Don't Be Decieved By Vibration Amplitude

By: Tyler Faucett, MSME; Mechanical Engineer

All too often when performing routine vibration analysis or condition monitoring, the one thing everyone wants to know is the vibration amplitude.  This, of course, is because amplitude is directly related to machine condition and fault severity, right?  Well, not quite.  When we collect vibration data on machinery with a case mounted accelerometer, the accelerometer is measuring the response of the machinery to the input forces.  In between this input and output is a complicated system with unique stiffness, mass, and damping properties that will dictate how much response amplitude will be measured versus how much force was inputted.  This relationship between input and output is usually referred to as a transfer function.  It is the ratio of input to output amplitude with respect to frequency.  If all system properties were known, then we could solve for a transfer function which would allow us to calculate the amplitude of the input force which, in turn, caused our corresponding response amplitude.  In the real world these parameters are not known and are, more often than not, difficult to extract.

As a result, the knowledge of the output response amplitude does not give the analyst knowledge of the total severity of input force. To say that a machine has a severe unbalance or misalignment based exclusively on the amplitude of the running speed vibration is not good practice. In order for this kind of statement to have any merit, the vibration amplitude caused by a known unbalance or misalignment on that machine must be known.

Since the transfer function is a frequency dependent ratio of input to output, it is possible to know that there is more force at a given frequency than there was previously.  That is to say more input force will always give more output response, but how much more is not known.  This is why the first steps in a dynamic balancing routine are to take an original amplitude and phase reading, then apply a known force in the form of a trial weight.  The difference between the original reading and the reading after the trial weight was applied gives us a transfer function between input force and output response.  This is only a single value known as the influence coefficient.  To fully understand the amplitudes shown in our collected response spectra, we would need influence coefficients for all frequencies at all collection points, and at all force input locations.  As stated before, the system parameters are difficult to extract.  In general it is only done mathematically for a system with a low number of degrees of freedom.  Shown below is a transfer function of input displacement to output displacement for a simple single degree of freedom, mass, spring, and damper system.  If the mass, stiffness, or damping of this system were to be changed this curve would be changed as well.

There are, however, times when we need to make sense of a system with a large number of degrees of freedom.  In this case, we can utilize modal testing to extract these system parameters and determine a transfer function for the points of interest.  With modal data it is possible to discern the true cause of the high amplitude vibration response.  It may be from a high input force or a magnification through system properties.

As you can now tell, amplitude is only one piece of the puzzle.  Without more information, its usefulness is questionable.  There seems to be a common tendency today to rely solely on amplitude to diagnose or evaluate machinery.   Hopefully a high amplitude reading will not be the end of analysis but will serve as a starting point.

Pioneer Engineering has extensive experience with collecting and analyzing vibration data, and performing modal analysis. We look at the whole picture the data provides to give our customers the best possible answers to their problems. For more information on how our team of vibration experts might be able to help you, please contact us at 970-266-9005 or here.