Displacement, velocity and acceleration
Vibration can be expressed three ways. They are related by frequency, so each one emphasises a different part of the spectrum:
| Quantity | Typical unit | Emphasises | Used for |
|---|---|---|---|
| Displacement | µm or mils, peak to peak | Low frequencies (below about 10 Hz) | Shaft motion in sleeve bearings (proximity probes), very slow machines |
| Velocity | mm/s or in/s, RMS | Mid frequencies (about 10 Hz to 1 kHz) | Overall machine condition and most severity standards (ISO 20816 series); unbalance, misalignment, looseness |
| Acceleration | g or m/s² | High frequencies (above about 1 kHz) | Bearing and gear defects, envelope analysis, impacts |
Almost all condition monitoring sensors measure acceleration. Velocity and displacement are calculated by integration, which amplifies low-frequency noise. That is why the sensor's low-frequency noise floor matters so much on slow machines.
MEMS or piezoelectric?
Two sensing technologies dominate industrial accelerometers.
| MEMS (micro-electro-mechanical) | Piezoelectric (ICP/IEPE or charge) | |
|---|---|---|
| How it works | A tiny silicon proof mass; movement changes a capacitance | A crystal or ceramic produces charge when stressed by a seismic mass |
| Low-frequency response | Down to 0 Hz (DC), so no low-frequency roll-off | Rolls off below a corner frequency, typically 0.5–3 Hz; special low-frequency models reach about 0.1–0.2 Hz |
| Upper usable frequency | Commonly a few kHz; better devices about 6–10 kHz; check the data sheet | Typically 10–15 kHz or more; resonance at 20–50 kHz |
| Noise floor | Higher; can hide small signals at low frequency and low amplitude | Lower; better for slow machines and early defects |
| Power | Very low, ideal for battery-powered wireless | Needs constant-current excitation; more power per measurement |
| Cost and size | Low, small, often several axes on one chip | Higher; triaxial piezo sensors are larger and cost more |
| Best fit | Standard-speed balance-of-plant on wireless sensors: motors, pumps, fans | Slow speed, high speed, gearboxes, critical assets, early bearing detection |
The practical rule
For standard-speed machines (about 600 to 3,600 rpm) where the frequencies you need stay below roughly 5 kHz, MEMS sensors on wireless nodes are usually enough and keep battery life and cost down. Choose piezo when the machine is slow, when you need clean data above about 6 kHz (gear mesh harmonics, high-speed machines, early bearing defects), or when the asset is critical enough to justify the best signal.
Other sensor specifications that matter
- Sensitivity (mV/g for piezo): 100 mV/g is general purpose; 500 mV/g suits slow machines with small signals; 10–50 mV/g suits high-amplitude, high-frequency applications.
- Measurement range (±g): must exceed the largest peaks, including impacts. Clipping destroys envelope and crest factor information.
- Resonant frequency: data near resonance is amplified and unreliable. Keep the useful range below about one third of the mounted resonance.
- Axes: triaxial sensors measure horizontal, vertical and axial directions at once. Uniaxial sensors are cheaper but see only one direction.
- Temperature range and ingress protection: check against the surface temperature, wash-down, and outdoor exposure.
- Hazardous area certification: required in classified areas (see the IIoT page).
Mounting changes the frequency response
The mount and the sensor form a spring-mass system with its own resonance. A stiff, light mount pushes that resonance high, so the sensor reads true up to high frequencies. A soft or heavy mount lowers it, and everything above is distorted or lost. Mounting can easily cost you the bearing fault frequencies you bought the sensor for.
Solid bars show the range most installations achieve; the lighter extension is the best case with careful preparation. Values are indicative; the sensor data sheet and your own surface preparation decide the real limit.
Mounting practice for permanent wireless sensors
- Prefer a stud on a spot-faced surface: machined flat, tapped perpendicular, a thin film of grease or coupling fluid, and the specified torque.
- Where drilling is not allowed, use an epoxy-bonded mounting pad: clean and degrease the surface, keep the bond line thin, use a curved-base pad on round housings, and let it cure.
- Avoid magnets for permanent installations: they can move, collect debris and lose high-frequency response. Use them for pilots and temporary checks.
