Post on 25-Jun-2015
description
12/20/2013
1
Predicting Net Traction on Soil Using a
Continuum Approach
Anoop Varghese1, John Turner1, Thomas Way2, Clarence
Johnson3, Brian Steenwyk1
1 Bridgestone Americas Tire Operations 2 National Soil Dynamics Lab 3 Auburn University
12/20/2013
2
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Agenda
1. Problem Definition
2. Challenges
3. Methodology
4. Results
5. Summary
2
AGV – 04/30/2012
12/20/2013
3
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Tilled Soil - Loose soil
- Somewhat controlled
Sod Soil - Organic content
- uncontrolled
Problem Definition
AGV – 04/30/2012
3
Problem: Predict net traction of an
AG tire in agricultural soil
Benefit of the study
Improve mechanistic understanding of tire traction performance
Improve product performance
Find the balance between compaction & traction
Reduce development cycle time
12/20/2013
4
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Challenges / Difficulties – 1/2
4
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
Model individual particles
Challenges: Clay particles are < 0.002 mm 1
mm3 of soil will contain ~ 106
particles
Capturing effect of moisture and
other microscopic interactions
Model soil as a continuum
Advantages: Use FEA to solve governing equations
Notes: Only average behavior of soil is captured
Approach #2
12/20/2013
5
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Challenges / Difficulties – 2/2
Spring
Non-linear
slider
1-D Soil Model based on Plasticity
5
Definition of slider
- When does it start to slide (yield function)
- How does it slide (flow potential)
R. Hill, The Mathematical Theory of Plasticity, 1950, Oxford University Press, Oxford
Notes about Bridgestone/Firestone model
- Satisfies consistency condition all the time
- Uses non-associated flow rule
- Enhancement of Drucker-Prager model
New Bridgestone/Firestone soil model for agricultural soil
Other Challenges
Very large & permanent deformations Instabilities in material
12/20/2013
6
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Methodology / Approach
6
Objective: Predict net traction of an AG
tire in tilled agricultural soil
L
H W
2R
Developed New
VDP Soil Model: New soil model for
improving physics
Triaxial Loading Rigid Wheel Rolling on Soil
(NSDL Test)
Plain Tread Rolling on Soil
33 , xX
11 , xX
22 , xX
v
F
h
1
3
12/20/2013
7
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Validation of the Soil Model in Triaxial Test
7
L
H W
2R
Triaxial Loading Rigid Wheel Rolling on Soil
(NSDL Test)
Plain Tread Rolling on Soil
1
3
33 , xX
11 , xX
22 , xX
v
F
h
Objective: Predict net traction of an AG
tire in tilled agricultural soil
Developed New
VDP Soil Model: New soil model for
improving physics
12/20/2013
8
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Validation of Bridgestone/Firestone Soil Model
8
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
12/20/2013
9
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Validation of the Soil Model in Rigid Wheel Analysis
9
L
H W
2R
Triaxial Loading Rigid Wheel Rolling on Soil
(NSDL Test)
Plain Tread Rolling on Soil
1
3
33 , xX
11 , xX
22 , xX
v
F
h
Objective: Predict net traction of an AG
tire in tilled agricultural soil
Developed New
VDP Soil Model: New soil model for
improving physics
12/20/2013
10
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Prediction of Net Traction of Rigid Wheel
10
AGV – 04/30/2012
y = 1.0506x + 0.3631
R² = 0.9826
y = 0.7495x + 0.4226
R² = 0.9618
0
1
2
3
4
5
0 1 2 3 4 5
Pre
dic
ted T
ractio
n [kN
]
Measured Traction [kN]
LSDYNA_VDP
ABAQUS_mod_DP
1:1 line
y = 1.0664x + 0.3447
R² = 0.9787
y = 0.697x + 0.4975
R² = 0.9809
0
1
2
3
4
5
0 1 2 3 4 5
Pre
dic
ted T
ractio
n [kN
]
Measured Traction [kN]
LSDYNA_VDP
ABAQUS_modDP
1:1 line
Norfolk Sandy Loam Decatur Clay Loam Load
[kN]
Slip
Rate
[%]
2.9 11&23
5.8 11&23
8.7 11&23
11.6 11&23
Test data from NSDL
Bridgestone/Firestone soil model is able to
predict net traction very well for a rigid
wheel
Bridgestone/Firestone
(LSDYNA) Bridgestone/Firestone
(LSDYNA)
W. Block, Analysis of Soil Stress Under Rigid Wheel Loading, PhD
Dissertation, Agricultural Engineering, Auburn University, 1991
0
50
100
150
200
Load=5.8kN
Slip Rate = 23%
Load=11.6kN
Slip Rate = 23%
Ru
t D
ep
th [m
m]
Measured
Predicted
12/20/2013
11
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Validation of the Soil Model in Plain Tread Traction
11
L
H W
2R
Triaxial Loading Rigid Wheel Rolling on Soil
