Using the Taylor's equation, $V T^{n} = C$ , calculate the percentage increase in tool life when the cutting speed is reduced by 50% (Assume n = 0.5 and C = 400)

300%

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400%

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100%

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50%

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Solution

The correct option is A 300%
Taylor's equation:

$V_{1} T_{1}^{n} = V_{2} T_{2}^{n}$

$V_{1} T_{1}^{0.5} = \frac{V_{1}}{2} T_{2}^{0.5}$

$T_{2} = 2^{1 / 0.5} T_{1}$

$T_{2} = 4 T_{1}$

$\frac{T_{2} - T_{1}}{T_{1}} \times 100$ %

$\frac{4 T_{1} - T_{1}}{T_{1}} \times 100$ % = 300%

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Using Taylor equation V T^{n} = C, what is teh percentage increase in tool life when the cutting speed is reduced by 75%. Tool life exponent is \frac{2}{3} .

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