Correct Answer - Option 4 : 4 min
Concept:
Tool life for a tool is given by,
VTn = C
V1T1n = V2T2n
where, V = Cutting velocity of tool, m/min
T = Tool life of a tool, min
n = Taylor’s tool life exponent
C = constant
Values of both ‘n’ and ‘C’ depend mainly upon the tool-work materials and the cutting environment (cutting fluid application).
Calculation:
Given:
V1 = 141.4 m/min, V2 = 100 m/min, V3 = 353.5 m/min
T1 = 25 min, T2 = 50 min, T3 = ?
V1T1n = V2T2n
141.4 × 25n = 100 × 50n
1.414 = 2n
ln 1.414 = n × ln 2
n = 0.5
V2T2n = V3T3n
100 × 500.5 = 353.5 × T30.5
\(\frac{100}{353.5} = \left (\frac{T_{3}}{50} \right )^{0.5}\)
\(\left (\frac{100}{353.5} \right )^{2} = \frac{T_{3}}{50} \)
T3 = 4 min