An FFT spectrum from an accelerometer looks intimidating the first time you see one — a forest of peaks at frequencies that mean nothing until you know what to look for. In practice, most of what you need comes from three numbers: the machine's running speed, its bearing geometry, and how many peaks line up with multiples of those two.

Start from running speed, not the highest peak

The instinct is to chase the tallest peak in the spectrum. The right first move is to mark the running speed frequency (1x) and its harmonics (2x, 3x...) instead. Unbalance shows up almost purely at 1x. Misalignment typically shows strong 2x and sometimes 3x content. Once those are identified and explained, whatever peaks are left over are the ones worth investigating.

Bearing fault frequencies aren't a guess

Ball bearings have four well-defined characteristic fault frequencies — for the outer race, inner race, rolling elements, and cage — computed directly from the bearing's geometry (ball diameter, pitch diameter, contact angle, number of rolling elements) and the shaft speed. They're not harmonics of running speed, which is exactly what makes them identifiable: a peak that lines up with a calculated outer-race frequency, with no obvious relationship to 1x or 2x, is a strong signal, not a coincidence.

For a bearing with $n$ rolling elements of diameter $B_d$, pitch diameter $P_d$, contact angle $\phi$, and shaft rotation frequency $f_r$, the outer and inner race fault frequencies are:

$$BPFO = \frac{n}{2} f_r \left(1 - \frac{B_d}{P_d}\cos\phi\right) \qquad\qquad BPFI = \frac{n}{2} f_r \left(1 + \frac{B_d}{P_d}\cos\phi\right)$$

The $(1 \mp \cos\phi \cdot B_d/P_d)$ term is the whole reason these frequencies are non-integer multiples of running speed — it comes from the rolling elements orbiting the cage at a different rate than the shaft itself, which is also why a good analyzer package computes all four fault frequencies straight from the bearing datasheet the moment you enter its part number:

function BEARING_FAULT_FREQUENCIES(n, Bd, Pd, phi_deg, fr):
    phi ← phi_deg * pi / 180
    ratio ← (Bd / Pd) * cos(phi)
    BPFO ← (n / 2) * fr * (1 - ratio)
    BPFI ← (n / 2) * fr * (1 + ratio)
    BSF  ← (Pd / (2 * Bd)) * fr * (1 - ratio^2)   # ball spin frequency
    FTF  ← (fr / 2) * (1 - ratio)                  # cage / fundamental train frequency
    return {BPFO, BPFI, BSF, FTF}

The trend matters more than a single reading

A single spectrum tells you what's happening right now. A trend — the same peak's amplitude tracked over weekly or monthly readings — tells you how fast it's getting worse, which is what actually drives a maintenance decision. A bearing fault frequency present at low amplitude and stable for months is a very different situation from the same frequency doubling in three weeks.

You don't need to be a vibration specialist to get real value from a spectrum — you need to know which frequencies to expect, and to treat any peak that doesn't line up with one of them as the thing worth explaining.