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# Predicting Net Traction on Soil Using a Continuum Approach Paper82111

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Anoop Varghese(1), John Turner(1), Thomas Way(2), Clarence Johnson(3), Brian Steenwyk(1)
1 Bridgestone Americas Tire Operations
2 National Soil Dynamics Lab
3 Auburn University

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### Predicting Net Traction on Soil Using a Continuum Approach Paper82111

1. 1. 12/20/2013 Predicting Net Traction on Soil Using a Continuum Approach Anoop Varghese1, John Turner1, Thomas Way2, Clarence Johnson3, Brian Steenwyk1 1 Bridgestone Americas Tire Operations National Soil Dynamics Lab 3 Auburn University 2 1
2. 2. 12/20/2013 Agenda 1. Problem Definition 2. Challenges 3. Methodology 4. Results 5. Summary The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 2 AGV – 04/30/2012 2
3. 3. 12/20/2013 Problem Definition Problem: Predict net traction of an AG tire in agricultural soil Tilled Soil - Loose soil - Somewhat controlled Sod Soil - Organic content - uncontrolled Benefit of the study     Improve mechanistic understanding of tire traction performance Improve product performance Find the balance between compaction & traction Reduce development cycle time The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 3 AGV – 04/30/2012 3
4. 4. 12/20/2013 Challenges / Difficulties – 1/2 Mechanistic Definition of Soil Solid Particles of different sizes and shapes Clay, Silt, Sand, etc Liquid Surface tension of water Air Important for root growth Approach #1 Approach #2 Model individual particles Model soil as a continuum Challenges: Notes:  Clay particles are < 0.002 mm  1 mm3 of soil will contain ~ 106 particles  Capturing effect of moisture and other microscopic interactions The leader in the field  Only average behavior of soil is captured Advantages:  Use FEA to solve governing equations Copyright © 2013 Bridgestone Americas, Inc. 4 4
5. 5. 12/20/2013 Challenges / Difficulties – 2/2 New Bridgestone/Firestone soil model for agricultural soil 1-D Soil Model based on Plasticity Definition of slider - When does it start to slide (yield function) Spring Non-linear slider - How does it slide (flow potential) Notes about Bridgestone/Firestone model - Satisfies consistency condition all the time - Uses non-associated flow rule - Enhancement of Drucker-Prager model Other Challenges Very large & permanent deformations Instabilities in material R. Hill, The Mathematical Theory of Plasticity, 1950, Oxford University Press, Oxford The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 5 5
6. 6. 12/20/2013 Methodology / Approach Objective: Predict net traction of an AG tire in tilled agricultural soil Developed New VDP Soil Model: New soil model for improving physics 2R F 1  h v X 2 , x2 3 X 1 , x1 H X 3 , x3 W L Triaxial Loading Rigid Wheel Rolling on Soil (NSDL Test) The leader in the field Plain Tread Rolling on Soil Copyright © 2013 Bridgestone Americas, Inc. 6 6
7. 7. 12/20/2013 Validation of the Soil Model in Triaxial Test Objective: Predict net traction of an AG tire in tilled agricultural soil Developed New VDP Soil Model: New soil model for improving physics 2R F 1  h v X 2 , x2 3 X 1 , x1 H X 3 , x3 W L Triaxial Loading Rigid Wheel Rolling on Soil (NSDL Test) The leader in the field Plain Tread Rolling on Soil Copyright © 2013 Bridgestone Americas, Inc. 7 7
8. 8. 12/20/2013 Validation of Bridgestone/Firestone Soil Model Loading Path 1 Loading Path 2 Loading Path 3  Bridgestone/Firestone model improves the prediction of shearing flow/deformation of soil under triaxial loading conditions A. C. Bailey and C. E. Johnson, Soil Critical State Behavior in the NSDL-AU model, ASAE Papers 941074 & 961064 The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 8 8
9. 9. 12/20/2013 Validation of the Soil Model in Rigid Wheel Analysis Objective: Predict net traction of an AG tire in tilled agricultural soil Developed New VDP Soil Model: New soil model for improving physics 2R F 1  h v X 2 , x2 3 X 1 , x1 H X 3 , x3 W L Triaxial Loading Rigid Wheel Rolling on Soil (NSDL Test) The leader in the field Plain Tread Rolling on Soil Copyright © 2013 Bridgestone Americas, Inc. 9 9
10. 10. 12/20/2013 Prediction of Net Traction of Rigid Wheel 5 Norfolk Sandy Loam y = 1.0506x + 0.3631 4 R² = 0.9826 3 y = 0.7495x + 0.4226 2 R² = 0.9618 Bridgestone/Firestone LSDYNA_VDP (LSDYNA) ABAQUS_mod_DP 1 1:1 line 0 0 200 Rut Depth [mm] Predicted Traction [kN] Predicted Traction [kN] 5 150 1 2 3 Measured Traction [kN] Decatur Clay Loam 11&23 11&23 y = 0.697x + 0.4975 8.7 11&23 R² = 0.9809 11.6 11&23 R² = 0.9787 3 2 Bridgestone/Firestone LSDYNA_VDP (LSDYNA) ABAQUS_modDP 1 1:1 line 0 5 2.9 y = 1.0664x + 0.3447 0 4 Slip Rate [%] 5.8 4 Load [kN] 1 2 3 Measured Traction [kN] 4 5 Measured Predicted Test data from NSDL Bridgestone/Firestone soil model is able to predict net traction very well for a rigid wheel 100 50 0 Load=5.8kN Load=11.6kN Slip Rate = 23% Slip Rate = 23% W. Block, Analysis of Soil Stress Under Rigid Wheel Loading, PhD Dissertation, Agricultural Engineering, Auburn University, 1991 The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 10 AGV – 04/30/2012 10
