# Chip Thickness Ratio

During cutting the cutting edge of tool is positioned a certain distance below the original. This corresponds to the thickness of the chip prior to chip formation t1 as the chip is formed along the shear plane its thickness increases to t2 ( after cut chip thickness).

Image Source : https://www.mecholic.com/2017/02/chip-thickness-ratio-cutting-ratio-equation.html

Chip Thickness ratio is defined as the thickness of metal before cutting to the thickness of metal after cutting.

We kmow that,
t1= chip thickness before cutting
t2= chip thickness after cutting
and let
r= Chip thickness ratio

Then,

r= t1 / t2.

Whenever there is high cutting ratio , it means the cutting action is good.

Now let
l1 = length before cutting
l2= length of chip after cutting
b1= width of chip before cutting
b2= width of chip after cutting
α = rake angle of tool
β = shear angle

Since the volume before cutting is equal to volume after cutting .In other words, volume of metal cut off from workpiece is equal to volume of the chip.
l1 b1 t1 = l2 b2 t2

Genrally b1=b2
Therefore, t1 l1 = t1 l2
or, t1 / t2 =l2 / l1

Then chip thickness ratio
r = t1 /t2 = l2 / l1

Image Source : https://www.mecholic.com/2017/02/chip-thickness-ratio-cutting-ratio-equation.html
Now from the diagram we have,
t1 = AB sinβ ……………… ( 1 )
t2= AB cos ( β − α ) ………………( 2 )

Then r = t1 / t2
From (1) and (2) we have
r = AB sinβ / AB cos ( β − α )
r = sinβ / cos ( β − α ) ….. (3)

### Shear Angle : –

As the tool is forced into the material, the chip is formed by shear deformation along a plane called shear plane which is oriented at an angle with the surface of work known as Shear angle. It is denoted by β.
From (3) we have ,

r = sinβ / cos ( β − α )
r cos ( β − α ) = sinβ
r (cosβ cosα + sinβ sinα) = sinβ
r cosβ cosα = (1 – r sinα ) sinβ
cosβ / sinβ = (1 – r sinα) / r cosα
tanβ = r cosα / 1 – r sinα ……(4)

This is the formula to find shear angle

Factors on which chip thickness ratio depends :-
1) Type of material.
2) Type of cutting fluid.
3) Geometry of cutting tool.
4) Cutting variables such as feed rate, speed depth.

### Coefficient of chip contraction or Chip reduction Coefficient

Coefficient of chip contraction or Chip reduction Coefficient is invese of Chip Thickness ratio. It is a quantitative measurement of plastic deformation occurred during the cutting process.

Chip reduction ratio ( k ) = t2/t1 = l1/l2 =1/r