It’s tempting to think vibration isolation is a simple matter of putting a vibration mount between an object and whatever it’s resting on. Anything must be better than no mount at all, right? Actually, it’s NOT always right. In some cases you can create problems by adding a vibration mount to a system. We’ll try to briefly summarize here the basic compromises in implementing vibration isolation.
In its simplest form, an isolated object can be represented as shown in the following figure. The object is rigid and sits on a mount, which has stiffness and damping properties. We are either trying to prevent forces being input to the object (a vehicle engine for example) from entering the structure (car body) or we are trying to prevent motion of a structure (a helicopter for example) from disturbing a sensitive object (an avionics box.)
In either case, the effectiveness of vibration isolation is usually represented by the “Transmissibility,” the ratio of either the Force out to the Force in or the Displacement out to the Displacement in. An effective isolation system has a transmissibility below 1.0 in the frequency range of interest. The relation is the same in either case, as shown below:
The terms r and ζ are nondimensional frequency and the system damping ratio, respectively. Detailed descriptions of these are readily available, but just think of ζ (zeta) as damping and remember that r=1.0 is the mounted natural frequency of the system, the frequency at which the peak response occurs. A graph of transmissibility for a range of ζ is shown below.
Another important quantity to know is the “static displacement” of the system. Placing the object on a compliant vibration isolator causes the system to deflect. This deflection due to gravity can be written as a function of the system’s natural frequency and the gravitational constant, or, , k=the isolator stiffness, g=the gravitational constant, m=the object’s mass.
So what lessons do we learn from this?
- Clearly you have potential problems if the system is excited at r=1.0, the mounted natural frequency. The vibration isolator causes amplification near this frequency for most practical levels of damping. Maybe not so obviously, at ALL frequencies below r=1.0 the best you can possibly do is to cause no amplification.
- Isolation systems are most effective at frequencies well above r=1.0, so we want the natural frequency of our mounting system to be low, below the disturbances we are concerned with. However, the static displacement increases with the square of natural frequency, so as we bring the frequency down we pay a price by letting our mounted object move around excessively. This is the first inherent compromise to be made in implementing vibration isolation. We would love to have a very low natural frequency in our car engine mounting system but we can’t have the engine hitting the radiator and the hood when we go over bumps.
- If we have vibration inputs near the natural frequency, r=1.0, it would be desirable to limit the motion of the system. That can be done with higher damping ratios, zeta (ζ). But you can also see that higher damping results in less vibration isolation at high frequencies. This is a second compromise to be made in implementing vibration isolation.
We’ll talk much more about the detailed considerations in controlling vibration in later posts.