Question

The number of teeth of a spur gear is 30 and it rotates at 200 rpm. What will be its pitch line velocity if it has a module of (6/π) mm?
1. 600 mm/s
2. 300 mm/s
3. 191 mm/s
4. 164 mm/s

Answer 1

Correct Answer - Option 1 : 600 mm/s

Concept:

Pitch line velocity (V_p) = Pitch radius × Angular velocity of the shaft

V_p = r × ω where, ω = 2πN/60

Also, module (m) = \(\frac{{\rm{d}}}{{\rm{T}}}\) where d = 2r = Pitch diameter, T = number of teeth.

Calculation:

Given:

T = 30, N = 200 rpm, m = 6/π 

m = \(\frac{{\rm{d}}}{{\rm{T}}}\)

d = m × T = (6/π) × 30

∴ r = (6/π) × 15 mm

ω = (2πN)/60

now, V_p = r × ω = \(\frac{6}{{\rm{\pi }}} \times 15 \times 2 \times {\rm{\pi }} \times \frac{{200}}{{60}}\)

V_p = 600 mm/s