I designed these very simple anti-vibration pads as part of an interesting forum discussion on vibrations resulting from running 3D-printers.

It is my hope, that these pads allow a better understanding of the theory of vibrations through free experimentation. As such, I'll outline a little background on why some things are a really good idea and how very simple means may be used by Makers to improve their set-up in a playfull manner.

At the end of this exploration, interested Makers should have learned:

• Why pavers are beautiful
• Why vibration insulation actually makes your printer bounce around more
• Why soft is better than hard
• Why mass matters (a little) more than damping

And most importantly:

• How to use these to take the next step and move from a Vibration Isolator to a Vibration Absorber

What you'll need:

• A 3D printer (obviously)
• A quarter of a dry roll of TPU 95A or TPU 95A HS to print this simple model a bunch of times using default settings
• A paver
• A wooden board (40X40cm or larger)
• Curiousity

A few words of warning though:

• The Anti-Vibration Pads go underneath a paver, NOT underneath a printer
• Use only TPU 95A or TPU 95A HS for these
• You should use at least four pads per 20kg supported by them
• The pads have only been tested in a relatively cold environment (<10°C): Use more pads if in doubt to counteract material softening
• Long term testing has not been done: You may want to check and maybe replace them frequently if you continue to use them after your experiment
• All experimentation is at your own risk!!!
• Be with your printer when you try this! Both getting it right and getting it wrong leads to movement where and how you may not expect it. You want to be ready to literally give your printer a steadying hand.

Table of Contents:

Chapter 1: Pavers are beautiful

Chapter 2: Becoming Dynamic: The Vibration Isolator

Chapter 3: The Vibration Absorber: From “Magic” to "Real Magic"

Chapter 4: A few short words on damping

Chapter 5: What to expect

Chapter 6: Final note

Chapter 1: Pavers are beautiful

So why are pavers beautiful when viewed through the goggles of vibration theory?

We'll, lets look at a printer. In my case, that is an X1C with AMS on top. It weighs in at something over 14kg (let's call that 15kg for simplicity) while a fully loaded AMS and something on the rear spool holder will add a little less than another 5kg. The print head has an acceleration of up to 20m/s and weighs round-about 150g (I think it is actually 163g but we do not want to be picky at this point).

Schematically, it looks like this:

By adding a paver, we get this:

So in this static model, we can turn an excitation acceleration at the print head of 20m/s² into a response acceleration of 0,075m/s² at the base of our slab of concrete versus a response acceleration of 0,2m/s² for just the printer without AMS and paver.

Note that you do not need to physically bolt your printer to the paver. You will notice if you have an insufficient printer-paver interface if your printer slides and bounces around on the paver. If it does not do this, you are fine with just putting it on top. Inversely, if you have vibration isolators between your printer and the paver, now is the time to remove them as you want the pavers' mass with your printer.

The response acceleration is of course translated into whichever surface the paver sits on as otherwise, the whole system would happily slide across the desk.

However, this location is where we want to isolate vibrations and become dynamic.

Chapter 2: Becoming Dynamic: The Vibration Isolator (Single-Degree-of-Freedom System)

We now place at least 8 Anti-Vibration Pad Mk I's underneath our paver. More if you want to be safer (but less efficient), less only if you have much lighter printers and/or pavers. Simplified, it looks like:

So now that we have finally implemented a dynamic system, we need to understand what it does. The best way to do this mentally is to give the whole system a quick, sharp knock on the head.

Don't do this physically though! A glas top just is not compatible with a hammer.

A Single-Degree-of-Freedom Mass-Spring-Damper system responds like this:

The system responds by an oscillation having a characteristic wavelength with oscillation peaks decaying depending on the damping.

But what happens if disturbances are introduced which do not take the form of a short sharp knock?

Well, fortunately for us, a few very smart people have solved a lot of really “Painful Descriptions of Experiments”, also known as “Partial Differential Equations”, so that we don't have to. Nevertheless, it does require some imagination to follow the translation from the system response in time, to the system response depending on frequency. Literally. The results come in two parts: A “Real” part and an “Imaginary” part. The “Real” part (left) describes how strongly the system responds to a given input frequency. The “Imaginary” (right) part describes how quickly a system responds to a given input frequency.

Before going into what this actually means, it is probably best to explain “in-phase” and “out-of-phase”:

So an “In-phase” response mirrors whatever vibration is put into the system while an “Out-of-phase” response is in the opposite direction.

This explains, why a vibration insulator only really does something above its Eigenfrequency.

Below the Eigenfrequency, the system acts pretty much statically. Which underscores that:

• Our simplification in Chapter 1 is actually rather helpful
• For low frequency attenuation, we only really have mass to play
• Concrete pavers truly are the prom queens of the vibration ball

So what does this mean for the members our vibration insulator?

