Modal Resonance Simulation - Fusion 360

[Tenson]

Hi ya'll,

I haven't been following this forum for some years since I built my machine and stopped thinking about upgrades for a while.

Since then, Autodesk Fusion 360 has become available for general use and with that its powerful simulation capabilities.

I was wondering if there has been much uptake with DIY designs here making use of the modal simulation functions?

I remeber I think Jonathan did some static load simulation with Solidworks when working out the best gantry shape, but milling machines are not about static loads, they are about resonance / structural modes. Everything is a spring, as they say.

Despite building what I thought would be a pretty solid machine frame (and for the most part it is, especially when considering static loads), there has always been some low frequency resonance that I couldn't track down because I'd braced all I could and it's too fast to see by eye other than 'it's wobbling'.

Using the modal simulation in Fusion 360 has been very telling about the effect of frame geometry, specifically bracing placement. I'm only just beginning to fiddle around, but so far it seems to match reality pretty accurately - for example I've found that cross-corner type of bracing is far less effective than diagonal-to-diagonal type.
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I can also see that the layer damping I added to the short and long top beams was worthwhile, as they flex in the direction the damping is most effective :)

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[Mud]

You have some long unsupported lengths, and these will tend to large deflections (per force input) at lower frequencies.

Bracing across the corners of your frame will act against the global modes of the structure (like lozenging), but the local modes (like the beams deflecting individually) won't be as strongly affected.

When you add a brace to a beam, you will tend to split modes into two higher frequency modes (with a node where the brace is attached). When you brace half-way along a beam you will disrupt the first flexural mode, but the second flexural mode will be less effected (the S-shape deflection).

It's much easier to add stiffness than effective damping. Adding stiffness reduces deflection and pushes the resonant frequencies up.

Models are helpful, but joints will always reduce their accuracy.

[Voicecoil]

The other thing to remember is that it's difficult to damp at low frequencies (needs lots of stuff), so if by bracing you can push the frequencies up, then the damping becomes much easier. On my machine I found that 3mm damping sheet was very effective from about 2....3Khz upwards, but didn't do so much for the fundamental resonance of beams.

When you add a brace to a beam, you will tend to split modes into two higher frequency modes (with a node where the brace is attached). When you brace half-way along a beam you will disrupt the first flexural mode, but the second flexural mode will be less effected (the S-shape deflection).
This can be helped by taking care not to have the bracing points at integer sub-multiples of the beam length - i.e. avoid 1/2, 1/3, 1/4.

[Mud]

...
This can be helped by taking care not to have the bracing points at integer sub-multiples of the beam length - i.e. avoid 1/2, 1/3, 1/4.

True - and for the same reason our tendency to equi-space supports can be sub-optimal. It does make understanding the dangerous frequencies easier though if all the little sub-sections are similar, and at the extreme you can try to avoid exciting them.

For context, this is big-brain stuff, and unless you enjoy worrying is of diminishing returns past the first few modes.

[Tenson]

Good info, thanks.

Even just looking at what you called losenging, the full diagonal brace is much more effective than multiple cross corner ones (which are similarly effective as webbing).

Regarding damping, I think it is critical. You can make something stiffer but without a means to dissipate energy it will only ring at a higher frequency. I've used two methods for low frequency damping.

The top beams (two long ones have the Y rails on them) are made of two steel box sections bolted together with a 3mm layer of butyl tape between them. This is what I meant by layer damping. It converts the beam flex in to sheer strain against the damping material, so is far more effective at low frequencies than just a surface treatment of 3mm butyl tape. My Z axis plate is also dual layer with damping between.

The second method I have used for low frequency damping is to pour the 4 main upright box sections with concrete that was mixed with something called 'SBR'. SBR comes as a liquid that gets used in place of water in the concrete mix and cures as latex rubber. This is used commonly to provide damping in concrete structures for reduced foot-fall noise and such like.

https://www.researchgate.net/publication/226620051_Improving_the_vibration_damping_capacity _of_cement

[Mud]

This is a complex topic, but you ultimately seek to control displacement. At higher frequencies the displacement for a given input level will be lower. The methods of increasing damping you mention are largely velocity dependent, so will be more effective at higher frequencies (as Voicecoil said), so you still want stiffness to push those frequencies up.

Arguing stiffness vs. damping in a pure sense is meaningless, but as I said before, adding stiffness (and I really should also say mass) is easy, and should intuitively make sense in limiting system response. Trying to engineer in damping usually means allowing relative motion of elements of the system somehow, which undermines keeping it stiff.