What a vibration tells you, and what it doesn't

The machine repeats itself with every revolution

A rotating machine repeats itself revolution after revolution, defects included. That’s why you don’t reason in raw hertz but in multiples of the rotational frequency: they’re called orders. A motor at 1,480 rpm completes about 24.7 revolutions per second: its 1x sits around 24.7 Hz, its 2x around 49.3 Hz. If the speed changes, all the rotation-related lines move together. The ones that stay put are not born from rotation: that’s the case of the electrical component at 100 Hz, covered further on.

Without a speed signal, the 1x is an estimate. Without a tachometer or an encoder, the speed has to be derived from the signal itself. That works with a clean, dominant 1x and nearly constant speed. It remains an inference, not a measurement. And if the 1x falls, so does the judgment about what is 2x, what is 3x, and what is not an integer at all.

The typical signatures, and where they really come from

This is the table hanging on walls across half the world. It’s useful, and it’s an orientation, not a verdict.

Defect	In the signal	On the shop floor
Unbalance	Stable 1x at constant speed, strong phase change through the criticals	Grows with speed, uniform hum on the support
Shaft misalignment	1x, 2x, or higher harmonics. Sometimes axial as strong as the radials	Hot coupling, worn inserts, leaking seals
Mechanical looseness	1x and harmonics, sometimes subharmonics, erratic values between startups	Loose anchors, shims that shift, noise that changes
Rolling bearing degradation	Broadband high-frequency acceleration at the support, unstable and rising readings	Metallic whistle or rasp, support running hot
Pump cavitation	Noise floor rising between 1 and 10 kHz, typically above 2 kHz, without sharp lines	Gravel noise in the impeller, fluctuating flow, suction at its limit
Resonance	Amplification near a natural frequency, strong phase changes on the 1x	Explodes at a certain speed, calms down above and below it

Where this table comes from. The rows above, cavitation included, are consolidated engineering practice, not normative requirements. An ISO table resembling them sits in an informative annex of ISO 13373-1:2002. Informative means orientation, not requirement. ISO 13373-3:2015 also uses fault tables in the diagnostic path, but as good practice among experienced users, admitting other approaches. Neither is reproduced here: content restated, full texts available from UNI.

Three levels better not confused

The standard says so. Broadband severity, with zones, thresholds, and comparison against the baseline: territory of the ISO 20816 series. And the structured diagnostic path, territory of ISO 13373-3 and ISO 13379-1, which calls for amplitude and phase of 1x and 2x, multiple measurement points, machine data, and a declared confidence level.

It’s engineering practice. The signature-to-defect associations in the detail in which they circulate in training courses, the ladder of half-order harmonics in looseness, cavitation as a rise in the noise floor. Cavitation appears in no ISO table: ISO 13373-1 mentions it only in connection with the frequency range on pumps.

It’s your own reasoning. The hypothesis you put together knowing that machine, that process, that failure history. Legitimate, as long as it’s declared for what it is.

How slippery the second level is. In 1999, at IMAC, researchers induced controlled misalignments on a fourteen-channel test rig, varying the coupling, the magnitude, and the speed. No guaranteed characteristic spectrum: the dominant harmonic changed from run to run, often the 1x, in many cases with the 2x and 4x larger. The authors call the rules taught in courses “doubtful at best”. So no: a dominant 2x does not mean misalignment.

The limit that changes everything: without phase, many diagnoses don’t separate

Phase is the angular position of the vibration relative to a reference rotating with the shaft. It takes a second signal: a notch, an encoder, a probe that sees it. Without one, phase is not less precise: it simply isn’t there.

The four diagnoses that collapse into one. ISO 13373-3:2015 states, in restated form, that phase is an important diagnostic tool, that it requires a reference signal, and that it serves to distinguish misalignment, resonance, rubs, and unbalance. Those are the four causes a measurement without a phase reference cannot separate: they all produce energy at 1x or its multiples. The normative diagnostic path calls for amplitude and phase of 1x and 2x.

Add a trap of electrical machines. On the 50 Hz grid, the electromagnetic force generates an exact component at 100 Hz. A two-pole motor at full load runs between 2,900 and 2,950 rpm: its mechanical 2x falls between 96.7 and 98.3 Hz, a few hertz from the electrical 100 Hz. Without a speed reference and without sufficient resolution the two get confused. That high 2x may have nothing to do with the coupling.

This is not a limitation of cheap instruments, it’s a codified fact. ISO 13379-1:2012 requires assigning each failure mode four scores, including detectability and diagnostic confidence, which combine into a monitoring priority index. The low scores mark the failure modes whose symptoms are not repeatable, unknown, or indistinguishable from those of other modes.

Bearings: what can be calculated, what can only be seen

The characteristic frequencies of a bearing, outer race, inner race, rolling element, cage, are pure kinematics: they depend on the number and diameter of the rolling elements, on the pitch diameter and the contact angle, and they scale with shaft speed. Without geometry and without speed they cannot be calculated. Whoever declares an outer race defect without those two pieces of data is skipping a step.

And even when calculated they are not exact. The contact angle changes with load and the rolling elements slip: the real values deviate by a few percentage points and the higher harmonics smear instead of staying sharp lines. That is what distinguishes them from mechanical harmonics: they are not integer multiples of rotation.

A note on the word envelope, used carelessly. Classic envelope analysis demodulates a high-frequency resonance band. Which band depends on the bearing and on the structure holding it: the literature places it in a wide interval, and the historical application notes indicate the region around 8-10 kHz as typical. With a usable band of a few kilohertz you’re doing envelope analysis on lower resonances, of the machine and the support: different technique, different sensitivity. Always ask which band it’s done on.

What remains visible even without the bearing data.

• The level and trend over time of the high-frequency energy.
• The signal’s impulsiveness indicators, such as crest factor and kurtosis.
• A non-integer periodicity found blind in the envelope spectrum, which you’ll only be able to name after entering the bearing data.

What it takes to close a diagnosis

Severity scale and diagnostics are two different normative worlds. ISO 20816-3:2022 itself declares that the evaluation concerns broadband vibration, with no reference to frequency components or to phase, and that setting criteria on individual components is outside its scope; its scope also excludes the evaluation of bearings and gears. A zone A, B, C, or D is not a bearing diagnosis. And it doesn’t hold for just any rotating machine: rotodynamic pumps have ISO 10816-7, while rotary positive-displacement compressors, reciprocating machines, and submersible machines stay outside ISO 20816-3. Before naming a zone you need to know what machine you’re measuring on.

What to put in place before declaring a cause. Here’s the honest point, and it isn’t discouraging. A continuous measurement doesn’t make the diagnosis. It does something else, and does it well: it notices that something has changed, when, and how fast. It tells you where to look and when it’s worth going there, instead of opening everything up on a calendar. The diagnosis comes later, with more points, the phase, the speed, and someone who decides. And no measurement predicts the date of a failure: whoever promises you one is selling, not measuring.

1. Multiple measurement points, on every bearing and not on a single support.
2. The three directions: horizontal radial, vertical radial, axial.
3. A phase reference and a shaft speed signal.
4. The machine data: bearing geometry, gear ratios, number of blades or rotor bars.
5. The operating conditions at that moment: a measurement taken in a transient is not comparable.
6. Someone who knows that machine, and, for the fine reading, certified expertise.