Reciprocity: vibration isolation works the same, regardless of which way you look

Last month, I wrote about vibration isolator frequency, and why we have to pay attention to it when isolating rotating machinery (especially in highly-sensitive settings). That discussion centered around the notion of tuning between the spring and the machine it supports. This explains why -- in vibration-sensitive labs and fabs -- neoprene mounts are probably a terrible isolator choice for a 900RPM fan. Here, the isolation frequency is too close to the primary fan vibration frequency; they're "tuned" to each other, and the isolator acts like an amplifier instead of an attenuator.

It's worth pointing out that other tunings can happen, too. And they can be equally problematic. Not only can the isolator be tuned to the machine frequency; the system could also end up tuned to the natural frequency of the structure itself. 

You can think of these systems from two different directions. That earlier post looked at the machine isolation problem of a vibrating payload isolated from a sensitive structure. Now, however, let's invert the problem and say that the structure is the vibration source while the payload is sensitive; imagine an optical microscope sitting on a lab bench. The Principle of Reciprocity insures that all the same concepts apply to both.

Isolation systems act the same, whether you're trying to isolate the building from the payload (like a pump) or trying to isolate the payload from the building (like a microscope). If you understand one, then you'll understand the other. You can thank Maxwell for figuring this out.

In our microscope isolation system, the same kind of problematic tuning can arise. If the structure's natural frequency matches the isolated system's natural frequency, then we're going to have problems.

Imagine that you're installing a microscope in a lab, and you choose mounts that result (via pad stiffness and microscope mass) in a 12Hz system resonance. That means that if you bump into the microscope, the entire isolated system will "ring," bouncing back and forth 12 times per second. What if the laboratory is on an upper floor of the building, and the structure -- unbeknownst to you -- also exhibits a natural frequency at 12Hz?  

Every time someone walks by, that 12Hz floor resonance is going to get excited greatly; since your isolation system is itself tuned to 12Hz, all that vibratory motion very efficiently finds it way into the microscope. In fact, those vibrations will end up getting amplified rather than attenuated, and your images are probably going to get a lot worse. The same thing would happen even if the frequencies aren't so perfectly aligned; the common wisdom is that the frequencies have to be separated by at least 40% to avoid strong interaction. 

So, even when you're isolating microscopes rather than machines, frequency still matters. I didn't choose 12Hz randomly; that's a common number for rubber-type mounts, and it's also common for vibration-designed laboratory floors. So, this isn't just a theoretical risk.

Everything has a natural frequency: the structural floor, the lab bench, the vibration-isolated system. Even the microscope itself has internal resonances; these are the reason why the instrument is sensitive to vibrations in the first place. And when it comes to vibration isolation, allowing these resonances line up (in frequency) is usually not what we want.

Machine vibration isolation failures

I've been writing a lot recently about machine vibration isolation, and it occurred to me that it might make sense to bring out a review article I wrote on failures in isolation systems.

I originally wrote this for a conference in 2010, and it ended up in Sound and Vibration Magazine as "Small Deviations and Big Failures in Vibration and Noise Isolation". It's still relevant, and it takes a high-level look at problems at all points, from concept design to isolator/hardware selection, to fabrication and installation. And while it's written from the perspective of high-end laboratories and imaging suites, the concepts are broadly applicable.

Part of what's vexing for machine isolation is the sheer number of options, and the fact that machine vibration impacts evolve over time. In contrast to the structural vibration design (for which there are only so many kinds of steel and concrete materials, concepts, and techniques), machine vibration isolation is heavily product-driven and sensitive to installation variability. And while that structure doesn't much change over the years, rotating machinery encounters wear-and-tear while isolators don't always stay in alignment. 

It's no surprise that all isolator products are not created equal; quality and performance can vary considerably from vendor to vendor. What might not be obvious, however, is the degree to which "robustness" matters in the face of realistic installations. Many isolator concepts and products work very well in principle, but age poorly or demand impossibly-perfect installation conditions / workmanship. Since we want the building to work well not only at startup but also many years into the future, it makes sense to pay attention to these issues.  

Anyway, take a look at that article if you're interested in good machine vibration isolation. And if you want to bounce some ideas off of me, note that the contact information given in that paper is now out-of-date.

Why vibration isolation frequency matters

I've written a lot about the isolators that we make use of on vibration-sensitive laboratory projects (including the variety of ways that things can go wrong). These are supports like the big steel-coil springs that you've seen pumps and fans sitting on:

Above: an unhoused steel spring from Mason, which I just learned can be purchased on Amazon, of all places (sadly, it's not eligible for Prime).

