## What Is Chip Thickness Ratio?

Chip thickness ratio is defined as **the thickness of the metal before cutting divided by the thickness after cutting**. Important factors that influence chip thickness include cutting speed, feed rate, depth of cut, and tool geometry.

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 the 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)**

## 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.

## Frequently Asked Questions (Faqs) That Could Be Included in Your Article on Chip Thickness Ratio in Metal Cutting:

### What Is Chip Thickness Ratio (Ctr) in Metal Cutting?

Chip thickness ratio (CTR) is a ratio that compares the thickness of the metal before cutting (t1) to the thickness after cutting (t2). It is a crucial parameter in machining processes that affects tool performance and chip formation.

### How Is Chip Thickness Ratio Calculated?

CTR is calculated using the formula: r = t1 / t2, where t1 is the thickness of the chip before cutting and t2 is the thickness after cutting.

### What Factors Influence Chip Thickness Ratio?

Several factors influence CTR, including cutting speed, feed rate, depth of cut, tool geometry (such as rake angle and nose radius), type of cutting material, and the use of cutting fluids.

### Why Is Chip Thickness Ratio Important in Metal Cutting?

CTR affects various aspects of metal cutting operations, including tool wear, surface finish of the workpiece, and the generation of heat. Optimal CTR helps in achieving efficient cutting with minimal tool wear and improved machining accuracy.

### How Does Chip Thickness Ratio Relate to the Coefficient of Chip Contraction?

The coefficient of chip contraction (k) is the inverse of chip thickness ratio (k = t2 / t1 or k = l1 / l2). It quantifies the longitudinal contraction of the chip during cutting and is influenced by factors like cutting angle and nose radius.

### What Are Typical Values of Chip Thickness Ratio and Coefficient of Chip Contraction?

Chip thickness ratios are generally less than unity, with higher values indicating more efficient cutting conditions. Coefficients of chip contraction can vary significantly depending on cutting parameters, often reaching values as high as 8 under optimal cutting conditions.

### How Can Engineers Optimize Chip Thickness Ratio in Metal Cutting Processes?

Engineers can optimize CTR by adjusting cutting parameters such as speed, feed rate, depth of cut, and tool geometry. Choosing appropriate cutting fluids and materials also plays a crucial role in achieving desired chip formation and machining efficiency.

### What Role Does Shear Angle Play in Chip Formation and Chip Thickness Ratio?

Shear angle (β) determines the orientation of the shear plane during metal cutting. It influences chip formation and directly affects the calculation of chip thickness ratio through trigonometric relationships involving the rake angle (α).