Environmental Engineering Reference
In-Depth Information
R
C
S
w
s
w
r
w
c
(a)
(b)
Figure 2.20 Epicyclic gear set and definitions: (a) definition of planetary gear
components and (b) illustration of planetary gear set (from UQM)
A planetary gear set is composed of sun gear at the centre of the diagram, a set
of pinion gears (planets) arranged around the sun and held by the carrier and the
ring gear. Bearings support the three sets of gears. The basic ratio,
k
, of an epicyclic
gear set is defined as the ratio of ring gear teeth to sun gear teeth, or the ratio of
their corresponding radii,
R
r
and
R
s
,as
k
=
R
r
/R
s
. Given the basic ratio, the
governing equation for epicyclic gear as a speed summing device is
w
s
þ
k
w
r
ð
k
þ
1
Þw
c
¼
0
ð
2
:
2
Þ
In (2.2),
w
s
,
w
c
and
w
r
correspond to angular speed of the sun, carrier and ring
gears, respectively. S/A sun gear speed,
w
s
, runs backward with respect to the
engine speed,
w
c
, in order to match road dependant speed at the ring gear. Con-
trolling the power transferred via the S/A at a given speed sets its reaction torque
level against the ICE via the ratio
G
cs
. The torque levels at sun and carrier gear
can be expressed in terms of the ring gear torque,
M
, the gear mesh efficiencies,
h
(generally a loss of 2%/mesh), the polar inertias,
J
, and accelerations as shown
in (2.3):
1
k
h
r
M
r
J
s
1
k
J
r
h
s
M
s
w
s
þ
w
r
¼
0
ð
2
:
3
Þ
k
þ
1
k
k
þ
1
k
h
c
M
c
þ
h
r
M
r
J
c
w
c
J
r
w
r
¼
0
Figure 2.21 is a plot of vehicle speed,
V
, versus
w
s
,
w
c
and
w
r
to illustrate how
each of these propulsion components responds during acceleration at WOT. For
example, suppose the ICE is rated 80 kW peak power for a Focus sized 4 or 5 door
passenger vehicle and further suppose that MG1 is rated 32 kW and MG2 is rated
16 kW. The vehicle accelerates from standstill to 60 mph (26.82 m/s) in 6.8 s with
the ICE operating at approximately 2,500 rpm.
