# Machining Power Calculator and Formulas

Calculating the power required (in kW or HP) from a CNC machine to perform particular milling, turning, or drilling operation is essential to validate that our equipment can execute the machining operation without getting too close to its power limit. Use our Online Calculator or learn how to compute it (Including detailed formulas).

## What is Machining Power?

In physics, power is defined as the amount of energy transferred per unit of time. In the case of CNC machining, the electrical network passes energy to the spindle’s electric motor, which passes it to the cutting tool. The cutting tool uses this energy to extract material from a workpiece. Assuming the efficiency is 100%, the power required to remove the material is the same as the power used by the machine’s motor. Each machine has a maximum power limit that it can handle. Therefore, it is helpful to calculate the power required to perform a machining operation such as milling or turning and compare it to our machine’s ability. For example:

• The Machine: 3 axis milling machine with a maximum power of 30 HP (22 kW)
• The Operation: Facemilling of stainless steel with a 4″ cutter, at a depth of cut of 0.5″, feed per tooth of 0.005″ and cutting speed of 300 SFM. (100 mm, 12.7 mm, 0.13 mm/tooth, 100 m/min).
• The power required in this case is about 28 HP (21 KW)
• From the calculation, we can see that we can do the job, but it would require the machine to run at near full power, and it would be better to select a machine with a higher power capacity.

## How is machining power calculated?

In mechanics, the power of a motor is the product of the torque and the shaft’s angular velocity. In machining, this translates to the Torque acting on the spindle multiplied by the spindle speed:

• In rotating Applications (Milling and Drilling), it is the force acting on the cutting edge times the cutter’s radius times the tool rotation speed ( the spindle speed).
• In Non-Rotating applications (Turning and Grooving), it is the force acting on the workpiece times the workpiece’s radius times the workpiece rotation speed (the spindle speed).

The problem is that calculating the cutting force is a rather complex computation that cannot be summarized into simple formulas. Luckily there is a workaround that is simple to implement and yields relatively accurate results (about +/- 15%).

The method is to multiply the Metal Removal Rate (MRR) by the Specific Cutting Force (KC)

• Metal Removal Rate (Q): The volume of material (in Cm3 or Inch3) that the machining operation removes in one minute. Learn More
• Specific Cutting Force (KC): A material property that indicates the required force needed to extract a chip out of the workpiece. Material charts on the web (or in catalogs) list the KC value per raw material or material group. (Learn more about Specific Cutting Force )
$$\begin{matrix} &\text{Q}& & \text {KC} & & \text {To get KW or HP}\\ \large POWER = &\overbrace{\text{Metal Removal Rate}} &\times&\overbrace{\text{Specific Cutting Force}} &\times&\overbrace{\text {Unit Constant}} \end{matrix}$$
$$\begin{matrix} \text{POWER = }\\ \text{Metal Removal Rate (Q)}\,\,\times\\ \text{Specific Cutting Force (KC)}\,\,\times\\ \text{Unit Constant (To get KW or HP)} \end{matrix}$$

## Cutting Power Formulas

Calculating the cutting power requires 4 steps:

### Step 1 – Calculating the Metal Removal Rate (Q)

Material removal rate (MRR) is the volume of material removed per time unit during machining operations such as milling, turning, drilling, and grooving. It is designated by the letter Q and measured in cubic Inches per minute or cubic centimeters per minute.

( For detailed explanations, check our in-depth MRR article )

Application Metric [Cubic Cm] Inch [Cubic Inch]
Milling $$\LARGE \frac {A_p \times\, A_e \times\, V_f }{1,000}$$
$$\large A_p \times A_e \times V_f$$
Turning $$\large A_p \times F_n \times V_c \$$
$$\large A_p \times F_n \times V_c\ \times 12$$
Drilling $$\LARGE \frac {D \times\, F_n \times\, V_c }{4}$$
$$\large D \times F_n \times V_c\ \times 3$$
Grooving $$\large W \times F_n \times V_c \$$
$$\large W \times F_n \times V_c\ \times 12$$

Units used in the above table:

• Ap, Ae, D, W – mm or Inch
• Vf – m/min or inch/min
• Vc – m/min or feet/min (SFM)
• Fn – mm/rev or Inch/rev
• MRR – Metal Removal Rate CM3/min or Inch3/min

### Step 2 – Obtaining the materials Specific Cutting Force (KC1.1)

Each material has a Specific Cutting Force coefficient that expresses the force in the cutting direction, required to cut a chip area of one square millimeter that has a thickness of 1 millimeter with a top rake angle of 0°, hence the name KC1.1. In addition to KC1., each material has an MC constant that indicates how KC varies as it gets further away from its normalized point. KC1.1and MC values are listed in charts like the one on the bottom of this page or in cutting tool technical guides. (Learn more about Specific Cutting Force )

