# If N is the number of strokes per minute, L is stroke length in mm, C is cutting ratio (cutting time/total time) the cutting speed of shaper in m/min

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If N is the number of strokes per minute, L is stroke length in mm, C is cutting ratio (cutting time/total time) the cutting speed of shaper in m/min is given by

1. NL/1000C
2. NLC/1000
3. 1000L/NC
4. 1000LC/N

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Correct Answer - Option 1 : NL/1000C

Explanation:

Cutting speed in a shaper is the average linear speed of the tool (m/min) during the cutting stroke. It depends on the number of ram strokes per minute and the stroke length.

Cutting speed of shaper is given by;

$V = \frac{{{\rm{NL\;}}\left( {1{\rm{\;}} + {\rm{\;m}}} \right)}}{{1000}}\;m/min$

where

V = Cutting speed of shaper, N = Number of double stroke per minute, L = length of stroke

m = Quick return ratio = $\frac{{{\rm{Time\;of\;return\;stroke}}}}{{{\rm{Time\;of\;cutting\;stroke}}}}$

Given:

$C=\frac{{Cutting~time}}{{Total~time}}=\frac{{Cutting~time}}{{Return~time\;+\;Cutting~time}}$

$\frac{{1}}{{C}}=\frac{{Cutting~time\;+\;Return~time}}{{Cuttting~time}}=1+m$

$\therefore V = \frac{{{\rm{NL\;}}\left( {1{\rm{\;}} + {\rm{\;m}}} \right)}}{{1000}}=\frac{{NL}}{{1000C}}$ m/min.