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Planetary gear trains

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(1)

Planetary gear trains

(2)

Gear train - tasks

Gear train

motor/engine

driven link (links) from which required forces and motions are obtained

in

M

in

out

M

out

If efficiency  = 1

out out

in

in

M

M  = 

(3)

Gear box – example 1

(4)

Gear box – example 2

(5)

h a gear pair

helical h  0

a  0

worm h  0

a = /2

bevel (conical) h = 0

a  0 h  0 cylindrical a = 0

gear type a h

Gear train types

(6)

helical h  0

a  0

worm h  0

a = /2

bevel (conical) h = 0

a  0

cylindrical h  0

a = 0

gear type a h

(7)

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

(8)

Planetary gear nomenclature

A simple planetary gear

(9)
(10)

Planetary gear box of the power split device

(11)

Simple planetary gear train (obtained from unmovable axes train)

carrier

FRAME → CARRIER

1 → FRAME

(12)

FRAME → CARRIER 2 → FRAME

Simple planetary gear train (obtained from unmovable axes train)

(13)

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)

(14)

One planet gear Ability to transfer large forces (power)

(15)

Planet gear 3 Planet gear 1

Planet gear 2

3 gear pairs take part in force transfer Ability to transfer large forces (power)

(16)

Mass 87 kg Mass 1400 kg

Gears with unmovable gear axes

Planet gear trains

420x320 610x520 850x510 1150x600

The same power and ratio !

Compare

(17)

One motor can drive few links (two wheels)

(18)

engine

(19)

po-line.sam

Planetary mechanism – trajectory (1)

(20)

po-stop.sam

Planetary mechanism – trajectory (2)

(21)

Planetary mechanism – trajectory (3)

po-ham.sam

(22)

Examples of trajectories

(23)

Examples of trajectories

(24)

Velocity ratio External gear

2 2

1 1

v v

R R

=

=

( ) 1

1 2 1

2 2

1

= = −

 

 

z z R

R

 z

2 R = m

(25)

Velocity ratio Internal gear

2 2

1 1

v v

R R

=

=

( ) 1

1 2 1

2 2

1

= = +

 

 

z z R

R

(26)

Analytical method

(27)

Idea of analytical method

1 3 2

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

(28)

3

J

1

2

( )

i

J s

J u

sJ

uJ

= f z

= −

( ) 1

1 3

1

= −

z z

J

J

0 

3

=

( ) 1

1 3 3

1

= −

z z

J

J

( ) ( )

 

 +

 

 

 −

=

 =

 

• 

 

 

= 

= −

1 1

2 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 3

1

z

z

J

(29)

50

; 99

; 51

; 101 :

numbers tooth

Assume z1 = z2 = z3 = z4 =

5049 1 51

99

50 1 101

3

= −

− 

=

J

( ) ( ) 1 1

3 4 2

1 1

3

= + +

z z z

z

J

J

„seen” from the carrier J:

1

= 0

Since:

2 3

4 1

3

1

z z

z z

J

 =

Then:

1 3

2 4

J

?

3

=

J

(30)

Graphical method (Velocity analysis)

(31)

1 2

J

A B

2

J

M

1 2

J

A B

2

J

vB=ABJ M

1 2

J

A B

2

J

vB=ABJ M

S21

1 2

J

A B

2

J

vB=ABJ M

S21

 =2 vB R2 2 2

 =ABRJ

1 2

J

A B

2

J

vB=ABJ M

S21

2

=S M vM 21

 =2 vB R2 2 2

 =ABRJ

2

2

R

J

AB

 = 

2

1

R

R AB = +

( )

2 2 1

2

R

R

J

R +

= 

2

2 1

2

2 1

2 1 2

1

mz

mz

J

mz

 

 +

=

( )

2 2 1

2

z

z

J

z +

= 

(32)

1 2

J

A B

2

J

M

1

C D

1 1

2

J

A B

2

J

vB=ABJ M

1

1 C=R v C

D

1

vD=vC

1 1

2

J

A B

2

J

vB=ABJ M

S20

1

1 C=R v C

D

1

vD=vC

1 1

2

J

A B

2

J

vB=ABJ M

S20

2

=S M vM 20

1

1 C=R v C

D

1

vD=vC

1

v

B

.

1 

J

D C

1

v v

.

2  → =

frame) (0

.

3 S

20

Two driving gears (gear 1 and carrier)

(33)

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

J vB=ABJ

C D

1

3

1 2

J

A B

2

J vB=ABJ

C D

1

2

3

S23

1 2

J

A B

2

J vB=ABJ

C D

1

2

3

S23

2 D=2R

v 2

1 2

J

A B

2

J vB=ABJ

1

C D

1

2

3

S23

2 D=2R

v 2

v =vC D

J B = AB v

2

1 R

R AB = +

2

2 R

vB

= J

R R

R

2 2 1 2

= +

2

2R2

D =

v vD = 2(R1 + R2)J

D

C v

v = vC = 2(R1 +R2)J

1

1 R

vC

=

1 2 1 1

) (

2

R R R J

= +

R J

R



 

 +

=

1 3

1 1

J B =(R1+R2) v

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