- Record the mounting method in the asset register. A change in mounting looks like a change in machine condition.
Where to place sensors
- On the bearing housing, as close as possible to the bearing and in the load zone, with the shortest, stiffest path from bearing to sensor.
- Not on fan covers, thin sheet metal, guards or end bells far from the bearing. Avoid crossing joints and gaskets.
- One sensor per bearing is ideal. With a limited budget, put one triaxial sensor at the drive-end bearing of the motor and one at the drive-end bearing of the driven machine; these see most coupling, alignment and bearing faults.
- Orientation: on horizontal machines, radial horizontal usually has the highest amplitude (lowest stiffness); vertical carries gravity and load; axial shows misalignment and thrust. On vertical machines, measure two radial directions 90° apart at the top bearing.
- Gearboxes: one sensor per shaft bearing if possible, at least input and output; place near the bearing carrying the gear load.
- Overhung and belt-driven machines: measure on the bearing nearest the load or pulley.
- Consistency: the same point, direction and mount every time. Mark and label locations.
| Machine train | Ideal sensor count | Minimum practical (wireless budget) |
|---|---|---|
| Motor + centrifugal pump, 4 bearings | 4 triaxial | 2 triaxial (motor drive end, pump drive end) |
| Motor + fan, overhung impeller | 4 triaxial | 2 triaxial (motor drive end, fan bearing nearest impeller) |
| Motor + single-stage gearbox + driven machine | 6–8 | 3 triaxial (motor drive end, gearbox input, gearbox output) |
| Close-coupled pump (motor and pump share a shaft) | 2 | 1 triaxial at the pump end |
| Vertical pump | 2–3 at the motor top and bottom bearings | 1 triaxial at the motor top bearing |
Data settings: Fmax, lines and record length
Every spectrum is defined by a few settings:
- Fmax, the highest frequency in the spectrum. It must cover the fault frequencies you care about and a few harmonics.
- Sampling rate: Fs = 2.56 × Fmax in most instruments, which leaves room for the anti-aliasing filter.
- Lines of resolution: the number of frequency bins. Resolution Δf = Fmax ÷ lines.
- Record length: T = lines ÷ Fmax seconds. Finer resolution needs a longer record, which uses more battery and is more affected by speed changes.
- Envelope (demodulation) band: a high-frequency band, often around 1–10 kHz on standard machines, in which bearing impacts excite structural resonances. Envelope analysis recovers the impact rate from it.
Common rules of thumb: Fmax of at least 10× running speed for unbalance and misalignment, about 40× running speed or 4× the inner race frequency for rolling bearings, and 3× gear mesh frequency for gearboxes. Choose enough lines that the resolution is a tenth of running speed or finer, which also means each record covers at least ten shaft revolutions.
Bearing frequencies here use the rough approximation BPFO ≈ 0.4 × rolling elements × running speed and BPFI ≈ 0.6 × rolling elements × running speed. Use the bearing manufacturer's geometry when you know the bearing number. Slide the speed down to 60 rpm and watch the record length grow: slow machines need long, quiet records, which is exactly where low-noise piezo sensors earn their cost.
Variable speed machines
When speed changes during a record, spectral peaks smear across several bins. Remedies: trigger measurements only within a speed and load window, record speed (from a tachometer, from the 1× peak, or from the drive), normalise spectra to orders of running speed, and keep records short enough that speed is stable. For machine learning models, record operating state alongside each measurement so baselines compare like with like.
Key takeaways
- Sensors measure acceleration; velocity is best for overall condition, acceleration for bearings and gears.
- MEMS suits standard-speed wireless monitoring; piezo suits slow, high-speed, gear and critical applications.
- Mounting sets the usable frequency range: stud best, epoxy next, magnets for temporary work only.
- Place sensors on bearing housings in the load zone; at minimum, the drive-end bearings of motor and driven machine.
- Set Fmax from the fault frequencies, and lines so each record covers ten or more revolutions.
Try it in the apps
The Program Setup app applies these rules to every asset in your list: sensor count, triaxial or uniaxial, MEMS or piezo, mounting, Fmax, lines and record length.