Table of Contents

## Metal Removal Rate Calculator

## how to calculate MRR ?

**The Metal Removal Rate is calculated by multiplying the area of the chipâ€™s cross-section by the linear velocity in the direction perpendicular to it.**

Letâ€™s look at a simple milling application as an example:

- The chip Area is A
_{p}x A_{e} - The Perpendicular Speed is the table feed (Vf).

(In a full plunging operation, the chip area would be *Ï€*Â xÂ D^{2}Â /Â 4, and the speed would be feed in the spindleâ€™s direction.)

The result is multiplied by a constant depending on the units used (Metric/Inch) to get the final result in either cubic inches or cubic centimeters.

\large MRR =

\\

\large \text {Chip Area} \times

\\

\large \text { Perpendicular Speed} \times

\\

\large \text { Unit Constant}

\end{matrix} \)

## Metal Removal Rate Formulas

**( For detailed explanations check the sections below on each application)**

Application | Metric [Cubic Cm] | Inch [Cubic Inch] | ||
---|---|---|---|---|

Milling |
\(\LARGE \frac {A_p \times\, A_e \times\, V_f }{1,000}\) |
\( \large A_p \times A_e \times V_fÂ \) |
||

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:**

- A
_{p}, A_{e}, D, W â€“ mm or Inch - V
_{f}â€“ mm/min or inch/min - V
_{c}â€“ m/min or feet/min (SFM) - F
_{n}â€“ mm/rec or Inch/rev - MRR â€“ Metal Removal Rate CM
^{3}/min or Inch^{3}/min

## MRR formulas explained

**As explained in the introduction, Metal Removal Rate is defined as:**

\large MRR =

\\

\large \text {Chip Area} \times

\\

\large \text { Perpendicular Speed} \times

\\

\large \text { Unit Constant}

\end{matrix} \)

**We will break down this basic formula for the main machining applications**

**Metal Removal Rate in Milling**

- A
_{p}â€“ Axial depth of cut in mm or inches. - A
_{e}â€“ Radial depth of cut in mm or inches. - V
_{f}â€“ Table Feed in mm/min or inches/min - MRR â€“ Metal Removal Rate in CM
^{3}/min or Inch^{3}/min

\(

\begin{matrix}

&\text{Chip Area}& & \text {perpendicular Speed} & & \text {Unit Constant}\\

\large MRR = &\overbrace{A_p\,\times\,A_e} &\times&\overbrace{V_f} &\times&\overbrace{K}

\end{matrix}

\)

- InÂ
**imperial units**, all the parameters are in Inches,Â therefore**K=1**to get the final result in Inch^{3}. - InÂ
**metric units**, Ap and Ae are in mm, while V_{f}is in meters. therefore,**K=0.001**get the result in Cm^{3}.

\(

\large MRR\,[\frac {Cm^{3}}{min}] = \LARGE \frac{A_p\,\times\,A_e\,\times\,V_f}{1,000} \\

\)

\(

\large MRR\,[\frac {Inch^{3}}{min}] = A_p\,\times\,A_e\,\times\,V_f

\)

**Metal Removal Rate in Turning**

- A
_{p}â€“ Depth of cut in mm or inches. - F
_{n}â€“ Feedrate n in mm or inches. - V
_{c}â€“ Cutting Speed in m/min or feet/min (SFM). - MRR â€“ Metal Removal Rate in CM
^{3}/min or Inch^{3}/min

\(

\begin{matrix}

&\text{Chip Area}&&\text {perpendicular Speed}&&\text {Unit Constant}\\

\large MRR = &\overbrace{A_p\,\times\,F_n}&\times&\overbrace{V_c} &\times&\overbrace{K}

\end{matrix}

\)

- InÂ
**imperial units**, the speed is given in SFM and**K equals12 to**Â convert the speed into Inches/min and get the final result in Inch^{3}. - InÂ
**metric units**, K=1 to get the result in Cm^{3}

