Question

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

Cutting speed $\left(m/min\right)$	Tool life $\left(minutes\right)$
$60$	$81$
$90$	$36$

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

• A. $n=0.5$ and $k=540$
• B. $n=1$ and $k=4860$
• C. $n=-1$ and $k=0.74$
• D. $n=-0.5$ and $k=1.155$

Answer 1

The correct option is A $n=0.5$ and $k=540$

Cutting speed $\left(m/min\right)$	Tool life $\left(minutes\right)$
$60$	$81$
$91$	$36$

Taylor's tool life equations,
$V{T}^n=$ constnat $=K$
$\left(60\right)(81{)}^n=K$ .... (i)
$\left(90\right)(36{)}^{=}K$ .... (ii)
Divide the Equ. (i) and Equ. (ii)
$\frac{\left(60\right)(81{)}^n}{\left(90\right)(36{)}^n}=1$
$\Rightarrow {\left(\frac{81}{36}\right)}^n=\left(\frac{90}{60}\right)$
$\Rightarrow (2.25{)}^n=1.5$
$\Rightarrow nln\left(2.25\right)=ln1.5$
$\Rightarrow n=0.5$
Keep the value of $n$ in Equ. (i)
$\left(60\right)(81{)}^{0.5}=K$
$\Rightarrow K=540$