NAZARIN B. NORDIN [email protected]. What you will learn: Tractive effort, tractive resistance,...
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Transcript of NAZARIN B. NORDIN [email protected]. What you will learn: Tractive effort, tractive resistance,...
BTE 1013ENGINEERING SCIENCES
12. TRACTIVE EFFORT AND TRACTIVE RESISTANCE
NAZARIN B. [email protected]
What you will learn:
• Tractive effort, tractive resistance, braking efficiency
• Tractive resistance components: rolling/ gradient/ air resistance
• Energy dissipated/ power required at constant velocity on level plane, accelerating/ braking forces applied on level plane, braking efficiency
Vehicle Dynamics
CEE 320Steve Muench
Outline
1. Resistancea. Aerodynamicb. Rollingc. Grade
2. Tractive Effort3. Acceleration4. Braking Force5. Stopping Sight Distance (SSD)
Main Concepts
• Resistance• Tractive effort• Vehicle acceleration• Braking• Stopping distance
grla RRRmaF
Resistance
Resistance is defined as the force impeding vehicle motionWhat is this force? 1. Aerodynamic resistance2. Rolling resistance3. Grade resistance
grla RRRmaF
Aerodynamic Resistance Ra
Composed of:1. Turbulent air flow around vehicle body (85%)2. Friction of air over vehicle body (12%)3. Vehicle component resistance, from radiators
and air vents (3%)2
2VACR fDa
3
2VACP fDRa
sec5501
lbfthp
from National Research Council Canada
Rolling Resistance Rrl
Composed primarily of 1. Resistance from tire deformation (90%)2. Tire penetration and surface compression ( 4%)3. Tire slippage and air circulation around wheel ( 6%)4. Wide range of factors affect total rolling resistance5. Simplifying approximation:
WfR rlrl
147101.0
VfrlWVfP rlrlR
sec5501
lbfthp
Grade Resistance Rg
Composed of – Gravitational force acting on the vehicle
gg WR sin
gg tansin
gg WR tanGg tan
WGRg
For small angles,
θg W
θg
Rg
Available Tractive Effort
The minimum of:1. Force generated by the engine, Fe
2. Maximum value that is a function of the vehicle’s weight distribution and road-tire interaction, Fmax
max,mineffort tractiveAvailable FFe
Tractive Effort Relationships
Engine-Generated Tractive Effort
• Force
• Power
r
MF de
e
0
2
minsec
60
rpm engine
550
lbft torque
sec
lbft550 hp
Fe = Engine generated tractive effort reaching wheels (lb)
Me = Engine torque (ft-lb)
ε0 = Gear reduction ratio
ηd = Driveline efficiency
r = Wheel radius (ft)
Vehicle Speed vs. Engine Speed
0
12
irn
V e
V = velocity (ft/s)
r = wheel radius (ft)
ne = crankshaft rps
i = driveline slippage
ε0 = gear reduction ratio
Typical Torque-Power Curves
Maximum Tractive Effort
• Front Wheel Drive Vehicle
• Rear Wheel Drive Vehicle
• What about 4WD?
LhL
hflW
F
rlf
1
max
LhL
hflW
F
rlr
1
max
DiagramR
a
Rrlf
Rrlr
ma
Wθ
g
Fbf
Fbr
h
h
lf
lr
L
θg
Wf
Wr
Vehicle Acceleration
• Governing Equation
• Mass Factor (accounts for inertia of vehicle’s rotating parts)
maRF m
200025.004.1 m
ExampleA 1989 Ford 5.0L Mustang Convertible starts on a flat grade from a dead stop as fast as possible. What’s the maximum acceleration it can achieve before spinning its wheels? μ = 0.40 (wet, bad pavement)
1989 Ford 5.0L Mustang Convertible
Torque 300 @ 3200 rpm
Curb Weight 3640
Weight Distribution Front 57% Rear 43%
Wheelbase 100.5 in
Tire Size P225/60R15
Gear Reduction Ratio 3.8
Driveline efficiency 90%
Center of Gravity 20 inches high
Braking Force
• Front axle
• Rear axle
L
fhlWF rlr
bf
max
L
fhlWF rlf
br
max
Braking Force
• Ratio
• Efficiency
rear
front
fhl
fhlBFR
rlf
rlr
maxg
b
Braking Distance
• Theoretical– ignoring air resistance
• Practical
• Perception
• Total
grlb
b
fg
VVS
sin2
22
21
Gga
g
VVd
2
22
21
pp tVd 1
ps ddd
a
VVd
2
22
21
For grade = 0
Stopping Sight Distance (SSD)
• Worst-case conditions– Poor driver skills– Low braking efficiency– Wet pavement
• Perception-reaction time = 2.5 seconds• Equation
rtV
Gga
g
VSSD 1
21
2
Stopping Sight Distance (SSD)
from ASSHTO A Policy on Geometric Design of Highways and Streets, 2001
Note: this table assumes level grade (G = 0)
SSD – Quick and Dirty
a
VVV
V
Ggag
VVd
222
221
22
21 075.1
2.11075.1
2.11
1
2
47.1
02.322.112.322
047.1
2
1. Acceleration due to gravity, g = 32.2 ft/sec2
2. There are 1.47 ft/sec per mph
3. Assume G = 0 (flat grade)
ppp VttVd 47.147.1 1
V = V1 in mpha = deceleration, 11.2 ft/s2 in US customary unitstp = Conservative perception / reaction time = 2.5 seconds
ps Vta
Vd 47.1075.1
2
Primary References
• Mannering, F.L.; Kilareski, W.P. and Washburn, S.S. (2005). Principles of Highway Engineering and Traffic Analysis, Third Edition). Chapter 2
• American Association of State Highway and Transportation Officals (AASHTO). (2001). A Policy on Geometric Design of Highways and Streets, Fourth Edition. Washington, D.C.
THANK YOU