Carmine Senatore*, Paramsothy Jayakumar†, and Karl Iagnemma* *Massachusetts Institute of Technology, Cambridge, MA, USA †U.S. Army TARDEC Warren, MI, USA

1. 12/20/2013
Experimental Study Of Lightweight Tracked
Vehicle Performance On Dry Granular Materials.
Carmine Senatore*, Paramsothy Jayakumar†, and Karl Iagnemma*
* Massachusetts Institute of Technology, Cambridge, MA, USA
†U.S. Army TARDEC Warren, MI, USA
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2. 12/20/2013
Motivation
• Evaluate the performance
of lightweight tracked
vehicles on granular media
• Understand modeling
shortcomings
• Highlight future directions in
track modeling
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2

3. 12/20/2013
Outline
• Experimental Setup
– Terramechanics test rig
– Single track device
•
•
•
•
•
Experimental Plan Overview
Experimental results
Semi-Empirical Modeling
Experiments vs. Models
Conclusions
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4. 12/20/2013
Terramechanics Test Rig
A motor drives
the horizontal
carriage.
Draw-wire encoder
for sinkage
measurement
Vertical
load
control
6-axis
F/T
Sensor
Torque
sensor
A motor
drives the
track
Mojave Mars
Simulant
Quikrete
Medium Sand
Quikrete
All Purpose Gravel
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Single Track
92 shore A durometer toothed belt
Tensioner
Trailing arms
Road Wheels
5.5 mm
33 mm
250 mm
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6. 12/20/2013
Single Track
DC Motor
Torque
Sensor
Flexible
Coupling
Bevel
Gears
Drive
Pulleys
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7. 12/20/2013
Experimental Plan Overview
Fz Range
Slip Levels
Terrains
Mars Simulant
125 N
155 N
190 N
± 50 %
Medium Sand
Gravel
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9. 12/20/2013
Traction Coefficient - Fx/Fz
0.6
Mars
Sand
Fz = 125 N
Fz = 155 N
Fz = 190 N
0.4
0.2
0
-0.2
-0.4
-0.6
-0.6
-0.4
-0.2
0
0.2
0.4
Slip
30
10
Sinkage [mm]
Torque - T [Nm]
8
6
4
2
0
-2
-0.6
25
20
15
9
-0.4
-0.2
0
Slip
0.2
0.4
-0.6
-0.4
-0.2
0
0.2
0.4
Slip
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10. 12/20/2013
Traction Coefficient - Fx/Fz
0.4
Medium
Sand
Fz = 125 N
Fz = 155 N
Fz = 190 N
0.2
0
-0.2
-0.4
-0.6
-0.5
8
0.5
45
40
Sinkage [mm]
6
Torque - T [Nm]
0
Slip
4
2
35
30
25
20
0
15
-2
10
-0.5
0
Slip
0.5
10
-0.4
-0.2
0
Slip
0.2
0.4
0.6
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Fz = 125 N
Fz = 155 N
Fz = 190 N
Traction Coefficient - Fx/Fz
0.4
Gravel
0.2
0
-0.2
-0.4
-0.6
-0.5
0.5
35
10
30
Sinkage [mm]
8
Torque - T [Nm]
0
Slip
6
4
2
25
20
15
10
0
5
-2
0
11
-0.5
0
Slip
0.5
-0.5
0
Slip
0.5
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12. 12/20/2013
Comparison for Fz = 125 N
Mars
Gravel
Medium Sand
Traction Coefficient - Fx/Fz
0.6
Mars
Medium Sand
Gravel
0.4
0.2
0
-0.2
-0.4
-0.6
-0.6
-0.4
-0.2
0
Slip
0.2
0.4
0.6
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13. 12/20/2013
Modeling
• Excluding numerical-intensive approaches (DEM/FEA)
the vast majority of models for tracked vehicles are
based on Bekker, Wong, and Muri’s work.
• Sinkage is calculated through Bekker’s pressure-sinkage
equation:
• Maximum traction is deduced from Mohr-Coulomb failure
criterion
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14. 12/20/2013
Modeling
0
• For frictional materials
cohesion is zero and
friction dominates trust.
Material
Mars
1.4
846
6708
600
35
0.0006
Medium Sand
1.0
-20
3130
1500
34
0.0006
Gravel
n/a
n/a
n/a
n/a
30
n/a
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15. 12/20/2013
Modeling
• Basic Wong Model (BWM) over estimates drawbar
mostly because it does not predict sinkage correctly
• Model Assumptions:
– Track is rigid
– Uniform ground pressure
– Continuous shear stress representation
Drawbar - Fx [N]
100
BWM @ Fz = 190 N
BWM @ Fz = 190 N
BWM @ Fz = 125 N
BWM @ Fz = 125 N
25
Sinkage [mm]
150
50
0
-50
20
15
10
-100
5
-150
-0.6
-0.4
-0.2
0
Slip
0.2
0.4
-0.6
-0.4
-0.2
0
0.2
15
0.4
Slip
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16. 12/20/2013
Modeling
• Advanced Wong Model (AWM) assumptions:
Track is a flexible belt
Belt tension between road wheels is function of shear stress
Terrain reaction force follows Bekker pressure-sinkage equation
Shear Stress resets when normal load decreases
Fx
Sinkage [m]
0.4
Fz
0.2
0
-0.2
0.05
0.1
0
Stress [kPa]
–
–
–
–
0.15
Length [m]
0.2
0.25
-5
-10
16
0.05
0.1
0.15
Length [m]
0.2
0.25
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17. 12/20/2013
Modeling
• AWM produces results closer to the measured data.
• AWM does not incorporate slip-sinkage effects (i.e,
sinkage response is flat)
120
100
100
AWM @ Fz = 125 N
80
80
Drawbar - Fx [N]
Drawbar - Fx [N]
120
AWM @ Fz = 190 N
60
40
Mars
20
0
60
40
20
Medium Sand
0
-20
-20
-40
0
0.1
0.2
Slip
0.3
0.4
0
0.1
0.2
0.3
0.4
17
0.5
Slip
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18. 12/20/2013
Conclusions
• The experiments highlighted that track performances are
mildly sensitive to the three granular materials under
investigation.
• Basic Wong Model showed to be inappropriate for
detailed analysis.
• Advanced Wong Model produced better predictions of
track performance.
• Both models showed to be sensitive to pressure-sinkage
parameters while the experiments showed that track
performances are not influenced by pressure-sinkage
behaviour.
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