Although vibration dampers are among the most used systems for vibration reduction, their operation and application methods remain largely misunderstood by non-experts. Vicoter is a company specialized in field measurements and tests and it often finds itself in the position of assessing the need to use antivibration mounts or verifying the effectiveness of those already in use.
In the following article, you will understand how the synergy between design and knowledge of the dynamic behaviour of the equipment is essential for properly sizing a vibratin damper device that can effectively perform its job without unexpected issues. You will see how knowing the frequency range in which the apparatus to isolate operates is a crucial requirement for selection and how the stiffness of the elastic mount is the key parameter for everything to function optimally. With numerical examples, you will verify how low frequencies are the most challenging to isolate and how overly rigid dampers are often completely ineffective.
Do you want to know why? Keep reading…
Anti-vibration devices can be found in a wide range of applications: from airplane engines to hydraulic presses, from bulldozer cabins to home air conditioners, from hydraulic pumps to special packaging. Yet, they all operate based on the same principle.
Figure 1. Examples of damper installations tested by Vicoter.
Contrary to what many believe, vibration dampers are not designed to dissipate vibrational energy by converting it into heat through the hysteresis cycles of rubber. In fact, to be precise, anti-vibration devices do not dissipate energy at all! As proof of this, there is an entire category of dampers made exclusively of metal, which, as is well known, exhibit a perfectly linear behavior.
Figure 2. Examples of commercial anti-vibration mounts. Rubber (left), metallic spring (central) and metallic wire rope (right) mounts.
The true purpose of using vibration dampers is to reduce the transmission of vibrations from a device that generates them—let’s call it the “source” (e.g., a home air conditioner)—to a structure that receives them, which we’ll refer to as the “receiver” (e.g., the house wall it’s mounted on). The effectiveness of a damper lies in its ability to isolate the receiver from the source, but it happens only above a certain frequency.
For a vibration damper to work, it must be physically placed between the force-generating source and the structure where vibration needs to be minimized. Additionally, a crucial point to remember is that there must be no alternative transmission paths between the two (e.g. rigidly mounted pipes); otherwise, the damping system (and the money spent on it) would be rendered useless.
But how does an anti-vibration device physically reduce the oscillations of the receiver?
To understand this, we need to turn to a bit of mathematics and the most beloved (and often overused) model among structural dynamics experts: the single-degree-of-freedom (SDOF) mass-spring-damper system.
To avoid confusion, let’s clarify from the start that real-world situations are slightly more complex than what we are about to explain. However, if the following two assumptions hold, our simplifications remain accurate:
- The system behaves as a rigid body, meaning it can be represented as a simple mass because its stiffness is sufficiently high. In technical terms, the first natural elastic frequency of the body is much higher than the frequency introduced by the anti-vibration device, causing the two behaviors to be decoupled (but since this is an explanatory article, we’ll keep it simple.)
- The six degrees of freedom of a rigid body can be treated separately, meaning that analyzing one at a time does not affect the generality of the solution.
In most practical cases, the problem falls into one of these two scenarios:
- You want to reduce the vibrations transmitted to the floor (receiver) by an operating machine (source), such a pump positioned exactly on the rooftop of the CEO’s office.
- You want to reduce the vibrations transmitted to a device (receiver) by the floor (source), such as your new high-end turntable worth tens of thousands of euros in your living room—unfortunately, your house is right next to a subway station, and the needle keeps skipping.
In both cases, we assume that the magnitude (and frequency) of the forces—whether they are the loads generated by the pump in case (1) or the floor oscillations in case (2)—are beyond your control, meaning you cannot relocate or reduce the source in any way. (After all, who would put a pump right above the CEO’s office if it’s not indispensable in other case?)
The only viable solution, then, is to block the vibrations using dampers.
Case 1. Reduction of vibrations transmitted to the ground
The simplest model to understand how an antivibration device works is the mass-spring system. Although damping is present, it is small compared to the other forces at play (trust us!) and only comes into effect near the resonance frequency—so we can safely ignore it.
Figure 3. Model of a SDOF mass-spring system (left) and force equilibrium (right) for an imposed force.
Let’s model the pump generating the force as a mass, M, and the anti-vibration device with its stiffness, K, as a simple spring. We call F the load generated by the source, which, without losing generality, we can assume to be sinusoidal (think of a slightly unbalanced fan—classic case!). If the system operates at different rotational speeds, as we’ll soon see, the lowest one is the most critical to consider.
From the equilibrium of forces acting on the mass, we obtain the well-known equation that brought in the Fourier domain and manipulated opportunely, derives the Frequency Response Function (FRF), which expresses the ratio between the absolute displacement of the mass and the input force as a function of frequency:
where ω represents the angular frequency, i.e., the frequency multiplied by 2π.
However, our real concern is reducing the force exerted on the ground. This force corresponds to the reaction transmitted by the spring to the ground (our model makes this clear!). Since this force is simply kX, we get:
which qualitatively follows the trend shown in Figure 4.
