arc Automotive Research Center Case Study: Tracked Vehicles

Case Study II
Dynamic Analysis and Design of
Tracked Vehicles
arc Automotive Research Center Case Study: Tracked Vehicles

Objectives

● Create a flexible simulation environment for the

efficient prediction of track vibration, powertrain
performance, and vehicle dynamics

● Provide an efficient tool for the assessment of

designs for tracked vehicles

● Develop a distributed, object-oriented

environment to perform design optimization
 arc Automotive Research Center Case Study: Tracked Vehicles

M1 Abrams Tank
● Main battle tank

● Weight: approx. 70 tons

● Max. speed: approx. 45 mph

 arc Automotive Research Center Case Study: Tracked Vehicles

M1 Abrams Tank

Track
Turret
Support Roller Hull

Idler Wheel
Torsion Bar Drive Sprocket
Track
Road Arm
Adjusting
Link Road Wheel
 arc Automotive Research Center Case Study: Tracked Vehicles

Outline

● Modeling and simulation

of tracked vehicles
◆ Track vibration models
◆ Vehicle multi-body
dynamics models

● Integration of powertrain
and structure models

● System integration for

track and road arm
analysis and design
arc Automotive Research Center Case Study: Tracked Vehicles

Modeling and Simulating

Tracked Vehicles
arc Automotive Research Center Case Study: Tracked Vehicles

Track Models
MULTI-BODY CHAIN
QUASI-STATIC

HYBRID DISCRETE-CONTINUOUS ELEMENT

 arc Automotive Research Center Case Study: Tracked Vehicles

Dominant Deformation Modes

TRANSVERSE
IN-PLANE RESPONSE
LONGITUDINAL
 arc Automotive Research Center Case Study: Tracked Vehicles

Research Plan
Continuous Experimental Implementation into
Element Validation DADS vehicle model
Model

Longitudinal
Vibration

Coupled
Longitudinal
and
Transverse
Vibration
arc Automotive Research Center Case Study: Tracked Vehicles

Experimental Validation
 arc Automotive Research Center Case Study: Tracked Vehicles

Vertical Accelerometer

7.2 Hz

Acceleration
Magnitude

0 20 40 60 80 100 120 140

Frequency (Hz)
 arc Automotive Research Center Case Study: Tracked Vehicles

Transverse Vibration Element Model

V - track speed
u2(s,t) d - static sag
s, u1(s,t) k - static curvature
d T - static tension
f(t) - dynamic strain
V
s

(quasi-static)
0 ∫
Longitudinal Response u1 ( s, t ) = f (t )s + k u2 (η, t )dη

Transverse m(u2, tt + 2Vu2, st + V 2u2, ss ) + kEAf (t ) = Tu2, ss

Response
−k L
f (t ) = ∫
L 0
u2 (η, t )dη
arc Automotive Research Center Case Study: Tracked Vehicles

Vibration Mode Shapes

f1 = 3.7 Hz f2 = 5.5 Hz

f3 = 7.3 Hz f4 = 7.6 Hz
arc Automotive Research Center Case Study: Tracked Vehicles

Mixed Eulerian/Lagrangian
Description of Motion

Eulerian Description of Motion

Lagrangian Description of Motion

arc Automotive Research Center Case Study: Tracked Vehicles

Component Mode Synthesis Method

for Discretization

● Rigid body mode

● Constraint mode

● Longitudinal vibration
modes

● Transverse vibration
modes
arc Automotive Research Center Case Study: Tracked Vehicles

General Track Element Models

Six Variations
● Static (spring-damper) model

● Lumped mass-spring-damper model

● Quasi-static (Guyan reduction) model

● Dynamic model with longitudinal vibration

● Dynamic model with transverse vibration

● Dynamic model with coupled longitudinal and

transverse vibration
arc Automotive Research Center Case Study: Tracked Vehicles

M1 Tank Traversing Profile 4

arc Automotive Research Center Case Study: Tracked Vehicles

Track Transverse Vibration

 arc Automotive Research Center Case Study: Tracked Vehicles

Dynamic Tension

35000

long. & trans.

