We can tell from the spectrum it is a 2-pole motor. Focusing on the failures, it may be helpful if you can explain:
1 - bearing type (sleeve or anti-friction, and if anti-friction what type)
2 - horizontal or vertical motor
3 - lubrication (oil or grease, and preferably identify the type)
4 - Driven equipment. And is it a high-temperature such that thermal growth is expected.
5 - intermediate equipment (coupling type, presence of belts or gearbox)
6 - Do the failures occur while coupled or uncoupled?
7 - roughly how many horsepower (probably not important to the question, but it's difficult to visualize the machine if we don't know if it is 1hp or 10000hp)
8 - vfd present?
9 - what do the bearings looks like after the failures.
10 - If ball beairngs, is it an inboard-fixed and outboard floating arrangement, or is it a cross-locating arrangement. With cross locating arrangement when uncoupled (and tagged out) you can move the shaft noticeably, perhaps 1 / 16". We have similar symptom on cross-locating bearing motor... haven't quite figured it out yet.
Assuming these are deep groove ball bearings, there are a number of possible causes for these sidebands:
A - Lack of preload on the bearings such as from no wavey washer or improperly sized wavey washer.
B - Process oscillation at the sideband frequency (approx 10hz).
C - machine mounted on flexible base with resonant frequency similar to sideband frequency (10hz). I don't know why this occurs, but I have seen it.
D - Series of running-speed/multiple-running-speed sidebands around BPFO and aournd BPFI that masquerade as sidebands around running speed. Remember BPFO and BPFI always add up to a whole number (the number of rolling elements), so if BPFO is 0.2 orders above a running speed harmonic, then BPFI is 0.2 below a running speed harmonic and the series of 1x sidebands around these peaks can look like 0.2 sidebands around running speed harmonics. For example 8-ball bearing with BPFO=3.2, BPFI =4.8, you can have series of peaks (in orers)
0.8X = BPFI-4X
1X = 1X
1.2X = BPFO-2X
1.8X = BPFI=3X
2X = 2X
2.2 = BPFO-1X
2.8X = BPFI=1X
3X = 3X
3.2 = BPFO
3.8X = BPFI-1X
4X = 4X
4.2 = BPFO+1X
As you can see, it looks like a series of 0.2x sidebands around 1x, 2x, 3x, 4x etc, when in fact it is 1x, 2x, 3x plus series of running speed/multiple-running-speed sidebands around BPFO plus series of running speed/multiple-running-speed sidebands around BPFI. It is easy to tell the difference if you put the spectra on log scale and examine all the peaks to fit them into a pattern. For example in the above case if it is actually bearing frequencies, then we expect to see 2*BPFO = 3.6X and 2*BPFI = 10.6x also showing up. If those frequencies don't show up even on a log scale, then you can throw this scenario (D) out the window.
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(2B)+(2B)' ?