Predicting Net Traction on Soil Using a Continuum Approach Paper82111

12/20/2013

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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

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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

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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

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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

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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

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Validation of the Soil Model in Triaxial Test

7

L

H W

2R


(NSDL Test)


1

3

33 , xX

11 , xX

22 , xX

v

F

h



Developed New


improving physics

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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

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Validation of the Soil Model in Rigid Wheel Analysis

9

L

H W

2R


(NSDL Test)


1

3

33 , xX

11 , xX

22 , xX

v

F

h



Developed New


improving physics

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Prediction of Net Traction of Rigid Wheel

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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

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Validation of the Soil Model in Plain Tread Traction

11

L

H W

2R


(NSDL Test)


1

3

33 , xX

11 , xX

22 , xX

v

F

h



Developed New


improving physics

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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

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Validation of Soil Model in Full AG tire Analysis

13

L

H W

2R


(NSDL Test)


1

3

33 , xX

11 , xX

22 , xX

v

F

h

Developed New


improving physics

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Prediction of Net Traction for a Full AG tire

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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

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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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AGV – 04/30/2012

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Thank You

Questions

AGV – 04/30/2012

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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]

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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

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AGV – 04/30/2012

Spring

Friction is

a function

of pressure

and shear

stress

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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

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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

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National Soil Dynamics Lab (@ Auburn)

Top of soil bins & testing facility

Indoor soil bin

Single wheel traction tester

AGV – 04/30/2012

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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

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W. Block, Analysis of Soil Stress Under Rigid Wheel Loading, PhD Dissertation, Agricultural Engineering, Auburn University, 1991

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Columbiana AG Tire Test Facility

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An instrumented tractor that can

generate drawbar-pull of 38,400 lbs-f

Testing is done in a prepared/tilled field

http://images.google.com/url?sa=i&rct=j&q=columbiana+test+firestone&source=images&cd=&cad=rja&docid=egNJxDGp7WruBM&tbnid=nxeZ9_T0a7CYpM:&ved=0CAUQjRw&url=http://www.agweb.com/blog/Machinery_Journal_138/?Year=2012&Month=8&ei=fauCUay0H8jBrQHkxIBY&bvm=bv.45960087,d.aWM&psig=AFQjCNHVt_w3zWV6Db019fYTNeGChgcOww&ust=1367604461538964

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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

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Verification of Bridgestone/Firestone Soil Model

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AGV – 04/30/2012

Triaxial Loading Test

Applied

Lateral

Pressure, 3

Applied Normal

Pressure, 1

Automotive

Predicting Net Traction on Soil Using a Continuum Approach Paper82111