30000
Dynamic Tension At 2nd Roller (lbs)

static long. only

25000

20000

15000

10000

5000

0
14 14.2 14.4 14.6 14.8 15 15.2 15.4 15.6 15.8 16
Time (seconds)
 arc Automotive Research Center Case Study: Tracked Vehicles

FFT of the Dynamic Tension

300

270
long. & trans.
FFT of Dynamic Tension At 2nd Roller (lbs)

240

210 long. only

180

150 static
120

90

60

30

0
2 4 6 8 10 12 14 16 18 20 22
Frequency (Hz)

f1 trans=3.7Hz f1 long=14.0Hz
 arc Automotive Research Center Case Study: Tracked Vehicles

FFT of Normal Contact Force

800

700
FFT of Normal Force On the 2nd Roller (lbs)

long. & trans.

600

500

400

300
static
long. only
200

100

0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Frequency (Hz)

f1 trans=3.7Hz f2 trans=5.5Hz
 arc Automotive Research Center Case Study: Tracked Vehicles

Integration

● Integration of powertrain
and structure models

● System integration for

track and road arm
analysis and design
arc Automotive Research Center Case Study: Tracked Vehicles

Integration of
Powertrain and Structure Models

POWERTRAIN Torque
STRUCTURE
TM TM
Matlab RPM DADS

Drive Sprocket
arc Automotive Research Center Case Study: Tracked Vehicles

Tank System Integration in the

Distributed Computing Environment

Load Torque Sprocket Angular Velocity

Engine Speed and Torque Sprocket Drive Torque

Air Exhaust Exhaust Air

gas gas

C T T C

INTER- INTER-
COOLER COOLER

T Trans-
I E E I
C mission D
M M M M

FUEL
Multi-Body
SYSTEM

V12 ENGINE Vehicle Dynamics

.
Diesel Engine W
Drivetrain Includes Longitudinal and
System Transverse Track Vibrations

TM TM
Matlab-SIMULINK DADS
arc Automotive Research Center Case Study: Tracked Vehicles

Integrated Simulation 1 Results

● Terrain: Flat

● Driver Demand: 90%

 arc Automotive Research Center Case Study: Tracked Vehicles

Integrated Simulation 1: Torque

4
x 10
3.5

2.5
Torque (Nm)

1.5

Drive Sprocket
1
Torque Converter Out
0.5
Engine Out

0
0 5 10 15 20 25 30
Time (seconds)
 arc Automotive Research Center Case Study: Tracked Vehicles

Integrated Simulation 1: Track Tension

13450

13400

13350

13300
Track Tension (lbs)

13250

13200

13150

13100

13050
10 12 14 16 18 20 22 24 26 28 30
Time (Seconds)
 arc Automotive Research Center Case Study: Tracked Vehicles

Integrated Simulation 1: Track Deflection

-0.09

-0.095
Transverse Deflection At Midpoint (in)

-0.1

-0.105

-0.11

-0.115
f1 = 3.7 Hz

-0.12
10 12 14 16 18 20 22 24 26 28 30
Time (Seconds)
arc Automotive Research Center Case Study: Tracked Vehicles

Integrated Simulation 2 Results

● Terrain: Profile 4

● Driver Demand: 90%

arc Automotive Research Center Case Study: Tracked Vehicles

Integrated Simulation 2: Sprocket Torque

35000

30000
Profile 4

Torque On the Sprocket (lbs-in)

25000

20000

15000

10000

5000 Flat Terrain

0
0 5 10 15 20 25 30 35
Time (Seconds)

Vertical
Displacement
of Vehicle CG
 arc Automotive Research Center Case Study: Tracked Vehicles

Integrated Simulation 2: Rotational Speed

1600

1400 Engine
1200

1000
Shaft Speed (rpm)

800

600
Transmission In
400
Transmission Out
200

Drive Sprocket
0

200
0 5 10 15 20 25 30
Time (seconds)

Vertical
Displacement
of Vehicle CG
arc Automotive Research Center Case Study: Tracked Vehicles

Integrated Simulation 2: Track Tension

26000

24000

22000 Profile 4
20000

18000

Dynamic Tension (lbs)

16000

14000

12000

10000

8000

6000

4000
Flat Terrain
2000
5 10 15 20 25 30 35
Time (Seconds)

Vertical
Displacement
of Vehicle CG
 arc Automotive Research Center Case Study: Tracked Vehicles

System Integration for Track and

Road Arm Analysis and Design
● GOAL: Integrate models, analysis and design tools
◆ developed and located at different locations
◆ for distributed analysis and design optimization
◆ within a CORBA (Common Object Request Broker Architecture)
environment

● VEHICLE: M1 Abrams tank

● PARTICIPANTS:
◆ University of Michigan (UM):
DADS vehicle and track dynamics models
◆ University of Iowa (UI):
Road arm life prediction/optimization (DRAW & DSO tools)
arc Automotive Research Center Case Study: Tracked Vehicles

Model and Tool Integration with CORBA

● Architecture for distributed object communication

● Platform and language independent

● Allows interchangeable components

client side server side

Analysis Wrapper
Optimization Model
...
...
ORB ORB Eval(x,y){
analysis->Eval(x,y)
...
... sys
} tem
cal
l
analysis
tool
y = f(x)
arc Automotive Research Center Case Study: Tracked Vehicles

Track Optimization
● DESIGN OBJECTIVE:
Maximize Road Arm Life Prediction (UI’s DRAW tool)

● DESIGN VARIABLES:
Track Parameters (UM’s DADS models)
◆ Stiffness
◆ Density
◆ Initial/static tension

● OPTIMIZATION APPROACHES:
Sample design objective on a grid of design points
Snyman-Fatti multistart trajectory method:
◆ Global
◆ Gradient-based
◆ Noise insensitive
arc Automotive Research Center Case Study: Tracked Vehicles

Integration of Models, Analysis and

Design Tools for Track Optimization
UM ROAD ARM UI
LOAD HISTORY
Vehicle & Track Road Arm Durability
Dynamics Models Prediction Tools
DADS DRAW

TRACK DESIGN
VARIABLES
ROAD
ARM LIFE
PREDICTION
Track
Optimization
Algorithm

UM
arc Automotive Research Center Case Study: Tracked Vehicles

CORBA Software Integration:

Track Optimization
CORBA::RUN()
UM Control

UM

DATA
DATA DATA
‘DADS’ ‘DADS_RDR’ ‘DADS_RDR’
||||||||| |||||||||
Analysis Object Data Get Object Data Get Object
CORBA::GET()
UM UM UI

CORBA::RUN(x) DONE e-mail Dynamic

notification
Stress
Computation
UI
CORBA::RUN()
‘M1TankProb’ ‘DRAW_RDR’
OptModel Object Analysis Object
DATA Fatigue Life
UM UI Prediction

Objective
CORBA::EVAL(x) DRAW
Function UI

DATA
‘Trajectory’ |||||||||
Optimizer Object

UM
 arc Automotive Research Center Case Study: Tracked Vehicles

Track Optimization Results

● TRACK STIFFNESS:
4000
◆ Nominal: 2.5e6 lbs.
3500
◆ Range: 0.625e6 to 5e6 lbs.

Road Arm Life Prediction (hrs.)

3000
48% LIFE
IMPROVEMENT
2500
● LIFE IMPROVEMENT:
2000
◆ 48% for a 25% increase in
track stiffness 1500
25%
● COMPUTATIONAL COST: 1000

◆ Dynamic and life 500

prediction analyses take NOMINAL
together about one day 0
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
6
Track Stiffness (lbs.) x 10
arc Automotive Research Center Case Study: Tracked Vehicles

Integration for Road Arm

Shape Optimization
DROW
UM ROAD ARM UI
LOAD HISTORY
Vehicle & Track Road Arm Durability
Dynamics Models Prediction Tools
DADS DRAW

ROAD
ROAD ARM
ARM LIFE
SHAPE
PREDICTION

Road Arm Shape

Optimization
DSO (DOT)

UI
arc Automotive Research Center Case Study: Tracked Vehicles

CORBA Integration:
Road Arm Shape Optimization
Parametric &
FE Models

UI

DATA
‘DADS’ DATA DATA Dynamic
‘DADS_RDR’ ‘DADS_RDR’ Stress
Multibody ||||||||| ||||||||| Computation
Data Get Object Data Get Object
Dynamics
CORBA::GET()
UM UM UI

