Environmental Engineering Reference
In-Depth Information
An equivalent mass,
m
eq
, has been defined in (1.5) that accounts for passenger
loading and all rotating inertia effects. Passenger loading is determined by taking
the number of passengers,
N
p
, including the driver, times the standard human
passenger mass,
m
p
, of 75.5 kg. The mass factor,
f
m
, accounts for all wheel, dri-
veline, engine with ancillaries, and hybrid M/G component inertias that rotate with
the wheels. The remaining terms on the right-hand side of (1.5) account for tractive
force,
F
trac
, aerodynamic force,
F
aero
, front rolling resistance,
F
rf
, rear rolling
resistance,
F
rr
and road grade. Rolling resistance is split front and rear to account
for their different contributions to overall resistance due to the vehicle's mass
distribution and tyre rolling resistance coefficients. There may be some minor
differences in coefficient of rolling resistance front to rear axle due to different
specifications on tyre pressure, but these second order effects will be ignored. The
mass factor,
f
m
, is now defined as the translational equivalent of all rotating inertias
reflected to the wheel axle:
J
eng
z
i
z
FD
m
v
r
w
þ
J
ac
z
i
z
FD
m
v
r
w
4
J
w
m
v
r
w
þ
f
m
¼
1
þ
ð
1
:
6
Þ
Mass factor is derived from equating rotational energy to its equivalent trans-
lational energy and solving for the equivalent translating mass. In (1.6),
r
w
is the
wheel dynamic rolling radius (approximately equal to standing height minus one-
third deflection),
m
v
is the vehicle curb mass, and
J
x
s are the respective inertias. The
factors
z
i
2
and
z
FD
2
are the transmission ratios in the
i
th gear and final drive ratio,
respectively. The appropriate gear ratios
z
i
and
z
FD
are listed in Table 1.11. Before
mass factor can be calculated the component inertias must be known. Notice also
that in (1.6) the right-hand terms are mass ratios, that is a component's equivalent
mass divided by vehicle's curb mass. Inertias are generally not available without
very detailed specifications for the components. Table 1.12 lists some representa-
tive inertia values. These values are generic in nature, but some approximations will
attest to their validity. The inertia values listed, and their counterpart equivalent
masses will be sufficient for the purposes of simulations in this topic. To begin,
recall that inertia of a rotating, symmetric object such as a disc or rod is defined as
p
2
hri
hr
0
ð
kgm
2
J
0
¼
Þ
ð
1
:
7
Þ
In (1.7),
h
is the disc thickness or rod length and
r
0
its radius. An average mass
density
hri
has been assigned. For electric machines such as claw pole Lundell
alternators with rotating copper wound field bobbins, or smooth rotor, cast alumi-
nium cage type, induction S/A, estimates for average mass density that prove useful
in approximations are 2,500 and 5,500 kg/m
3
, respectively. Some examples will
reinforce this assertion. A typical 120 A Lundell alternator has a rotor thickness of
~40 mm and a diameter of 100 mm. When these values are substituted into (1.6),
the approximate polar moment of inertia comes out to
J
0
= 0.00098 kg m
2
. Without
loss of applicability use 0.001 kg m
2
. As another example, a crankshaft mounted
induction S/A designed for 42 V applications has a rotor thickness of 50 mm, a