Looking at the Real part of the system response, we can see that the only dynamic isolation occurs above the Eigenfrequency. So we want that as low as possible to affect as much energy as possible.

Therefore, for vibration isolation, we want:

• The softest possible spring (while still keeping the printer, AMS and paver safely upright)
• The highest sensible (!) mass
• Some damping (we'll get to that later)

Keep in mind that in this model, we did not actually magically make energy dissapear. That is not possible. While some energy is taken up, converted and dissipated by the dampener, the majority is just kept from travelling through the insulator. It is instead kept in the printer.

That is why mounting a printer on springs will actually increase its own vibrations. It can no longer dissipate these into the surface it is standing on.

That was the tough part. It get's easier from here on. There are still a few Anti-vibration pads left over and we have not yet touched upon your real reason for reading through this saga.

Chapter 3: The Vibration Absorber: From “Magic” to "Real Magic"

It is at this point, that a lot of vibration discussions end, as attention is focussed on the dampener. Indeed there are many different ways in which a dampener can extract and convert energy from the system. Pneumatic, hydraulic or just by using internal friction to generate heat. Unfortunately, this means that an easy solution is often overlooked:

• You can easily convert some of the vibration energy back into kinetic energy

The schematic for the required Two-Degree-of-Freedom System is:

All you need to build this yourself are a few extra Anti-Vibration pads and a board to add some mass. You'll also want to make sure that all Anti-Vibration pads are on the same surface and in the same orientation everywhere. And of course use at least 4 per 20kg in each layer. Otherwise, there's no telling what system you have actually built.

Sounds, daunting?

It shouldn't be. It's as simple as that:

This type of kinetic Vibration Absorber will not eliminate all vibrations. It will also not magically stop your printer from vibrating. But it can make your life quieter and more peaceful (by dissipating neighbours reasons for banging on your floor or wall) or extract some vibrations that would interfere with your other printers.

By varying the mass of (or on) your Vibration Absorber board and changing the number or even the type of your Anti-Vibration pads, you are able to further tune your Vibration Absorber system.

Just do not do what I did on my first attempt: Adding mass to my board asymmetrically, I accidentally collapsed half my pads. Make sure you use enough pads to avoid collapse while keeping your spring stiffness low.

Chapter 4: A few short words on damping

So far, we did not really think much about damping as it is of surprisingly minor significance to the tuning of the Vibration Isolator and the Vibration Absorber.

Increasing damping will lower the peak response at and around the resonance frequency as well as slightly lowering the resonance frequency. The latter may point towards a desire to absolutely maximize damping, but that is unfortunately a misconception. To understand why, we need to look at the time response of a Single-Degree-of-Freedom system again.

Obviously, we do not want our system to ring like a bell. So we do want to have an underdampened system. However, if we have too much damping, our system will take ages to return to its origin, rendering it significantly less effective. Ideally, we want damping to allow only a very slight overshooting of its equilibrium state.

Chapter 5: What to expect

What can be expected from the Vibration Absorber experiment is very much dependant on what is put in:

• Printers which already benefit from the very effective Active Vibration Control directly at the source (such as the A1 and X1 series at the time of writing) do not actually have much of a problem to be solved. Nevertheless, I was able to feel my DIY Vibration Absorber doing its job. And using half-filled glasses of water (careful, do not spill (!!!)) as magnifiers, a possitive effect can be visualized even for these advanced set-up's.
• Printers which do not (yet) have Active Vibration Control will evidently benefit much more from this approach.

Also, the expert use of vibration theory is clearly observable in the industry and in particular by Bambu Labs. Eigenfrequency determination during z-homing, Anti-Ghosting and of course the Active Vibration Control directly at the print head are a testament to their expertise. As such, and without actually owning them, my personal expectation is that it would be very difficult to actually improve on the specifically designed Vibration Isolators for the X1/P1.

Except for:

• using more of them firmly fixed underneath a paver rather than underneath the printer
• and also using them for the Vibration Absorber.

Since that is a bit costly, you may want to first try this model to build and tune your own vibration absorber.

Chapter 6: Final note

• If you have found this experiment helpful, for example for your own vibration isolator or vibration absorber designs, I'd appreciate a link and mention.
• You are of course free to remix the pads. Just make sure the remix is not trivial but actually meaningful, thought-out and functional. So please do not just change dimensions but actually create something with additional or better tuned functionalities.
• Regarding print profiles, just use default settings. And please do not upload profiles that exceed default speeds and accelerations. It may be safe for you, but you do not know that it will be safe for a Maker with a different set-up. And you certainly do not know where the human acceptance thresholds of individual Makers are when pushing them over default settings.