Question

Comprehension

A 20º full depth involute spur pinion of 4 mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm.

Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factors intensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material is

1. 242.0
2. 166.5
3. 121.0
4. 74.0

Answer 1

Correct Answer - Option 2 : 166.5

Concept

The force transmitted by the gear is given by,

\({F_t} = \frac{{{\sigma _b} \times b \times Y \times m}}{{{f_s}}}\)

where σ_b   = Minimum allowable stress for gear material

              Y = Tooth geometry factor

             f_s  Combined effect of dynamic load and allied factors intensifying the stress.

              b = Face width of the tooth

              m = Module of the gear

Calculation:

Given:

Tooth geometry factor, Y = 0.32

The combined effect of dynamic load and allied factors intensifying the stress, f_s = 1.5

Face width of the tooth, b = 25 mm

The module of the gear, m = 4 mm

Force transmitted, 

\({F_t} = \frac{{{\sigma _b} \times b \times Y \times m}}{{{f_s}}}\)

\(3552 = {\rm{}}\frac{{{\sigma _b} \times 25 \times 0.32 \times 4}}{{1.5}}\)

σ _b = 166.5 MPa