11. 11. 12/20/2013 Validation of the Soil Model in Plain Tread Traction Objective: Predict net traction of an AG tire in tilled agricultural soil Developed New VDP Soil Model: New soil model for improving physics 2R F 1  h v X 2 , x2 3 X 1 , x1 H X 3 , x3 W L Triaxial Loading Rigid Wheel Rolling on Soil (NSDL Test) The leader in the field Plain Tread Rolling on Soil Copyright © 2013 Bridgestone Americas, Inc. 11 11
12. 12. 12/20/2013 Prediction of Net Traction of a Plain Tread Tire Year Load [kN] Inflation Pressure [kPa] Slip Rate [%] 2009 44.5 kN (10,000 lbs-f) 70 kPa (10 psi) 240 kPa (35 psi) 5, 10, 15 2010 66.7 kN (15,000 lbs-f) 70 kPa (10 psi) 240 kPa (35 psi) 5, 10, 15 Testing done by Firestone on tilled soil on a tire size 710/ 70 R 42 Soil Model is for Decatur Clay Loam The predicted vs. measured correlation is 85% (very good) The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 12 AGV – 04/30/2012 12
13. 13. 12/20/2013 Validation of Soil Model in Full AG tire Analysis Objective: Predict net traction of an AG tire in tilled agricultural soil Developed New VDP Soil Model: New soil model for improving physics 2R F 1  h v X 2 , x2 3 X 1 , x1 H X 3 , x3 W L Triaxial Loading Rigid Wheel Rolling on Soil (NSDL Test) The leader in the field Plain Tread Rolling on Soil Copyright © 2013 Bridgestone Americas, Inc. 13 13
14. 14. 12/20/2013 120 Measured Predicted 100 Normalized Net Traction Index Measured Net Traction [kN] Prediction of Net Traction for a Full AG tire 80 60 120 100 80 60 Competitor Tire Firestone RAT_DT 40 20 0 2009 Sep-24-2010 1 2 3 4 5 6 Sep-30-2010 7 8 9 Measurement is the average of nine tests – tilled condition 40 20 0 Firestone Tire Competitor Tire (RAT_DT - 710/70R42) (710/70R42) Inflation = 23 psi (160 kPa) Vertical Load = 14,792 lbs-f (65.8 kN) Speed = 3 mph Tire Size = 710/70R42 Bridgestone/Firestone model is able to - rank the performance of these tires. - predicted absolute performance reasonably well The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 14 14
15. 15. 12/20/2013 Summary Problem Definition: Predict traction of AG tires in tilled soil using a continuum approach Developed new Bridgestone/Firestone soil model – Validated the soil model in triaxial loading conditions Predicted Net Traction successfully in the following cases – Rigid wheel – AG tire without lugs – AG tire with lugs Successfully predicted net traction using continuum approach and Bridgestone/Firestone soil model The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 15 AGV – 04/30/2012 15
16. 16. 12/20/2013 Thank You Questions The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 16 AGV – 04/30/2012 16
17. 17. 12/20/2013 Bridgestone/Firestone Soil Model 1-D Model of Soil pressure 3-D Model of Soil: Yield Surface Component 1: Normal Consolidation Curve 4E-16 Volumetric Strain -0.05 Spring Friction increases with deformation -0.1 -0.15 -0.2 -0.25 -0.3 -0.35 0 100 200 300 400 500 Hydrostatic Pressure [kPa] pressure Pressure vs. soil compaction curve This function determines soil compaction The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 17 AGV – 04/30/2012 17
18. 18. 12/20/2013 Bridgestone/Firestone Soil Model 1-D Model of Soil shear 3-D Model of Soil: Yield Surface Component 2: Shear Failure Surface Shear Stress [kPa] 400 Spring Friction is a function of pressure and shear stress Shear Failure Surface 300 200 100 0 0 shear 100 200 300 Pressure [kPa] 400 500  Determines when soil fails (flows like a liquid)  Direct influence on traction The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 18 AGV – 04/30/2012 18
19. 19. 12/20/2013 Mechanics of Traction Normal Contact Forces direction of motion x1 e Motion Resistance x2 n Tpve + Tfve soil surface rut surface soil strength - driving Contact pressure Tpve Frictional Tangential Contact Forces direction of motion x1 e x2 n Net Traction Tfve - Tpve - Tfve soil surface rut surface Tfve friction - driving Friction Tfve The leader in the field Contact Pressure Copyright © 2013 Bridgestone Americas, Inc. 19 AGV – 04/30/2012 19
20. 20. 12/20/2013 National Soil Dynamics Lab (@ Auburn) Indoor soil bin Top of soil bins & testing facility The leader in the field Single wheel traction tester Copyright © 2013 Bridgestone Americas, Inc. 20 AGV – 04/30/2012 20
21. 21. 12/20/2013 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, Rolling Speed [m/s] 0.15 Wheel Size 1.372 m x 0.305 m Soil Bin Size 57.3 m x 6.1 m x 1.8 m 23.0 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, 1991 The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 21 AGV – 04/30/2012 21
22. 22. 12/20/2013 Columbiana AG Tire Test Facility An instrumented tractor that can generate drawbar-pull of 38,400 lbs-f Testing is done in a prepared/tilled field The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 22 22
23. 23. 12/20/2013 Challenges / Difficulties – 3/3 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 (soil model) Explicit analysis The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 23 23
24. 24. 12/20/2013 Verification of Bridgestone/Firestone Soil Model Triaxial Loading Test Applied Normal Pressure, 1 Applied Lateral Pressure, 3 The leader in the field Copyright © 2013 Bridgestone Americas, Inc. 24 AGV – 04/30/2012 24