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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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12/20/2013
1
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
12/20/2013
2
Motivation
• Evaluate the performance
of lightweight tracked
vehicles on granular media
• Understand modeling
shortcomings
• Highlight future directions in
track modeling
2
12/20/2013
3
Outline
• Experimental Setup
– Terramechanics test rig
– Single track device
• Experimental Plan Overview
• Experimental results
• Semi-Empirical Modeling
• Experiments vs. Models
• Conclusions
3
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4
Terramechanics Test Rig
4
Vertical
load
control
6-axis
F/T
Sensor
Mojave Mars
Simulant
Torque
sensor
Draw-wire encoder
for sinkage
measurement
A motor drives
the horizontal
carriage.
A motor
drives the
track
Quikrete
Medium Sand
Quikrete
All Purpose Gravel
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Single Track
5
Road Wheels
92 shore A durometer toothed belt
250 mm
Tensioner
33 mm
5.5 mm
Trailing arms
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Single Track
6
DC Motor Torque
Sensor
Flexible
Coupling Bevel
Gears
Drive
Pulleys
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Experimental Plan Overview
7
125 N
155 N
190 N
Fz Range Slip Levels Terrains
Gravel
Medium Sand
Mars Simulant
± 50 %
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8
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Mars
Sand
9
-0.6 -0.4 -0.2 0 0.2 0.4
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Slip
Tra
ctio
n C
oe
ffic
ien
t -
F
x/Fz
Fz = 125 N
Fz = 155 N
Fz = 190 N
-0.6 -0.4 -0.2 0 0.2 0.4-2
0
2
4
6
8
10
Slip
To
rqu
e -
T [N
m]
-0.6 -0.4 -0.2 0 0.2 0.4
15
20
25
30
Slip
Sin
ka
ge
[m
m]
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10
10
Medium
Sand
-0.5 0 0.5-0.6
-0.4
-0.2
0
0.2
0.4
Slip
Tra
ctio
n C
oe
ffic
ien
t -
Fx/F
z
Fz = 125 N
Fz = 155 N
Fz = 190 N
-0.5 0 0.5
-2
0
2
4
6
8
Slip
To
rqu
e -
T [N
m]
-0.4 -0.2 0 0.2 0.4 0.6
10
15
20
25
30
35
40
45
Slip
Sin
ka
ge
[m
m]
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11
11
Gravel
-0.5 0 0.5
-0.6
-0.4
-0.2
0
0.2
0.4
Slip
Tra
ctio
n C
oe
ffic
ien
t -
Fx/F
z
Fz = 125 N
Fz = 155 N
Fz = 190 N
-0.5 0 0.5
-2
0
2
4
6
8
10
Slip
To
rqu
e -
T [N
m]
-0.5 0 0.5
0
5
10
15
20
25
30
35
Slip
Sin
ka
ge
[m
m]
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12
Comparison for Fz = 125 N
12 -0.6 -0.4 -0.2 0 0.2 0.4 0.6
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Slip
Tra
ctio
n C
oe
ffic
ien
t -
Fx/F
z
Mars
Medium Sand
Gravel
Mars Medium Sand Gravel
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13
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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Modeling
14
• For frictional materials
cohesion is zero and
friction dominates trust.
0
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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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
15 -0.6 -0.4 -0.2 0 0.2 0.4
-150
-100
-50
0
50
100
150
Slip
Dra
wb
ar
- F
x [N
]
BWM @ Fz = 190 N
BWM @ Fz = 125 N
-0.6 -0.4 -0.2 0 0.2 0.4
5
10
15
20
25
Slip
Sin
ka
ge
[m
m]
BWM @ Fz = 190 N
BWM @ Fz = 125 N
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16
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
16
0.05 0.1 0.15 0.2 0.25
-0.2
0
0.2
0.4
Length [m]
Sin
ka
ge
[m
]
0.05 0.1 0.15 0.2 0.25
-10
-5
0
Length [m]
Str
ess [kP
a]
Fz
Fx
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0 0.1 0.2 0.3 0.4 0.5
-40
-20
0
20
40
60
80
100
120
Slip
Dra
wb
ar
- F
x [N
]
0 0.1 0.2 0.3 0.4
-20
0
20
40
60
80
100
120
Slip
Dra
wb
ar
- F
x [N
]
AWM @ Fz = 190 N
AWM @ Fz = 125 N
Modeling
• AWM produces results closer to the measured data.
• AWM does not incorporate slip-sinkage effects (i.e,
sinkage response is flat)
17
Mars Medium Sand
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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.
18
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