Post on 24-Sep-2020
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Planetary gear trains
Gear train - tasksGear train
motor/engine
driven link (links) from
which required forces and
motions are obtained
ininM
outoutM
If efficiency = 1
outoutinin MM =
Gear box – example 1
Gear box – example 2
h a
gear pair
helicalh 0a 0
wormh 0a = /2
bevel (conical)h = 0a 0
cylindricalh 0a = 0
gear typeha
Gear train types
helicalh 0a 0
wormh 0a = /2
bevel (conical)h = 0a 0
cylindricalh 0a = 0
gear typeha
Planetary gear train definition
Most of simple and compound gear trains have the restriction that
their gear shafts may rotate in bearings fixed to the frame.
If one or more shafts rotate around another
shaft a gear train is called a planetary (or
epicyclic) gear train
Planetary gear nomenclature
A simple planetary gear
Planetary gear box of the power split device
Simple planetary gear train (obtained from unmovable axes train)
carrier
FRAME → CARRIER
1 → FRAME
FRAME → CARRIER
2 → FRAME
Simple planetary gear train (obtained from unmovable axes train)
Properties of planetary gear train
Interesting trajectories of planet gear points
Gears and other parts must be manufactured in very high
accuracy → COSTS !!!
Large velocity ratio (for compact gear train)
A few motors can drive one machine
Ability to transfer large forces (and power)
One motor can drive few links (car differentials)
One planet
gear
Ability to transfer large forces (power)
Planet gear 3
Planet gear 1
Planet gear 2
3 gear pairs take part in force transfer
Ability to transfer large forces (power)
Mass 87 kg Mass 1400 kg
Gears with unmovable
gear axes
Planet gear trains
420x320 610x520 850x510 1150x600
The same power and ratio !
Compare
One motor can drive few links (two wheels)
engine
po-line.sam
Planetary mechanism – trajectory (1)
po-stop.sam
Planetary mechanism – trajectory (2)
Planetary mechanism – trajectory (3)
po-ham.sam
Examples of trajectories
Examples of trajectories
Velocity ratio
External gear
2
2
1
1
v
v
R
R
=
=
( )11
2
1
2
2
1 −==
z
z
R
R
z
2
mR =
Velocity ratio
Internal gear
2
2
1
1
v
v
R
R
=
=
( )11
2
1
2
2
1 +==
z
z
R
R
Analytical method
Idea of analytical method
1
23
J
1 J
3
J
1
2
Gear train seen
from carrier
Revolutions in
frame (gear 3)
Revolutions seen from
carrier J
gear 1 n1 n1J = n1 - nJ
gear 2 n2 n2J = n2 - nJ
gear 3 n3 = 0 n3J = n3 - nJ
Carrier J nJ 0 30
min
rev
s
1
=
n
3
J
1
2 ( )i
Js
Ju
sJ
uJ zf=−
−=
( )11
31 −=−
−
z
z
J
J
03 =
( )11
3
3
1 −=−
−
z
z
J
J
( ) ( )
+
−=
=
•
=
−
−=
112
3
1
2
3
2
2
1
3
1
3
1
z
z
z
z
J
J
J
J
J
J
J
J
+= 1
1
31
z
zJ
50;99;51;101:numberstooth Assume 4321 ==== zzzz
5049
1
5199
5010113 −
=
−=
J
( ) ( )113
4
2
1
1
3 ++=−
−
z
z
z
z
J
J
„seen” from the carrier J:
01 =
Since:
23
413 1zz
zz
J
−=
Then:
13
2 4
J
?3 =J
Graphical method (Velocity analysis)
1
2
J
A
B
2
J
M
1
2
J
A
B
2
J
vB J=AB M
1
2
J
A
B
2
J
vB J=AB M
S21
1
2
J
A
B
2
J
vB J=AB M
S21
=2vB2R
22 = R
JAB
1
2
J
A
B
2
J
vB J=AB M
S21
2=S MMv 21
=2vB2R
22 = R
JAB
2
2R
ABJ =
21 RRAB +=
( )
2
212
R
RRJ +=
2
21
2
2
1
2
1
2
1
mz
mzmzJ
+
=
( )
2
212
z
zzJ +=
1
2
J
A
B
2
J
M
1
C
D
11
2
J
A
B
2
J
vB J=ABM
1
1=RCv
C
D1
Dv C=v
11
2
J
A
B
2
J
vB J=ABM
S20
1
1=RCv
C
D1
Dv C=v
11
2
J
A
B
2
J
vB J=ABM
S20
2=S MMv 20
1
1=RCv
C
D1
Dv C=v
1
Bv.1 →J
DC1 vv.2 =→
frame)(0.3 20 −S
Two driving gears (gear 1 and carrier)
Planetary gear train – graphical method
1
2
J
A
B
2
C
D
1
3
1
2
J
A
B
2
J
C
D
1
3
1
2
J
A
B
2
JvB J=AB
C
D
1
3
1
2
J
A
B
2
JvB J=AB
C
D
1
2
3
S23
1
2
J
A
B
2
JvB J=AB
C
D
1
2
3
S23
2=2RDv 2
1
2
J
A
B
2
JvB J=AB
1
C
D
1
2
3
S23
2=2RDv 2
Cv =vD
JB AB=v
21 RRAB +=
2
2R
Bv=
JR
RR
2
212
+=
222 RD =v JD RR )(2 21 +=v
DC vv =JC RR )(2 21 +=v
1
1R
Cv=
1
211
)(2
R
RR J
+=
JR
R
+=
1
31 1
JB RR )( 21 +=v