CNC

Calculating the feed rate of a CNC mill

last updated: 06/04/20

Definitions and tips

• `Rotation speed n in RPM`:
This is the speed of the spindle in Revolutions Per Minute (RPM)!

• `Cutting speed vc in m/min`:
Speed of a tool (cutter) when cutting normally in `m/min`. The cutting speed depends on the material. Typical values range from `50 to 500 m/min`. It is the speed of a rotating tooth! and we get it from tables. If needed it can be calculated with the diameter of the tool `d` in mm and the spindle speed `n` in RPM (Revolutions Per Minute): `vc = (d·π·n)/1000`. With a maximum spindle speed of 20000 1/min we get: `vc = d·63 m/min`. This shows, that we can get a higher speed rate by choosing a bigger diameter of our tool.

• `Feed rate (feed speed) vf in mm/min`:
Tool’s distance travelled during one spindle revolution.

• `Diameter in mm`:
Diameter of the tool (cutter).

• `Number of teeth`:
Number of teeth (cutting edges, flutes) of the used tool (cutter).

• `Tooth feed fz in mm/tooth`:
Also chip load (cpt: chip per tooth) is the amount of material, which should be removed by each tooth of the cutter as it rotates and advances into the work.

The rate of material removal, but also the power requirements and the finish quality of the surface are determined by the feed rate and the cutting speed. They are mostly determined by the material that’s being cut. Softer material need lower cutting speeds. Harder cutting tool material need higher cutting speeds.

Calculating the feed rate

First we need to calculate the rotation speed in RPM with the following formula (`n` = rotation speed in RPM, `vc` = cutting speed in m/min, `d` = diameter in mm)

Formula to calculate the spindle speed:

`n = (vc·1000)/(π·d)`

The cutting speed for e.g. wood is selected from a table.

Material Cutting speed in m/min
Wood (soft) 500
Hardwood and MDF 450
Brass, Bronze, Copper 360
Aluminium (wrought alloy) 300
Cast-Aluminium > 6 % Si 200
Softplastic 150
Hardplastic 100
Steel 90

We get 500 m/min. This gives us a speed for the cutter resp. our spindle of 500000/3.1415 = 159160 RPM (revolutions/min) if we use an 1 mm tool. Ok, here is a problem! The max. speed of my spindle is 20000 RPM! So we stay with 20000 RPM for the next formula to calculate the feed speed:

Formula to calculate the feed rate:

`vf = n·z·fz`

In the following table (sorotec.de) we find the tooth feed in mm/tooth for spiral toothed cutter (solid carbide, fishtail, upcut-spiral, 3,175mm (1/8")).

Material Tooth feed in mm/tooth for d (mm) 0.5 1 1.5 2 2.5 3
Wood (soft)   0.01 0.012 0.015 0.02 0.025 0.03
Hardwood   0.008 0.01 0.012 0.015 0.018 0.02
MDF   0.01 0.012 0.015 0.017 0.02 0.025
Brass, Bronze, Copper   0.003 0.004 0.006 0.008 0.012 0.015
Aluminium (wrought alloy)   0.003 0.004 0.006 0.008 0.012 0.016
Cast-Aluminium > 6 % Si   0.002 0.003 0.005 0.007 0.011 0.015
Softplastic   0.008 0.015 0.03 0.04 0.05 0.06
Hardplastic   0.004 0.006 0.010 0.012 0.015 0.018
Steel   0.001 0.003 0.004 0.006 0.008 0.01

The table gives only rough values! to be able to calculate the feed rates. Optimum feed rate will be determined from experience. A good approach is to start off with half of the calculated feed rate and gradually increased to the capacity of the machine and the finish desired.

With our 20000 RPM we get a feed rate of 20000·2·0.01 = 400 mm/min for a 1 mm cutter in wood or 1200 mm/min for a 3 mm cutter.

Tables

Here I will try to document settings that worked for me (spindle 3000-20000 RPM).

Material Cutter Feed rate in mm/min
plywood birch 4 mm spiral diamond 1 mm 400