What size does my gantry tube need to be for a DIY CNC

This is a simple and very quick post regarding gantry tube sizing.

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”.

DIY CNC
Midspan load representation

Resource #1 Moment of inertia calculator

2022 09 14 17 29 32 Free Online Moment of Inertia Calculator SkyCiv
SkyCiv 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.

Beam Deflection Calculator1
Beam deflection calculator

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.

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Spikee
Spikee

Hi, My name Is spikee and I'm the Author of this post.
I have been active on various cnc communities over the past few years.

On this website I share tips&tricks, reviews and intresting resources relating to diy cnc and cnc router topics.

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7 Comments

  1. Its great to see someone putting in some design effort into a homebuilt router instead of just eyeballing everything! Simplifying systems into something easy to model (like a beam) is key.

    Something that surprised me when I did the math on my own router design was that the x/y deflections of the gantry tended to be much more significant than the z axis deflections. This is driven not only by the horizontal cutting forces but also the dynamic loading from accelerating the spindle around. If you want to check out the specifics you can take a look at my post here: https://burksbuilds.com/2021/12/20/cnc-router-stiffness-analysis/#Results

    You have a later blog post on millalyzer and mentioned that you bought a license. For the cutting cases that you expect to encounter on this machine what kind of loads are you expecting? How does that new information impact this beam model?

    Thanks for all the great content!

    • Hi Andrew those are great insights. X/Y deflections are the highest because it is basically a big mechanical lever. Double carriages (with a big as possible distance between) can help to limit this.
      In addition to oversizing gantry/riser construction. I have not done the full calculations for my new build yet. But it is something I’m working on.

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