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# Chip Thickness Ratio

During cutting action of a metal, the thickness of the deformed or upward flowing chip in more than the actual depth of cut. It is because the chip flows upwards at a slower rate than the velocity of the cut. The velocity of the chip flow is directly affected the shear plane angle. The smaller the shear plane angle the slower will be the chip flow โ velocity and therefore longer will be the thickness of the chip.

Since tc in always greater than t, the value of chip thickness ratio r is always less than unity. The higher the value of r, the better is supposed to be cutting action. The reverse of r is known as chip reduction co efficient. If k is the chip reduction co efficient

In orthogonal cutting the width of the chip equals the width of the cut. Considering specific gravity of the metal as constant, the volume of the chip produced will be equal to the volume of the metal cut. Width of both being equal, the product of the chip thickness and its length will, therefore be equal to the product of the thickness of the metal cut and length of metal cut. If L1 and L2 are lengths of the metal cut and chip respectively.

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## Merchants Force Diagram:

FHย = Horizontal cutting force exerted by the tool on work piece.

FVย = Vertical or tangential force which helps in holding the tool in position and acts on tool nose.