Simulation of Tracked Vehicles

8/19/2019 Simulation of Tracked Vehicles

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arc Automotive Research Center

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

Documents

Simulation of Tracked Vehicles