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90
cent. Actually, such a speed ratio is impossible to realize in practice
because it requires that
0
=
KBJA
dddd . Also, since the value of this
diameter ratio cannot be negative, m
p
= +1 is the theoretical maximum
limit for positive speed ratios in this train.
When
)1(
tt
R η−=η , η
t
= 0. For η
t
= 0.97 this condition corresponds
to m
p
=+0.03. When the speed ratio is negative, η
t
=0 corresponds
approximately to 031.0−=
p
m . Efficiency increases as the absolute
value of speed ratio increases, approaching the value of η
t
asymptotically as a higher limit. For m
p
=-25, the efficiency of the train
is 0.9688. This value may be considered as highly satisfactory for a
planetary gear train of this type. However, this type of train can be
designed only for relatively small speed ratios, having a maximum
absolute value that is approximately of the same magnitude as may be
obtained by two pairs of gears in a conventional gear train.
Modified Differential System: In another type of differential
planetary gear train, Fig. 9, the sun gears are in the form of internal
gears A and K. In this particular train, gear A is fixed and K is connected
to the output shaft. Planet cage G is connected to input shaft D.
For this train, as in the arrangement shown in Fig. 7a, speed ratio is
given by Equation 20. These two differential systems also have the same
expressions for η
t
and R. Here again, two principal cases must be
considered: (1)
1
<
KBJA
dddd and (2) 1>
KBJA
dddd . In the first case,
gear K' is the driver in the equivalent train with the planet cage stopped,
and Equations 23, 24 and 25 must be used for efficiency calculations.
For the second case, gear A' becomes the driver and Equations 28 and 29
are pertinent.
The only difference
between the two train
arrangements, Figs. 7a and 9,
lies in the values for ∆
1
, ∆
2
,
and η
t
of the train. The losses
in internal gears, if all other
factors remain the same, are
somewhat lower than for
comparable external gear pairs.
Therefore, the value of η
t
may
be considerably smaller for the
internal gear arrangement, Fig. 9, than for the external gear system, Fig.
7a. Total efficiency for a planetary train of this type will thus be higher
for a given speed ratio if internal gears are used.
Sun gear, A
(fixed)
Output shaft, H
Sun gear, K
Planet cage, G
Planet gear, J
Input shaft, D
Planet gear, B
Fig. 9-Modified differential system in
which the sun gears are internal gears
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