Question

During the turning of a 20 mm diameter steel bar at a spindle speed of 400 rpm, a tool life of 20 minute is obtained. When the same bar is turned at 200 rpm, the tool life becomes 60 minute. Assume that Taylor's tool life equation is valid. When the bar is turned at 300 rpm, the tool life (in minute) is approximately

• A. 25
• B. 32
• C. 40
• D. 50

Answer 1

The correct option is B 32

Cutting velocities:
$V_1=\pi D\times 400m/min;T_1=20min$
$V_2=\pi D\times 200m/min;T_2=60min$

Now using Taylor's equation

$V_1{T}_1^n=V_2{T}_2^n$

$\pi D\times 400\times {\left(20\right)}^n=\pi D\times 200\times {60}^n$

$n=0.6309$

When the bar is turned at 300 rpm, the tool life (in minute) is

$V_3=\pi D\times 300m/min;T_3=?$

Now using Taylor's equation
$V_1{T}_1^n=V_2{T}_2^n=V_3{T}_3^n$

$\pi D\times 400\times {\left(20\right)}^{0.6309}=\pi D\times 300\times T_3^{0.6309}$

$\therefore T_3=31.55min=32min$