How Vibration is Measured: A Look at Sine Waves, FFT, and More

Machinery vibration continues is an indispensable tool for knowing the condition of machine components.  While analyzing vibration can sometimes be complex, understanding the basics of what a vibration signal is can simplify the process.

Taking a vibration measurement on equipment typically requires two components – an accelerometer, and a device, such as a vibration analyzer to process and display the data. Accelerometers are made up of a mass, which moves within a coil.  The movement comes from the accelerometer being mounted to the machine, and from the machine moving due to vibration.  The more movement, the more voltage, and the higher the level of vibration. In its simplest form, an accelerometer is a device that generates a voltage.  

The analyzer displays:

• The amount of voltage, typically displayed as either displacement, velocity, or acceleration.  The amount of voltage, and the sensitivity of the accelerometer, determines the amplitude, or severity of the vibration.
• The rate of change in the voltage determines the frequency of the vibration, in essence, how many times per minute (or second) the voltage is generated.

Let’s use an unbalanced, belt driven fan as an example.  If we mount the sensor (connected to an analyzer) to a fan bearing, and start the unbalanced fan up, the sensor will generate a voltage:

• The amount of voltage, which would give us the amplitude, or how much vibration is occurring,
• The rate of change of the voltage, which would tell us the frequency of the vibration, or how many times a minute (or second) the change occurs.

The fan would vibrate at one time per revolution.  This would be a simple sine wave.  But there’s more!

The motor probably operates at a different speed than the fan.  The belts have a different rotational speed as well.  Each of these would also have their own frequency and amplitude of vibration.  If the fan had a damaged bearing, the bearing itself would generate a vibration, which would be picked up by the sensor.  A bent fan shaft might generate a different signal than an unbalanced fan.

Pretty soon, we have a complex sine wave.  Measuring this in the time domain can be complicated.  But measuring in the frequency domain can simplify the signal.

As opposed to a time domain signal, where amplitude is displayed versus time, a signal in the frequency domain (often called an FFT) would display amplitude versus frequency.  Each peak in the frequency domain would represent the events occurring in, and processed from, a time signal.

A vibration analyst (or automated diagnostics software)  will analyze these signals, knowing the fundamental frequency (running speed of the machine components) to determine the condition of the machine, and its components.

The fan speed is 555 cpm.  So we can use a cursor to mark the running speed of the fan. 

The frequency of the vibration peak is 555 cpm.  The amplitude for each direction (vertical, horizontal, and axial) is defined by the scale (to the left, and amplitude levels are displayed in the boxes on top.

Axial = 0.062 inches per second

Horizontal = 0.079 in/sec

Vertical = 0.064 in/sec

On the same spectrum, we can use a cursor to mark the running speed of the motor (1770 cpm).

Axial = 0.164 in/sec

Horizontal = 0.087 in/seec

Vertical = 0.143 in/sec

This cursor marks a vibration at 7200 cpm, or 120 Hz.  In the US, electrical current is typically on a 60 Hz cycle.  So this peak marks the vibration in the motor due to electrical current ( 2 x 60Hz).  

Axial = 0.026 in/sec

Horizontal = 0.176 in/sec

Vertical = 0.046 in/sec

Based on the frequencies and amplitudes of each peak, the analyst may determine that:

• The fan is well balanced
• The motor is in fair balance condition 
• But the vibration at 60 Hz (from the electrical current) might be questionable.
• The lesser peaks (not marked) might be from duct vibration, looseness, belt-induced vibration, etc.  

The analyst or automated diagnostics would examine each of these peaks, based on the running speed of the equipment, to determine if any other faults (such as a bearing problem) are present.