Question

ENGR4803 Mechatronics and Lab mechanical engineering hw part

(Introduction to Mechatronics and Measurement Systems 5th Edition by David Alciatore)

mechanical engineering hw part

mechanical engineering hw part

2. A 40-tooth gear and a 16-tooth gear are both 12 pitch and need to be meshed. How far apart should the shafts be?

Answer 1

Sol.

Note:-

1. There is no unit provided in the problem for pitch. hence the answer will be given in terms of "units". Users can put any suitable unit of distance in the solution as the numerical value will remain the same.
2. Type of pitch is not mentioned in the problem, so the diametral pitch is considered on the bases of the following reasons.  

The data provided in the problem are:-

Both gears have pitch =P_d1= P_d2= 12, Number of teeth in the gear 1 = T₁ = 40, Number of teeth in the gear 2 = T₂ = 16.

Now,

In order to mesh two gears, their module must be the same.

The module is defined as the ratio of the diameter of the gear to the number of teeth in the gear. ( m = D/T)

Therefore, it can be said that the inverse of the module should also be the same for both gears in order to mesh.

(ie. (1/m₁) = (1/m₂))

The inverse ratio of the module is defined as the diametral pitch. Hence, to mesh two gears diametral pitch of that gears must be the same.

Also, industrially the gears are made in accordance with the diametral pitch.

Thus considering the given pitch as diametral pitch.

Now,

For gear 1,

P_d1 = T₁ /D₁

12 = 40 / D₁

$\therefore$ D₁ = 3.334 units

For gear 2,

P_d2 = T₂ /D₂

12 = 16 / D₂

$\therefore$ D₂ = 1.334 units

The distance between the shafts of the gears is given by:-

Shaft distance = ( Diameter of gear 1 + Diameter of gear 2) / 2

$\therefore$ Shaft distance = (D₁ +D₂) / 2

Shaft distance = (3.334 + 1.334) / 2

Shaft distance = 2.334 units

Hence, the shafts can be placed 2.334 units apart without considering any clearance.