In a simple gear train, 1^st gear (Driver) has 40 number of teeth, 2^nd gear has 20 number of teeth and last gear has 80 number of teeth. The train value of the gear train is -

Concept:

Velocity Ratio is:

\(Velocity~ratio = \frac{{Speed~of~driver}}{{Speed~of~follower}}\)

Train value is:

The reciprocal of velocity ratio is known as train value of the gear train.

\(Train~value= \frac{1}{velocity~ratio}\)

The velocity ratio of a simple gear train

When the driver and intermediate gear are in mesh

\(\frac{{{N_1}}}{{{N_2}}} = \frac{{{T_2}}}{{{T_1}}}\)

When the intermediate and followers are in mesh.

\(\frac{{{N_2}}}{{{N_3}}} = \frac{{{T_3}}}{{{T_2}}}\)

Multiplying both the equations,

\(\frac{{{N_1}}}{{{N_2}}} \times \frac{{{N_2}}}{{{N_3}}} = \frac{{{T_2}}}{{{T_1}}} \times \frac{{{T_3}}}{{{T_2}}}\)

\(\frac{{{N_3}}}{{{N_1}}} = \frac{{{T_1}}}{{{T_3}}}\)

\(Speed~ratio = \frac{{Speed~of~driver}}{{Speed~of~follower}} = \frac{{No.~of~teeth~on~follower}}{{No.~of~teeth~on~driver}}\)

Calculation:

Given:

T₁ = 40, T₂ = 20, T₃ = 80

\(Velocity~ratio=\frac{{T_3}}{{T_1}} = \frac{{80}}{{40}} = 2\)

\(Train~value = \frac{{1}}{{velocity~ratio}} = \frac{1}{2} = 0.5\)