Question

4. Tests are performed to determine the Tool Life of a high speed steel single edge cutting tool. At a cutting speeds (v) of 180 m/min and 110 m/min the corresponding tool life is 4.25 min and 35 min., respectively. Except for the cutting speed, the cutting conditions for the test are the same. Calculate the value of n in the Taylor Tool Life Equation. Answers are rounded to three (3) decimal place (x.xxx). (A) 0.234 (B) 1.263 (C) 0.199 (D) 0.492 (E) None of the above

Answer 1

Answer:(a)   n=0.233

Step-by-step explanation:

Given

We Know according to Taylor tool life

$VT^n=c$

V=cutting speed

T=tool life

n=tool life exponent

c=constant

$180\times \left ( 4.25\right )^n=110\times \left ( 35\right )^n$

$\frac{180}{110}=\left ( \frac{35}{4.25}\right )^n$

$1.636=\left ( 8.235\right )^n$

taking log both side

$\ln \left ( 1.636\right )=n\ln \left ( 8.235\right )$

n=0.233