\(

\large MRR\,[\frac {Cm^{3}}{min}] = A_p\,\times\,F_n\,\times\,V_c

\)

\(

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

\)

**Metal Removal Rate in Drilling**

- D â€“ Drill diameter in mm or inches.
- F
_{n}â€“ Feed per Revolution in mm or inches. - V
_{c}â€“ Max Cutting Speed in m/min or feet/min (SFM). - MRR â€“ Metal Removal Rate CM
^{3}/min or Inch^{3}/min

\(

\begin{matrix}

&\text{Chip Area}&&\text {perpendicular Speed}&&\text {Unit Constant}\\

\large MRR = &\overbrace{D\,\times\,F_n\,\times\,0.5}&\times&\overbrace{V_c\,\times\,0.5} &\times&\overbrace{K}

\end{matrix}

\)

- The
**chip area**is the radius (D/2) of the drill times the feed per revolution.Â - The
**speed**starts with zero at the center of the drill and reaches its maximum at the OD. Therefore, we use**the average speed, which is Vcmax/2**. - InÂ
**imperial units**, the speed is given in SFM, andÂ Â**K equals12 to**Â convert the speed into Inches/min and get the final result in Inch^{3}. - InÂ
**metric units**, K=1 to get the result in Cm^{3}

\(

\large MRR\,[\frac {Cm^{3}}{min}] = \LARGE \frac{D\,\times\,F_n\,\times\,V_c}{4} \\

\)

\(

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

\)

**Metal Removal Rate in Parting and grooving**

- W â€“ Width of Groove in mm or inches.
- F
_{n}-Feedrate in mm or inches. - V
_{c}â€“ Cutting Speed in m/min or feet/min (SFM). - MRR â€“ Metal Removal Rate in CM
^{3}/min or Inch^{3}/min

\(

\begin{matrix}

&\text{Chip Area}&&\text {perpendicular Speed}&&\text {Unit Constant}\\

\large MRR = &\overbrace{W\,\times\,F_n}&\times&\overbrace{V_c} &\times&\overbrace{K}

\end{matrix}

\)

- InÂ
**imperial units**, the speed is given in SFM and**K equals12 to**Â convert the speed into Inches/min and get the final result in Inch^{3}. - InÂ
**metric units**, K=1 to get the result in Cm^{3}

\(

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

\)

\(

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

\)

## What is MRR used for ?

**The Metal Removal Rate is used for two main purposes:**

**1) Estimating the machine power consumption for a given set of machining conditions**

Each raw material has aÂ **Specific Cutting Force**Â property, designated by Kc. The constant is in pressure units (Force per Area) and is usually listed in Mpa (N/mm^{2}) or N/Icnh^{2}. The specific cutting force indicates how much force is needed to shear a chip from the raw material, and multiplying it with the Metal Removal Rate yields theÂ **required Machining Power**. This method of machining power calculation is an indirect estimation; however, due to its simplicity and decent accuracy, it is the most widely used way to compute machining power.

**2)** **Comparing the productivity of two machining processes**

Suppose we need to mill a cube in the dimensions of 1â€³ X 1â€³ X 1â€³ with a 0.5â€³ diameter endmill. Two workers suggest different approaches to perform the task.

- Worker #1 r suggests to use a 1/2â€³ 4 fulte endmill with cutting conditions: A
_{p}=0.5â€³, A_{e}=0.25â€³, f_{z}=0.004 Inch/rev and V_{C}=300 SFM. - Worker #2 suggest to use a 1/2â€³ 6 fulte endmill with cutting conditions: A
_{p}=0.5â€³, A_{e}=0.1â€³, f_{z}=0.005 Inch/rev and V_{c}=350 SFM .

To evaluate which options yield the best productivity we can compare the MRR of both options:

**Worker #1:**

**Worker #2:**

By comparing the MRR value of the options, we can see that the approach suggested by worker #1 provides higher productivity.