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Using the Taylor Equation for tool life and letting n = 0.5 and C = 120, calculate the percentage increase in tool life when the cutting speed is reduced by 50%.

Using the Taylor Equation for tool life and letting n = 0.5 and C = 120, calculate the percentage increase in tool life when the cutting speed is reduced by 50%. Correct Answer 300%

Since n = 0.5, the Taylor equation can be rewritten as VT0.5 = 120. Let’s denote V1 as the initial speed and V2 the reduced speed; thus, V2 = 0.5 V1. Because C is the constant 120, we have the relationship 0.5V1 sqrt T2 = V1sqrt T1 Simplifying this equation, T2/T1 = 1/0.25 = 4. This indicates that the change in tool life is (T2 – T1/ T1) = (T2/T1) – 1 = 4 – 1 = 3, or that tool life is increased by 300%. Thus, a reduction in cutting speed has resulted in a major increase in tool life. Note also that, for this problem, the magnitude of C is not relevant.

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