About this 3D model

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 g