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

Since n = 0.5, the Taylor equation can be rewritten as VT^0.5 = 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.