Bma4723 Vehicle Dynamics Chap 22
Bma4723 Vehicle Dynamics Chap 22
Bma4723 Vehicle Dynamics Chap 22
By
Dr. Gan Leong Ming
Semester 20122013-II
Limit of the Longitudinal Acceleration
Engine power for high speed
Traction limit for low speed
Depend on vehicle speed
Power Limited Acceleration
Engine
- Source of power
- Characterized by torque and power curve
2000
4000 6000 RPM
Power
Torque
Specific fuel consumption
1000
2000 3000
RPM
Specific fuel consumption
Torque
Power
Gasoline engine Diesel engine
Difference between Gasoline and Diesel Engine
Gasoline Engine
- govern by the
induction system
- Most efficient at
0.4ib/hp-hr sfc
Diesel Engine
- Govern by the fuel
injection system
- Most efficient at
0.2ib/hp-hr sfc
Relationship between power, torque and horsepower
5252 / Speed) x (Torque Horsepower
Speed x Torque Power
=
=
HP x 0.746 (kW) Power =
radius x Force (Nm) Torque =
From Newtons Second Law:
wheels drive at the force Tractive F
direction forward in the on Accelerati a
W/g vehicle the of Mass M
where
F a M
x
x
x x
=
=
= =
=
Since the drive power = Tractive force x forward speed
(kg) vehicle the of weight W
(W) power Engine P
(m/s) speed Forward V
) m/s 9.81 (g constant nal Gravitatio g
where
V
P
W
g
F
M
1
a
2
x x
=
=
=
= =
= =
V
1
a
x
It shown that
acceleration
capability
decrease with
increasing speed
Power Train The Primary Elements
? Drivetrain To Torque Actual Torque Output Engine >
Engine
Transmission Driveshaft
Differential
Axle shaft
c
T
d
T
a
T
e
T
Engine
Torque
Clutch
Torque
Driveshaft
Torque
Axle
Torque
Torque to Clutch
on accelerati rotational Engine
inertia rotational Engine I
data) dynamic (from speed given a at torque Engine T
ion) transmiss the (input to clutch at the Torque T
where
I - T T
e
e
e
c
e e e c
=
=
=
=
=
Torque to Driveshaft
side) engine the from seen (as ion transmiss the of inertia Rotational I
ion transmiss the of ratio Numerical N
driveshaft the output to Torque T
where
N ) I - T ( T
t
t
d
t e t c d
=
=
=
=
Torque on the axles
drive final the of ratio Numerical N
driveshaft the of on accelerati Rotational
driveshaft the of inertia Rotational I
wheels the of on accelerati Rotational
shafts axles and wheels the of inertia Rotational I
wheels the of Radius r
ground at the force Tractive F
axles on the Torque T
where
N ) I - T ( I r F T
f
d
d
w
w
x
a
f d d d w w x a
=
=
=
=
=
=
=
=
= + =
Rotational Acceleration
w f t d t e
w f d
N N N
and
N
= =
=
Solving all the equations,
( ) { }
drive final and ion transmiss of ratio Combined N
where
r
a
I N I N I I
r
N T
F
tf
2
x
w
2
f d
2
tf t e
tf e
x
=
+ + + =
Continue
( ) { }
drive final and ion transmiss of efficiency Combined
where
r
a
I N I N I I
r
N T
F
losses, viscous and mechanical to due ncies ineffiecie the include By
tf
2
x
w
2
f d
2
tf t e
tf e
x
=
+ + + =
tf
( ) { }
2
x
w
2
f d
2
tf t e
tf e
x
r
a
I N I N I I
r
N T
F + + + =
tf
E
n
g
i
n
e
s
p
e
e
d
Road speed
1
1
st
gear 2
nd
gear 3
rd
gear 4
th
gear
Selection of Gear Ratios
Actual gear ratios selection also reflect the realities
of the pressures for fuel economy and emissions.
