cee 320 fall 2008 road vehicle performance cee 320 anne goodchild
TRANSCRIPT
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Road Vehicle Performance
CEE 320Anne Goodchild
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Outline
1. Resistancea. Aerodynamicb. Rollingc. Grade
2. Tractive Effort1. Maximum Tractive Effort2. Engine Generated Tractive Effort
3. Acceleration4. Braking
1. Stopping Sight Distance
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Review
• Force (N): – influence that tends to change motion– mass (kg) * acceleration (m/s2)
• Torque (Nm):– infleunce that tends to change rotational motion– Force * lever arm
• Work (Nm):– Force * distance
• Power (Nm/s):– Rate of doing work (work/time)
Units matter!
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Primary Opposing Forces
• Resistance (N): Force impeding vehicle motion• Tractive Effort (N): Force available at the roadway
surface to perform work
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Primary Opposing Forces
• Resistance (N): Force impeding vehicle motion• Tractive Effort (N): Force available at the roadway
surface to perform work
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Sum forces on the vehicle
grla RRRmaF
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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
from National Research Council Canada
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Power required to overcome Ra
• Power– work/time – force*distance/time
– Ra*V
3
2VACP fDRa
sec5501
lbfthp
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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 resistance
5. Simplifying approximation:
WfR rlrl
147101.0
Vfrl
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Power required to overcome rolling resistance
• On a level surface at maximum speed we could identify available hp
WVfP rlrlR
sec5501
lbfthp
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Grade Resistance Rg
Composed of – Gravitational force acting on the vehicle– The component parallel to the roadway
gg WR sin
gg tansin
gg WR tanGg tan
WGRg
For small angles,
θg W
θg
Rg
G=grade, vertical rise per horizontal distance (generally specified as %)
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Available Tractive Effort
The minimum of:1. Force generated by the engine, Fe2. Maximum value that is a function of the
vehicle’s weight distribution and road-tire interaction, Fmax
max,mineffort tractiveAvailable FFe
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Engine-Generated Tractive Effort
• Force
r
MF de
e
0
Fe = Engine generated tractive effort reaching wheels (lb)
Me = Engine torque (ft-lb)
ε0 = Gear reduction ratio
ηd = Driveline efficiency
r = Wheel radius (ft)
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Engine Generated Tractive Effort: Power
1000
2
2speed engine torquetime
torquepower
eee
nMP
Pe in kW
550
2 eee
nMhP
hPe in hp
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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
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Diagram
Ra
Rrlf
Rrlr
ma
Wθg
Fbf
Fbr
h
h
lf
lr
L
θg
Wf
Wr
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Maximum Tractive Effort
• Front Wheel Drive Vehicle
• Rear Wheel Drive Vehicle
= coefficient of road adhesion
LhL
hflW
F
rlf
1
max
LhL
hflW
F
rlr
1
max
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Tractive Effort Relationships
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Typical Torque-Power Curves
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Vehicle Acceleration
• Governing Equation
• Mass Factor (accounts for inertia of vehicle’s rotating parts)
maRF m
200025.004.1 m
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Braking
• Maximum braking force occurs when the tires are at a point of impending slide.– Function of roadway condition– Function of tire characteristics
• Maximum vehicle braking force (Fb max) is– coefficient of road adhesion () multiplied by
the vehicle weights normal to the roadway surface
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Braking Force
• Front axle
• Rear axle
L
fhlWF rlr
bf
max
L
fhlWF rlf
br
max
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Braking Force
• Maximum attainable vehicle deceleration is g
• Maximum obtained when force distributed as per weight distribution
• Brake force ratio is this ratio that acheives maximum braking forces
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Braking Force
• Ratio
• Efficiency
rear
front
fhl
fhlBFR
rlf
rlrrf
max
maxg
b
We develop this to calculate braking distance – necessary for roadway design
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Braking Distance
• Theoretical
– Assumes effect of speed on coefficient of rolling resistance is constant and calculated for average of initial and ending speed
– Ignores air resistance
– Minimum stopping distance given braking efficiency• For population of vehicles, what do you assume about rolling
resistance, coefficient of adhesion, and braking efficiency?
grlb
b
fg
VVS
sin2
22
21
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Braking Distance
• Practical
• For 0 grade
Gga
g
VVd
2
22
21
a
VVd
2
22
21
typically assume a = 11.2 ft/sec2
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Response time
• Perception time
• Total stopping distance
pp tVd 1
ps ddd
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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
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Stopping Sight Distance (SSD)
from ASSHTO A Policy on Geometric Design of Highways and Streets, 2004
Note: this table assumes level grade (G = 0)