For tool A, Taylor's tool life exponent (n) is 0.45 and

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For tool A, Taylor's tool life exponent (n) is 0.45 and constant (K) is 90. Similarly for tool B, n = 0.3 and K = 60. The cutting speed (in 'm/ min) above which tool A will have a higher tool life than tool B is

1. 26.7
2. 42.5
3. 80.7
4. 142.9

Correct Option: A

Taylor’s tool life equation is
VTⁿ = Constant
∴ k₁ = v₁T₁^n₁ and k₂ = v₂T₂^n₂
Given conditions for both tools:
Tool A : constant, k₁ = 90 ;
exponential constant, n₁ = 0.45
Tool B: Constant, k₂ = 60 ;
exponential constant, x₂ = 0.3

∴		k₁		=		v₁		T₁^0.45
		k₂				v₂		T₂^0.3

At point of intersection
v₁ = v₂ and T₁ = T₂ = T

∴	3	=	T^0.45	= T^0.15
	2		T^0.3

⇒ T = (3/2)^1/0.15 = 14.92 min
∴ 90= v₁(14.92)^0.45
⇒ v₁ = 26.7 m/min
Above v₁ = 26.7 m/min, tool A will have a higher tool life them too B.