# The Chip Thickness Ratio (Cutting Ratio) and Chip Reduction Coefficient with Equation

### Chip thickness ratio

In the metal cutting process, the chip flow of the metal is shorter and thicker than the metal prior to the cutting because of plastic deformation. The extent of this variance in dimension is denoted by the chip thickness ratio or cutting ratio. The chip thickness ratio or cutting ratio is defined as the ratio of chip thickness before cutting to the thickness after cutting.

Chip thickness ratio depends on

Let
t1 = chip thickness before cutting or depth of cut
t2 = chip thickness after cutting
Then chip thickness ratio
Higher cutting ratio denotes that the cutting action is good.

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

The volume before cutting is equal to the volume after cutting. i.e., the volume of metal cut off from workpiece equal to the volume of the chip.

l1 b1 t1 = l2 b2 t2
Normally b1= b2, then
t1 l1 = t2 l2
Then chip thickness ratio

The shear angle can be easily determined by measuring chip thickness ratio, depth of cut and the rake angle of tool

### Coefficient of chip contraction or Chip reduction coefficient

The shortening of chip length is known as the longitudinal chip contraction. The inverse of chip thickness ratio is known as chip reduction coefficient. The coefficient of chip contraction or chip reduction coefficient is a quantitative measurement of plastic deformation occurred during the cutting process.

Chip reduction ratio

The value of k may be high as 8 depending on cutting condition.

Contraction of chip increases when
Read: Chip Reduction Coefficient Plot Against Cutting Speed, Feed, and Type of Cutting Fluid
Remember:
• The chip thickness ratio is always less than unity. Coefficient of chip contraction is always more than one