In a machine tool the range of cutting speeds used is 10 m/min to
In a machine tool the range of cutting speeds used is 10 m/min to 200 m/min and range of diameters of jobs used is 100 mm to 500 mm. The speed range ratio of the machine tool is
A. 100
B. 4
C. 1000
D. 400
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Concept:
\(V=\frac{\pi DN}{1000}\)
where V = velocity in (m/min)
N = revolution per minute
D = diameter in mm
\(N=\frac{1000V}{\pi D}\)
\(N_{max}=\frac{1000V_{max}}{\pi D_{min}}\)
\(N_{min}=\frac{1000V_{min}}{\pi D_{max}}\)
Speed range ratio:
\(\frac{N_{max}}{N_{min}}=\frac{V_{max}}{V_{min}}\times\frac{D_{max}}{D_{min}}\)
Calculation:
Given:
Vmin = 10 m/min, Vmax = 200 m/min, Dmin = 100 mm and Dmax = 500 mm.
Speed range ratio \(= \frac{{{V_{max}} \;\times\; {D_{max}}}}{{{V_{min}} \;\times\; {D_{min}}}} = \frac{{200\; \times\; 500}}{{10 \;\times\; 100}} = 100\)