Traction Prediction of a Smooth Rigid Wheel in Soil Using Coupled Eulerian-Lagrangian Analysis

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1 Traction Prediction of a Smooth Rigid Wheel in Soil Using Coupled Eulerian-Lagrangian Analysis Anoop Varghese 1, John Turner 1, Thomas Way 2, Clarence Johnson 3, Hans Dorfi 1 1 Bridgestone Americas Tire Operations LLC 2 National Soil Dynamics Laboratory 3 Auburn University 1

2 Agenda Problem Definition What is soil? Physics of Soil Deformation Permanent deformation, instabilities, etc Modeling Soil Continuum approach Analysis of Rigid Wheel Summary 2

Problem Definition Big Problem: Predict traction

understanding of tire traction performance Improve

Problem: Predict traction of a rigid wheel in controlled

81 m/s 2 F 2R h Removed pneumatics of the tire Removed

3 Problem Definition Big Problem: Predict traction performance of a tire in the field Improve mechanistic understanding of tire traction performance Improve product performance Reduce development cycle time Smaller Problem: Predict traction of a rigid wheel in controlled soil Acceleration due to gravity, 9.81 m/s 2 F 2R h Removed pneumatics of the tire Removed lugs/complex geometric features of a tire Soil is well controlled H L v X, x 2 2 X, x 1 1 X 3, x 3 W 3

4 What is Soil? - 1/3 Solid Liquid Air Clay Silt Sand Gravel < mm 0.05 to mm 2 to 0.05 mm >2 mm 4

5 What is Soil? - 2/3 Solid Liquid Air Sand [2 to 0.05 mm] Silt [0.05 to 0.002mm] Clay [<0.002 mm] Moisture/Liquid affects the strength of soil significantly Dry beach sand flows like water Mud (saturated soil) also flows like water Moist sand/soil is stronger than uncompacted (or loose) dry soil and mud (due to surface tension of water) 5

6 What is Soil? - 3/3 Solid Liquid Air Sand [2 to 0.05 mm] Silt [0.05 to 0.002mm] Clay [<0.002 mm] Moisture/Liquid affects the strength of soil significantly Air(voids) is a measure of compaction/voids in soil. 6

density achieved (only shearing deformation) Soil becomes denser and stiffer More available

7 Physics of soil deformation Loading Further Loading Volumetric compression; (permanent initially) + Shearing deformation (permanent) Max. density achieved (only shearing deformation) Soil becomes denser and stiffer More available traction Important for soil compaction & traction Critical State (shear failure / instability landslide) Important for max. available traction 7

Model soil as a continuum Challenges: Clay

002 mm 1 mm 3 of soil will contain ~ 10 6

other microscopic interactions Notes: Only

Individual particles, clumps in soil are

element is much larger than largest soil

8 Approaches to Modeling Soil Approach #1 Approach #2 Model individual particles Model soil as a continuum Challenges: Clay particles are < mm 1 mm 3 of soil will contain ~ 10 6 particles Capturing effect of moisture and other microscopic interactions Notes: Only average behavior of soil is captured Individual particles, clumps in soil are ignored Applicable only if smallest finite element is much larger than largest soil particle Advantages: Can use continuum mechanics Use FEA to solve governing equations Practical 8

Physics to be Modeled Very large deformations

laws in soil Lagrangian: speedometers inside a car

Theory of plasticity (soil model) Instabilities Theory

American Institute of Aeronautics and Astrophysics,

9 Physics to be Modeled Very large deformations Continuum mechanics Eulerian formulation of balance laws in soil Lagrangian: speedometers inside a car Eulerian: sensors on the road Permanent deformations Theory of plasticity (soil model) Instabilities Theory of plasticity (part of soil model) Explicit analysis Landslides R. C. Batra, Elements of Continuum Mechanics, 2005, AIAA: American Institute of Aeronautics and Astrophysics, Reston, VA R. Hill, The Mathematical Theory of Plasticity, 1950, AGV Oxford 04/30/2012 University Press, Oxford 9

10 Soil Model 1/3 1-D Model of Soil Spring Non-linear slider 10

11 Soil Model 1/3 Volumetric Strain 1-D Model of Soil 3-D Model of Soil: Yield Surface pressure Component 1: Normal Consolidation Curve Spring Pressure hardening of sliding Hydrostatic Pressure [kpa] pressure Pressure vs. soil compaction curve This function determines soil compaction 11

