The tool life equation for HSS tool is VT0.14f0.7d0.4 =

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The tool life equation for HSS tool is VT^0.14f^0.7d^0.4 = Constant. The tool life (T) of 30 min is obtained using the following cutting conditions: V= 45 m/min, f = 0.35 mm, d =2.0 mm. If speed (V), feed (f) and depth of cut (d) are increased individually by 25%, the tool life (in min) is

1. 0.15
2. 1.06
3. 22.50
4. 30.0

Correct Option: B

VT^0.14 f ^0.7 d^0.4 = C
⇒ T₁ =30 min,
V₁ =45 m/min,
f₁ =0.35 min,
d₁ =2.0 mm,
⇒ C =V₁ (T₁) ^0.14 (f₁) ^0.7 (d₁) ^0.4
C =45(30)^0.14 (0.35)^0.7 (2)^0.4
C =45.8425
V₂ (T₂) ^0.14 (f ₂) ^0.7 (d₂) ^0.4 = 45.8425
(1.25 × 45)(T₂) ^0.14 (1.25 × 0.35)^0.7 (1.25 × 2)^0.4
= 45.8425
⇒ T₂ =1.06 min