Rolling bearings: the four stages of failure and what the FFT spectrum shows in each

Rolling bearings do not fail out of the blue. They give warning, and they do it in stages: first at frequencies only a high-response sensor can pick up, then at their own natural frequencies, then at the fault frequencies any velocity spectrum shows, and finally in the broadband noise that comes before seizure. Whoever can read these stages replaces the bearing in the right shutdown, with the part already on hand.

This article explains the four stages, the characteristic frequencies of each bearing component, what enveloping is and how trend-based alerts anticipate the replacement. It is written for the vibration technician and for the manager who wants to understand why "still in zone B" does not mean "still fine."

The fault frequencies

A rolling bearing has four components that generate vibration when they are defective: the outer race, the inner race, the rolling elements (balls or rollers) and the cage. Each one produces a characteristic frequency, calculated from the bearing geometry and the running speed:

• BPFO (Ball Pass Frequency Outer): the rate at which the rolling elements pass a point on the outer race.
• BPFI (Ball Pass Frequency Inner): the same for the inner race.
• BSF (Ball Spin Frequency): the rotation of each element about its own axis.
• FTF (Fundamental Train Frequency): the rotation of the cage.

The formulas use the number of rolling elements (n), the element diameter (d), the pitch diameter (D) and the contact angle (a), with f being the shaft rotation frequency:

• BPFO = (n ÷ 2) × f × (1 − (d ÷ D) × cos a)
• BPFI = (n ÷ 2) × f × (1 + (d ÷ D) × cos a)
• BSF = (D ÷ 2d) × f × (1 − ((d ÷ D) × cos a)²)
• FTF = (f ÷ 2) × (1 − (d ÷ D) × cos a)

Manufacturers publish these values per bearing model. When the model is unknown, the field approximations apply: BPFO around 0.4 × n × f, BPFI around 0.6 × n × f and FTF around 0.4 × f. For a 9-ball bearing on a shaft turning at 29 Hz (a 4-pole motor on a 60 Hz grid), BPFO comes out at about 105 Hz and BPFI at about 157 Hz.

The detail that saves the analyst: these frequencies are non-integer multiples of running speed (3.6x, 5.4x and so on). Unbalance, misalignment and looseness show up at integer multiples. A peak at 5.4x running speed, with no integer harmonic nearby, is a bearing until proven otherwise, even without knowing the model.

The four stages

Stage 1: the damage is still subsurface. There is no visible peak at the fault frequencies in the velocity spectrum. The first indications appear in the ultrasonic range and are picked up by high-frequency techniques: demodulation, spike energy, shock pulse. At this stage the defect is microscopic, and poor lubrication may be the cause. Most of the bearing's life is still ahead of it.

Stage 2: the bearing's natural frequencies wake up. The impacts of each pass over the defect excite the natural frequencies of the bearing components, usually between 500 Hz and 1.5 kHz (30,000 to 90,000 cpm). They appear in the acceleration spectrum, with sidebands at running speed. This is the stage where enveloping shines, and where the replacement can be planned without rushing.

Stage 3: the fault frequencies appear in the velocity spectrum. The overall RMS rises. BPFO, BPFI or BSF become visible along with their harmonics, and BPFI is usually the first to develop 1x running-speed sidebands, because a defect on the inner race rotates and moves in and out of the load zone on every revolution. At this point replacement is no longer optional; it is a question of when.

Stage 4: the bearing comes apart. The amplitude of 1x running speed and its harmonics rises (clearance has increased), 1x sidebands appear around everything, noise and temperature climb, and the discrete fault frequencies disappear, replaced by a random broadband noise floor. Remaining life is measured in hours or days, and a shutdown at this point is an emergency shutdown.

What enveloping is

In stages 1 and 2 the impacts are small and buried under the machine's normal vibration. The envelope technique (or demodulation) filters the acceleration signal in a high band, around the excited natural frequencies, extracts the envelope of these repetitive impacts and runs an FFT on that envelope. The result shows the rate at which the impacts repeat, which is precisely BPFO, BPFI or BSF, long before they appear in the velocity spectrum. It requires a sensor with high-frequency response and rigid mounting; a magnet on paint will not deliver.

How trend-based alerts anticipate the replacement

With RMS velocity and temperature recorded several times a day on each bearing, the transition from stage 2 to stage 3 shows up as a slope in the curve, weeks before the value crosses into zone C. ISO 20816-3 provides the criterion: a change greater than 25% of the B/C boundary, at the same point and under the same conditions, is significant and calls for investigation, wherever it falls in the table.

On our platform, each reading is compared with the sensor's thresholds, only a change of level sends a notification (email and WhatsApp), and the trend is fitted over the history to project when the alarm threshold would be reached, with the confidence of the estimate stated. One caveat we always make: a wearing bearing accelerates at the end, so the projection is a maximum deadline, not a scheduled date. The on-demand FFT spectrum is the next step: the engineer opens the spectrum, looks for the non-integer multiples and confirms which component is failing.

The practical sequence:

1. The trend rises: alert. Open the spectrum and confirm it is the bearing.
2. Stage 2 or early stage 3: buy the bearing and schedule the shutdown in the production window.
3. Replacement done while the machine is still intact: shaft, housing and seal survive.
4. New baseline recorded.

What to do now

1. Find out the bearing models on your critical machines and calculate (or ask the manufacturer for) the four frequencies at the operating speed.
2. Make sure the bearings that matter have rigid mounting and a sensor with response above 1 kHz.
3. Record the baseline with the machine in good condition.
4. Treat the slope of the trend as the first sign, and the spectrum as confirmation.

If you want to know what your plant needs, talk to one of our engineers.

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Sources: Ludeca, 4 Stages of Bearing Failures (reference guide, 2021); ISO 20816-3:2022, clause 6.3 (Criterion II, change in vibration magnitude); fault-frequency formulas as given in the vibration analysis literature (Mobius Institute; Acoem; Power-MI).