Damping Test of Concrete & Steel Tube

[Tenson]

Hi Everyone!

Over at CNCZone I was discussing a build that will use a steel tube frame and I said I was planning to fill it with concrete / SBR mixture. SBR is basically a liquid latex that adds flexibility and waterproofing to concrete. Styrene Butadiene Rubber.

Another user mentioned that he did some calculations and thought that: A) The steel would carry nearly all the stress/strain and so the concrete core would not offer much lossy damping, only increase mass. B) Therefore, might as well buy thickest steel tube and not bother filling.

As I have the acoustics tools to measure damping I thought it would be an interesting experiment.

I took two 90cm lengths of 40x40 steel tube. (I didn't have 1m scraps). One had a 2mm wall, the other had a 3mm wall. I hung them so they were free to resonate and attached an exciter transducer and an accelerometer.

https://i.imgur.com/Gg0DeBN.jpg

This is the result for the hollow tube, before filling.

Thin Tube Hollow.
https://i.imgur.com/u2s6vHQ.png

Thick Tube Hollow.
https://i.imgur.com/1aHCqJC.png

We can see the first strong resonance frequency in each tube is pretty much the same frequency 138Hz (thin) vs. 128Hz (thicker). However we can see a significant difference in amplitude. The thin walled tube has higher amplitude and the width 'Q' of the resonance is more narrow. The thicker walled tube resonance is -5dB in comparison, which is a lot. 3dB is a halving of amplitude. It has a broader 'Q' which usually indicates higher damping factor, but we can look at that more closely in a moment.

Below we look at the same data, but in a different way, this a waterfall plot and shows the decay of energy over time.

Thin Tube Hollow.
https://i.imgur.com/InM1dIF.png

Thick Tube Hollow.
https://i.imgur.com/fxdv3fh.png

Now we start to see the difference between 'lossy damping' and simply increasing mass. Yes, in terms of amplitude adding mass damps the resonances. However when we look at energy decay in the system we can see that the thicker higher mass tube actually has slower energy decay.

This is not surprising really. A higher mass object will not move as far as a lighter one given the same energy input, but it has greater inertia so it will keep moving for longer once in motion.

We do see a cleaner decay in the range below the big resonance on the thicker tube. I think this is probably a reflection of simple increased rigidity but I'm not entirely sure.

Okay lets fill the beams! I used a pre-mix concrete bag, but instead of water I used only SBR mixture.

I gave them about 10 days to cure during the hot weather at the time.

Thin Tube Filled.
https://i.imgur.com/oj6jFOK.png

Thick Tube Filled.
https://i.imgur.com/0ckZU7h.png

Thin Tube Filled.
https://i.imgur.com/V92etoW.png

Thick Tube Filled.
https://i.imgur.com/NxbkJdt.png

Wow there is a difference there! I'm surpised just going 2mm to 3mm wall thickness did that.

The filling gave a significant increase in mass and has reduced the initial amplitude of the resonances in both tubes by over -10dB (that's HUGE!). They are now equal in terms of initial amplitude, probably because the filling equalises the difference in mass.

Looking at the decay of energy we see now the thin walled tube decays significantly faster than the thicker filled tube. Both are improved over the decay rate of the hollow tubes.

So in conclusion, Does the SBR concrete mixture contribute lossy damping or only mass? It clearly is able to contribute lossy damping. Great!

Looking at the results we can also conclude that the thinner walled tube is passing more of the stress/strain to the concrete core and this benefits from greater lossy damping. There is of course a catch, that you still want a steel tube with enough outright stiffness to be suitable for your machine design, concrete is good in compression but weak in tension so you can not rely only on the concrete to give the structure strength.

In my own design I was wondering if I should go for 2mm walled tube and fill, or go for 5mm tube with/without filling. The choice for me is clearly in favour of the thin tube filled, as that still offers easily enough stiffness for my planned design with improved lossy damping.

At frequencies below the resonances, the stiffness and mass still dominate over lossy damping. So if you know a machine will not excite those higher frequencies, stiffness is all that needs to be considered. However, also remeber that longer beams and larger structures will have lower frequency resonances than these ~1 meter samples.

I'd very much like to try a thin walled tube with concrete filling under compressive pre-load. In buildings they sometimes cure concrete around steel bars stretched under tons of load. When the concrete is set, the steel is released from it's load and it contracts on the concrete putting it under a massive compressive pre-load. I imagine this would get the best of the visco-elastic damping at higher frequencies, while also gaining great stiffness and at the lowest frequencies. Trouble is, that isn't so easy in a complex shape.

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[Clive S]

Very interesting. Have you thought about the concrete shrinking and so not adhering to the tube ?

[Tenson]

SBR reduces shrinkage compared with water, so hopefully it won't be a problem. However for my real build I will source expanding cement, or at least 'non-shrink' variety.

You can also get synthetic cement such Polycrete (Granite Resin Mortar) which is supposedly good at damping and really stiff.

https://www.vubaresinproducts.com/epoxy-resin-concrete-repair-mortar.html

[Voicecoil]

Very interesting. Have you thought about the concrete shrinking and so not adhering to the tube ?

You could maybe add a very little bit of aluminium powder? this will cause the concrete to foam a bit.

[Muzzer]

Yes, apparently that's how they make the foam cement bricks and it doesn't seem to take much. I often wondered how they made them.

