Question

Linked Question
Orthogonal turning is performed on a cylindrical workpiece with shear strength of $250MPa$. The following conditions are used: cutting velocity is $180m/min,$ feed is $0.20mm/rev$, depth of cut is $3mm$, chip thickness ratio $=0.5$. The orthogonal rake angle is $7^o$. Apply Merchant's theory for analysis.

The cutting and thrust forces, respectively, are

• A. $568N;387N$
• B. $565N;381N$
• C. $440N;342N$
• D. $480N;356N$

Answer 1

The correct option is B $565N;381N$

Ratio of cutting force and shear force:
$\frac{F_C}{F_S}=\frac{cos(\beta -\alpha )}{cos(\varphi +\beta -\alpha )}$
$F_C=F_S\times \frac{cos(\beta -\alpha )}{cos(\varphi +\beta -\alpha )}$
$F_C=320\times \frac{cos({41}^o-7^o)}{cos({28}^o+{41}^o-7^o)}$

Cutting force:
$F_C=565.08N$

The ratio of thrust froce and cutting force:
$\frac{F_T}{F_C}=tan(\beta -\alpha )$
$F_T=F_{C}tan(\beta -\alpha )$
$=565tan({41}^o-7^o)$
$=565tan{34}^o=381.55N$
Trust force:
$F_T=381.55N$