Rolling-Element Bearing Faults: Frequencies, Enveloping and Evidence

From Mechanical Maintenance to Vibration Analysis - Part 6

In Part 5 - From Spectral Peaks to Fault Hypotheses, we learned to separate an observation from a diagnosis and test competing explanations.

Now we apply that discipline to one of the most important and frequently misunderstood subjects in vibration analysis: rolling-element bearing faults.

A peak near a calculated bearing frequency is evidence. It is not, by itself, permission to replace the bearing.

Bearing signals may be weak, high-frequency and affected by load, lubrication, mounting, sensor position, structural resonance and speed variation. A reliable conclusion therefore combines the correct bearing geometry, good measurements, trending and physical evidence.

Why a local bearing defect creates vibration

When a rolling element repeatedly passes over a pit, crack or spall, it produces a short impact. That impact excites high-frequency resonances in the bearing, housing and sensor mounting path. The impacts repeat according to the geometry and speed of the bearing component involved.

The raw time waveform may show a train of impacts, while the FFT and envelope spectrum help reveal the repetition rate. Because bearing geometry is not normally synchronized to an exact integer multiple of shaft speed, many bearing frequencies appear at non-integer orders such as 3.58X or 5.42X.

The four calculated bearing frequencies

Frequency	Component represented	Typical supporting clues
BPFO Ball Pass Frequency Outer race	Rolling elements passing a fixed outer-race location	BPFO harmonics; amplitude may be strongest close to the loaded outer-race zone
BPFI Ball Pass Frequency Inner race	Rolling elements passing a defect rotating with the inner race	BPFI harmonics with possible 1X running-speed sidebands
BSF Ball Spin Frequency	Rotation of a ball or roller	BSF or its harmonics with possible cage-frequency modulation
FTF Fundamental Train Frequency	Cage rotational frequency	A low, sub-synchronous component; possible cage, lubrication or load-zone involvement

Use the manufacturer and exact bearing model whenever possible. Calculated frequencies depend on the number and size of rolling elements, pitch diameter and contact angle. Actual frequencies may shift slightly because of slip, load and operating condition, so software cursors should allow a sensible tolerance rather than demanding perfect alignment.

A practical frequency example

Consider a motor running at 1,800 rpm:

• Shaft speed = 1,800 / 60 = 30 Hz.
• Suppose the bearing database gives BPFO = 3.58X, BPFI = 5.42X, BSF = 2.35X and FTF = 0.40X.
• BPFO = 3.58 x 30 = 107.4 Hz.
• BPFI = 5.42 x 30 = 162.6 Hz.
• BSF = 2.35 x 30 = 70.5 Hz.
• FTF = 0.40 x 30 = 12 Hz.

If the envelope spectrum contains peaks near 107.4, 214.8 and 322.2 Hz, BPFO and its first two harmonics become a reasonable outer-race fault hypothesis. The analyst must still verify the bearing identity, actual speed, trend, sensor position and competing impact sources.

Why enveloping helps detect early damage

Early bearing impacts may contain little energy compared with normal shaft vibration. In a conventional velocity spectrum, strong 1X and 2X components can dominate the display while the bearing signal remains hidden in the high-frequency noise floor.

Envelope analysis, also called demodulation, typically:

1. Measures acceleration at a suitable sample rate.
2. Uses a high-pass or band-pass filter around a high-frequency resonance excited by the impacts.
3. Rectifies the filtered signal so the ringing transients can be followed.
4. Applies a low-pass stage and calculates the envelope spectrum to expose the lower-frequency impact repetition rate.

The result may reveal BPFO, BPFI, BSF or FTF before those components become obvious in a normal velocity spectrum. Enveloping does not replace the waveform or conventional spectrum; it adds another view of the same machine behaviour.

Envelope setup matters

The filter band and sampling rate determine what the instrument can reveal. The high-pass or band-pass filter should reject strong lower-frequency machine vibration while retaining a resonance band excited by short bearing impacts. The envelope-spectrum Fmax must then be high enough to display the bearing frequencies and several harmonics.

As a practical starting point, the Mobius Category II manual recommends an envelope-spectrum Fmax of roughly 3.5 to 5 times the calculated BPFI. If the bearing is unknown and has approximately 8 to 12 rolling elements, it suggests starting near 15X to 20X running speed. These are setup guides, not alarm limits; adjust them for the bearing, machine and instrument.

Choose the resonance band carefully. Motor-bar and variable-frequency-drive switching activity, gearmesh, reciprocating-machine impacts, rotating looseness and cavitation can also generate high-frequency energy. A strong envelope reading therefore proves that repetitive impacts or modulation are present, not automatically that the bearing is damaged.

Conventional velocity: useful for overall machine condition and lower-to-mid-frequency faults such as unbalance, misalignment and looseness.

Acceleration: sensitive to higher-frequency energy and impacts.

Envelope spectrum: useful for identifying the repetition rate hidden inside high-frequency impact energy.

Read harmonics and sidebands as modulation clues

A single peak close to a calculated frequency is weak evidence. Confidence improves when a physically meaningful family appears.

• Harmonics: repeated impacts can generate BPFO, 2xBPFO, 3xBPFO and higher multiples.
• 1X sidebands around BPFI: an inner-race defect rotates through the bearing load zone, so impact amplitude may be modulated once per shaft revolution.
• FTF sidebands around BSF: rolling-element damage may change as the element moves around the bearing and contacts the inner and outer raceways.
• Rising noise floor: more distributed surface distress, contamination or poor lubrication can create broadband high-frequency energy.

Sideband spacing matters. Do not call every cluster a bearing fault; measure the spacing and relate it to shaft speed, FTF or another credible modulating frequency.

High-frequency vibration normally attenuates more rapidly through a structure than low-frequency vibration. Compare equivalent high-frequency readings at nearby bearings: a signal concentrated at one housing provides useful location evidence, while the same low-frequency pattern at several points may be transmitted from another source.

A simplified progression of bearing deterioration

Bearing damage does not always follow a neat universal sequence, but analysts often see a progression similar to this:

1. Earliest indication: high-frequency energy or the envelope trend rises while conventional velocity changes little.
2. Localized race defect develops: a bearing-frequency family and harmonics become visible, often first for one race.
3. Damage spreads: more harmonics and sidebands appear; rolling-element or cage-related activity may join the race frequencies, and impacts become clearer in acceleration and the waveform.
4. Advanced deterioration: broadband energy and the noise floor rise, discrete peaks may become less distinct, clearances and internal geometry may change, and conventional velocity can become significant.

Do not misinterpret falling discrete peaks as recovery. Severe loss of internal geometry can reduce the clear transmission of individual frequencies while broadband energy and random impacts continue to increase.

Do not use this sequence as a countdown clock. Remaining life depends on the size and number of defects, the components involved, loss of internal geometry, rate of progression, load, speed, lubrication, service time and experience with genuinely comparable machines. No two cases are identical.

Do not confuse the damaged component with the root cause

A vibration pattern may identify where damage is occurring without explaining why it occurred. Possible contributors include:

• Insufficient, excessive, incorrect or contaminated lubricant.
• Water or solid-particle contamination.
• Misalignment, unbalance, belt forces or excessive external load.
• Incorrect fits, loss of internal clearance or installation damage.
• Electrical discharge or fluting in motors and variable-frequency-drive applications.
• Resonance, looseness or impacts transmitted from a nearby machine component.

Replacing the bearing without correcting the cause may simply restart the failure cycle.

Worked example: motor drive-end bearing

A motor runs at 1,780 rpm, or approximately 29.67 Hz. The correct bearing model gives BPFI = 5.45X. The analyst observes:

• Envelope peaks near BPFI and 2xBPFI.
• Sidebands around BPFI spaced at approximately 1X running speed.
• The envelope trend has doubled over six weeks at comparable load.
• Conventional velocity has increased only slightly.
• The drive-end bearing temperature is stable.
• Lubrication history shows a recent change in grease quantity.

Observation: a growing, speed-related impact family aligns with BPFI and includes 1X sidebands.

Leading hypothesis: developing inner-race-related distress.

Competing explanations: an incorrect bearing number, transmitted impacts, electrical activity, lubrication-related friction or a mounting problem.

Recommended actions: confirm actual speed and bearing identification; review the grease type, quantity and procedure; inspect motor current and grounding evidence where relevant; increase measurement frequency; and plan inspection or replacement according to risk and trend rate. After maintenance, inspect the removed bearing and document the failure mode rather than recording only “bearing replaced.”

A seven-step bearing diagnosis workflow

1. Verify the bearing and operating condition. Record model, speed, load, temperature and lubrication state.
2. Verify the measurement. Use a repeatable point, firm sensor mounting, suitable frequency range and adequate sampling.
3. Review multiple displays. Compare velocity, acceleration, envelope spectrum, waveform and trends.
4. Overlay the correct frequencies. Look for harmonics and meaningful sideband spacing, allowing for reasonable slip.
5. Compare locations and history. Check nearby bearings, directions, baselines and comparable machines.
6. Test the root-cause and false-positive hypotheses. Review lubrication, contamination, load, alignment, fits, electrical switching, gearmesh, cavitation and other impact sources.
7. Verify the intervention. Inspect the removed bearing and repeat measurements under a comparable condition.

High-frequency methods are deliberately sensitive. Unless risk, trend rate or a low-speed application justifies earlier action, avoid overhauling a machine from one envelope spectrum alone. Seek confirmation in repeatable trends, the conventional spectrum, waveform, lubrication condition or another independent technique.

How software helps - and where judgement remains essential

System 1 and other condition-monitoring platforms can store bearing data, calculate or import defect frequencies, apply frequency markers, trend amplitudes, display waveforms and spectra, and generate alarms. These features improve consistency and make developing patterns easier to see.

However, the software cannot guarantee that the installed bearing matches the database, that the speed is correct, that the sensor is well mounted, or that the peak comes from the bearing. The analyst still has to connect the signal to the machine and select the next discriminating test.

Final takeaway

• BPFO, BPFI, BSF and FTF are geometry-based diagnostic frequencies, not automatic failure verdicts.
• Early bearing damage is often easier to see in high-frequency acceleration and envelope data than in overall velocity.
• Harmonics, sidebands, waveforms and trends provide stronger evidence than a single peak.
• A damaged bearing is not necessarily the root cause of the failure.
• The best diagnosis combines vibration, operating condition, lubrication history and physical inspection.

Coming in Part 7

Part 7: Gearbox Faults and Sideband Analysis. We will examine gear mesh frequency, harmonics, sidebands, modulation and how to separate gear damage from shaft-speed and bearing-related activity.

Discussion question: Which bearing evidence do you trust most in your plant - envelope trends, defect-frequency patterns, temperature, lubrication findings or inspection results?

References and further learning

• Emerson Process Management, Basic Vibration Analysis - Course 2031, Section 5: Rolling Element Bearings.
• Mobius Institute, Category II Vibration Analysis Manual, Chapter 13: Rolling Element Bearing Analysis.
• SKF, Spectrum Analysis.
• SKF Evolution, Vibrations Help Find Faulty Components.
• Fluke, How Demodulation Helps You Detect Bearing Faults Early.
• Fluke, Smarter Bearing Monitoring.

Educational note: The patterns are simplified learning guidance, not universal fault rules, alarm limits or remaining-life predictions. Apply approved site procedures, bearing-manufacturer guidance and qualified engineering judgement to real machinery.

A Horrible Noise That Disappeared: Diagnosing a Loose Motor Cooling-Fan Part

A strange mechanical noise does not have to remain present for the fault to be real.

In a Bently Nevada success story from an offshore oil and gas platform, a technician heard a “horrible noise” from a dissolved-salts pump motor during routine vibration data collection. The noise disappeared shortly afterward, but the measurements taken during the event preserved the evidence. What followed is a valuable lesson in combining human observation, spectral analysis, waveform interpretation and focused inspection.

A transient sound may disappear before an inspection begins, but correctly captured vibration data can preserve the mechanical signature of the event.

The operating context

The machine was considered moderately critical and was monitored periodically using a portable Scout 220 data collector. Offshore technicians collected the readings, uploaded them to a System 1 server and requested remote diagnostic support from Bently Nevada Machinery Diagnostic Services engineers.

This arrangement matters. It shows how a condition-monitoring program can connect three important capabilities:

• People near the machine who notice abnormal sound, smell, heat or movement.
• Portable measurements that preserve the spectrum and time waveform.
• Diagnostic expertise that can interpret the data and guide a targeted inspection.

What the vibration data showed

The measurement taken while the noise was present contained a single prominent peak at approximately 1210 Hz, accompanied by 1X and 2X running-speed sidebands. The unusual vibration appeared only at the motor non-drive end and was absent from the later measurement taken after the noise stopped.

The 1210 Hz component did not match an expected forcing frequency for the machine. This prevented the analyst from simply assigning it to a normal rotating or electrical source. Instead, the spectrum and waveform suggested that repeated impacts were exciting a local resonance near 1210 Hz. The 1X and 2X sideband spacing showed that the high-frequency response was being modulated at running-speed-related intervals.

Measured observation: A 1210 Hz peak with 1X and 2X sidebands appeared at the motor non-drive end during the audible event.

Interpretation: Periodic impact or rubbing was likely exciting a structural resonance.

Location hypothesis: A loose rotating part or contact between rotating and stationary parts near the overhung cooling fan.

Discriminating action: Open the fan cover and inspect the cooling-fan assembly.

Why sidebands were important

A sideband is a spectral component that appears on either side of a carrier frequency. In this case, the carrier was the resonance near 1210 Hz. Regular variation in the amplitude of that vibration produced sidebands separated by the modulating frequencies.

The key point is not merely that sidebands existed. Their spacing connected the high-frequency resonance to a once-per-revolution and twice-per-revolution mechanical event. That relationship supported a hypothesis involving a rotating component repeatedly contacting, striking or changing load as the shaft turned.

Sidebands should always be interpreted with the waveform, machine speed, measurement location and equipment geometry. They describe modulation; they do not identify the damaged component by themselves.

Why the noise was so noticeable

The abnormal frequency was high enough to be heard clearly by the technician. Baker Hughes noted that it was near the frequency range where human hearing is particularly sensitive. This helps explain why the event sounded severe even though it was temporary.

Human senses remain useful screening tools in maintenance. An experienced technician may recognize a change before an alarm is triggered. However, the safest workflow is to treat sound as an observation, capture objective data and avoid approaching or opening moving equipment until it is isolated under the approved procedure.

The inspection confirmed the diagnosis

Because the abnormal response was localized at the non-drive end, the diagnostic team suspected the overhung cooling fan. They recommended removing the fan cover and looking for abnormalities.

The inspection found part of a broken retaining ring loose inside the cover. The ring belonged to the fan assembly and had separated. The technician replaced it, and the machine returned to service less than 48 hours after the abnormal measurement.

According to the source case study, failure to detect the problem could have allowed the fan to separate from the rotor and destroy the motor. The estimated replacement cost of the motor was approximately €40,000. The larger value, however, also included avoided secondary damage, unplanned downtime and operational risk.

A practical diagnostic workflow

1. Record the human observation. Note what was heard, where it was strongest, when it began and whether operating conditions changed.
2. Preserve event data. Save the spectrum, time waveform, speed, load, measurement direction and timestamp. Do not overwrite an abnormal reading with a later normal one.
3. Compare locations. A response isolated to one end or one direction can greatly reduce the search area.
4. Identify measured facts. List the dominant frequency, sideband spacing, waveform features and differences from the baseline.
5. Develop more than one hypothesis. Consider loose parts, rubbing, impacts, bearing faults, aerodynamic effects, electrical sources and structural resonance as appropriate.
6. Use machine geometry. Ask which component near the measurement point could physically produce the observed periodic event.
7. Choose a focused inspection. Inspect the suspected area under proper isolation instead of dismantling the entire machine.
8. Verify after repair. Repeat comparable measurements and confirm that the abnormal sound and vibration signature are gone.

Lessons for a condition-monitoring program

• Intermittent faults deserve immediate attention. Disappearance of the symptom is not proof that the defect corrected itself.
• Keep the abnormal dataset. Event measurements may contain evidence that routine follow-up readings no longer show.
• Use both spectrum and waveform. Frequency-domain sidebands reveal modulation, while the time waveform helps show the underlying impact pattern.
• Measurement location matters. Localization to the motor non-drive end directed attention toward the cooling fan.
• Combine technology with technician experience. The technician’s report of abnormal noise gave essential context to the data.
• Convert diagnosis into a specific action. The recommendation was not simply “monitor closely”; it identified the fan cover as the next safe inspection point.
• Moderately critical assets can still create major losses. Periodic portable monitoring can prevent expensive failures outside the permanently monitored machine population.

Final takeaway

This case is a strong example of evidence-based vibration analysis. A temporary noise was captured as a localized high-frequency resonance with running-speed sidebands. The pattern suggested impact or rubbing near the motor cooling fan, and a focused inspection revealed a broken retaining ring.

The successful diagnosis did not come from one spectral rule. It came from linking sound, timing, location, spectrum, waveform, machine geometry and physical inspection. That is the habit that turns condition-monitoring data into reliable maintenance decisions.

Source and further reading

This educational analysis is based on the Baker Hughes/Bently Nevada success story Loose Part on Motor Cooling Fan, authored by Håkon Myklestad of Norway MDS. Refer to the original case study for its spectrum, waveform and damaged-component images.

Educational note: This article summarizes a published case and expands on its diagnostic lessons. Actual machinery decisions must follow approved isolation procedures, manufacturer guidance, applicable standards and qualified engineering judgement.

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From Spectral Peaks to Fault Hypotheses: Unbalance, Misalignment and Looseness

From Mechanical Maintenance to Vibration Analysis - Part 5

In Part 4 - Understanding the Time Waveform and FFT Spectrum, we learned how running speed, harmonics, sidebands and acquisition settings help us read vibration data.

Now we take the next step: turning observed patterns into fault hypotheses.

A spectral peak is a measured fact. A fault name is an interpretation. Evidence must connect the two.

This distinction is essential. A strong 1X peak may support an unbalance hypothesis, but it may also be influenced by resonance, eccentricity, a bent shaft, looseness or transmitted vibration. Good analysts do not stop at pattern recognition; they test competing explanations.

Separate observation, interpretation and confirmation

Use three levels when communicating a diagnosis:

1. Observation: What does the data actually show?
2. Interpretation: Which mechanisms could reasonably produce it?
3. Confirmation: What additional evidence distinguishes the leading hypothesis?

For example:

Observation: Pump outboard radial velocity has a dominant, stable 25 Hz peak. The machine runs at 1,500 rpm.

Interpretation: The peak is 1X running speed; unbalance is one plausible cause.

Confirmation: Check radial direction, phase stability, response at both bearings, operating-speed behaviour, rotor cleanliness and evidence of resonance before recommending balancing.

Build the fault hypothesis from multiple clues

A useful hypothesis combines more than frequency. Review:

• Frequency: Is the component at 1X, 2X, a harmonic, subharmonic or another calculated frequency?
• Amplitude: Is it significant relative to the baseline, alarm criteria and nearby locations?
• Direction: Is the response mainly horizontal, vertical or axial?
• Phase: Is phase stable, and how does it compare across bearings, directions and the coupling?
• Waveform: Is the motion sinusoidal, impacted, clipped, modulated or irregular?
• Operating condition: Does the pattern change with speed, load, temperature, flow or pressure?
• Machine geometry: Where are the bearings, coupling, overhung components, supports and potential clearances?
• History: What changed after cleaning, overhaul, alignment, pipe work or process adjustment?

Hypothesis 1: Rotor unbalance

Unbalance exists when the mass centre of a rotating component does not coincide with its rotational axis. The resulting centrifugal force rotates once per revolution and increases strongly as speed increases.

Patterns that may support unbalance

• A prominent 1X running-speed component.
• Vibration is commonly stronger in radial directions than axial direction.
• The time waveform may look relatively sinusoidal when 1X dominates.
• 1X phase is often reasonably stable when speed and load are steady.
• The response may increase markedly near a structural or rotor resonance.

Possible physical causes include product buildup, erosion, a missing balance weight, an incorrectly installed component, rotor damage, casting variation or eccentric mass distribution.

Why 1X alone is not enough

A shaft rotates once per revolution, so many mechanical conditions can produce 1X. A bent shaft, eccentric sheave, resonance, misalignment, looseness, rub or external vibration may all contribute. A large 1X peak identifies a synchronous response; it does not identify the root cause by itself.

Useful confirmation checks

• Compare horizontal, vertical and axial readings at both bearings.
• Measure 1X phase with a reliable tachometer and check repeatability.
• Inspect the rotor for deposits, missing material or loose components.
• Review startup or coast-down data for resonance amplification.
• Check whether the vibration changed after cleaning or mechanical work.
• Before adding correction weight, confirm that looseness, soft foot and alignment are acceptable.

Hypothesis 2: Shaft misalignment

Misalignment means the shaft centre-lines of coupled machines are not collinear under their normal operating condition. It may be angular, offset or a combination. Thermal growth, pipe strain, soft foot, foundation movement and assembly errors can all alter the running alignment.

Patterns that may support misalignment

• Elevated 1X and/or 2X components near the coupling.
• Significant axial vibration, particularly with angular misalignment.
• Radial response on both sides of the coupling, especially with offset misalignment.
• A repeatable phase relationship across the coupling that is inconsistent with simple unbalance.
• Coupling temperature, bearing temperature or seal problems may accompany the vibration evidence.

The exact spectrum depends on coupling type, machine stiffness, bearing arrangement, load and degree of misalignment. Some misaligned machines show a strong 2X component; others are dominated by 1X. Therefore, the absence of a large 2X peak does not rule misalignment out.

Useful confirmation checks

• Compare axial and radial readings on both sides of the coupling.
• Take phase readings at consistent locations and directions across the coupling.
• Check coupling condition and temperature.
• Verify soft foot, base condition, hold-down bolts and pipe strain.
• Review cold alignment targets and expected thermal growth.
• Perform precision alignment using an approved method, then compare vibration before and after correction.

Hypothesis 3: Mechanical looseness

Mechanical looseness is excessive movement between parts that should remain fixed or move within a controlled clearance. It can occur at a machine foot, baseplate, foundation, bearing housing, bearing fit, shaft fit, coupling or structural joint.

Patterns that may support looseness

• A family of running-speed harmonics: 1X, 2X, 3X and higher.
• Sometimes subharmonics such as 0.5X, depending on contact and clearance behaviour.
• An impacted, truncated or asymmetric time waveform.
• Amplitude and phase that may be unstable between repeated measurements.
• Large differences between nearby points or directions.
• A nonlinear response: relatively small changes in load or speed produce large vibration changes.

Harmonics develop because looseness can distort an otherwise sinusoidal motion. Contact, clearance and changing stiffness create a non-sinusoidal waveform, which the FFT represents as multiple harmonics.

Useful confirmation checks

• Inspect hold-down bolts, grout, baseplate, welds and structural joints.
• Check bearing and housing fits where permitted by the maintenance procedure.
• Compare casing points immediately above and below suspected joints.
• Look for fretting, polished contact surfaces, cracked paint or movement marks.
• Perform a controlled bump or impact test if resonance or structural flexibility is suspected.
• Check whether phase is repeatable; erratic phase may support intermittent movement.

Comparison table: clues, not rigid rules

Evidence	Unbalance hypothesis	Misalignment hypothesis	Looseness hypothesis
Spectrum	Often dominant 1X	Often 1X and/or 2X	Often multiple running-speed harmonics; possible subharmonics
Direction	Usually radial emphasis	Axial and/or radial near coupling	Any direction; may differ sharply across a joint
Waveform	May be near sinusoidal	Periodic but often more complex	Impacted, clipped, asymmetric or irregular
Phase	Often stable at constant condition	Cross-coupling relationships can be diagnostic	May be unstable or inconsistent
Physical checks	Deposits, erosion, missing weight, rotor damage	Alignment, thermal targets, coupling, soft foot, pipe strain	Bolts, fits, grout, cracks, fretting and structural movement

Important: These are tendencies, not universal acceptance rules. Faults can coexist, and resonance can amplify any forcing frequency.

Worked motor-pump example

A direct-coupled motor-pump runs at 1,500 rpm, so 1X equals 25 Hz. The analyst records:

• Motor drive-end axial: strong 25 Hz and 50 Hz.
• Pump drive-end axial: strong 25 Hz and 50 Hz.
• Radial readings: moderate 25 Hz.
• Phase readings across the coupling: repeatable but significantly different.
• Coupling temperature: higher than its established baseline.
• Inspection history: pump pipe work was modified during the last shutdown.

Observation: 1X and 2X are elevated, axial vibration is significant on both sides of the coupling, cross-coupling phase is repeatable, and temperature has increased.

Leading hypothesis: Misalignment or externally imposed strain affecting alignment.

Competing explanations: Coupling defect, bent shaft, looseness, soft foot or structural amplification.

Next actions: Check pipe strain, soft foot, hold-down condition, coupling condition and hot-versus-cold alignment requirements before moving the machine. Repeat vibration and phase readings after any correction.

This conclusion is stronger than saying, “The spectrum has 2X, therefore the machine is misaligned.” It connects the spectrum with direction, phase, temperature, maintenance history and physical checks.

A practical hypothesis-testing workflow

1. Verify the data. Confirm point, direction, units, mounting, speed, load and acquisition settings.
2. State the observation. Record frequencies, amplitudes, directions, waveform features and phase behaviour without naming a fault.
3. List plausible mechanisms. Include at least one competing explanation.
4. Rank the hypotheses. Use machine design, operating condition and history.
5. Choose a discriminating test. Ask which measurement or inspection will separate the leading possibilities.
6. Correct the verified cause. Do not balance, align or tighten components merely because a pattern looks familiar.
7. Verify the result. Repeat measurements under a comparable condition and document the change.

How to write a defensible recommendation

Avoid:

The pump is unbalanced because the spectrum has 1X.

Prefer:

Radial vibration at the pump outboard bearing is dominated by a stable 1X component that has increased from its comparable-load baseline. Rotor unbalance is a leading hypothesis. Inspect the impeller for buildup or damage, check hold-down integrity and resonance response, and collect repeatable 1X phase data before deciding whether field balancing is appropriate.

Final takeaway

• Unbalance often emphasizes stable radial 1X, but 1X is not unique to unbalance.
• Misalignment may produce axial and radial 1X/2X near a coupling, but the exact pattern varies.
• Looseness may generate harmonics, impacts and unstable behaviour, but harmonics alone do not prove it.
• Direction, phase, waveform, operating condition, history and inspection turn a pattern into a testable hypothesis.
• The repair result is part of the diagnosis. Always verify the post-maintenance condition.

Coming in Part 6

Part 6: Rolling-Element Bearing Faults. We will examine bearing defect frequencies, high-frequency acceleration, enveloping, harmonics and sidebands—and why lubrication, load and installation must be considered before condemning a bearing.

Discussion question: Which fault have you found hardest to distinguish in the field—unbalance, misalignment or looseness?

References and further learning

• Fluke, Diagnosing Imbalance, Misalignment, Looseness, and Bearing Wear.
• Fluke, Mechanical Looseness: What It Is and How to Detect It.
• Fluke Reliability, Phase in Vibration Analysis: Theory, Applications, and Examples.
• Bently Nevada, Vibration and Dynamic Measurements.

Educational note: The patterns are simplified learning guidance, not universal fault rules or alarm limits. Apply approved site procedures, applicable standards, manufacturer guidance and qualified engineering judgement to real machinery.

Understanding the Time Waveform and FFT Spectrum

From Mechanical Maintenance to Vibration Analysis - Part 4

In Part 3 - Displacement, Velocity and Acceleration, we learned that the measurement quantity changes which part of a vibration signal is emphasized.

Now we move to the two plots an analyst uses most often:

The time waveform shows what the vibration did over time. The FFT spectrum shows how that vibration is distributed across frequency.

They are not two unrelated measurements. The spectrum is calculated from the sampled time waveform. Each view organizes the same signal differently, and each can reveal evidence that is difficult to see in the other.

Start with the time waveform

A time waveform plots:

• Amplitude on the vertical axis - displacement, velocity or acceleration; and
• Time on the horizontal axis - normally seconds or milliseconds.

The waveform answers questions such as:

• Is the motion smooth and repeating?
• Are there impacts, clipping, beats or modulation?
• How far apart are repeated events?
• Is the signal symmetrical?
• Does the vibration change during the record?

A clean sinusoidal waveform suggests that one frequency dominates. A complex machine waveform usually contains several vibration sources at the same time: shaft rotation, coupling forces, gears, bearings, blades, hydraulic activity, structural response and background noise.

Period and frequency

If a feature repeats every T seconds, its frequency is:

Frequency (Hz) = 1 / period (seconds)

Running frequency (Hz) = speed (rpm) / 60

For a motor running at 1,500 rpm:

1,500 / 60 = 25 Hz

One shaft revolution therefore takes:

1 / 25 = 0.04 seconds, or 40 milliseconds

If a waveform contains a strong event every 40 ms, the repetition rate is synchronous with running speed. That is useful evidence, but it does not by itself prove unbalance or any other single fault.

What the FFT spectrum does

The Fast Fourier Transform, or FFT, is a mathematical method that separates a sampled waveform into frequency components. The resulting spectrum normally plots:

• Amplitude on the vertical axis; and
• Frequency on the horizontal axis, commonly in hertz, cycles per minute or orders.

Instead of asking when an event happened, the spectrum helps us ask:

• Which frequencies contain the most vibration?
• Do peaks correspond with shaft speed or component frequencies?
• Are harmonics or sidebands present?
• Which peaks are changing over time?

A spectrum makes repeating components easier to separate. However, it removes much of the timing shape that can make impacts, modulation and transient behaviour obvious in the waveform.

Time waveform versus FFT spectrum

Question	Time waveform	FFT spectrum
Horizontal axis	Time	Frequency or order
Especially useful for	Impacts, beats, modulation, clipping, non-stationary events and waveform shape	Separating periodic components, identifying orders, harmonics, sidebands and component-related frequencies
What may be hidden	Closely spaced frequency components can overlap visually	The timing and shape of individual events can be difficult to recognize
Best practice	Review both views with the same units, point, direction, speed, load and acquisition settings.

Understanding 1X, 2X and harmonics

Analysts often express frequency as a multiple of shaft-running speed:

• 1X means once per shaft revolution.
• 2X means twice per shaft revolution.
• 3X means three times per shaft revolution.

For the 1,500 rpm motor:

• 1X = 25 Hz
• 2X = 50 Hz
• 3X = 75 Hz
• 4X = 100 Hz

Integer multiples of a fundamental frequency are called harmonics. A series at 1X, 2X, 3X and higher orders tells us that the waveform contains repeating non-sinusoidal content related to shaft rotation.

A harmonic family is a pattern, not a diagnosis. Several conditions can generate harmonics, and the same fault can look different on different machines.

Before attaching a fault name, compare the pattern with measurement direction, phase, machine construction, clearances, operating condition, history and physical inspection.

Worked motor-pump example

Consider a direct-coupled motor and centrifugal pump running steadily at 1,500 rpm. The pump impeller has six vanes.

1. Running speed: 1,500 / 60 = 25 Hz.
2. Shaft period: 1 / 25 = 0.04 s.
3. Vane-pass frequency: 6 vanes × 25 Hz = 150 Hz, or 6X.

Suppose the spectrum contains peaks at 25, 50 and 150 Hz.

• The 25 Hz peak is synchronous with shaft rotation.
• The 50 Hz peak is 2X running speed.
• The 150 Hz peak matches the calculated vane-pass frequency.

Those identities are defensible because they are based on measured speed and machine geometry. The cause still requires testing.

For example, a 1X peak could be influenced by unbalance, bent shaft, eccentricity, resonance, transmitted vibration or other mechanisms. A vane-pass peak may be influenced by normal hydraulic excitation, operating away from the best efficiency point, recirculation, clearance problems or structural amplification. The frequency tells us where to investigate; it does not complete the diagnosis.

What the waveform adds

If the waveform is smooth and repeats every 40 ms, shaft-synchronous motion may dominate. If sharp impacts repeat at the same interval, looseness, contact or another once-per-revolution event may be exciting a resonance. If the amplitude rises and falls in a regular envelope, modulation or beating may be present.

This is why the analyst should move between waveform and spectrum instead of relying on one display.

Sidebands and modulation

Sidebands are peaks spaced equally around a central frequency. Their spacing is important because it can identify the modulating frequency.

For example, peaks around 150 Hz separated by 25 Hz would be described as 1X sidebands around the vane-pass frequency:

125 Hz, 150 Hz and 175 Hz

The spectrum shows the spacing clearly, while the waveform may show the related rise and fall of amplitude. Sidebands are useful evidence of modulation, but their mechanical source must still be confirmed.

FFT settings can change what you see

A spectrum is not independent of its acquisition settings. Poor settings can hide peaks, merge nearby frequencies or display misleading amplitudes.

1. Frequency span or maximum frequency

The selected span must include the frequencies relevant to the suspected condition. A low span may show running-speed components clearly but exclude bearing or gear activity. A very high span can provide inadequate detail at low frequency if the number of spectral lines is unchanged.

2. Spectral lines and resolution

A useful approximation is:

Frequency resolution Δf ≈ frequency span / number of lines

Longer time record → finer frequency resolution

If the span is 1,000 Hz with 800 lines, the line spacing is approximately 1.25 Hz. Two components only 0.5 Hz apart will not be cleanly separated by that setup. To improve frequency resolution, the analyzer normally needs a longer time record.

3. Sampling rate and alias protection

The signal must be sampled fast enough for the selected frequency range. Frequencies above the usable range can fold into the displayed spectrum as false lower-frequency components, a problem called aliasing. Modern analyzers normally use anti-alias filtering, but the analyst must still use a suitable acquisition range and instrument configuration.

4. Window function and leakage

A finite time record rarely begins and ends at perfectly matching points in the vibration cycle. The FFT can then spread energy from a true component into adjacent frequency bins. This is called spectral leakage.

A window function reduces the discontinuity at the record ends. A Hanning window is common for general machinery spectra, while other windows may suit transient or amplitude-accuracy applications. Window choice involves trade-offs; it does not repair an unstable or incorrectly collected signal.

5. Averaging

Averaging several records can stabilize random variation and make repeatable components easier to see. Too much averaging can hide short-lived events. Select the averaging method and number of averages to match the machine behaviour and diagnostic question.

Orders versus hertz

Hertz is absolute frequency. Order is frequency divided by a selected reference speed.

At 1,500 rpm, 25 Hz is 1X. If speed changes to 1,800 rpm, 1X becomes 30 Hz. The physical shaft-related event remains once per revolution even though its frequency in hertz changes.

Order-based analysis is especially useful when speed varies. It helps distinguish components tied to rotational speed from frequencies that remain fixed. Accurate speed information from a tachometer, keyphasor or reliable speed measurement becomes essential.

A practical reading sequence

1. Confirm data quality. Check the point, direction, sensor mounting, units, range, overload status, speed and load.
2. Read the waveform first. Look for periodicity, impacts, modulation, clipping, beats and changes during the record.
3. Calculate known frequencies. Include shaft speeds, gear mesh, blade or vane pass and available bearing frequencies.
4. Read the spectrum. Identify dominant peaks, harmonics, subharmonics, sidebands and broadband regions.
5. Match frequencies to the machine. Use measured speed and actual component geometry, not guesswork.
6. Compare locations and directions. Horizontal, vertical and axial responses help test a hypothesis.
7. Compare with history. Trend amplitudes and patterns under similar operating conditions.
8. Seek confirmation. Use phase, high-resolution data, envelope analysis, temperature, oil analysis, process data or inspection as appropriate.
9. State uncertainty. Separate what the data proves from what it merely suggests.

Five common mistakes

Mistake 1: Diagnosing from the tallest peak

The tallest peak may be important, but amplitude can be influenced by structural response, measurement location, direction and operating condition. Identify the frequency and test the mechanism.

Mistake 2: Assuming every 1X peak means unbalance

Unbalance often produces running-speed vibration, but 1X is not unique to unbalance. Phase, direction, machine geometry and inspection evidence are needed.

Mistake 3: Ignoring the time waveform

A spectrum can make frequencies clear while hiding impact shape and timing. Always inspect the waveform when impacts, looseness, rubs or modulation are possible.

Mistake 4: Comparing spectra with different settings

Changes in span, lines, window, averaging, units or operating condition can change the display. Trend like with like.

Mistake 5: Trusting software labels without verification

Software can calculate peaks, orders and alarms quickly. It does not know every change in machine configuration, process condition, sensor installation or maintenance history. The analyst remains responsible for validation.

Final takeaway

The waveform and spectrum are two views of the same vibration signal.

• The time waveform preserves timing, shape and transient behaviour.
• The FFT spectrum separates repeating components by frequency.
• Running speed and machine geometry give peaks physical meaning.
• Acquisition settings determine what can be seen and resolved.
• A familiar pattern is evidence, not proof.

A good analyst does not ask, "Which plot gives the answer?" The better question is, "What does each view reveal, and what additional evidence will confirm the hypothesis?"

Coming in Part 5

Part 5: From Spectral Peaks to Fault Hypotheses. We will examine how unbalance, misalignment and mechanical looseness can influence 1X, 2X, harmonics, direction and phase - and how to distinguish a plausible pattern from a confirmed diagnosis.

Discussion question: When diagnosing a difficult machine problem, which view has helped you more - the time waveform or the FFT spectrum - and why?

References and further learning

• SKF, Spectrum Analysis, guidance on identifying and trending component frequencies in machinery FFT spectra.
• Bently Nevada, Vibration and Dynamic Measurements, examples of waveforms, spectra, 1X components and phase references.
• Fluke, What Is Vibration Analysis? A Complete Guide, overview of time-waveform and FFT analysis.
• Fluke, Vibration Spectrum Analysis versus Overall Vibration Analysis, explanation of time-domain collection and FFT conversion.

Educational note: The examples are simplified for learning and d

From Mechanical Maintenance to Vibration Analysis - Part 4

In Part 3 - Displacement, Velocity and Acceleration, we learned that the measurement quantity changes which part of a vibration signal is emphasized.

Now we move to the two plots an analyst uses most often:

The time waveform shows what the vibration did over time. The FFT spectrum shows how that vibration is distributed across frequency.

They are not two unrelated measurements. The spectrum is calculated from the sampled time waveform. Each view organizes the same signal differently, and each can reveal evidence that is difficult to see in the other.

Start with the time waveform

A time waveform plots:

• Amplitude on the vertical axis - displacement, velocity or acceleration; and
• Time on the horizontal axis - normally seconds or milliseconds.

The waveform answers questions such as:

• Is the motion smooth and repeating?
• Are there impacts, clipping, beats or modulation?
• How far apart are repeated events?
• Is the signal symmetrical?
• Does the vibration change during the record?

A clean sinusoidal waveform suggests that one frequency dominates. A complex machine waveform usually contains several vibration sources at the same time: shaft rotation, coupling forces, gears, bearings, blades, hydraulic activity, structural response and background noise.

Period and frequency

If a feature repeats every T seconds, its frequency is:

Frequency (Hz) = 1 / period (seconds)

Running frequency (Hz) = speed (rpm) / 60

For a motor running at 1,500 rpm:

1,500 / 60 = 25 Hz

One shaft revolution therefore takes:

1 / 25 = 0.04 seconds, or 40 milliseconds

If a waveform contains a strong event every 40 ms, the repetition rate is synchronous with running speed. That is useful evidence, but it does not by itself prove unbalance or any other single fault.

What the FFT spectrum does

The Fast Fourier Transform, or FFT, is a mathematical method that separates a sampled waveform into frequency components. The resulting spectrum normally plots:

• Amplitude on the vertical axis; and
• Frequency on the horizontal axis, commonly in hertz, cycles per minute or orders.

Instead of asking when an event happened, the spectrum helps us ask:

• Which frequencies contain the most vibration?
• Do peaks correspond with shaft speed or component frequencies?
• Are harmonics or sidebands present?
• Which peaks are changing over time?

A spectrum makes repeating components easier to separate. However, it removes much of the timing shape that can make impacts, modulation and transient behaviour obvious in the waveform.

Time waveform versus FFT spectrum

Question	Time waveform	FFT spectrum
Horizontal axis	Time	Frequency or order
Especially useful for	Impacts, beats, modulation, clipping, non-stationary events and waveform shape	Separating periodic components, identifying orders, harmonics, sidebands and component-related frequencies
What may be hidden	Closely spaced frequency components can overlap visually	The timing and shape of individual events can be difficult to recognize
Best practice	Review both views with the same units, point, direction, speed, load and acquisition settings.

Understanding 1X, 2X and harmonics

Analysts often express frequency as a multiple of shaft-running speed:

• 1X means once per shaft revolution.
• 2X means twice per shaft revolution.
• 3X means three times per shaft revolution.

For the 1,500 rpm motor:

• 1X = 25 Hz
• 2X = 50 Hz
• 3X = 75 Hz
• 4X = 100 Hz

Integer multiples of a fundamental frequency are called harmonics. A series at 1X, 2X, 3X and higher orders tells us that the waveform contains repeating non-sinusoidal content related to shaft rotation.

A harmonic family is a pattern, not a diagnosis. Several conditions can generate harmonics, and the same fault can look different on different machines.

Before attaching a fault name, compare the pattern with measurement direction, phase, machine construction, clearances, operating condition, history and physical inspection.

Worked motor-pump example

Consider a direct-coupled motor and centrifugal pump running steadily at 1,500 rpm. The pump impeller has six vanes.

1. Running speed: 1,500 / 60 = 25 Hz.
2. Shaft period: 1 / 25 = 0.04 s.
3. Vane-pass frequency: 6 vanes × 25 Hz = 150 Hz, or 6X.

Suppose the spectrum contains peaks at 25, 50 and 150 Hz.

• The 25 Hz peak is synchronous with shaft rotation.
• The 50 Hz peak is 2X running speed.
• The 150 Hz peak matches the calculated vane-pass frequency.

Those identities are defensible because they are based on measured speed and machine geometry. The cause still requires testing.

For example, a 1X peak could be influenced by unbalance, bent shaft, eccentricity, resonance, transmitted vibration or other mechanisms. A vane-pass peak may be influenced by normal hydraulic excitation, operating away from the best efficiency point, recirculation, clearance problems or structural amplification. The frequency tells us where to investigate; it does not complete the diagnosis.

What the waveform adds

If the waveform is smooth and repeats every 40 ms, shaft-synchronous motion may dominate. If sharp impacts repeat at the same interval, looseness, contact or another once-per-revolution event may be exciting a resonance. If the amplitude rises and falls in a regular envelope, modulation or beating may be present.

This is why the analyst should move between waveform and spectrum instead of relying on one display.

Sidebands and modulation

Sidebands are peaks spaced equally around a central frequency. Their spacing is important because it can identify the modulating frequency.

For example, peaks around 150 Hz separated by 25 Hz would be described as 1X sidebands around the vane-pass frequency:

125 Hz, 150 Hz and 175 Hz

The spectrum shows the spacing clearly, while the waveform may show the related rise and fall of amplitude. Sidebands are useful evidence of modulation, but their mechanical source must still be confirmed.

FFT settings can change what you see

A spectrum is not independent of its acquisition settings. Poor settings can hide peaks, merge nearby frequencies or display misleading amplitudes.

1. Frequency span or maximum frequency

The selected span must include the frequencies relevant to the suspected condition. A low span may show running-speed components clearly but exclude bearing or gear activity. A very high span can provide inadequate detail at low frequency if the number of spectral lines is unchanged.

2. Spectral lines and resolution

A useful approximation is:

Frequency resolution Δf ≈ frequency span / number of lines

Longer time record → finer frequency resolution

If the span is 1,000 Hz with 800 lines, the line spacing is approximately 1.25 Hz. Two components only 0.5 Hz apart will not be cleanly separated by that setup. To improve frequency resolution, the analyzer normally needs a longer time record.

3. Sampling rate and alias protection

The signal must be sampled fast enough for the selected frequency range. Frequencies above the usable range can fold into the displayed spectrum as false lower-frequency components, a problem called aliasing. Modern analyzers normally use anti-alias filtering, but the analyst must still use a suitable acquisition range and instrument configuration.

4. Window function and leakage

A finite time record rarely begins and ends at perfectly matching points in the vibration cycle. The FFT can then spread energy from a true component into adjacent frequency bins. This is called spectral leakage.

A window function reduces the discontinuity at the record ends. A Hanning window is common for general machinery spectra, while other windows may suit transient or amplitude-accuracy applications. Window choice involves trade-offs; it does not repair an unstable or incorrectly collected signal.

5. Averaging

Averaging several records can stabilize random variation and make repeatable components easier to see. Too much averaging can hide short-lived events. Select the averaging method and number of averages to match the machine behaviour and diagnostic question.

Orders versus hertz

Hertz is absolute frequency. Order is frequency divided by a selected reference speed.

At 1,500 rpm, 25 Hz is 1X. If speed changes to 1,800 rpm, 1X becomes 30 Hz. The physical shaft-related event remains once per revolution even though its frequency in hertz changes.

Order-based analysis is especially useful when speed varies. It helps distinguish components tied to rotational speed from frequencies that remain fixed. Accurate speed information from a tachometer, keyphasor or reliable speed measurement becomes essential.

A practical reading sequence

1. Confirm data quality. Check the point, direction, sensor mounting, units, range, overload status, speed and load.
2. Read the waveform first. Look for periodicity, impacts, modulation, clipping, beats and changes during the record.
3. Calculate known frequencies. Include shaft speeds, gear mesh, blade or vane pass and available bearing frequencies.
4. Read the spectrum. Identify dominant peaks, harmonics, subharmonics, sidebands and broadband regions.
5. Match frequencies to the machine. Use measured speed and actual component geometry, not guesswork.
6. Compare locations and directions. Horizontal, vertical and axial responses help test a hypothesis.
7. Compare with history. Trend amplitudes and patterns under similar operating conditions.
8. Seek confirmation. Use phase, high-resolution data, envelope analysis, temperature, oil analysis, process data or inspection as appropriate.
9. State uncertainty. Separate what the data proves from what it merely suggests.

Five common mistakes

Mistake 1: Diagnosing from the tallest peak

The tallest peak may be important, but amplitude can be influenced by structural response, measurement location, direction and operating condition. Identify the frequency and test the mechanism.

Mistake 2: Assuming every 1X peak means unbalance

Unbalance often produces running-speed vibration, but 1X is not unique to unbalance. Phase, direction, machine geometry and inspection evidence are needed.

Mistake 3: Ignoring the time waveform

A spectrum can make frequencies clear while hiding impact shape and timing. Always inspect the waveform when impacts, looseness, rubs or modulation are possible.

Mistake 4: Comparing spectra with different settings

Changes in span, lines, window, averaging, units or operating condition can change the display. Trend like with like.

Mistake 5: Trusting software labels without verification

Software can calculate peaks, orders and alarms quickly. It does not know every change in machine configuration, process condition, sensor installation or maintenance history. The analyst remains responsible for validation.

Final takeaway

The waveform and spectrum are two views of the same vibration signal.

• The time waveform preserves timing, shape and transient behaviour.
• The FFT spectrum separates repeating components by frequency.
• Running speed and machine geometry give peaks physical meaning.
• Acquisition settings determine what can be seen and resolved.
• A familiar pattern is evidence, not proof.

A good analyst does not ask, "Which plot gives the answer?" The better question is, "What does each view reveal, and what additional evidence will confirm the hypothesis?"

Coming in Part 5

Part 5: From Spectral Peaks to Fault Hypotheses. We will examine how unbalance, misalignment and mechanical looseness can influence 1X, 2X, harmonics, direction and phase - and how to distinguish a plausible pattern from a confirmed diagnosis.

Discussion question: When diagnosing a difficult machine problem, which view has helped you more - the time waveform or the FFT spectrum - and why?

References and further learning

• SKF, Spectrum Analysis, guidance on identifying and trending component frequencies in machinery FFT spectra.
• Bently Nevada, Vibration and Dynamic Measurements, examples of waveforms, spectra, 1X components and phase references.
• Fluke, What Is Vibration Analysis? A Complete Guide, overview of time-waveform and FFT analysis.
• Fluke, Vibration Spectrum Analysis versus Overall Vibration Analysis, explanation of time-domain collection and FFT conversion.

Educational note: The examples are simplified for learning and do not establish universal alarm limits or fault rules. Apply approved site criteria, applicable standards, manufacturer guidance and qualified engineering judgement to real machinery.

o not establish universal alarm limits or fault rules. Apply approved site criteria, applicable standards, manufacturer guidance and qualified engineering judgement to real machinery.

Displacement, Velocity and Acceleration: What Each Vibration Measurement Tells You

From Mechanical Maintenance to Vibration Analysis - Part 3

In Part 2 - From a Measurement to a Maintenance Decision, we followed the complete vibration-analysis workflow: understand the machine, collect repeatable data, validate the measurement, analyse the evidence, recommend an action and verify the result.

Now we address a question every new analyst meets:

Should I measure displacement, velocity or acceleration?

All three describe the same vibrating motion, but they emphasize different parts of the frequency range. Selecting the right quantity can make a machine condition easier to see. Selecting the wrong one can reduce or hide useful evidence.

Begin with one simple motion

Imagine a point on a bearing housing moving back and forth around its normal position:

• Displacement tells us how far the point moves.
• Velocity tells us how fast it moves.
• Acceleration tells us how quickly its velocity changes.

For a simple sinusoidal vibration at frequency f:

Velocity peak = 2 π f × displacement peak

Acceleration peak = 2 π f × velocity peak

Therefore, acceleration peak = (2 π f)² × displacement peak

This relationship explains the main selection principle:

• Displacement emphasizes lower-frequency motion.
• Velocity provides a useful balance across a broad middle-frequency range.
• Acceleration emphasizes higher-frequency activity.

This is not a rule that one quantity is always better than another. The right choice depends on the machine, bearing type, sensor, expected fault, speed and frequency range of interest.

1. Displacement: how far the vibration moves

Displacement is the change in position of the vibrating surface or shaft. Common units include:

• micrometres, or µm;
• millimetres, or mm; and
• mils, where 1 mil equals 0.001 inch.

Displacement is often displayed as peak-to-peak because that value represents the total travel from one extreme of the waveform to the other. Always confirm the convention in the instrument or software; µm peak, µm peak-to-peak and µm RMS are not interchangeable.

Where displacement is especially useful

• Low-frequency vibration and slow movement
• Shaft-relative vibration on machines with fluid-film bearings
• Large turbo-machinery where non-contact proximity probes observe shaft motion relative to the bearing housing
• Clearance-related questions where actual movement matters

A proximity probe measures the changing gap between the probe tip and the shaft. This is a different physical measurement from an accelerometer mounted on the bearing housing. One represents shaft-relative motion; the other normally represents absolute casing vibration. They should not be treated as if they were the same measurement.

Important limitation

As frequency increases, the displacement produced by high-frequency impacts can become extremely small. A developing rolling-element bearing defect may therefore be difficult to recognize in a displacement plot even though it is clear in acceleration or an appropriate demodulated measurement.

2. Velocity: how fast the vibration moves

Velocity is the rate of change of displacement. Common units are:

• millimetres per second, or mm/s; and
• inches per second, or in/s.

Overall casing velocity is frequently displayed as RMS. RMS is useful because it represents the effective energy of a varying signal, but you must still confirm the instrument configuration and frequency band before comparing values.

Where velocity is especially useful

• General condition monitoring of many rotating machines
• Broad assessment of casing vibration over a middle-frequency range
• Common mechanical conditions such as unbalance, misalignment and looseness when their frequencies fall inside the configured measurement band
• Trending overall machine condition under comparable operating states

Velocity does not give every frequency equal importance in every real measurement. Sensor response, integration, filtering and the selected frequency band still matter. However, compared with displacement and acceleration, velocity often provides a practical balance for general machinery monitoring.

Important limitation

An overall velocity value can tell you that vibration energy changed, but it cannot identify the cause by itself. Two machines can have the same overall velocity and completely different spectra. The analyst must review frequency, direction, location, phase, waveform, process condition and machine history.

3. Acceleration: how quickly velocity changes

Acceleration is the rate of change of velocity. Common units include:

• metres per second squared, or m/s²; and
• g, where 1 g is approximately 9.81 m/s².

Industrial accelerometers commonly use piezoelectric sensing elements. They are versatile, robust and capable of measuring a wide frequency range when the sensor, mounting and acquisition settings are suitable.

Where acceleration is especially useful

• Higher-frequency vibration
• Rolling-element bearing impacts
• Gear-mesh activity
• Blade- or vane-related frequencies
• Impulsive events and resonance excited by impacts

Acceleration is also commonly the original signal collected by a portable data collector. The instrument or software may mathematically integrate that signal to display velocity and, in some applications, displacement.

Important limitation

High-frequency acceleration can be sensitive to mounting quality. A hand-held probe, magnet, adhesive pad and stud do not provide identical frequency response. A loose or inconsistent mounting method can distort the very high-frequency information the analyst wants to examine.

A practical comparison table

Quantity	What it describes	Common display units	Often useful for
Displacement	How far the vibration moves	µm peak-to-peak, mils peak-to-peak	Low-frequency motion and shaft-relative vibration
Velocity	How fast the vibration moves	mm/s RMS, in/s peak or RMS	General casing-vibration condition monitoring
Acceleration	How quickly velocity changes	g peak, g RMS, m/s2	High-frequency, bearing, gear and impact-related activity

The entries are starting points, not universal rules. A specific monitoring program must follow the machine design, sensor specifications, applicable standards, original-equipment-manufacturer guidance, site procedures and engineering judgement.

Worked example: the same 1X vibration in three quantities

Consider a motor running at 1,500 rpm:

Frequency = 1,500 / 60 = 25 Hz

Suppose the 1X displacement is 100 µm peak-to-peak. For a simple sinusoid:

1. Displacement peak is half of peak-to-peak: 50 µm, or 0.000050 m.
2. Velocity peak = 2 π × 25 × 0.000050 = 0.00785 m/s, or 7.85 mm/s peak.
3. Velocity RMS = 7.85 / √2 = approximately 5.55 mm/s RMS.
4. Acceleration peak = 2 π × 25 × 0.00785 = approximately 1.23 m/s², or 0.126 g peak.

The motion has not changed. Only the quantity and amplitude convention used to describe it have changed.

Never compare 100 µm peak-to-peak directly with 5.55 mm/s RMS or 0.126 g peak as if they were competing severity numbers. They are different descriptions of the same sinusoidal motion.

Why frequency changes what you see

For the same displacement amplitude, increasing frequency increases velocity in direct proportion to frequency and acceleration in proportion to frequency squared.

This explains why:

• a slow shaft movement may look large in displacement but modest in acceleration;
• a high-frequency bearing impact may look small in displacement but strong in acceleration; and
• velocity often serves as a useful middle ground for general rotating-machine casing vibration.

It also explains why a single overall value cannot cover every failure mode equally well. A monitoring program may need overall velocity, acceleration spectra, bearing-condition measurements and shaft-relative displacement, depending on the asset.

Peak, peak-to-peak and RMS: do not ignore the convention

For a pure sine wave:

• Peak-to-peak = 2 × peak
• RMS = peak / √2

These simple conversions apply exactly to a pure sinusoid. Real machine vibration is usually a combination of frequencies, impacts and noise. Do not convert a broadband overall RMS value to peak or peak-to-peak using the sine-wave factors and assume the result represents the real waveform.

Before comparing readings, confirm all of the following:

• same physical quantity;
• same unit;
• same amplitude convention;
• same frequency band and filtering;
• same sensor and mounting method;
• same measurement point and direction; and
• comparable speed and load.

The sensor and the displayed quantity are not always the same

An accelerometer measures acceleration, but software can integrate its signal once to display velocity and twice to display displacement. This does not mean every converted result is equally reliable.

• Integration can magnify low-frequency noise, drift and sensor-settling effects.
• High-pass filters may remove low-frequency content.
• Sensor mounting and frequency response limit the usable high-frequency range.
• The selected acquisition range and resolution determine what enters the calculation.

Always check the actual sensor, its mounting, the acquisition setup and the displayed engineering units. Software cannot reconstruct information that the sensor and acquisition system did not capture correctly.

A practical selection guide

1. Define the machine and bearing type. A rigid-bearing motor and a fluid-film-bearing turbine do not require identical measurements.
2. Identify the failure mode of interest. Are you looking for slow shaft movement, general mechanical vibration, or high-frequency impacts?
3. Estimate the relevant frequency range. Use running speed, bearing geometry, gear teeth, blade or vane count and known excitation frequencies.
4. Select a suitable sensor and mounting. Confirm its usable frequency and amplitude range.
5. Select the quantity and convention. Record whether the result is displacement, velocity or acceleration and whether it is RMS, peak or peak-to-peak.
6. Trend like with like. Keep the point, direction, operating condition, band and setup consistent.
7. Use more than one view when needed. Combine overall trends with spectra, waveforms and other diagnostic techniques.

Three mistakes new analysts should avoid

Mistake 1: Asking which quantity is best

There is no universal best quantity. Ask which one is most sensitive and meaningful for the machine condition and frequency range being investigated.

Mistake 2: Comparing values without reading the units

A value of 5 can mean 5 mm/s RMS, 5 µm peak-to-peak or 5 g peak. The number alone is meaningless.

Mistake 3: Treating an overall value as a diagnosis

Overall vibration is useful for screening and trending. Diagnosis requires the frequency content, location, direction, time behaviour, operating condition and machine context.

Final takeaway

Displacement, velocity and acceleration are not three unrelated measurements. They are three connected ways of describing vibration.

Displacement answers how far. Velocity answers how fast. Acceleration answers how quickly the velocity changes.

The analyst's job is not to select a familiar unit automatically. It is to match the measurement quantity, sensor, frequency range and amplitude convention to the machine and the suspected condition.

Coming in Part 4

Part 4: Understanding the Time Waveform and FFT Spectrum. We will explain what each plot shows, how frequency relates to machine speed, what 1X and harmonics mean, and why a spectrum pattern should be treated as evidence rather than proof.

Discussion question: Which quantity do you use most often in your plant - displacement, velocity or acceleration - and what type of machine are you monitoring?

References and further learning

• Emerson, Vibration Analysis for Machinery Health Diagnosis, especially the comparison of typical sensors, units and applications.
• SKF, Introduction Guide to Vibration Monitoring, sections on displacement, velocity and acceleration.
• NI, What Is Vibration Monitoring?, sensor and measurement overview.
• Emerson Process Management, Basic Vibration Analysis - Course 2031, measurement-parameter fundamentals.
• Vibration Analysis Guide, beginner sections on amplitude, frequency and measurement quantities.

Educational note: The worked example assumes a pure sinusoidal signal and is intended to demonstrate the mathematical relationship between quantities. It is not a universal alarm limit. Apply approved site criteria, applicable standards, manufacturer guidance and qualified engineering judgement to real machinery.