I guess the resonance you need to damp in a machine tool isn't the ringing of the tube itself but of the structure formed by it. So if you were to stick a large mass (gantry, machine head etc) on the end of said tube and give it a knock, you'd get a much lower resonant frequency as the mass swung back and forth. That's the motion you'd need to damp in a machine tool isn't it? I expect the damping effect of that different structure at the lower frequency is likely to be different.

Nice equipment to be able to play with, not least the analyser for logging and plotting the measurements! Can you do another experiment now, with a mass on the end of one of those beams and the other end anchored? Easier said than done, I appreciate.

[redfedoradog]

Very interesting, I've been doing similar tests on my own build.

Have you tried measuring the loss factor (https://my.mech.utah.edu/~bamberg/research/PrinciplesOfRapidMachineDesign/Principles%20of%20Rapid%20Machine%20Design.pdf)? It's the energy dissipated (as a ratio of initial energy) over a number of cycles. It's used in measuring damping of larger/more complex systems because bolts and bearings are supposed to contribute significant amounts of damping.

I attached a phone IMU to my frame, hit it with a mallet and recorded the acceleration. Not sure if I did it right, I got a value of 0.08 for the assembled frame versus 0.0005 for the individual beams.

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[Tenson]

I did try a measurement with one end of the beam clamped to my drill press and the other end free. I saw the same modes but they were all more suppressed, I assume damped by the clamping interface. This is probably why they use quite thin samples in the industry standard procedure.

When the beams are longer and part of a structure, the resonances will also be lower. The lossy damping will be less effective at lower frequencies. There is less internal friction generated in the structure at lower speeds of vibration. That's why friction welding uses high speed vibration.

One way to improve damping at the lower frequencies is to use constrained damping layers. Outer skin - Damping layer - inner core. However that becomes more difficult than simply pouring a filler in the structure. I also wonder how that would effect over-all stiffness compared to a directly coupled core.

I believe you can calculate loss factor as a ratio of the upper and lower -3dB points on the main resonance before and after damping. However I don't think it will provide any data that can be compared with other info found on the web. My test set up is not industry standard. Also as this test demonstrates a simple loss factor figure only looks at damping of the initial amplitude, ignoring energy storage. EDIT: Although if you calculate energy loss over a number of cycles like you suggest maybe it is more representative than the method I mentioned. I can provide the impulse response if you want to have a crack at it? Maths is not my strong suit.

[redfedoradog]

I can provide the impulse response if you want to have a crack at it?

Yeah sure, send it over. Not sure if we can compare between different test setups, but it can't hurt.

Maybe the best test for hobbyists is to assemble the whole machine, place it where it's going to be used and start whacking it with a mallet? It'll be affected by the floor material, friction, etc but in the same way as when it's running.

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This test was done very similarly to yours and I've been using it as a reference.

[Voicecoil]

I guess the resonance you need to damp in a machine tool isn't the ringing of the tube itself but of the structure formed by it. So if you were to stick a large mass (gantry, machine head etc) on the end of said tube and give it a knock, you'd get a much lower resonant frequency as the mass swung back and forth. That's the motion you'd need to damp in a machine tool isn't it? I expect the damping effect of that different structure at the lower frequency is likely to be different.

The tube resonance (or rather resonances) seems to be of some importance for the gantry at least on my machine, being a "raised sides" design, the long (y in my case) axis seems to be well constrained due to it's large attachment area to the base/bed with multiple fixing points and shows very little vibration even when properly thugging through metal. When the z-axis is in the middle of the gantry it will obviously load it and reduce the frequency of the fundamental resonance however it won't affect the 2nd harmonic much at all, similarly for other positions where it's sitting over a node. I found that damping out the higher harmonics with constrained layer damping was quite easy, the lower ones were less easy which is an issue to my mind as on typical sized machines they can fall into the same frequency range as cutter flute impact frequencies and low harmonics thereof.

[Tenson]

Yeah sure, send it over.

I uploaded the files to a google drive folder. There is an install file for the (free) software to view and analyse the files. The only limitation of the free version is that you can't save.

Once you open the file it will directly display the impulse response. You can zoom vertical and horizontal axis and scroll with the buttons at the side.

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EDIT: Helps if I link the folder! https://drive.google.com/drive/folders/10kElTXKHVxLkhIpGyd-QKREfY40SM_j9?usp=sharing

[Tenson]

Thin Hollow
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Thick Hollow
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Thin Filled
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Thick Filled
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[Bongo]

This is all really fascinating, thanks for sharing! So I made an 8 x 4 machine frame from I beam profile filled with concrete mix (vid of it being made, concrete mix design details etc & it cutting: https://youtu.be/cqYJS27aC4w ) and wish I had made more video recordings of how the concrete changed the vibration characteristics. I actually used a vibration monitor on my smartphone, and had the data, but that phone got hit by a freak flying phone seeking branch when we cut a dead ash tree down :(

I suspect you have seen it, but I haven't seen mention of it here yet: Bamberg's "Principles of Rapid Machine Design" (https://my.mech.utah.edu/~bamberg/research/PrinciplesOfRapidMachineDesign/Principles%20of%20Rapid%20Machine%20Design.pdf) In it he describes a similar concrete-filled tube, but he adds constrained layer damping... Worth a look if you haven't seen it - page 96 on.