The exponent (n) and constant (k) of the Taylor's tool life

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Direction: In a machining experiment, tool life was found to vary with the cutting speed in the following manner:

Cutting speed (m/min)	Tool life (minutes)
60	81
90	36

The exponent (n) and constant (k) of the Taylor's tool life equation are

1. n = 0.5. and k = 540
2. n = 1 and k = 4860
3. n = –1 and k = 0.74
4. n = –0.5 and k = 1.155

Correct Option: A

According to Taylor’s equation
VTⁿ = C
where, V = cutting speed in m/s
T = tool life (min)
C = constant (Taylors constant)
∴ V₁T₁ⁿ = V₂T₂ⁿ
or 60 × (81)ⁿ = 90 × (36)ⁿ

or	60	=		36		ⁿ
	90			81

or	2	=		4		ⁿ
	3			9

Taking log of both sides

log	2	= n log	4
	3		9

∴ n =	log	2	= 0.5
		3

	log	4
		9

∴ Taylor’s constant C = V₁T₁ⁿ
= 60 × (81)^0.5
= 60√81= 60 × 9 = 540