About planetary gear box

1. Simple Epicyclic Gear Trains
Epicyclic gear trains have a number of new
definitions not found in simple gear trains:
Ring gear or annulus gear (R)

2. Kinematics of Epicyclic
Gear Trains
Planet gear P can rotate freely on a pin
attached to carrier C
Carrier C rotates freely about the axis of sun
gear S
Only one planet gear P is needed to transmit
motion
Multiple planet gears can be added for balance,
strength, and smooth operation
Extra planet gears DO NOT
change the speed ratios of
epicyclic gear trains

3. Ring gears typically have internal teeth
Ring gears can have external teeth
meshing with additional gears
External gears are not part of the epicyclic
gear train
P
S
R
C
Simple Epicyclic Gear Trains

4. Advantage of epicyclic gear trains:
P
S
R
C
Simple Epicyclic Gear Trains
• Compact
• Gears are constantly in mesh
• Loads are shared between several gears

5. Advantage of epicyclic gear trains:
P
S
R
C
Simple Epicyclic Gear Trains
• Reverse can be achieved without the need
for additional shaft

6. Advantage of epicyclic gear trains:
P
S
R
C
Simple Epicyclic Gear Trains
• Several gear (speed) ratios can be obtained
• Three shafts available for selection of input
and output shafts

7. Input/Output Shafts
• Two shafts can be selected for input and
output (e.g. sun and carrier) and one shaft is
locked (ring gear)
• Sun gear or carrier can be locked and the
remaining two components are used to
determine the speed ratio

8. How many teeth should each gear
have?
Gear Teeth Number
Relationships

9. Gear Teeth Number
Relationships
rR
rS
rS
rR
dP
dP
We can determine the required size of all the
gear components visually.
(1)
P
S
R
P
s
R
P
S
R
d
2
d
d
d
2
r
2
r
2
d
r
r







10. 10
rR
rS
dP

11. Module
Recall that the module is the length of pitch
circle diameter per tooth
1
P
n
d
m 

To mesh, two
gears must have
the same module.
To mesh, two
gears must have
the same module.
Gear Teeth Number
Relationships

12. Gear Teeth Number
Relationships
rR
rS
rS
rR
dP
dP
Using the equation for the module, we can
write:
(2)
Module
n
m
d
n
d
m


Lecture Outline
Compound gear
train example
Epicyclic gear
trains
Analysis of
epicyclic gear
trains
Examples

13. (1)
P
S
R
P
s
R
P
S
R
d
2
d
d
d
2
r
2
r
2
d
r
r






(2)
Module
n
m
d
n
d
m


(3)
(2)
and
(1)
From
P
s
R
P
S
R
n
2
n
n
n
m
2
n
m
n
m




Gear Teeth Number
Relationships
rR
rS
rS
rR
dP
dP
We now have a relationship for
the number of teeth of each
gear.

14. Gear Teeth Number
Relationships
rD rE
dB dC
rA
A compound epicyclic gear train is shown
If we know how many teeth are on gears A, B, C &
D, how many teeth are on gear E?

15. n
n
n
n
m
m
n
m
n
m
n
m
n
m
m
m
d
d
d
d
r
r
r
r
r
r
r
r
C
B
A
E
C
B
A
E
C
B
A
E
C
B
A
E
C
B
A
E
















,
If
ly
respective
D,
-
B
-
A
and
C
-
E
for trains
modules
the
are
and
If
2
2
2
2
2
1
1
2
2
1
2
1
Gear Teeth Number
Relationships
rD rE
dB dC
rA

16. Schematics of Epicyclic Gears
Left: The epicyclic gear train
Right: An example of an epicyclic gear sketch
Teeth are indicated by “T”
A
B C
E
D
F
The gears and carrier are labelled

17. Another example...
Schematics of Epicyclic Gears

18. Analysing speed ratios
Consider here that the sun gear is held stationary
What might the ratio of the ring gear shaft to the
carrier shaft be…?