017 Kristian Lardner ABSTRACT Significant time and cost savings can be realized through the use of virtual simulation of testing procedures across diverse areas of research and development. Fully detailed virtual truck models using the simplified off-road rigid-ring model parameters may further increase these economical savings within the automotive industry. The determination of the off-road rigid-ring parameters is meant to facilitate the simulation of full vehicle models developed by Volvo Group Trucks Technology. This works features new FEA (Finite Element Analysis) tire and SPH (Smoothed Particle Hydrodynamics) soil interaction modeling techniques. The in-plane and out-of-plane off-road rigid-ring parameters are predicted for an RHD (Regional Haul Drive) truck tire at varying operating conditions. The tire model is validated through static and dynamic virtual tests that are compared to previously published literature. Both the in-plane and out-of-plane off-road rigid-ring RHD parameters were successfully predicted. The majority of the in-plane parameters are strongly influenced by the inflation pressure of the tire because the in-plane parameters are derived with respect to the mode of vibration of the tire. The total equivalent vertical stiffness on a dry sand is not as heavily influenced by the inflation pressure compared to predictions on a hard surface. For perspective, at 110 psi, the dry sand total vertical stiffness is nearly nine times smaller than that determined on the hard surface, while the lateral stiffness on soft soil (Dry Sand) is at a minimal of three times higher than that of the corresponding values tested on a hard surface. The cornering stiffness is primarily load dependant because the inflation pressure is only noticeably influential at high vertical loads. More importantly, the soil builds in front of the tire, creating what is called a bulldozing effect, during high slip angles. The additional lateral force of the soil exerted onto the tire during cornering maneuvers may contribute to higher than expected results and may be confirmed through future investigation of the cohesion of the soil model. Key Words: FEA (Finite Element Analysis), SPH (Smoothed Particle Hydrodynamics), RHD (Regional Haul Drive truck tire), Off-Road Rigid-Ring Tire Model i TABLE OF CONTENTS 1.1 Motivation ................................................................................................. 1 1.2 Problem Statement .................................................................................... 1 1.3 Objectives and Scope ................................................................................ 2 1.4 Working Fundamentals ............................................................................. 2 1.4.1 Construction of Pneumatic Tires ......................................................... 3 1.4.2 Dynamics of Pneumatic Tires ............................................................. 4 1.5 Thesis Outline ........................................................................................... 6 2.1 Chapter Introduction ................................................................................. 7 2.2 Tire Modeling ............................................................................................ 7 2.2.1 Analytical Tire Modeling .................................................................... 7 2.2.2 FEA Tire Modeling ........................................................................... 14 2.3 Soil Modeling .......................................................................................... 18 2.3.1 Terra-mechanics ................................................................................ 18 2.3.2 FEA Soil Modeling ........................................................................... 21 ii 2.3.3 SPH Soil Modeling ........................................................................... 23 2.3.4 Hybrid Soil Modeling........................................................................ 27 2.4 Chapter Summary .................................................................................... 29 3.1 Chapter Introduction ............................................................................... 32 3.2 RHD Tire Modeling ................................................................................ 32 3.2.1 Final FEA Tire Model ....................................................................... 34 3.2.2 Tire Validation .................................................................................. 36 3.3 Dry Sand SPH Soft Soil Modeling .......................................................... 40 3.3.1 Pressure-Sinkage Relationship .......................................................... 40 3.3.2 Shear Strength ................................................................................... 44 3.4 Chapter Summary .................................................................................... 46 4.1 Chapter Introduction ............................................................................... 47 4.2 Drum-Cleat Testing Procedure................................................................ 49 4.3 Drum-Cleat Results and Observations .................................................... 51 4.4 Determination of the Sidewall Damping Coefficient .............................. 55 4.5 Chapter Summary .................................................................................... 55 5.1 Chapter Introduction ............................................................................... 57 5.2 List of In-Plane Rigid-Ring Parameters .................................................. 57 5.3 Total Equivalent Vertical Stiffness, 풌풕풐풕, 푯풂풓풅 푺풖풓풇풂풄풆 .................. 59 5.4 Vertical Stiffness and Residual Vertical Stiffness, 풌풃풛 and 풌풗풓 ........... 61 iii 5.5 Total Vertical Damping and Residual Damping Constant, ctot and cvr ..................................................................................................... 63 5.6 Rotational Stiffness and Damping Constant, 풌풃휭 and 풄풃휭 .................. 65 5.7 Total Equivalent Vertical Stiffness, 풌풕풐풕, 푫풓풚 푺풂풏풅 ........................... 68 5.8 Longitudinal Tire Stiffness, 풌풌, 푫풓풚 푺풂풏풅 ........................................... 71 5.9 Chapter Summary .................................................................................... 74 5.9.1 13.34 kN In-Plane Parameter Summary ............................................ 75 5.9.2 26.69 kN In-Plane Parameter Summary ............................................ 76 5.9.3 40.03 kN In-Plane Parameter Summary ............................................ 77 6.1 Chapter Introduction ............................................................................... 78 6.2 List of Out-of-Plane Rigid-ring Parameters ............................................ 78 6.3 Translational Stiffness and Damping Constant, 풌풃퐲 and 풄풃퐲 ............... 80 6.4 Rotational Stiffness and Damping Constant, 풌풃후 and 풄풃후 .................... 83 6.5 Lateral Tire Stiffness and Damping Constant, 풌풍 and 풄풍 ........................ 87 6.6 Lateral Tire Stiffness and Damping Constant, kl, Dry Sand and cl, Dry Sand .......................................................................... 90 6.7 Steering Characteristics on Dry Sand, 풌풇, 푫풓풚 푺풂풏풅 ........................... 94 6.8 Self-Aligning Moment Stiffness on Dry Sand, 푴풛, 푫풓풚 푺풂풏풅............. 97 6.9 Relaxation Length on Dry Sand, 흈푫풓풚 푺풂풏풅 ....................................... 99 6.10 Rolling Resistance Coefficient on Dry Sand, 푹푹푪푫풓풚 푺풂풏풅 .......... 99 6.11 Chapter Summary .............................................................................. 101 6.11.1 13.34 kN Out-of-Plane Parameter Summary ................................ 102 6.11.2 26.69 kN Out-of-Plane Parameter Summary ................................ 103 iv 6.11.3 40.03 kN Out-of-Plane Parameter Summary ................................ 104 7.1 Conclusions ........................................................................................... 105 7.2 Future Work .......................................................................................... 108 v LIST OF FIGURES Figure 1-1: Pneumatic (Radial-Ply) Tire Construction [5] ..................................... 3 Figure 1-2: Radial-Ply Pneumatic Tire [1] ............................................................. 4 Figure 1-3: Forces and Moments Acting on a Tire in the SAE Coordinate System [1] ............................................................................................................... 5 Figure 2-1: Point Contact Mechanism by Captain et al. [6] ................................. 8 Figure 2-2: Loo's Flexible Rigid-Ring Model [9] ................................................... 9 Figure 2-3: Basic Rigid-Ring Tire Model [10] ..................................................... 10 Figure 2-4: Bruni’s Rigid-ring Tire Model [12] ................................................... 11 Figure 2-5: Chae's Out-of-Plane Rigid-ring Model [16] ...................................... 12 Figure 2-6: Slade's In-Plane Off-Road Rigid-Ring Model [17] ........................... 13 Figure 2-7: Slade's Out-of-Plane