Lathe Tools

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University Math Help?

A lathe tool has to accommodate work between 25mm and 300mm in diameter. Six spindle speeds are required and cutting speed is 25m/min Find the six speeds if they are in a) AP, b) GP Use Spindle speed N = S/(piD) S is cutting speed and D is diameter

Represent on a graph with N, S on x, y axis AND on y,x axis separately

WHICH is preferable and WHY?

The equation you have been given, N = S/(piD), only works if S and D are in the SAME units. You have been given S and D in different units. You should change S from 25 m/min to 25000 mm/min.

Smallest diameter: N = 25000 / (25.pi) = 320 rpm.
Largest diameter: N = 25000 / (300.pi) = 26.5 rpm.

GP = 26.5, 43.6, 72, 118, 195, 320
AP = 26.5, 85, . . .

AP is a disaster, because the worst case of a medium-sized workpiece needing about 47.5 rpm for a cutting speed of 25 m/min would have to be cut at either 14 m/min or 45 m/min. The GP is the one which gives you a closer fit to the ideal cutting speed over all possible sizes, although only 6 sizes can be cut at exactly 25 m/min - other sizes will be somewhere between 19.5 and 32 m/min.

A slightly adjusted GP of 32.6, 49.4, 75, 113, 172, 260 gives an even closer fit, between 20.3 and 30.7 over all possible sizes, but that's probably beyond the scope of your question.

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