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

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* \left ( 4.25\right )^n=110* \left ( 35\right )^n`

`(180)/(110)=\left ( (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