Important Point

## What Is Chip Thickness Ratio?

The tool is positioned at a fixed distance below the core while cutting. This chip formation corresponds to the thickness of the chip before **t1** as the chip is formed along the shear plane. Its thickness increases to **t2** (after the cut chip thickness).

The chip thickness ratio is defined as the thickness of the metal before cutting to the thickness of the metal after cutting. Chip thickness ratio or cuttings ratio is defined as the ratio of chip thickness before cutting to thickness after cutting.

It depends on the chip thickness ratio.

- Type of material to be worked
- The geometry of the cutting tool
- Types of cutting fluids
- Other cuttings variables such as feed rate, speed, depth.

Let

**t1 =** thickness of chip before cutting or at depth

**t2 =** chip thickness after cutting

Then Chip Thickness Ratio

and let

**r=** Chip thickness ratio

Then,

**r= t1 / t2.**

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

Now let

**l1 =** length before cutting.

**l2=** length of the chip after cutting.

**b1=** width of the chip before cutting.

**b2=** width of the chip after cutting.

**α =** rake angle of the tool.

**β =** shear angle.

Since the volume before cutting is equal to volume after cutting. In other words, the volume of metal cut off from the workpiece is equal to the volume of the chip.

**l1 b1 t1 = l2 b2 t2**

Generally **b1=b2**

Therefore, **t1 l1 = t1 l2**

or, **t1 / t2 =l2 / l1**

Then chip thickness ratio.

**r = t1 /t2 = l2 / l1**

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)**

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## Shear Angle of Chip Thickness Ratio:

As the tool is forced into the materials, the chip is formed by shear deformation along a plane called the shear plane, which is oriented at an angle with the surface of work known as the Shear angles. 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 a shear angle.

## Factors on Which Chip Thickness Ratio Depends:

- Type of material.
- Type of cutting fluid.
- The geometry of the cutting tool.
- Cuttings variables such as feed rate, speed depth.

## Coefficient of Chip Contraction or Chip Reduction Coefficient:

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

**k=t2/t1 =l1/l2**

The values of k may be high as 8, depending on the condition of the cutting.

Contraction of chip increases when

- Increase cuttings angle or smaller positive rake angle.
- Increases in nose radius.
- The chip thickness ratios are always less than unity. The coefficient of chip contraction is always more than one.

### Chip Thickness Ratio

**Chip Thickness ratio** is defined as the **thickness** of metal before cutting to the **thickness** of metal after cutting. Then, r= t1 / t2. Whenever there is high cutting **ratio** , it means the cutting action is good.

### Cutting Ratio

As applied to metal **cutting**, the **ratio** of depth of **cut** to chip thickness for a given shear angle.

### Chip Reduction Coefficient

**Chip reduction coefficient** (Ks) is defined as the **ratio** of **chip** thickness (S1) to the uncut **chip** thickness (S). This factor, Ks, is an index of the degree of deformation involved in **chip** formation process during which the thickness of layer increases and the length shrinks.

### Chip Thickness

Equivalent chip thickness is the thickness of the layer removed at wheel speed. Depth of cut is **0.02 mm** (or 0.00079 in.), work speed is 0.3 m/s (or 709 in./min) and wheel speed is 40 m/s (or 7874 ft/min). Calculate equivalent chip thickness.

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