E
n
g
i
n
e
s
p
e
e
d
Road speed
1
st
gear 2
nd
gear 3
rd
gear 4
th
gear 5
th
gear
Problem
We are given the following information about the engine and drivetrain components for a
passenger car :
Engine inertia 0.0904kgm
2
RPM/Torque (Nm) 800/162.8 1200/179.0 1600/196.7 2000/217.0 2400/237.4 2800/245.5
3200/257.7 3600/268.5 4000/271.3 4400/272.6 4800/268.5 5200/244.1
Transmission Data Gear 1 2 3 4 5
Inertia (kgm
2
) 0.1469 0.1017 0.091 0.0565 0.0339
Ratios 4.28 2.79 1.83 1.36 1.00
Efficiencies 0.966 0.967 0.972 0.973 0.970
Final drive inertia 0.1356kgm
2
Ratio 2.92
Efficiency 0.99
Wheel inerties Drive 1.243kgm
2
Non-drive 1.243kgm
2
Wheel size 497.7 rev/km 2.0 m circumference 31.98 cm radius
a. Calculate the effective inertia of the drive-train components in first gear
b. Calculate the maximum tractive effort and corresponding road speed in first and fifth gears
of the car described above when inertial losses are neglected.
Traction Limited Acceleration
Limited by the coefficient of friction between the tire and road. Therefore,
wheels drive on Weight W
friction of t coefficien Peak
where
W F
x
=
=
=
** The weight on a drive wheel then depends on the (Static load + Dynamic load)
due to acceleration, and on any transverse shift of load due to drive torque.
Transverse Weight Shift
- Due to drive torque
- Occurs on all solid drive axles (front/rear)
s
T
d
T
t y
r
W
2
W
+
y
r
W
2
W
** Torque delivered to wheels will be limited by the traction limit on the most
lightly loaded wheel
0
Writing NSL at point O
ratio drive Final N
radius Tire r
s rear wheel two the from force drive Total F
where
r/N F T
and
)/t T - (T W
or
0 T T )t/2 W /2 W W /2 (W T
f
x
f x d
s d y
d s y r y r 0
=
=
=
=
=
= + + + =
r
f
sr
sf
=
=
=
=
=
For Low Speed Acceleration
L
h
g
a
W W
L
h
g
a
L
b
W W
L
h
g
a
W W
L
h
g
a
L
c
W W
x
rs
x
r
x
fs
x
f
+ =
+ =
=
=
Traction Limits Rear Wheel Drive
Based on the relationship and assumptions,
Maximum tractive force for solid rear axle with a
non-locking differential:
f
f
max
x
K
K
t N
r 2
L
h
- 1
L
Wb
+
=
Dynamic Load
transfer
Lateral load transfer
for lower traction
force limited wheel
Static load
distribution
cof of the driving wheel
Additional Traction limits
When no lateral load transfer, both driving wheels has
the same traction force limit, where
L
h
- 1
L
Wb
K
K
t N
r 2
L
h
- 1
L
Wb
f
f
max x
=
+
=
0
True for independent rear suspension because the
driveline torque reaction is picked up by the chassis-
mounted differential
Traction Limits Front Wheel Drive
For the solid front drive axle with non-locking differential,
r
f
max
x
K
K
t N
r 2
L
h
1
L
Wc
+ +
=
For solid front drive axle with locking differential, or independent
front drive axle,
L
h
1
L
Wc
F
max
x
+
=
Problems
Find the traction-limited acceleration for the rear-drive
passenger car with and without a locking differential on a
surface of moderate friction level. The information that will be
needed is as follows:
Weights Front 952 kg Rear 839 kg Total 1791 kg
CG height 53.34 cm Wheelbase 274.3 cm
Coefficient of friction 0.62 Wheel track 149.86 cm
Final drive ratio 2.90 Tire size R13/200/65
Roll Stiffness Front 1559.7 Nm/deg Rear 379.8 Nm/deg
Problems
Find the traction-limited performance of a front-
wheel-drive vehicle under the same road conditions
as the problem above. The essential data are:
Weights Front 885 kg Rear 522 kg Total 1407 kg
CG height 48.26 cm Wheelbase 266.7 cm
Coefficient of friction 0.62 wheel track 152.4 cm
Final drive ratio 3.70 Tire size 12.59 in
Roll Stiffness Front 1288.5 Nm/deg Rear 840.9 Nm/deg
Nissan Sentra Engine Curve
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