simulation of tracked vehicles
TRANSCRIPT
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Simulating Track/Sprocketand Track/Wheel/Terrain Contact
in Tracked VehiclesZ.-D. Ma
C. Scholar
N. C. PerkinsUniversity of Michigan
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ObjectiveEfficient simulation of vehicle response including track vibration, track/sprocket contact, and track/wheel/terrain
interaction.
n
Overview of recent efforts
n New effort: Track/SprocketContact
n New effort: Track/Wheel/TerrainInteraction
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Track Models
QUASI-STATICMULTI-BODY CHAIN
HYBRID DISCRETE-CONTINUOUS ELEMENT
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Continuous Track Model
LONGITUDINAL
TRANSVERSEIN-PLANE RESPONSE
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Continuous Track Model
u1( s,t ) = f (t ) s + k u
2(η, t )d η
0
s
∫
m(u2,tt + 2Vu2, st + V 2u2, ss ) + kEAf (t ) = Tu2, ss
f (t ) = − k
Lu2 (η,t )d η0
L
∫
s, u1(s,t)
u2(s,t)
d
V
V - track speed
d - static sag
k - static curvature
T - static tension
f(t) - dynamic strain
Longitudinal Response
(quasi-static)
Transverse
Response
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Experimental Validation
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M1 Tank Traversing Profile 4
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Track Transverse Vibration
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Including Track/Sprocket Contact
P&H 4100A Crawler
Objective: To model of dynamic shoe-tumblerseating process
n
Inputs: shoe pitchelongation, tumbler lugwear, track tension,interface friction, appliedtorque, ground conditions.
n Outputs: pin loading,shoe/tumbler contactforces, animation of
seating process
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P&H 4100A Crawler
n Operating weight:1,200 tons
n
Max. speed: 0.56mph.
n Max. appliedtorque: 1,580,000ft-lbs
n Max. designtension: 1,480,000lbs
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Shoe/Tumbler Seating Process
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Hybrid Track Model
Multibody Model of Shoes Continuous Model of Track Segments
Tumbler Rear Idler
Front Idler Rollers
Guide
Shoes
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Shoe/Tumbler Interface
a) Slight Wear b) Heavy Wear
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Prescribed Tumbler Velocity
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Machine Travel Speed
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Shoe/Tumbler Normal Contact Force
For Shoe 3-7
shoe 7
shoe 6
shoe 5 shoe 4
shoe 3
3
4
5
67
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Vertical Load For Pins 01 to 03 Under
Rear Idler
pin 01 pin 02 pin 03
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Case: Slight Wear, Very Tight
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Case: Heavy Wear, Extremely Loose
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Including Track/Wheel/Terrain Contact
Track/Wheel/Terrain Interaction
Objective: To developtrack/wheel/terrain interface
model to efficiently predictthe loading on the vehicledue to the ground pressureand shear.
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Track/Wheel/Terrain Interaction Model
(Force Element)
l
X
Z
x
z
A
O
x
Wheel 1
Wheel 2
α
g
B P ( x,z )
z t ( x)
O1 ( X 1, Z 1)
O2 ( X 2
, Z 2)
Terrain
s
o
φ1
φ2
F X 1
F Z 1
F X 2
F Z 2τ1
τ2
Inputs
( X 1, Z 1, φ1)( X 2, Z 2, φ2)
z t ( x)
Outputs
( F X 1, F Z
1, τ1)( F X
2, F Z 2, τ2)
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Track/Wheel/Terrain Interaction
T
T+dT f z ds
f x
dsθ+d θ
θ
x
z
o
P
dsθ+d θ
θ
x
z
o
dx
dz
d ρ
P
Equilibrium
Kinematic Relationships
Constitutive Law
dsdsd EAT /)( −= ρ
0)cos()(cos =−+++− ds f d dT T T xθθθ
0)sin()(sin =−+++− ds f d dT T T z θθθ
dsd
dx
ds
d
d
dxd
d
dx
+=+=
ρρθθ
ρθ )cos(,cos
dsd
dz
ds
d
d
dz d
d
dz
+=+=
ρρθθ
ρθ )sin(,sin
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Contact Models
f
-f z
-f x
O1( x1, z 1)
P ( x, z )
x
z
r 1 z - z 1
x- x1
z
A
x
α
g
B
P ( x,z )
( xt , z
t )
Terraino f z
f x
Track/Wheel Track/Terrain
(Janosi & Hanamoto)
(Bekker)
≥
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Solution Procedure
n Re-write BVP in incremental form
n Discretize by FE
n (Modified) Newton-Raphson Iteration of nonlinear BVP
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Example: Case of Zero Sinkage
Trapezoid Bump
Round Bump
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Example: Case of One Inch Sinkage
Trapezoid Bump
Round Bump
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Example: Effect of Ground Stiffness
K=3.6e4
K=1.8e4
K=0.9e4
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Effect of Track Extensibility
EA (lbs) Tension (lbs) Fx (lbs) Fz (lbs)
2.5e6 0.188e6 0.153e6 0.110e6
2.5e7 0.837e6 0.759e6 0.354e62.5e8 0.154e7 0.148e7 0.428e6
2.5e9 0.189e7 0.184e7 0.445e6
5.0e9 0.192e7 0.187e7 0.447e6
1.0e10 0.194e7 0.189e7 0.447e6
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Continuous to Multibody Formulation
Nel Tension (lbs) FX (lbs) FZ (lbs)100 0.188e6 0.153e6 0.110e6
20 0.188e6 0.152e6 0.130e6
6 0.208e6 0.138e6 0.442e6
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Conclusions
Continuous track model
n Captures low frequency track vibration in anefficient manner
n Can be married to multibody track models(track/sprocket contact)
n
Can be extended to capture track/wheel/terraininteraction