Reading a spectrum graph for vibration analysis

Thank you for the replies, but if you don't mind, can you please explain to me why are harmonics important? I mean in this case, the shaft is rotating at 1500rpm, it will not rotate at 3000rpm or 4500rpm, so why is harmonics important, and how does one even measure the amplitude at harmonic frequencies in the 1st place?

And secondly, "why" does unbalanced shaft only have 1x amplitude and not both 1x and 2x? Is there any physical reason for it, or is it just base on experiments?

Thank you!

A very good question!

A perfectly balanced shaft will not generate any vibrations, but as we all know nothing is perfect. The easiest frequency to excite is the fundamental frequency because the least amount of spring constants must be flexed and these springs will have the lowest spring coefficient being the longest shaft lengths. The next harmonic will require twice as many springs to be flexed with shorter, stiffer shaft lengths, and so on.

Now depending on where along the length of the shaft the imbalance resides will partly determine the ratio of the energy distributed to all of the possible frequencies. This is why on a guitar, the closer the string gets picked to the end of the string the more harmonics in the fundamental note exists.

Simarly to the guitar amplifier being able to output the harmonics of the fundamental note, the FFT analysis itself will measure and display the higher harmonics that exist.

Thank you for trying to explain it to me, but I guess I am a bit slow :(

I am still not understanding as to why 2x frequency is important and how did we even managed to measure the amplitudes of the harmonics in the first place since the shaft only stayed at 1500rpm?

And in terms of "it is easier to excite the fundamental frequency", wouldn't it be just because fundamental frequency is at a lower rpm, which mean less rotational force is required etc...? But I still don't understand why or how a misaligned shaft managed to have a amplitude at both 1x and 2x frequency while unbalanced shaft only managed to have at 1x? It felt almost as if it is because misaligned shafts is easier to "vibrate" than an unbalanced shaft, but then I would have thought that misaligned shaft should just have a higher amplitude at 1x frequency...

And another question arise is that if 2x and 3x frequencies are important, why not 2.3, 2.6 or 3.4x frequencies important as well? Even though I can understand that the maximum amplitude will occur at harmonics due to resonance only occurs at harmonics, but that doesn't mean the rest of the frequencies are not important?

Thank you very much for your patience!

Ok, one last try because you're on the edge of an important understanding.

First a little understanding of what and how a FFT analysis works. This is a well understood mathematical analysis of a large collection of data samples taken at a regular interval of time. (All of the data points obtained by a digitizing oscilloscope.)This analysis takes these incremental data points and translate them from a voltage versus time information, into a an amplitude versus frequency display. There are a variety of mathematical limitations and distribution effects that happens when a frequency that actually exists in the data taken does not exactly correlates to a specific frequency that can be displayed but this gets into a very complicated side discussion. The general rules of thumb are that one wants to sample as fast as possible and to use as many samples as possible for reasonable resolutions. The raw mathematics of this process is typically at least a half semester in a undergraduate engineering program. So for now let's just accept that it works.

Now onto why an integer times the driving frequency is so important to examine. The FFT analysis will display the amplitude of all frequencies that exist in your data and not just multiples of the driving frequencies. So the frequencies that are not multiples of the drive frequency are not there because of the driving frequency. There present from another source. So to see if the mechanical driving signal is finding a non-linear load, like a damaged bearing, then one would expect to see more high frequency multiples of the fundamental frequency to appear. This way one can test and ispect the operational quality of the whole machine without a physical teardown and failures prior to becoming a catastrophic failure can be detected.