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)

win

wout

rin

rout

in

outVRw

w

out

in

N

N

out

in

r

r

반대방향

Number of teeth

F

• 토크 비 (Torque Ratio: TR)

out

in

in

out

NN

w

w

in

out

in

out

rF

rF

T

TTR

(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

Dm p

Module:

기초원 (Root circle)

A1

A1R1 & A2R2 : Perpendicular to the Involute curve

: Tangent to the root circle

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)

k

1i iDriven

Drivernv N

N)1(m

Number of external meshes

Number of stages

Example

win wout

2 3 4 5N2

N3

N4 N5

Idle gear

5

4

4

3

3

22v N

N

N

N

NN

)1(m

5

22

NN

)1(

out

in2

N

N)1(

기어 열

9.8 복합 기어열 (Compound gear trains)

• 속도 비 (Velocity Ratio: VR)

k

1i iDriven

Drivernv N

N)1(m

N2

N3

N4 N5

5

4

3

22v N

N

NN

)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 4.13180 > 10

• 3 stages 6.51803 < 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 25o

pressure angle to avoid interference.

4. Verification

Practical consideration

1801

7014

8414

8414

)1(m 3v

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

5432 rrrr

5432 NNNN

2. Gear ratio

18 ( 6 ) X ( 3 )

3. Number of teeth

(2)

(2) (1) :

72

63

(1)

61

N

N

3

2

23 N6N

31

N

N

5

4 45 N3N

4422 N3NN6N 74

N

N

4

2

N2=12 & N4=21