Question

Details pertaining to an orthogonal metal cutting process are given below:
Chip thickness ratio $0.4$
Undeformed thickness $0.6mm$
Rake angle $+{10}^o$
Cutting speed $2.5m/s$
Mean thickness of $25microns$ primary shear zone
The shear strain rate in $s^{-1}$ during the process is

• A. $0.1781\times {10}^5$
• B. $0.7754\times {10}^5$
• C. $1.0104\times {10}^5$
• D. $4.397\times {10}^5$

Answer 1

The correct option is C $1.0104\times {10}^5$

$r=0.4;t_1=0.6mm;\alpha ={10}^o$
$V_C=2.5m/s;t_m=25\mu m$
$tan\varphi =\frac{rcos\alpha }{1-rsin\alpha }=0.4233$
$\Rightarrow \varphi ={22.9}^o$
Shear strain rate
$=\frac{V_{c}cos\alpha }{cos(\varphi -\alpha )\times t_m}$
$=\frac{2.5cos10}{cos129\times 25\times {10}^{-6}}$
$=1.0104\times {10}^5/s$