Planetary gear drive
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Subramanian Vinoth
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) A simplified approach tor determining power losses and efficiency of Planeta,y Gear Drives By Eugene I. Radzimovsky Associate Professor of Mechanical Engineering University of II1inois Urbana, 111. .' '. N A PLANETARY gear drive, the power circulating within the system elements may differ appreciably from that being transmitted. This unique characteristic, which is a result of the relative motion of the gear members, is present in some degree in all planetary gear trains and has a significant effect on the performance and efficiency of systems transmitting power continuously. Power losses become a function of the power developed in the gearing rather than of the actual power transmitted through the train. Several methods for determination of power losses and efficiencies of planetary gearing have been propo:sed, and expressions for a number of specific gear arrangements have been developed. Most of these analyses are based on the principle I of equilibrium of moments first suggested by Massot. 1 This article presents a new approach to the problem and offers a general method of solution, utilizing the concept of an "equivalent" conventional gear train in conjunction with the particular kinematic characteristics of planetary systems. Several representative planetary gear arrangements are analyzed to illustrate application of the principles discussed. Basic Considerations: Certain general concepts of gear performance will be useful in analysis of planetary gear systems and perhaps should be reviewed. 'References are tabulated at end of article, Nomenclature = Pitch diameter of gear, in. e t = Overall efficiency of planetary gear train F = Tangential force acting at the pitch circle of the driving gear, Ib L = Tooth mesh power loss in a planetary gear pair, ftlb per sec L t = Total tooth mesh power loss in a planetary gear train, ftIb per sec J = Tooth mesh loss in a conventional gear pair, ftlb per sec It = Total tooth mesh loss in a conventional gear train, ftIb per sec m = Speed ratio of gear pair d e = Efficiency of planetary gear pair February 9, 1956 = Overall speed ratio of planetary gear train = Number of meshing pairs in a gear train Pi, Po = Input and output power, respectively, itlb per sec R = Planetary velocity ratio defined by Equation 6 v = Pitchline velocity of gear pair, fps e = Velocity of engagement of a gear pair, fps A = Ratio of tooth mesh loss to input power in a gear pair 7/ = Efficiency of conventional gear pair mp n...
)
Drives
'References
are
tabulated
at
end
of
article,
Basic
Considerations:
Certain
general
concepts
of
gear
performance
will
be
useful
in
analysis
of
planetary
gear
systems
and
perhaps
should
be re
viewed.
of
equilibrium
of
moments
first
suggested
by
Mas
sot.
1
This
article
presents
a
new
approach
to
the
problem
and
offers a
general
method
of
solution,
utilizing
the
concept
of
an
"equivalent"
conven
tional
gear
train
in
conjunction
with
the
particular
kinematic
characteristics
of
planetary
systems.
Several
representative
planetary
gear
arrange
ments
are
analyzed
to
illustrate
application
of
the
principles
discussed.
.'
'.
Planeta,y
Gear
By
Eugene
I.
Radzimovsky
Associate Professor
of
Mechanical Engineering
University
of
II1inois
Urbana,
111.
A
simplified
approach
tor
determining
power
losses
and
efficiency
of
I
N A
PLANETARY
gear
drive,
the
power
circu
lating
within
the
system
elements
may
differ
appreciably
from
that
being
transmitted.
This
unique
characteristic,
which
is a
result
of
the
relative
motion
of
the
gear
members,
is
present
in
some
degree
in
all
planetary
gear
trains
and
has
a
significant
effect
on
the
performance
and
efficiency
of
systems
transmitting
power
continu
ously.
Power
losses
become a
function
of
the
power
developed
in
the
gearing
rather
than
of
the
actual
power
transmitted
through
the
train.
Several
methods
for
determination
of
power
losses
and
efficiencies
of
planetary
gearing
have
been
propo:sed,
and
expressions
for
a
number
of
specific
gear
arrangements
have
been
developed.
Most
of
these
analyses
are
based
on
the
principle
Nomenclature
d =
Pitch
diameter
of
gear,
in.
e =
Efficiency
of
planetary
gear
pair
e
t
=
Overall
efficiency
of
planetary
gear
train
F =
Tangential
force
acting
at
the
pitch
cir
cle
of
the
driving
gear,
Ib
L =
Tooth
mesh
power
loss
in
a
planetary
gear
pair,
ftlb
per
sec
L
t
=
Total
tooth
mesh
power
loss
in
a
planetary
gear
train,
ftIb
per
sec
J =
Tooth
mesh
loss
in
a
conventional
gear
pair,
ftlb
per
sec
It
=
Total
tooth
mesh
loss
in
a
conventional
gear
train,
ftIb
per
sec
m =
Speed
ratio
of
gear
pair
m
p
=
Overall
speed
ratio
of
planetary
gear
train
n =
Number
of
meshing
pairs
in
a
gear
train
Pi, Po =
Input
and
output
power,
respectively,
itlb
per
sec
R =
Planetary
velocity
ratio
defined
by
Equa
tion
6
v =
Pitchline
velocity
of
gear
pair,
fps
V
e
=
Velocity
of
engagement
of
a
gear
pair,
fps
A =
Ratio
of
tooth
mesh
loss
to
input
power
in
a
gear
pair
7/
=
Efficiency
of
conventional
gear
pair
7/t =
Overall
efficiency
of
conventional
gear
train
'"
=
Angular
velocity,
radians
per
sec
February
9, 1956
101
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Planetary gear drive

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Planetary gear drive
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