This document details the development and validation of a new Bridgestone/Firestone soil model aimed at predicting the net traction of agricultural tires on tilled soil. The study outlines challenges in modeling soil mechanics and presents methodologies, including the use of a continuum approach to increase accuracy in predicting tire performance under various loading conditions. The results show successful traction predictions for rigid wheels and different types of agricultural tires, providing a solid foundation for future developments in tire technology.

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
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2. 12/20/2013
Agenda
1. Problem Definition
2. Challenges
3. Methodology
4. Results
5. Summary
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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
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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
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 Only average behavior of soil is captured
Advantages:
 Use FEA to solve governing equations
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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
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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)
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Plain Tread Rolling on Soil
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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)
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Plain Tread Rolling on Soil
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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
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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
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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
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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
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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)
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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
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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
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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
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16. 12/20/2013
Thank You
Questions
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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
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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
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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
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Contact
Pressure
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20. 12/20/2013
National Soil Dynamics Lab (@ Auburn)
Indoor soil bin
Top of soil bins & testing facility
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Single wheel traction tester
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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
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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
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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
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24. 12/20/2013
Verification of Bridgestone/Firestone Soil Model
Triaxial Loading Test
Applied Normal
Pressure, 1
Applied
Lateral
Pressure, 3
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