Environmental Engineering Reference
In-Depth Information
The complete road load model developed thus far is given as (1.24), where the
terms from (1.5) have been expanded:
d 2 x
dt 2 ¼
T M = G z i z M = G h EM
r w
0 : 5 r air C d A f ð V V air Þ
T e z 0 h TM
r w
ð f m m v þ N p m p Þ
þ
R 0 g B
2
L m v cos ðaÞ
ð 1 : 24 Þ
R 0 g A
L m v cos ðaÞ
m v g sin arctan %grade
100
where provision is made for the M/G torque to be summed into the propulsion
system at a gear ratio other than the transmission times final drive ratio, z 0 .
Aerodynamic modelling includes the effect of head/tail winds and rolling resistance
accounts for front to rear axle mass partitioning. For completeness, a cos( a ) grade
term is included that multiplies both rolling resistance terms in (1.24).
Due to wheel slip, driveline and engine speeds can be as much as 20% over
the freewheeling vehicle speed to engine speed relationship. To correctly model
the driveline and engine speeds, the tractive effort must be equated to the wheel
slip curve modelled in Figure 1.27. The slip s is determined by solving (1.25) and then
substituting this slip value into (1.26) for engine speed for a given vehicle speed:
h
i g
z 0
r w ¼
m us
2
B
L ð m a þ N p m p Þþ
m pk ½ a ð 1 e bs
ð T e h TM þ T M = G h EM Þ
Þ cs
ð 1 : 25 Þ
Solve (1.25) for slip, s , for a given engine torque, T e , at engine speed, n e ,
determined from
60
2 p
z 0
n e ¼
V ð rpm Þ
ð 1 : 26 Þ
r w ð
1
s
Þ
The vehicle performance model described in this section is referred to as a
backward model because the vehicle speed is the state that determines the road load
and from this the engine operating points. A forward simulationmodel is more difficult
to implement and requires an accurate engine model so that fuel control becomes the
input command that results in an output torque and speed at the engine crankshaft, plus
an algorithmic decision process to actuate the transmission gears. The resultant for-
ward path gives the tractive effort at the tyre patch and from this the vehicle speed.
The second performance attribute is fuel economy and the topic of the next
section.
Example 4: Vehicle tyres are designed to provide a safe and smooth ride. This
means sufficient road holding ability to not only meet acceleration and braking
traction needs but cornering performance as well. Calculate the approximate tyre
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