NOTE: for a quick read, skip ahead to where it says “Here’s How” below…
At KCF, we are passionate about eliminating needless machine failures, and vibration is our best tool. A practical problem that often comes up is this: how much is something vibrating, in a way I can understand? Displacement (distance traveled by an object, in time) is something we can all understand: how many inches is my something vibrating, where something can be a pipe, a motor, a pump, a fan, a beam, ceiling, floor, etc. There are sensors that measure displacement directly, accelerometers, especially wireless accelerometers, make it much easier because we can mount externally on a machine with a magnet.
With software and a simple calculation, you can use the accelerometer measurement to calculate the displacement, and get an accurate estimate of how many inches (or milli-meters for our Canadian and European friends) something is vibrating. The fundamental equation for vibration, or any oscillating motion is:
In a simple oscillating vibration, A (t) = A1cos(f1*t) + A2cos(f2*t) + … (where A1 is the amplitude at frequency f1, etc.)
By integration, the velocity, V (t) = A1/f1*sin(f1*t) + A2/f2*sin(f2*t) + …
Integrating again, displacement, D (t) = A1/f21*cos (f1*t) + A2/f22*cos(f2*t) + …
But fortunately, the software does most of the work for you, and it’s much easier to get a rough estimate, especially when you have one dominant vibration frequency.
1) Use the software to find the peak velocity at a given frequency (inches/second). NOTE: The software has already integrated to convert acceleration to velocity.
2) Identify the frequency of that peak (RPM)
Example: we had a customer recently in a well completion operation, and they were seeking to know the amplitude of vibration of a high-pressure pipe. They were using a practical and proven method, duct-taping a sharpie to the pipe and duct-taping a piece of cardboard to the adjacent structure. A great practical solution, and it answered the question, but there is an easier way! Just follow these steps:
1) Peak Velocity = 15 in/s (it was a high-amplitude application)
2) Identify the frequency of the dominant peak = 943 RPM (15.7 Hz)
3) Displacement = 10 X 15 / 943 = 0.15 inches.
Answer: the pipe is vibrating a little more than 1/8th of an inch. It’s not exact, but it’s accurate enough to be very useful and answer a question, and it doesn’t require duct tape!