If you are mechanically- or electrically-inclined, it's natural to think of these elements as presenting an impedance discontinuity at the support. That means that some frequencies "reflect" off of the discontinuity, their energy (mostly) doomed to stay trapped in the machine instead of spreading into the building. However, that also means there are some frequencies at which the spring is acting as an impedance-matching element, and it actually helps (rather than hinders) the transfer of vibrational energy into the structure. That's what's happening at the resonance, and it makes matters worse instead of better.

This is why we are usually leery of neoprene-style isolators in highly vibration-sensitive settings like nanotech labs or buildings with high-end imaging suites.

Most neoprene mounts are 12Hz (or so) isolators. Remember, though, that a "vibration isolator" only isolates at frequencies above 1.4x the spring resonance. And all isolators of this sort provide more attenuation at higher frequencies, and less attenuation at lower frequencies. That means that neoprene is great for acoustical problems: a 12Hz isolator might provide attenuation for frequencies as low as 17Hz (12 x 1.4). That's well below most people's range of hearing, and it's operating pretty well by the time you get up to the frequencies that people hear easily.

But a 12Hz isolator isn't helping much on any machine operating below about 1200RPM, and it's actually amplifying vibrations from slower machines. 

Above: a quick comparison of vibration isolation effectiveness for a double-deflection mount and an unhoused steel spring. In general, these isolators perform better at higher frequencies and worst at lower ones. The neoprene mount is fine for many applications, but when you need a lot of attenuation or have intense vibration sensitivities, then it's hard to beat springs.

That's right: if your fans run at 900RPM, you might be better off just bolting them directly to the structure rather than using neoprene. The neoprene might reduce some of the audible (higher-frequency) fan noise, but it's only making structural vibrations worse. And remember, lots of systems these days run on VFD, meaning that your 1800RPM fan might sometimes operate at 900RPM when demand is low.

So when your vibration consultant tells you that he or she really thinks you should use springs instead of neoprene pads for something, there's probably a reason! Frequency matters, and it's actually possible for the wrong kind of "isolator" to make building vibrations worse instead of better.

We need a better word than "isolator"

Most of our projects depend on liberal application of vibration isolation systems on mechanical equipment. Especially in nanotech labs and other high-tech settings, you simply can't throw enough concrete and steel at the problem. It's far better -- and far cheaper -- to just minimize the vibrational forces that get applied to the structure in the first place. 

But it bears repeating: resilient-support isolation systems can't eliminate vibrations. At best, they can only only reduce vibrations. Critically: the effectiveness of vibration isolators depends on frequency. In fact, they actually make matters worse if mis-applied.

This means that the exact same "isolator" that works great in one application might be worse-than-useless in another. That's right: your isolator can become an amplifier if you're not careful.

The plot below shows the force transmissibility of a simple spring vibration isolator system, something like the free-standing springs that you often see base-building machinery (like pumps, fans, and chillers) installed upon.

Isolation transmissibility curve for a steel spring with 1" static deflection, which works out to be a 3Hz isolator. Note that the x-axis is shown both in Hz and the equivalent RPM. Of course, this is somewhat simplified; real springs don't perform quite so beautifully at high frequencies. 

Here's how to read the above plot: "transmissibility" is the ratio of output force to input force. Above, we've expressed this in decibels, but you could use decimal notation too. The "input" is the force produced by the machine, like the imbalance force that shows up at the shaft speed. This gets applied to the top of the spring system. The "output" is the force that shows up at the bottom of the springs and gets applied to the building structure. 

Positive numbers (in decibels) mean amplification and negative numbers mean attenuation. Zero dB means that there's no change: the output force is the same as the output force. At the very lowest frequency (0Hz), nothing is moving, and the transmissibility tends to zero decibels. This should be obvious, since all of the static weight of the machine gets transmitted to the floor. At high frequencies, the transmissibility is negative: the output forces applied to the floor are lower than the input forces generated by the machine. This is the attenuation we were looking for. But between the two, around the spring resonance, we actually get amplification. Just how much amplification depends on the damping in the system. As a practical matter, isolators are only useful for frequencies well above the spring frequency times the square root of 2.

Now, there's a ton of ways that machine vibration isolation can go wrong, but I think it would help if we at least had a better word for these systems. When you hear "isolator" it's easy to forget that these systems just don't isolate at all frequencies.