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The number of teeth of a spur gear is 30 and it rotates at 200 rpm. What is the pitch line velocity if it has a module of 2 mm ?
1. 341.7 mm/s
2. 497.2 mm/s
3. 628.3 mm/s
4. 758.5 mm/s

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Correct Answer - Option 3 : 628.3 mm/s

Concept:

Rolling velocity/Pitch line velocity:

Rolling velocity = Pitch line velocity = ω × r

where ω = angular velocity (rad/sec) and r = pitch circle radius.

Module:

\(m=\frac{D}{T}\;ot\;D=mT\)

\(r=\frac{mT}{2}\)

where T = number of teeth and m = module.

Calculation:

Given:

T = 30, m = 2 mm, N = 200 rpm

Pitch line velocity:

V = ωr

\(V =\frac{2\pi N}{60}\times\frac{mT}{2}\)

\(V =\frac{2\pi\;\times\;200}{60}\times\frac{2\;\times\;30}{2}=628.3\;mm/s\)

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