### Step 3 – Calculating the actual Specific Cutting Force (KC)

Since KC1.1 is normalized to 1 mm at 0° rake, we need to calculate the actual specific cutting force KC suitable for our conditions. It is the most complicated part of the process, and it differs depending on the application. To perform the calculations we will need to obtain 4 parameters.

$$\large \bf KC = KC1.1\,\times\,HM^{-MC}\,\times\,\left (1\,- \,0.01\,\times\, GAMF\right )$$
$$\large KC = KC1.1\,\times\,HM^{-MC}\,\times$$
$$\large \left (1 – 0.01\,\times\, GAMF\right )$$
1. KC1.1 – Normalized Specific cutting Force [KPSI] or [KW] – Obtained from the below chart
2. MC – Curve slope of the KC graph. – Obtained from the below chart
3. GAMF – Top rake angle. – Obtained from the tool/insert catalog or drawing.
4. HM – Chip thcikness [Inch] or [mm] – Needs to be calclated per application.

#### c) Top Rake (Radial) Angle -GAMF

Each cutting tool has a radial rake angle. The angle is measured between the cutting edge and the workpiece. Therefore when an indexable insert is mounted on a tool holder, you should use the combined angle (the angle of the top rake relative to the tool’s clamping plane when the insert is mounted in the pocket). A reputable tool supplier will provide this angle in his catalogs. If you have trouble obtaining it use +7° as a default value since most cutting tools have a slight positive rake angle.

#### d) Chip thickness (HM) Is calculated differently depending on the application:

• When the approach angle is 90° (or more), use the feed per revolution as the chip thickness HM=FN
• As the approach angle gets smaller, the chip thickness is reduced according to the formula: HM = FN X SIN(KAPR)
• Milling The chip thciness depends on two factors:

Approach angle (KAPR):

• When the approach angle is 90° (Standard straight cutters), use the feed per revolution as the chip thickness HM=FN
• As the approach angle gets smaller, the chip thickness is reduced according to the formula: HM = FN X SIN(KAPR)
• For round shapes the formula is more complicated and is not covered here.

• When AE>=D/2, use the feed per tooth as the chip thickness HM=FN
• When AE<D/2, the chip thickness is reduced according to the Radial Chip Thinning Factor (RCTF). HM=FZ/RCTF
• Detailed formulas for radial chip thinning (RCTF) are explain in-depth here

### Step 4 – Converting the result to kW or HP

• Assuming the input values are in Inches and KC is in KPSI the result should be divided by 400 to get the power in HP units.
• Assuming the input values are in millimeters and KC is in Mpa (N/mm2) the result should be divided by 60,000 to get the power in kW.
• Hence, the final formulas are:
$$\large P[HP] = \LARGE \frac{Q\,\times\,KC}{400}$$

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

## Factors affecting Cutting power

By understanding each parameter’s effect on machining power consumption, we can decide what to change when we want to optimize an application for less power consumption.

### Factors affecting directly the machining power formulas

#### Raw Material:

The workpiece material type is by far the most significant factor. The specific cutting force (KC) ranges from 700 MPa for Aluminum up to 3,500 Mpa for nickel-based alloys. Machining a stock of Inconel will consume 400% more power than aluminum (At the same cutting conditions).

#### Rake Angle:

Every single degree of rake angle increases/decreases the power consumption by about 1%. Radial rake angles (GAMF) range from +20° on high positive inserts up to -20° for inserts with a K-land. Therefore, the maximum potential of rake angle influence is 40%

#### Approach Angle:

The approach angle (KAPR) on most cutting tools is 90°. However, there are many tools with 45° and high feed cutters with approach angles as low as 12°. As the angle decreases, chip thickness is reduced by SIN(KAPR). Since the chip thickness is one of the components of the formula of the specific cutting force (see above), it indirectly influences also the required machining power. As the approach angle decreases, the machining power rises. The maximum potential of approach angle influence is 30%

There are additional factors that are not included in the formulas but have a significant effect on the actual machining power requirements.

#### Cutting Edge Wear

The cutting power formulas are based on a new insert without wear. As the cutting edge gradually wears, the cutting forces increase, and the power rises. The difference between the power consumption of a fresh insert and a worn insert can be up to 50%.

#### Machine efficeincy

So far, we have learned how to estimate the theoretical machining power. It is the mechanical power required to extract the chips from the workpiece. The value we are interested in is the power requirements from the CNC machine’s motor. The factor between these two figures is machine efficiency and is denoted with μ. It is influenced by the motor and power transmission technology and the machine’s age and mechanical condition. In the below table you can find typical efficiency values:

## Specific Cutting Force chart

Typical values of KC1 and MC values are shown in the below table. The difference between specific materials within the material groups is not significant and the accuracy is good enough in most cases. You can find more detailed charts here

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