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In milling, the depth of cut is two-dimensional. The Radial depth of cut (AE or RDOC) is the length that the tool engages a workpiece perpendicular to its axis direction. The Axial depth of cut (AP or ADOC) is the length in its axis direction. They are both measured perpendicular to the table feed direction.

The two parameters are interlinked, and finding the best value for each of them and the proportion between them is critical to achieving a balanced milling process (Productivity, Safe process, and tool-life)

## Axial Depth of Cut (Cut Depth)

• The Axia depth of cut is also called Stepdown and Cut depth.
• It is designated by ap or ADOC.
• The maximum possible depth depends mainly on the cutter’s diameter.
• For large diameter cutters (Above 3/4″, 20 mm), It is up to 4D (4 times the diameter).
• For small diameter cutters (Below 1/8″, 3 mm) it is up to 10D.

### Optimal Cut Depth Calculators

The typical (and wrong!) opinion is that the larger the depth, the more vibrations will be in the cut. However, there are optimized cut depths that create minimum vibrations.

#### Optimal Depth of Cut Calculator

The calculator below shows the cut depths (ap), which yield the least vibrations. (Read below why)

#### Optimal Milling Cutter for a given Depth

The calculator below shows the diameters and helix angle combinations, which yield the least vibrations for a given depth. (Read below why)

#### Reducing vibrations by optimizing the depth of cut

The cutting force during a milling operation depends on the depth of cut, chip load, raw material, cutting angles, and the total length of engagement between the cutting edges of the endmill and the material being cut. All the parameters stay constant throughout the operation except for cutting-edge engagement. The length of the helix, which is in contact with the material, varies as the cutter rotates.

Therefore, a typical graph for the cutting forces acting on a solid carbide endmill as a function of time (or rotation angle) is like shown here.

However, specific combinations of diameters, number of flutes, helix angles, and depth of cut yield a constant contact length independent of the rotation angle, therefore, a constant force.

Since the diameter, helix angle, and flute count of the milling cutter can not be changed. We can find an optimal cut depth that will yield a constant cutting force:

You can use our above calculator to find out this depth of cut. All the multiples of this depth will also yield constant force.
When you machine with a constant force, you will get less vibrations, a better surface finish, and a longer too-life.

You can also use this theory in another effective way. Suppose you have a mass-production job and must constantly machine at a certain depth. If you reverse the formulas, you can find specific combinations of diameter, flute count, and helix angles to yield constant force and smooth machining. The result will be non-standard figures. But it may be well worth designing and purchasing a special cutter according to these parameters for a mass-production job.
You can use our above calculator to find out the optimal milling cutter geometry for your required depth of cut.

## Radial Depth of Cut (Cut Width)

• The Radial depth of cut is also called Stepover and Cut Width.
•  It is designated by ae or RDOC.
• The maximum possible radial depth is the cutter’s diameter.
• When the radial depth is larger or equal to the cutter’s radius, the chip load is similar to the feed per tooth.
• The chip load is reduced for smaller cut widths because of the chip thinning effect. (See below)

Chip Thinning Effect

Chip Thinning allows dramatic productivity gain since you can multiply the Feed by the Chip Thinning Factor (RCTF) while keeping the Chip Load within the recommended range! Learn more about it in our detailed guide about chip thinning

$$\large RCTF =$$

$$\huge \frac{1}{\sqrt{1-\left ( 1 – 2 \times \frac{Ae}{D} \right )^{2}}}$$

## Depth Of Cut Effects On Machining

If we understand each effect, we can make informed decisions about changes in radial or axial depth of cut to solve the problem we have on hand. Assuming that the Cutting speed, spindle speed, cutter diameter, and feed are constant, let’s have a look at what changes in AE and AP are affecting.

#### Productivity:

The productivity of the machining process is measured by its Metal Removal Rate (MRR).

$$\large MRR\,[\frac {Inch^{3}}{min}] = W\,\times\,F_n\,\times\,V_c\,\times\,12$$

We can see from the formula two things:

• As we increase both AP and AE, we gain more productivity.
• Both depth directions have the same effect. So a process with AE=0.5″ and AP=0.75″ will yield the same output as a process with AE=0.75″ and AP=0.5″.

We would increase AP and AE extensively in an ideal world to gain high productivity. Unfortunately, this is not the case in real life, as we will have many more parameters to consider.

The chip load during a milling process depends on cutter geometry, cutting speed, table feed, and radial depth of cut. The axial depth of cut has a zero effect on the chip load. (Learn More)

We cannot exceed a certain chip load for each geometry without damaging the cutting edge or hurting the tool-life. AP has zero effect on the chip load. but AE does according to the Chip Thinning Factor. So, we can keep the same productivity and decrease the chip load by “playing” with the proportion between AP and AE.

• A process with AE=0.5″ and AP=0.75″ will yield the same productivity as a process with AE=0.75″ and AP=0.5″, but the latter will have a lower chip load depending on the chip thinning factor.

#### Machining Power Consumption:

The power consumption in a milling process is calculated by the Metal Removal Rate (MRR) times the Specific Cutting Force (KC).

$$\large P[HP] = \LARGE \frac{MRR\,\times\,KC}{400}$$

$$\large P[kW] = \LARGE \frac{MRR\,\times\,KC}{60,000}$$

We saw above that MRR depends on AP and AE in the same proportion. However, the second parameter in the formula is the Specific Cutting Force (KC). It depends mainly on the workpiece material but also on the chip thickness and the radial depth. For the same MRR, a reduction in AE (and an increase in AP) will yield lower power consumption. For Example:

• A process with AE=0.5″ and AP=0.75″ will yield the same productivity as a process with AE=0.75″ and AP=0.5″, but the latter will require lower power consumption from the CNC machine.

#### Bending Force:

Both AP and AE increase the bending force when they are larger. However, the axial depth of cut is much more influential. Therefore, if you face problems related to bendings, such as chatter or non-straight walls, you should decrease the AP before you touch your AE.

#### Heat Removal:

As seen in the sketch, each cutting edge absorbs heat when it is engaged with the material and cools downs when it is in contact with air. The “air time” percentage depends on the radial depth of cut. Therefore, you can reduce the AE if you have fast wear associated with overheating. The Axial depth has no direct influence on heat removal.

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