Topic: Manufacturing Processes
The useful tool life of a HSS tool machining MS at $18~m/min$ is 3 hours. Calculate the tool life when the tool operates at $24~m/min$ Assume 'n' (exponent) which depends on cutting conditions as 0.125?
- A. 28 min
- B. 18 min
- C. 14 min
- D. 22 min
Answer: B. 18 min
Explanation: According to Taylor's tool life equation: $V_1 T_1^n = V_2 T_2^n$.
$V_1 = 18~m/min$, $T_1 = 3~hours = 180~min$, $V_2 = 24~m/min$, $n = 0.125$.
$18 \times (180)^{0.125} = 24 \times (T_2)^{0.125}$.
$\left(\frac{T_2}{180}\right)^{0.125} = \frac{18}{24} = 0.75$.
$\frac{T_2}{180} = (0.75)^{\frac{1}{0.125}} = (0.75)^8 = 0.1001129$.
$T_2 = 180 \times 0.1001129 \approx 18.02~min$. So, 18 min is the correct answer.