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How To Calculate the Depth Of Cut In Machining?


If you decide that CNC machining operation is the method you need to get your piece done, then you need to know that Depth of Cut (DOC) is one of the top 3 most important parameters affecting the quality of the machining product.

This article will help you understand what is meant by Depth of Cut in machining, why you need to control it, what the difference between chip thickness and depth of cut, and how to calculate it.

What Is Depth Of Cut In Machining?
In the machining process, depth of cut is simply how deep the cutting tool gets into a workpiece and cuts through it to create a chip. In an ideal cutting process, when the CNC cutting tool moves to the left with a certain depth inside the workpiece’s surface, it creates a chip. This depth is named Depth of Cut or DOC. If you need a similar and simple application you can see how chocolate curls or chocolate shavings are cut.

turning process showing feed and depth of cut
The depth of cut values is measured either in inches or millimeters and usually varies between 0.1 to 1 mm.

Why Do You Need To Control Depth Of Cut In Machining?
Depth of cut has a direct effect on the machining process, such as:

The heat rises at the tool tip;
Tool wear rate;
Strength of the processed product;
The quality of the machined surface.
For example, there is a tendency for the Built-up Edge (BUE) formation with annealed metals than cold-worked ones in the cutting process. BUE chip type consists of layers of chips accumulating at the tool tip. Therefore, if the depth of cut is too deep, uncontrolled BUE also adversely affects the surface finish.

depth of cut in machining
How Does Depth Of Cut Interact With Other Machining Factors?
Depth of cut is one of the independent factors affecting the machining process, which means it is controlled by the operator. However, the depth of the cut interacts with other factors and affects the resultant surface of the workpiece and its properties.

Depth of Cut and Cooling Fluid
With decreasing the depth of cut the chip curvature decreases and the chip becomes curly. In this case and when heat rises at the tool tip, you might think that adding cooling fluid will cool up the process.

However, adding CNC coolant fluid makes the chip even more curlier, decreases the contact between the tool and the chip, and concentrates the heat at the tool which significantly increases the tool wear. In this case, a chip breaker might be handy.

Depth of Cut, Rake Angle, and Cutting Speed
Another example can be found in machining thermoplastics. Thermoplastics generally have low thermal conductivity and low elastic modulus. This means that they are greatly affected by heat fluctuations at the tool tip in machining. Depth of cut, rake angle, and cutting speed all have to be adjusted relative to each other to avoid temperature rise and the formation of gummy and sticky chips at the tool tip.

It is also worth to be known that depth of cut is one of the top three parameters affecting tool life along with cutting speed and feed.

How To Calculate The Depth Of Cut?
The significance of having quantitative relationships among different variables is obvious when you need depth of cut calculation, why the tool’s temperature is getting high? why is the surface finish poor? Why does the cutting tool wear rapidly? And many more.

In order to calculate the depth of cut, you need to specify the following parameters:

What is the machining process (Milling, Turning, etc.)
Workpiece material
Tool tip properties
Machine capabilities
Required surface finish and tolerance
Depth of Cut in Turning Process
In CNC turning, the workpiece rotates while the tool removes a layer of material as it moves along the length of the workpiece. The depth of cut can be the same as the feed or feed rate which is simply the distance the tool travels along the workpiece at each revolution over time, and it has the unit of mm/min.

Therefore, depth of cut can be simply defined by the thickness of the material removed and can be calculated from:

turning depth of cut calculation formula
depth of cut schematic of the turning process
Depth of Cut in Milling Process
In the CNC milling process, the tool rotates while the workpiece is steady. The depth of cut is simply how deep the tool cuts in the workpiece in one turn. Commonly, the cutting depth is 4 times the diameter of the cutting tool for large diameters above 20mm and 10 times the diameter size for smaller tool diameters.

depth of cut in milling process
Compare Chip Thickness Value Vs. Depth Of Cut Value
It is important to differentiate between chip thickness and the depth of cut because they are NOT the same and do NOT have the same value.

In order to explain it, we need to have a deeper look at Figure 1 of the ideal cutting process. The value of the depth of cut (let’s denote it with to) is different than the chip thickness (tc).

ideal cutting process
Figure 1: ideal cutting process

The chip removal process is done via shearing at a well-defined shear plane and with a defined shear angle ϕ as illustrated in the following Figure 2. This makes the value of the chip thickness always greater than the value of the depth of cut.

basic mechanism of chip formation
Figure 2: basic mechanism of chip formation

Cutting Ratio vs. Chip Compression Ratio
The ratio between the depth of cut to the chip thickness to/tc is called the cutting ratio or chip thickness ratio and is denoted by (r) and can be calculated as follows:

depth of cut to chip thickness ratio r
It can also be calculated from the shear angle ϕ and the rake angle α as shown in Figure 1 as follows:

r-value formula-shear angle ϕ and the rake angle α

ϕ: shear angle
α: rake angle

The reciprocal of this value is called chip-compression ratio or chip-compression factor which indicates how much the chip thickness is compared to the depth of cut.

Bonus: Depth Of Cut Versus Cutting Forces And Power
Knowing the cutting force and power is crucial in calculating the DOC. They can provide important parameters such as:

Tools with required strengths to avoid rapid wear and provide the best efficiency and surface finish.
Workpiece holders and fixtures that can withstand these forces with minimum distortion.
The power required is simply the product of the cutting force multiplied by the speed and can be calculated as follows:

cutting power calculation formula
Where Fc is the “cutting force” and is defined as the force exerted by the tool to cut through the workpiece, and is acting in the same direction as tool velocity V.

The total specific energy is the total energy required to perform the shearing force required to cut through the surface (us), in addition to the friction specific energy which is the energy required to overcome the friction between the tool and the surface (uf).

Shear-specific energy and friction-specific energy are related to the depth of cut and can be calculated as follows:

The chip speed is related to the cutting speed as follows:

calculation formula for depth of cut and shear specific energy
calculation formula for depth of cut and friction specific energy
forces acting in the cutting zone
Therefore, it is worth mentioning that these formulas can be used vice versa to calculate the depth of cut in case you have specific machine parameters.

chip speed and cutting speed calculation
XTJ Is A Reliable Partner For Your Machining Projects
Machining is a complex operation and it is not an easy process to establish quantitative values for all the parameters and determine the machinability of a certain material.

XTJ is your CNC machining expert offering efficient and affordable machining solutions. Our engineers will develop a comprehensive machining strategy to ensure that every machining parameter in the process meets the machining requirements. In addition, we employ 100% inspection for each project to meet your product specifications.

XTJ is your CNC machining expert


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