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 0.1 mm. If you deflect more, you can expect issues such as chatter, bad surface finish, etc.
Note: this is an oversimplification of the calculations needed. 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 CNCs it is safe to assume 100 N (10 kg) load. During this calculation we will assume the worst-case situation — the load being at the middle of the gantry. This is called midspan-load.
Gantry tube sizing calculation for a DIY CNC
A two-step calculation to sanity-check the size of your gantry tube before you commit to ordering steel. Uses two free online calculators.
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Pick a candidate tube and get its moment of inertia (Iₓ)
Use SkyCiv’s free online moment-of-inertia calculator. Enter the outer dimensions and wall thickness of your candidate tube (for example, 100×100×8 mm hollow rectangular). Work in centimetres to avoid unit conversions in step 2. Note the Iₓ value the calculator returns.
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Calculate midspan deflection
Plug the values into a beam-deflection calculator: unsupported gantry length (e.g. 1600 mm), midspan load of 100 N, modulus of elasticity 200 GPa for steel, and the Iₓ from step 1. The calculator returns maximum deflection under that load.
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Check against the 0.1 mm budget
If maximum deflection ≤ 0.1 mm, your tube is adequate for DIY CNC service. If it’s over, increase outer dimensions or wall thickness and repeat.
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Keep the calculator open
When you change gantry dimensions, the Iₓ changes too. Always re-run step 1 before re-running step 2 — don’t reuse an old Iₓ with a different tube.
Resource #1 — Moment of inertia calculator
With SkyCiv’s free online moment-of-inertia calculator, you calculate the moment of inertia values for your gantry tube. This is only based on its dimensions, not its material. I do these calculations in centimetres (cm) to prevent further unit changes when doing the beam deflection calculation.
In my worked example I use a hollow rectangular tube with the size of 100×100×8 mm.
Resource #2 — Beam deflection calculator
With a beam deflection calculator you can check what the mid-point deflection is for a given tube and force. The inputs of this specific example are: a 1600 mm long gantry tube (unsupported length), 100 N downward force, 200 GPa (steel) modulus of elasticity, and 47 cm⁴ of moment of inertia coming from the SkyCiv calculator above.
When you change your gantry tube dimension, you will get a different Iₓ value. Adjust the span length and beam size according to your specification. When the maximum deflection ≤ 0.1 mm, you will be OK for DIY CNC applications.
FAQ
Sizing a gantry for your own build? Join the Discord and share your numbers — happy to sanity-check.
