Question

Orthogonal machining of a steel workpiece is done with a HSS tool of zero rake angle. The ratio of the cutting force and the thrust force on the tool is 1 : 0.372. The length of cut chip is 4.71 mm while the uncut chip length is 10 mm. What is the shear plane angle $\varphi$ and friction angle $\beta$ in degree? Use Merchant's theory

• A. 32.49, 10.22
• B. 25.22, 20.41
• C. 64.78 20.41
• D. 25.22, 23.21

Answer 1

The correct option is B 25.22, 20.41

$\alpha =0,\frac{F_T}{F_C}=0.372$

$L_2=4.71mm,L_1=10mm$

$\tan (\beta -\alpha )=\tan \beta =\frac{F_T}{F_C}$

$\beta ={\tan }^{-1}\left(0.372\right)=20.71$

$r=\frac{L_2}{L_1}=\frac{4.71}{10}=0.471$

$\varphi ={\tan }^{-1}\left(\frac{0.471\cos \alpha }{1-0.471\sin \alpha }\right)$

$={\tan }^{-1}\left(0.471\right)={25.22}^{\theta }$