Figure 4. FRF of transmitted force on input force of a SDOF mass-spring system.
Now, let’s interpret what our calculations have revealed. Introducing anti-vibration mounts between the equipment and the floor creates a resonance that wasn’t present when the source was rigidly connected to the ground (that nice, undamped peak clearly visible in the diagram …). The frequency of this mode is determined by the mass of the object and the stiffness of the isolators, and it can be adjusted by varying the latter.
Thanks to inertia forces, at frequencies higher than the resonance, the amplitude of the transmitted force decreases—an immediate benefit in terms of perceived vibrations. A well-designed vibration suppression system is therefore based on understanding how the source operates and ensuring the dampers are flexible enough to create a clear separation between the two frequencies at play.
But what happens if we choose isolators that are too stiff for our application?
To understand this, let’s compare two cases: one where softer anti-vibration mounts are used and another where stiffer ones are selected—represented by the black and red lines in Figure 5, respectively. At the extreme, we could imagine the original scenario where the system is bolted to the ground as the case where the dampers have an infinite stiffness.
The stiffer the isolator, the higher the resonance frequency and it’s possible that this frequency surpasses the operating frequency of the equipment—well, let’s just say you don’t even want to think about what happens if the two frequencies coincide (but remember, Murphy’s Law is always lurking!). If the resonance exceeds the source frequency, Figure 5’s red line makes it painfully clear: the force transmitted to the ground remains unchanged. And there you are, after confidently assuring your CEO that their office would return to its peaceful, vibration-free state…
Figure 5. Comparison of the transmitted force for soft (black) and hard (red) stiffness of the dampers.
So, all we need to do is choose the softest anti-vibration mounts available on the market, and we’re done, right?
Hmm… unfortunately, no. As the saying goes, there’s no rose without thorns, and just like in many other things, the solution here isn’t so simple.
The price to pay for reducing the vibrations transmitted to the ground is the increase in the oscillations to which the source (our operating machine) is subjected. Now, the machine will vibrate on its supports, which have become elastic.
Let’s examine Figure 6, which shows the displacement of the mass as a function of frequency in the two cases: when softer (black line) or stiffer (red line) vibration dampers mounts are installed. The curves speak for themselves: the lower the resonance frequency, the greater the displacement of the body (after all, we’ve done everything to make it move and generate inertia forces in counter-phase with the input force!).
Thus, the two factors—low resonance frequency and limited displacement—are in opposition to each other. Although sometimes using a foundation might be a solution, increasing the vibrating mass allows the resonance frequency to decrease without reducing stiffness, generally a compromise between the two is the only possible approach.
Figure 6. Comparison of the source displacement for soft (black) and hard (red) stiffness of the dampers.
Case 2. Reduction of vibrations transmitted from the ground to an apparatus
In this second case, the situation is reversed compared to the previous one, but the factors at play remain the same. The floor is vibrating and the goal is to prevent these oscillations from reaching an object that needs to remain stationary in order to function properly, such as a microscope on a table. The mass-spring model can still be used to model the problem, but now it takes on a new form.
Figure 7. Model of a SDOF mass-spring system (left) and force equilibrium (right) for an acceleration imposed at the base.
Indicating with xm and xb the absolute displacements of the body to be isolated and those of the base, from the equilibrium of the forces acting on the mass, we get:
By bringing the problem into the frequency domain and performing the appropriate transformations (which I’ll spare you this time), it can be written as:
Figure 8. FRF of absolute displacement on base displacement of a SDOF mass-spring system.
The behavior of the curve in Figure 8 is the same as the previous one, but on the y-axis (it’s worth pointing this out…) the ratio between the absolute displacement of the receiver and that of the base is shown. Everything works as seen before: the displacement of the mass is smaller the greater the distance between the oscillation frequency of the floor and its natural frequency. A low stiffness of the antivibrators is therefore also positive in this case, as it reduces the absolute vibration of the body, while overly rigid dampers could be useless.
The downside of this solution, however, is the increase in relative displacement between the floor and the apparatus, shown in Figure 9. If the receiver is connected to other machinery that does not move with it, this can lead to damage and breakages if the joint is not sufficiently flexible.
Figure 9. FRF of relative displacement on base displacement of a SDOF mass-spring system.
Even from this brief information, where issues such as the stability of the apparatus, static strength of the vibration dampers, deformation under load, environmental compatibility, etc., have been omitted, it should be evident how the choice of antivibrators varies from installation to installation. The correct sizing of the vibration dampers requires knowledge of the operating frequencies of the source, otherwise the adopted solution will be ineffective, and there is also the possibility of using products calibrated for each specific need.
Vicoter has been working for years in the vibration suppression sector, boasting numerous successful cases. They provide a comprehensive service that starts with field vibration measurements and covers the choose, implementation and verification of the adopted intervention. Thanks to their proven expertise and experience, clients can rely on them for a solution that best meets their needs.
Read more about the activities that Vicoter performs in the field of vibration test on our page: Vibration test .
