The cutting and thrust forces, respectively, are

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

The cutting and thrust forces, respectively, are

1. 568 N; 387 N
2. 565 N; 381 N
3. 440 N; 342 N
4. 480 N; 356 N

Correct Option: B

F_H = F_S		cos(β − α)
		cos(φ β α)

where β is friction L.

Now by Merchant’s theory

φ =	π	−	1	= (β − α)
	4		2

∴ 28 = 45° –	β	+ 3.5°
	2

∴ β = 2(20.5) = 41°

∴ F_H = F_C		cos(34)		= 320 × 1.77 = 565 N
		cos(62)

Now,	F_V	= tan(β − α)
	F_H

∴ F_V = 565 × tan 34 = 381 N
Frictional force F from the figure can be written as,
F = F_H sin + F_V cos α
= 68 + 381 = 447N Hence none of the options seems to be correct.