Fatigue Life
e-mail Prediction
notification

DRAW UI

UI
Design
Sensitivity
Analysis

Optimizer
(DOT)

DSO UI
arc Automotive Research Center Case Study: Tracked Vehicles

Shape Design Problem

● Objective Function - Minimize
Volume

● Fatigue Life is 2189 Hours at the

Initial Design

● 56 Constraint Functions - Fatigue

Life Longer Than 69444 Hours at
56 Critical Nodes

● 8 Shape Design Parameters

● MFD Algorithm Is Used for

Optimization
DP Value(in) Lower Bd Upper Bd DP Value(in) Lower Bd Upper Bd
db1 1.968 1.5 2.5 db5 2.635 2.2 3.1
db2 1.968 1.5 2.5 db6 5.057 4.9 5.5
db3 3.250 2.9 3.8 db7 3.038 2.6 3.5
db4 3.170 2.8 3.8 db8 2.909 2.7 3.5
arc Automotive Research Center Case Study: Tracked Vehicles

Shape Design Parameterization

• Section Dimensions (Heights and Widths) Are Selected as Design Parameters

Cubic Curves bi, i=1,2,5,6

Straight
Lines bi, i=3,4,7,8

x 3
Cross Sectional Shape
Design Parameters
b1,b2,b5,b6 Design Parameters
b3,b4,b7,b8

x Intersection 2
1 b2, b4 Intersection 3
b5, b7 Intersection 4
Intersection 1
b6, b8
b1, b3
Torsion Bar

Center of the
Roadwheel
arc Automotive Research Center Case Study: Tracked Vehicles

Design Optimization History

● Optimal Design Is Obtained in 12 Iterations

Cost Function History Design Parameter History

arc Automotive Research Center Case Study: Tracked Vehicles

Life Contour at Initial and Optimal Designs

Initial Design Optimal Design

Initial Optimal DP Initial (in) Optimal DP Initial (in) Optimal

b1 1.968 2.099 b5 2.635 2.718

Volume (in 3 ) 515.1 522.1
b2 1.968 2.488 b6 5.057 4.850
lowest life (hr) 2189 69623 b3 3.250 3.050 b7 3.038 2.897
b4 3.170 2.917 b8 2.909 2.701
arc Automotive Research Center Case Study: Tracked Vehicles

Future Work: Integration for Track and

Road Arm Shape Optimization
DROW
UM ROAD ARM UI
LOAD HISTORY
Vehicle & Track Road Arm Durability
Dynamics Models Prediction Tools
DAS DRAW

ROAD
ROAD ARM TRACK DESIGN ROAD ARM
ARM LIFE
PARAMETERS VARIABLES SHAPE
PREDICTION

Track Road Arm Shape

Optimization Optimization
Algorithm DSO (DOT)
ROAD ARM
UM LIFE PREDICTION UI
& SHAPE
 arc Automotive Research Center Case Study: Tracked Vehicles

CORBA Integration:
Track and Road Arm Shape Optimization
Parametric &
FE Models
CORBA::RUN()
UM Control
UI
UM

DATA
DATA DATA Dynamic
‘DADS’ ‘DADS_RDR’ ‘DADS_RDR’ Stress
||||||||| ||||||||| Computation
Analysis Object Data Get Object Data Get Object
CORBA::GET()
UM UM UI

CORBA::RUN(x) DONE CORBA::RUN(x) DONE Fatigue Life

Prediction

CORBA::RUN()
‘M1TankProb’ ‘DROW’ DRAW UI
OptModel Object Analysis Object
DATA
UM UI Design
Sensitivity
Analysis
Objective
CORBA::EVAL(x)
Function

Optimizer
‘Trajectory’ TRACK ROAD ARM SHAPE (DOT)
Optimizer Object OPTIMIZATION OPTIMIZATION
UM UI
DSO
arc Automotive Research Center Case Study: Tracked Vehicles

Contributions of Case Study

● Development of dynamic track model with
longitudinal and transverse vibration
TM
● Implementation of new track model in DADS
(with enhancements)

● Development of integrated powertrain/vehicle

models

● Integration of vehicle dynamics models, road arm

life prediction, and design tools across different
platforms and physical locations using CORBA
◆ Track optimization
◆ Road arm shape optimization