During milling conditions you do not want your gantry tube to deflect more than 0.1mm. If you deflect more you can expect issues such as chatter, bad surface finish etc.

Note: this is an oversimplification of the calculations needed. As there are moment forces etc. This is a simple calculation for DIY CNC projects such as the PrintNC to get an indication of required gantry tube size.

How do I calculate that?

you can actually calculate milling forces with a tool such as Millalyzer. But for now that is too complicated. For milling forces on DIY cnc’s it is safe to assume 100N (10kg) load. During this calculation we will assume the worst case situation thus the load being at the middle of the gantry. This is called “midspan-load”.

Resource #1 Moment of inertia calculator

With this calculator you calculate the moment of inertia values for your grantry tube. This is only based on it’s dimensions, not its material.

I do these calculations in centimeters (CM) to prevent further unit changes when doing the beam deflection calculation. In the above example I use a hollow rectangular tube with the size of 100x100x8 mm

Resource #2 Beam deflection calculator

With the beam deflection calculator you can check what the mid-point deflection is for a given tube / force.

The inputs of this specific example is a 1600mm long gantry tube (unsupported length) , 100N downward force, 200GPa (steel) modulus of elasticity

and 47 cm^4 of moment of inertia coming from the Skyciv moment of inertia calculator above.

Note: When you change your gantry tube dimension, you will get a different Ix value.

Adjust the Span length, beam size according to your specification

When the maximum deflection <= 0.1mm , you will be ok for DIY CNC applications.