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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