(NSDL Test)
Plain Tread Rolling on Soil
1
3
33 , xX
11 , xX
22 , xX
v
F
h
Objective: Predict net traction of an AG
tire in tilled agricultural soil
Developed New
VDP Soil Model: New soil model for
improving physics
12/20/2013
12
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Prediction of Net Traction of a Plain Tread Tire
12
AGV – 04/30/2012
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)
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
12/20/2013
13
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Objective: Predict net traction of an AG
tire in tilled agricultural soil
Validation of Soil Model in Full AG tire Analysis
13
L
H W
2R
Triaxial Loading Rigid Wheel Rolling on Soil
(NSDL Test)
Plain Tread Rolling on Soil
1
3
33 , xX
11 , xX
22 , xX
v
F
h
Developed New
VDP Soil Model: New soil model for
improving physics
12/20/2013
14
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Prediction of Net Traction for a Full AG tire
14
Measurement is the average of nine tests –
tilled condition
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
0
20
40
60
80
100
120
Firestone Tire
(RAT_DT - 710/70R42)
Competitor Tire
(710/70R42)
No
rma
lized N
et T
raction
Measured
Predicted
0
20
40
60
80
100
120
1 2 3 4 5 6 7 8 9
Ind
ex M
ea
su
red
Ne
t T
ractio
n [kN
]
Competitor Tire
Firestone RAT_DT
Sep-30-2010
Sep-24-2010
2009
12/20/2013
15
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
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
15
AGV – 04/30/2012
12/20/2013
16
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Thank You
Questions
AGV – 04/30/2012
16
12/20/2013
17
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Bridgestone/Firestone Soil Model
Spring
Friction
increases
with
deformation
1-D Model of Soil 3-D Model of Soil: Yield Surface
Component 1: Normal Consolidation Curve
Pressure vs. soil compaction curve
This function determines soil compaction
pressure
pressure
17
AGV – 04/30/2012
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
4E-16
0 100 200 300 400 500
Vo
lum
etr
ic S
train
Hydrostatic Pressure [kPa]
12/20/2013
18
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Bridgestone/Firestone Soil Model
1-D Model of Soil 3-D Model of Soil: Yield Surface
Component 2: Shear Failure Surface
Determines when soil fails (flows like a
liquid)
Direct influence on traction
0
100
200
300
400
0 100 200 300 400 500
Sh
ea
r S
tre
ss [kP
a]
Pressure [kPa]
Shear Failure Surface
shear
shear
18
AGV – 04/30/2012
Spring
Friction is
a function
of pressure
and shear
stress
12/20/2013
19
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Mechanics of Traction
n
e
1x
2x
pT ve
soil
surface rut surface
direction of motion
soil strength - driving
Normal Contact Forces
Tangential Contact Forces
Motion Resistance p
T ve
fT ve+
Contact
pressure Frictional
Friction Contact
Pressure
19
AGV – 04/30/2012
Net Traction
fT ve
fT ve
pT ve- -
n
e
1x
2x
fT ve
fT ve
direction of motion
soil
surface rut surface
friction - driving
12/20/2013
20
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
National Soil Dynamics Lab (@ Auburn)
Top of soil bins & testing facility
Indoor soil bin
Single wheel traction tester
AGV – 04/30/2012
20
12/20/2013
21
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Problem Definition - Validation
Rigid Wheel Rolling on Soil
Test Output
Net Traction
Rut Depth
Stresses beneath soil surface
AGV – 04/30/2012
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 1.372 m x 0.305 m
Soil Bin Size 57.3 m x 6.1 m x 1.8 m
21
W. Block, Analysis of Soil Stress Under Rigid Wheel Loading, PhD Dissertation, Agricultural Engineering, Auburn University, 1991
12/20/2013
22
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Columbiana AG Tire Test Facility
22
An instrumented tractor that can
generate drawbar-pull of 38,400 lbs-f
Testing is done in a prepared/tilled field
12/20/2013
23
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Challenges / Difficulties – 3/3
23
Very large deformations Continuum mechanics
Eulerian formulation of balance
laws in soil
Permanent deformations Theory of plasticity (soil model)
Lagrangian:
speedometers inside a
car
Eulerian: sensors on
the road
Instabilities Theory of plasticity (soil model)
Explicit analysis
12/20/2013
24
The leader in the field Copyright © 2013 Bridgestone Americas, Inc.
Verification of Bridgestone/Firestone Soil Model
24
AGV – 04/30/2012
Triaxial Loading Test
Applied
Lateral
Pressure, 3
Applied Normal
Pressure, 1