Gear Train

Three-Speed Transmission

Synchronizers cone clutch f

Before the teeth can engage, the cone clutch engages first, which brings the selector and gear to the same speed using friction.

First Gear

Second Gear

Third Gear (Direct Gear)

Shown below is a three- speed transmission. Gears 4,5 and 6 are free to spin about their shaft, while gears 3,7,8,9,10 and 11 are keyed to their respective shafts. Gear 10 is an idler gear whose centre is not in line with those of gears 6 and 11. C1 and C2 are synchronizers that fix one gear to the shaft each time, so power is transmitted from the input shaft to the output shaft.

Idler gear 10: reverses the direction of rotation without changing the gear ratio

Assume the following parameters:All gears have a diametral pitch

p=12center –to –center distance between

input shaft and counter shaft C=4 inapproximate speed ratios first gear e1=0.2, second gear

e2=0.51, third gear e3=1, reverse er=-0.22

idler gear: number of teeth =16, pitch diameterD10= D6/3, centre- to centre distance C10/11=2 in

drive

driven

wew

1in

Questions:

(1)Calculate the gears’ teeth number

(2)Calculate the gears’ diameters

Solution:Because all gears are to have the

same module and meshing gears must share a common center –to –center distance,

3 7 4 8 5 9C r r r r r r

3 7 4 8 5 9

2 2 2d d d d d d

C

r is pitch radiusd is pitch diameter

We know that the relationship between the number of teeth and the pitch diameter is

Ndp

where P is the diametral pitch.

3 7 4 8 5 92 2*12*4 96pC N N N N N N

3 7

4 8

5 9

969696

N NN NN N

3 9 7 51

7 5 7 5

(96 )(96 )0.2

N N N Ne

N N N N

The first gear speed ration is (1)drive

driven

wew

The second gear speed ration is 3 8 7 4

27 4 7 4

(96 )(96 ) 0.51N N N NeN N N N

(2)

The reverse gear speed ration is

3 10 7 1111

7 10 6 7 6

(96 )* * 0.22revN N N NNeN N N N N

(3)

From (1), (2), (3),we can get:

27

57 7

96 960.2 96

NN

N N

27

47 7

96 960.51 96

NNN N

11

76 11

960.22

NNN N

10 6

1010 10 6

66

13

13

D D

Nd N NpNdp

10 16N

6 3*16 48N

10 11 10 1110/11 10 11 2 2

d d N NC r rp

Nd

p

11 10/11 102 48 16 32( )N pC N teeth

117

6 11

27

57 7

27

47 7

96 72.18 720.22

96 96 600.2 96

96 96 37.9 380.51 96

NN teethN N

NNN N

NN teethN N

3 7

4 8

5 9

969696

N NN NN N

3 7

8 4

9 5

96 96 72 2496 96 38 5896 96 60 36

N N teethN N teethN N teeth

3 7 4 8 5 92 2*12*4 96pC N N N N N N

Ndp

Calculate gear diameters

33

44

55

66

77

24 21238 3.1671260 51248 41272 612

Nd inpNd inpNd inpN

d inpN

d inp

88

99

10 6

1111

58 4.8331236 312

1 4 1.333 3

32 2.66712

Nd in

pN

d inp

d d in

Nd inp