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82
0.97446. In this case, the velocity of engagement in the planetary train
is somewhat less than that in a corresponding conventional train
consisting of the same gears and having the same angular velocity and
power at the input shaft. Since the tangential forces acting on the gears
are the same, the power developed by the planetary gears is lower than
in the conventional train. Dynamic tooth loads and wear, which depend
upon the tangential force and the velocity of engagement, are also lower
in the planetary train.
Modified Train Arrangement: A planetary gear train similar to
the one just considered, but with gear A as the fixed member, is shown
schematically in Fig. 5. Internal gear C becomes the driver, and output
shaft C is connected to planet cage G. The speed ratio of this train can
be determined from the following relationship:
C
A
G
C
H
D
p
d
d
m +=
ω
ω
=
ω
ω
= 1 (16)
After the angular velocity —ω
H
is added to the entire system, as in
the previous analysis, the angular velocity of gear C becomes
−ω=ω−+ω=ω
′
p
CHCC
m
1
1)( (17)
The value of m
p
is always positive and greater then one; therefore,
the direction of ω
c
' is positive if ω
C
is positive. The torque acting on
Fig. 4—Typical
planetary gear
transmission design
employing the
basic arrangement
shown in Fig. 3a
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