how to solve 14

Question

3.1. a simple gear train, comprising of a pinion B with 30 teeth meshing internally with a ring gear A. the centre distances between the shaft is 45mm and the teeth module of 1,5mm. Calculate the following: 3.1.1. the number of teeth on the ring gear A 3.1.2. the pitch circle diameter of the ring gear 3.2. A simple gear train consists of a gear and pinion of which the shaft centre is approximately 635mm apart. Assume that the circular pitch is 31,46mm and that gears have a speed ratio 3,3:1 Calculate the following: 3.2.1. the number of teeth on each gear 3.2.2. the actual centre distance between the two shafts

Answer 1

3.1.1)

The number of teeth on ring gear can be calculated using the Centre distance formula .

a = ( d _g + d _p) / 2    ----------------(1)

Where d _g = gear pitch circle diameter & d _p = pinion pitch circle diameter 

pitch circle diameter  d = z . m   --------------------(2)

From (1) and (2)

a = ( Z₁ m + Z₂ m) / 2  

a =  m( Z₁  + Z₂ ) / 2  

Where Z₁  is number of teeth on pinion gear =30 .

           Z₂  is number of teeth on ring gear .

The Centre distances between the shaft is  (a) 45 mm .

Module  (m) is 1.5 mm .

45  =  1.5 ( 30  + Z₂ ) / 2  

1.5 ( 30  + Z₂ ) = 90

( 30  + Z₂ ) = 90/1.5

30  + Z₂  = 60

Z₂  = 60 - 30

Z₂  = 30 

Hence the number  of teeth on ring gear  (Z₂) is 30 .

Answer 2

3.1.2)

Module  (m) is 1.5 mm .

Pitch circle diameter of ring gear d =Z₂ . m 

Where m is module  (m)  = 1.5 mm .

Z₂ is the number  of teeth on ring gear  (Z₂) is 30 .                       [From 3.1.1]

The Pitch circle diameter of ring gear d =Z₂ . m .

d = 30*1.5

d = 45 mm

The Pitch circle diameter of ring gear is 45 mm .

Answer 3

3.2.1)

The number of teeth of gear and pinion can be evaluated using the formula of Centre distance .

a = ( d _g + d _p) / 2    ----------------(1)

Where d _g = gear pitch circle diameter & d _p = pinion pitch circle diameter 

pitch circle diameter  d = z . m   --------------------(2)

From (1) and (2)

a = ( Z₁ m + Z₂ m) / 2  

The given Gear ratio (Z₁:Z₂) is 3.3:1  .

Let the number of teeth of  pinion is Z₂ = x .

Then the number of teeth of  ring gear is Z₁ = 3.3x . 

a = ( 3.3x m + x m) / 2

a = m (3.3x  + x) / 2

635 = 10 (4.3x) / 2

10 (4.3x) = 1270

4.3x = 1270/10

4.3x = 127

x = 127/4.3

x = 29.49

So the number f teeth of  pinion is ≈ 29 .

The number of teeth of  ring gear is 3.3*29.49 = 97.25 .

So the number f teeth of ring gear is ≈ 97 .