How to separate mixed signals, 3 identical gears meshing together
Yes it would make sense to analyse the sound of the vibrations without the gear interactions if you can, and then delete that sound profile from the overall sound using a noise remover that works with a sample of the noise only prior to the noise + recorded signal. You should say roughly what frequencies you expect from the gears based on the RPM and number of teeth, because it affects analysis methods. On this and many other programs there is "noise reduction using noise sample profiling" http://wiki.audacityteam.org/wiki/Noise_Reduction it is tremendously efficient.

There are no obvious correlations or patterns in the graph, it is true. Read about engine vibration analysis. I found a paper on engine sound graphs when i was researchign SPWVD, and indeed it is 100ds of times more precise than FFT and pseudo smoothed wigner ville distribution makes waterfall graphs which show the clearest patterns of sound that are physically measurable.

To seriously analyse your vibrations, you should not use coarse FFT, instead use pseudo smoothed wigner ville distribution which is available as an addon. this program can do it too, see the graphs: http://www.christoph-lauer.de/sonogram