Vibration is motion, and as with any form of motion there are multiple ways to quantify these values. When I think about cars I am typically interested in how fast the car can accelerate, and what velocity or speed it can get up too. Others may prefer to know the maximum distance the car can travel, or its maximum displacement. These same principles apply to how we quantity machinery vibrations.

When we place a sensor on an instrument, we are typically measuring the accelerations that are occurring at that location. In large turbomachinery, special sensors, or proximity probes, are used to directly measure the distance the shaft is moving. Typical databases and software packages then have utilities that use calculus to convert acceleration to velocity, or displacement and vice-versa. This allows the analyst to look at vibrations in the following terms:

How fast is the equipment shaking at a given location? - Velocity
How fast is the velocity changing at a given location? - Acceleration
How far is the equipment moving back and forth at a given location? - Displacement

Each of these quantities has their own benefit in vibration analysis. The most widely used measurement is velocity. Velocity allows us to directly measure how the equipment is being fatigued, which has direct implications on eventual failure. The standard unit for velocity in the United States is inches per second, or ips. Acceleration is helpful for analyzing higher frequency content, and is a direct indicator of the overall force in a system. Just like on roller coasters and aircraft, we measure this quantity in g's.

Finally displacement, which is not a strong indicator of severity without knowing what frequency the vibration is occurring at. We typically measure displacement in mils, or thousandths of an inch. Let us imagine we have a fan that is moving two inches back and forth. If this fan is moving back and forth one time every few seconds, we may not be as concerned as opposed to if the same distance was being traveled 1,000 times every second. We can imagine that for the fan to move back and forth that fast it must have enormous velocity, which is why we typically analyze vibration data in terms of velocity.