Lecture-8 chip thickness ratio & shear angle

During the cutting action of metal it will be observed that the thickness of the deformed or upward flowing chip is 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 by the shear plane angle. The smaller this angle the slower will be the chip-flow-velocity and, therefore, larger will be the thickness of the chip. 

Fig. 8.1 An Orthogonal Cutting Operation. 

Refer to Fig. 8.1. Let, 

t ₁ = Chip thickness prior to deformation 

t ₂ = Chip thickness after deformation 

The above discussion leads to the result that t₂ > t₁ 

The Chip thickness ratio ' r' is given by: 

--------------------------------------------- (1) 

Since t₂ is always greater than t₁, the value of chip thickness ratio 'r' is less than unity. The higher the value of 'r' the better is supposed to be the cutting action.  

The reverse of 'r' is known as Chip Reduction Coefficient. If 'k' is the Chip Reduction Coefficient, then : 

--------------------------------------(2) 

Now, in Orthogonal Cutting, the width of the chip equals the width of the cut. Considering the specific gravity of the metal as constant, the volume of the chip produced will be equal to the volume of the metal cut. Widths of both being equal, the product of the chip thickness and its length will, therefore, be equal to the product of the thickness and the length of the metal cut. If L₁ and L₂ are the lengths of the metal cut and the chip respectively, it follows that: 

In the given Fig. 8.1, we have two right-angled triangles OAP and OBP. Considering the right-angled triangle OAP, we have: