Vibration Analysis: Acceleration vs Velocity vs Displacement (2026)
Acceleration vs velocity in vibration analysis — which parameter to measure at which frequency, units and conversion, and what an industrial sensor outputs to a PLC.
Acceleration is best for high-frequency faults (bearings, gears, >1 kHz). Velocity (mm/s RMS) is the standard for general rotating machinery (10–1,000 Hz). Displacement (µm or mils) suits low-speed shafts and journal bearing analysis (<10 Hz). Choosing the wrong parameter does not just produce noisy data — it masks the exact fault you are trying to catch.
The three parameters are mathematically related: velocity is the integral of acceleration, and displacement is the integral of velocity. Every vibration sensor measures one natively and derives the others through integration or differentiation in firmware or your PLC. Understanding which parameter carries useful signal at each frequency is the foundation of any condition monitoring strategy.
The Three Vibration Parameters Explained
Vibration is periodic motion. To describe that motion completely, engineers use three related but distinct physical quantities, each emphasising a different aspect of the waveform.
Acceleration
Acceleration is the rate of change of velocity over time. It is measured in g (gravitational units, where 1 g = 9.81 m/s²) or in m/s². Because acceleration is proportional to the square of frequency (a = ω² × d, where ω = 2πf), it amplifies high-frequency content strongly. A small, fast impact from a defective bearing race produces a large acceleration spike even if its displacement is only a few micrometres.
Piezoelectric accelerometers are the most common sensor type for acceleration measurement. They generate a charge proportional to the force applied and are robust enough for industrial environments rated to 120°C and beyond.
Velocity
Velocity describes how fast a surface is moving — the speed of the vibrating part, not just how far it travels. It is measured in mm/s (metric) or in/s (imperial), typically reported as RMS (root mean square), which correlates directly with the energy content of the vibration and therefore with mechanical stress and fatigue.
ISO 10816 and ISO 20816 — the primary international machinery vibration standards — specify velocity RMS in mm/s as the default measurement for assessing overall machine condition. For most rotating equipment running between 600 and 60,000 RPM, velocity provides the clearest picture of mechanical health.
Displacement
Displacement is the actual physical distance the vibrating surface travels, measured in µm (micrometres) or mils (thousandths of an inch). Because displacement is the double-integral of acceleration, it de-emphasises high frequencies and amplifies low-frequency motion. It is most useful when absolute shaft position matters — for example, in sleeve/journal bearings where shaft orbit relative to the bearing housing determines clearance and alignment.
Eddy-current proximity probes, mounted in the bearing housing, are the standard sensor for displacement. They measure shaft position without contact and are described in the API 670 standard.
Which Parameter to Use at Which Frequency
Frequency range is the single most important factor in parameter selection. At low frequencies, acceleration signals are tiny and easily lost in noise. At high frequencies, displacement values are so small they fall below sensor noise floors.
| Frequency Range | Best Parameter | Typical Application |
|---|---|---|
| < 10 Hz | Displacement (µm) | Low-speed machinery, journal bearings, reciprocating compressors |
| 10 Hz – 1,000 Hz | Velocity (mm/s RMS) | Motors, pumps, fans, gearboxes (overall machine health) |
| 1 kHz – 20 kHz | Acceleration (g peak or g RMS) | Rolling element bearings, gear mesh, cavitation |
| > 20 kHz | Acceleration (g, SEE, kurtosis) | Ultrasonic bearing defect detection, early-stage spalling |
The 10–1,000 Hz band is where most rotating machinery faults — imbalance, misalignment, looseness, resonance — produce their dominant energy. This is why velocity RMS is the default ISO measurement.
At frequencies above 1 kHz, the integration required to compute velocity amplifies low-frequency noise and makes the result unreliable. Acceleration in its native form is cleaner, and derived metrics such as envelope analysis and kurtosis extract fault-specific content from the raw acceleration waveform.
Why Acceleration for Bearings and Gears
Rolling element bearings fail through pitting, spalling, and fatigue cracks. Each contact event between a rolling element and a defect generates a brief, high-amplitude shock at characteristic defect frequencies (BPFI, BPFO, BSF, FTF). These events typically fall between 1 kHz and 20 kHz.
At 5 kHz, the equivalent displacement of a bearing fault may be only 0.01 µm — completely unmeasurable by an eddy probe and lost in the noise floor of a velocity transducer. The same event produces an acceleration spike of 5–10 g that a piezoelectric sensor captures clearly.
Gear mesh frequency follows the same logic. A 40-tooth gear running at 1,500 RPM produces mesh events at 1,000 Hz. Sidebands from a chipped tooth appear at the gear mesh fundamental and harmonics, well into the acceleration-sensitive range.
For vibration analysis basics including sensor mounting and frequency analysis, see our vibration analysis basics guide.
Why Velocity for General Machinery
The physical reason velocity works so well for general machinery is that mechanical stress is proportional to vibration velocity, not acceleration or displacement. A bearing race subjected to repeated stress cycles at high velocity fatigues faster regardless of frequency. ISO 10816-3 severity zones (A through D, from new machine to danger) are expressed entirely in mm/s RMS.
Practical thresholds for common equipment (ISO 10816-3, Group 1 — large machines > 15 kW):
| Zone | Velocity RMS (mm/s) | Meaning |
|---|---|---|
| A | 0 – 2.3 | Newly commissioned, acceptable |
| B | 2.3 – 4.5 | Acceptable for long-term operation |
| C | 4.5 – 7.1 | Alarm — schedule maintenance |
| D | > 7.1 | Danger — immediate action required |
Most modern IO-Link vibration sensors report velocity RMS in mm/s as their primary output precisely because these ISO thresholds are so widely understood. A field technician, a PLC programmer, and a maintenance engineer can all interpret 5.8 mm/s the same way without additional conversion.
For a deeper look at integrating condition monitoring into maintenance strategy, see condition monitoring vs predictive maintenance.
Why Displacement for Low-Speed Shafts
At shaft speeds below 600 RPM (10 Hz), a single revolution takes more than 100 milliseconds. Imbalance forces are low-frequency, and their acceleration values are extremely small — a 100-µm orbit at 5 Hz produces only 0.001 g of acceleration. No practical accelerometer can reliably resolve that signal above noise.
Displacement, however, makes the 100-µm shaft orbit directly visible and comparable against the bearing radial clearance (typically 150–250 µm for journal bearings). API 670 — the standard governing machinery protection systems for process-critical turbines, compressors, and pumps — mandates non-contacting eddy-current probes measuring displacement for all sleeve-bearing machines.
Reciprocating machinery (engines, reciprocating compressors) also uses displacement extensively because the piston stroke is the fundamental operating parameter, and its low-frequency harmonics carry diagnostic information about valve condition and rod load.
Units and Conversion Reference
The three parameters are linked by the frequency ω (in rad/s, where ω = 2πf):
- Velocity = Acceleration / ω (integration in frequency domain)
- Displacement = Velocity / ω = Acceleration / ω²
For sinusoidal vibration at a single frequency f (Hz):
| From | To | Formula (peak values) |
|---|---|---|
| Acceleration a (g peak) | Velocity v (mm/s peak) | v = (a × 9,810) / (2πf) |
| Velocity v (mm/s peak) | Displacement d (µm peak) | d = (v × 1,000) / (2πf) |
| Acceleration a (g peak) | Displacement d (µm peak) | d = (a × 9,810 × 10⁶) / (2πf)² |
RMS vs Peak: Peak = RMS × √2 for a pure sine wave. Real machinery vibration is broadband, so sensors report RMS over a frequency band, not peak of a single tone. Always confirm whether a sensor datasheet specifies g peak, g RMS, or g peak-peak before scaling in the PLC.
Worked example: A motor bearing running at 3,000 RPM (50 Hz) shows 4 g peak acceleration at the bearing defect frequency.
- Velocity peak = (4 × 9,810) / (2π × 50) = 39,240 / 314.2 = 124.9 mm/s peak (88.3 mm/s RMS)
- Displacement peak = 124,900 / (2π × 50) = 124,900 / 314.2 = 397 µm peak
At 50 Hz, 4 g is clearly significant; 397 µm is detectable but not obvious without the context of bearing clearance; 88 mm/s RMS is far above any ISO zone D threshold — all three representations confirm the same fault.
Signal and Noise Characteristics
Understanding signal quality at each frequency is as important as understanding the physics.
Acceleration sensors have a flat frequency response from roughly 1 Hz to 10–20 kHz (model-dependent). Below 1 Hz, DC offset and thermal drift dominate. Integration to velocity amplifies low-frequency drift significantly, which is why most sensors apply a high-pass filter (typically 10 Hz) before integration in firmware.
Velocity transducers (geophone or magnetic-inductive types) have a natural resonance around 10 Hz. Below resonance, sensitivity falls sharply. Above ~1 kHz, the output degrades. Their sweet spot perfectly matches the ISO 10816 general machinery band, which is why they were the industrial standard for decades.
Eddy-current proximity probes are DC-coupled and measure static position as well as dynamic vibration. They cannot measure high frequencies above ~10 kHz, but they resolve sub-micrometre position at very low speeds, which no other sensor type can do.
How to Choose the Right Parameter for Your Machine
Use this decision table when specifying a sensor or configuring a PLC alarm strategy:
| Machine Type | Speed Range | Primary Parameter | Secondary Parameter |
|---|---|---|---|
| Electric motor (rolling element bearings) | 1,000–3,600 RPM | Velocity RMS (mm/s) | Acceleration (g) for bearing health |
| Centrifugal pump | 1,000–3,600 RPM | Velocity RMS (mm/s) | Velocity spectrum for cavitation |
| High-speed spindle / milling head | 3,600–30,000 RPM | Acceleration (g) | Velocity for overall level |
| Gearbox | Any | Acceleration (g) | Velocity for overall housing level |
| Paper machine roll (slow) | 50–300 RPM | Velocity RMS (mm/s) | Displacement for shaft orbit |
| Steam turbine / large compressor | 1,500–3,600 RPM | Velocity RMS (mm/s) | Displacement (eddy probe, API 670) |
| Reciprocating compressor | 300–600 RPM | Displacement (µm) | Acceleration for valve knock |
| Cooling tower fan (very slow) | < 200 RPM | Displacement (µm) | Velocity for low-frequency imbalance |
The rule of thumb: if the machine has rolling element bearings and runs above 600 RPM, start with velocity for overall health and add acceleration for bearing-specific monitoring. If the machine uses sleeve/journal bearings or runs below 600 RPM, lead with displacement.
What an Industrial Vibration Sensor Actually Outputs — and How to Scale It in a PLC
This is where most implementation guides stop short. Knowing the physics is not enough; you need to know what signal arrives at the PLC analog input or digital fieldbus port.
IO-Link Vibration Sensors
Modern IO-Link vibration sensors (such as those from ifm, Balluff, and Pepperl+Fuchs) typically output two process data values simultaneously over the IO-Link digital channel:
- v-RMS in mm/s (overall velocity, 10–1,000 Hz band)
- a-peak in g (peak acceleration, 1–5 kHz band for bearing health)
Some models also provide temperature and a third value such as kurtosis or crest factor for early-stage bearing diagnostics. The IO-Link IODD (device description) specifies the exact scaling and data type for each value. In a Siemens or Allen-Bradley system, the IO-Link master maps each variable to a PLC data register automatically once the IODD is imported.
4–20 mA Analog Sensors
Traditional industrial vibration transmitters output a single 4–20 mA signal representing one parameter over a defined range. Common configurations:
| Output | Typical Range | PLC Scaling (12-bit ADC, 0–4,095 counts) |
|---|---|---|
| Velocity RMS | 0–25 mm/s | mm/s = (counts / 4,095) × 25 |
| Velocity RMS | 0–50 mm/s | mm/s = (counts / 4,095) × 50 |
| Acceleration peak | 0–10 g | g = (counts / 4,095) × 10 |
| Acceleration RMS | 0–5 g | g = (counts / 4,095) × 5 |
Always verify the sensor datasheet for the exact range. A 4 mA offset maps to 0 counts only if you subtract the 4 mA live-zero in the PLC scaling block. In ladder logic or structured text, the scaling function is:
Eng_Value := ((Raw_Count - Zero_Count) / (Span_Count - Zero_Count)) * Full_Scale_Eng;
Where Zero_Count = 819 (4 mA on a 0–20 mA ADC card mapped to 0–4,095), Span_Count = 4,095 (20 mA), and Full_Scale_Eng is the sensor's full-scale engineering value (e.g., 25.0 for a 0–25 mm/s transmitter).
PLC Alarm Strategy by Asset Class
Once the raw counts are scaled to engineering units, configure alarms in the PLC using ISO 10816 zone boundaries for velocity, or manufacturer-recommended thresholds for acceleration:
| Asset Class | Warning Alarm | Shutdown Alarm | Parameter |
|---|---|---|---|
| General motor / pump (ISO 10816-3 Group 1) | 4.5 mm/s RMS | 7.1 mm/s RMS | Velocity |
| General motor / pump (Group 2, < 15 kW) | 3.5 mm/s RMS | 5.6 mm/s RMS | Velocity |
| Rolling element bearing (trend-based) | Baseline + 3 dB | Baseline + 6 dB | Acceleration (g) |
| Journal bearing (API 670) | 75% of clearance | 90% of clearance | Displacement (µm) |
For a complete implementation reference covering sensor wiring, analog input modules, and alarm ladder rungs, see the PLC predictive maintenance complete guide. For the broader context of industrial sensor types and signal types, the types of industrial sensors guide covers transducer selection across temperature, pressure, and vibration. For connecting vibration systems over PROFINET, EtherNet/IP, or Modbus, see the PLC communication protocols complete guide.
Summary: Parameter Selection at a Glance
- Acceleration (g): High-frequency faults, bearings, gears, >1 kHz. Native output of piezoelectric sensors.
- Velocity (mm/s RMS): General rotating machinery health, 10–1,000 Hz, ISO 10816 compliance. Most IO-Link sensors report this as primary output.
- Displacement (µm or mils): Low-speed machinery, journal bearings, shaft orbit, API 670. Requires eddy-current probe.
- Conversion: All three parameters are mathematically linked through frequency; sensors integrate or differentiate internally, but integration amplifies low-frequency noise — always apply a high-pass filter before integration.
- In the PLC: Scale 4–20 mA counts to engineering units before comparing against ISO zone thresholds; IO-Link sensors deliver pre-scaled values directly over the digital channel.
Frequently Asked Questions
When should you use acceleration vs velocity in vibration analysis?
Use acceleration (measured in g) when diagnosing high-frequency faults above approximately 1 kHz — primarily rolling element bearing defects, gear mesh faults, and cavitation events. Use velocity (measured in mm/s RMS) for overall machine health assessment of rotating machinery running between 600 and 60,000 RPM, which is the frequency range covered by ISO 10816 and ISO 20816. The practical rule: acceleration for bearing-specific monitoring, velocity for machine-level trending and ISO compliance.
What is the difference between velocity and acceleration in vibration?
Acceleration is the rate of change of velocity — mathematically, acceleration = dv/dt. In vibration terms, acceleration is proportional to force and emphasises high-frequency, short-duration events like bearing impacts. Velocity is the speed of the vibrating surface and correlates directly with mechanical stress and fatigue energy. A piezoelectric accelerometer measures acceleration natively; velocity is obtained either from a dedicated velocity transducer (geophone) or by integrating the accelerometer signal in firmware. Because integration amplifies low-frequency noise, most sensors apply a 10 Hz high-pass filter before integration.
What units are used for vibration measurement?
The three standard vibration units are: g (gravitational units) or m/s² for acceleration; mm/s (or in/s) RMS for velocity; and µm (micrometres) or mils (1 mil = 25.4 µm) for displacement. ISO 10816 specifies velocity in mm/s RMS as the default unit for machinery condition assessment. API 670 — the standard for turbomachinery protection systems — specifies displacement in µm or mils peak-peak for shaft orbit measurement.
When do you use displacement in vibration analysis?
Use displacement (µm or mils) when monitoring low-speed rotating machinery (typically below 600 RPM) or machines equipped with sleeve/journal bearings. At low speeds, acceleration values from imbalance and misalignment are tiny and easily masked by sensor noise, but the corresponding shaft orbit displacement may be tens or hundreds of micrometres — easily measurable by a non-contacting eddy-current proximity probe. Displacement is also the mandatory measurement parameter under API 670 for process-critical machines (steam turbines, centrifugal compressors, large pumps) where shaft position relative to bearing clearance is the primary safety variable.