Soil Model 3/3 Shear Stress [kpa] 1-D Model of Soil 3-D Model of Soil: Yield Surface shear Component 2: Shear Failure Surface 400 Shear Failure Surface Spring

12 Soil Model 3/3 Shear Stress [kpa] 1-D Model of Soil 3-D Model of Soil: Yield Surface shear Component 2: Shear Failure Surface 400 Shear Failure Surface Spring Shear failure of slider shear Pressure [kpa] Determines when soil fails (flows like a liquid) Direct influence on traction 12

13 Verification of Soil Models 1. Mod. Drucker-Prager/Cap (ABAQUS) Shear failure surface Loading Path Mod. Drucker-Prager soil model is reasonable in this loading path other loading paths not shown here Norfolk Sandy Loam 13

14 National Soil Dynamics Lab Auburn) Indoor soil bin Top of soil bins & testing facility Single wheel traction tester 14

Problem Definition - Validation Rigid Wheel Rolling

15 Problem Definition - Validation Rigid Wheel Rolling on Soil Test Conditions Vertical Load [kn] 2.9, 5.8, 8.7, 11.6 Slip Rates [%] 11.1, 23.0 Rolling Speed [m/s] 0.15 Wheel Size m x m Soil Bin Size 57.3 m x 6.1 m x 1.8 m Test Output Net Traction Rut Depth Stresses beneath soil surface W. Block, Analysis of Soil Stress Under Rigid Wheel Loading, PhD Dissertation, Agricultural Engineering, Auburn University,

16 Mechanics of Traction Normal Contact Forces rut surface n e direction of motion x 2 soil surface x 1 Motion Resistance p T ve + f T ve soil strength - driving p T ve p T ve Contact pressure Frictional Tangential Contact Forces e direction of motion x 1 Net Traction n rut surface x 2 soil surface p T ve p T ve f T ve f T ve friction - driving f T ve slip plane f T ve Contact pressure Frictional 16

17 Video of Wheel Rolling on Soil Total Strain on Cap Surface (PEQC2) Predicts the slip plane under soil Permanent deformation of soil Strain has reached 2,700% Norfolk Sandy Loam Load = 11.6 kn Slip Rate = 11% 17

Traction Validation Norfolk Sandy Loam Predicted Traction [kn] 4 3 2 y = 1.0517x - 0.0764 R² = 0.9672 8.7 kn 11.

9 kn 0 1 2 3 4 Measured Traction [kn] Load; Slip Rate Measured Rut Depth [mm] Predicted Rut Depth [mm] 11.6kN; 23% 153 150 5.

18 Traction Validation Norfolk Sandy Loam Predicted Traction [kn] y = x R² = kn 11.6 kn Load [kn] 11 % Slip Rate 23 % Slip Rate 2.9 A1 A2 5.8 B1 B2 8.7 C1 C D1 D2 5.8 kn kn Measured Traction [kn] Load; Slip Rate Measured Rut Depth [mm] Predicted Rut Depth [mm] 11.6kN; 23% kN; 11% Very good comparison between predicted and measured net traction Predictions underestimate effect of slip rate Other data points for rut depth are not available 18

19 Traction Validation Decatur Clay Loam Predicted Traction [kn] y = 0.953x R² = kn 11.6 kn Load [kn] 11 % Slip Rate 23 % Slip Rate 2.9 A1 A2 5.8 B1 B2 8.7 C1 C D1 D2 5.8 kn kn Measured Traction [kn] Very good comparison between predicted and measured net traction Predictions underestimate effect of slip rate 19

20 Summary Problem: Predict traction of a rigid wheel rolling in soil Continuum approach to solve the problem Used continuum mechanics, theory of plasticity, & FEA Verified ABAQUS soil model Analysis of Rigid Wheel Rolling on Soil Solution predicted presence of slip surfaces Predicted and measured traction and rut depth compared very well Shows that continuum approach can be applied to soil 20

21 Thank You Questions 21

Traction Prediction of a Smooth Rigid Wheel in Soil using Coupled Eulerian-Lagrangian Analysis

Traction Prediction of a Smooth Rigid Wheel in Soil using Coupled Eulerian-Lagrangian Analysis Anoop G. Varghese 1, John L. Turner 1, Thomas R. Way 2, Clarence E. Johnson 3, Hans R. Dorfi 1 1 Advanced