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