9장. 기어 열

9장. 기어 열

(Chap 9. Gear Trains)

The earliest known reference to gear trains is in a treatise by Hero Alexandria. Gear trains are widely used in all kinds of mechanisms and machines from automobile engines to industrial robots. Whenever a change in the speed or torque of a rotating device is needed, a gear train or one of its cousins, the belt or chain drive mechanism, will usually be used.

This chapter will explore the theory of gear teeth action and its ubiquitous devices for motion control.

(Excerpted from the textbook)

기어 열

9.2 기어 이론 (Fundamental law of gearing)

• 속도 비 (Velocity Ratio: VR)

w_in w_out

r

r

in

VR out

w

 w

out in

N

 N



out in

r

 r



반대 방향

Number of teeth

F

• 토크 비 (Torque Ratio: TR)

out in in

Nout

N

w

 w





in out in

out

r F

r F T

TR T 

 





(Excerpted from the textbook)

9.2 기어 이론 (Fundamental law of gearing)

• 인벌류트 치형 (Involute tooth form)

R₁ R₂

A₂

A 피치원 (Pitch circle)

N m  D^p

Module:

기초원 (Root circle)

A₁

 

  ^ 

A₁R₁  AR₁ & A₂R₂  AR₂ 접점 궤적

(Excerpted from the textbook)

기어 열

9.2 기어 이론 (Fundamental law of gearing)

(Excerpted from the textbook)

기어 열

9.6 기어 형태 (Gear types)

(a) Spur (b) Bevel (straight) (c) Bevel (crossed)

(d) Worm (e) Helical (parallel) (f) Helical (crossed)

(Excerpted from the textbook)

기어 열

9.7 단순 기어열 (Simple gear trains)

기어열 (Gear trains)

• Any collection of two or more meshing gears.

(2개 이상의 맛물린 기어 조합)

• Classification (분류)

- Meshing (맞물림) : External (외접)

External

Internal

: Internal (내접) - Arragement (배열) : Simple (단순)

: Compound (복합) : Planetary (유성)

Each shaft carries only one gear

At least one shaft carries more than one gear

기어 열

9.7 단순 기어열 (Simple gear trains)

• 속도 비 (Velocity Ratio: VR)



 





 



 



1

i Driven i

Driver

v n

N

) N 1 ( m

Number of external meshes Number of stages

Example

w_in w_out

2 N₂ 3 4 5

N₃

N₄ N₅

Idle gear

















5 4 4

3 3

2 2

v N

N N

N NN

) 1 ( m









5 2 2

N ) N

1 (









out 2 in

N ) N

1 (

기어 열

9.8 복합 기어열 (Compound gear trains)

• 속도 비 (Velocity Ratio: VR)



 





 



 



1

i Driven i

Driver

v n

N

) N 1 ( m

N₂

N₃ N₄

N₅













5 4 3

2 2

v N

N N

) N 1 ( m

기어 열

9.8 복합 기어열 (Compound gear trains)

예제 9-2 복합 기어열 설계 (Compound Gear Train Design)

Design a compound train for an exact train ratio of 180:1.

Find a combination of gears which will give that ratio.

(Excerpted from the textbook)

Solution

예제 9-2 복합 기어열 설계

1. Number of stage

• 2 stages 180  13.4 > 10

• 3 stages ³180  5.6 < 10

X

2. Gear ratio

180 ( ) X ( ) X ( )6 6 5 3. Number of gear teeth

• 1st stage 6 X 14 = 84

• 2nd stage 6 X 14 = 84

• 3rd stage 5 X 14 = 70

Greater than 12 at 25^o pressure angle to avoid interference.

4. Verification

Practical consideration

1801 1470

1484 1484

) 1 (

m_v ³  



 



 



 



 



 



 



기어 열

9.8 복합 기어열 (Compound gear trains)

예제 9-3 Reverted gear train design

Design a reverted compound train for an exact train ratio of 18:1.

Output shaft concentric with the input shaft

(Excerpted from the textbook)

예제 9-3 Reverted gear train design Solution

1. Reverted

5 4

3

2 r r r

r   

5 4

3

2 N N N

N   

2. Gear ratio

18 ( 6 ) X ( 3 )

3. Number of teeth

(2)

(2)  (1) :

72 63

(1)

61 N

N

3

2  N₃  6N₂

31 N

N

5

4  N₅  3N₄

4 4

2

2 6N N 3N

N   

74 N

N

4 2 

N₂=12 & N₄=21