# Vibration measurement settings: Fmax, number of lines, window and averaging > Two people taking a reading from the same bearing housing will come back with different pictures. One gets a single thick peak in the spectrum; the other, at the same spot, gets three separate lines. Same instrument, same machine — the only difference is the settings. Below, we go through the numbers you set before a reading and what each one does to the picture on screen. **In short:** Three settings are rigidly linked: Δf = Fmax / N = 1 / T. Fmax decides what you'll see at all, the number of lines N decides how finely, and you get the record length T thrown in, with an obligation to hold the speed steady across the whole interval. For balancing, an Fmax of roughly ten times the running frequency and 400–1600 lines is enough. For bearings and gear meshes you need kilohertz on acceleration, and to separate two close lines, 6400 lines or more. Source: https://axiline.pt/en/articles/vibration-measurement-settings/ Publisher: AXILINE · Vila Nova de Gaia, Portugal · +351 931 831 229 · axilinegeral@gmail.com ## Three settings, tied together by one formula An instrument doesn't 'see' vibration as a whole. It records a finite length of signal and breaks it down into a finite number of frequency lines. Anything that falls outside that record, or between the lines of that grid, doesn't exist for you. Remember the relationship the whole rest of this piece grows out of: Δf = Fmax / N, and at the same time Δf = 1 / T. Here Fmax is the upper bound of the spectrum, N is the number of lines, Δf is the spacing between adjacent lines, and T is the record length. From this, T = N / Fmax. Read it this way. Fmax answers 'what will I see': above that frequency, there's nothing for you. The number of lines answers 'how finely': two peaks that land in one line merge into one. And you don't choose the record length at all — it's calculated automatically, and it's exactly what determines how many seconds the machine has to hold a steady mode. A one-line example. Fmax = 1000 Hz, N = 1600 lines. So Δf = 0.625 Hz, and the record lasts 1.6 s. Want twice the resolution? The record becomes 3.2 s. Want to raise Fmax to 10 kHz and keep the same 1600 lines? Resolution gets ten times coarser, to 6.25 Hz, and close lines merge. > Averaging plays no part in this formula. It stabilizes the amplitude and suppresses random noise, but it doesn't improve frequency resolution by even one hertz. This is the most common point of confusion for people just starting to collect their own data. ## Fmax: the upper bound, chosen for the task Set Fmax by the highest frequency you're actually looking for, and add a threefold margin. Not 'ten times, just in case': a wide view costs you resolution and adds high-frequency noise to the reading. For overall level and for the 'balance or not' decision, a wide band isn't needed. What you need is the running-speed component 1x — the vibration at the rotation frequency — and its first few harmonics (frequencies that are multiples of it). A fan at 1450 rpm gives 1x = 24.2 Hz; an Fmax of 250–500 Hz covers 1x…20x with margin to spare, and resolution at 1600 lines comes out very fine. Separately, check which band your standard is defined in: overall vibration under ISO 20816 is assessed as mm/s RMS (root mean square, also called RMS) in the 10–1000 Hz band, and your instrument's band needs to cover that standard, or the numbers aren't comparable. Bearings and gear meshes live higher up. Early rolling-element bearing defects excite high-frequency resonances roughly in the 2–10 kHz range and show up in acceleration, not velocity. A typical benchmark: a gearbox with a 3.2 kHz mesh frequency needs an Fmax around 10 kHz on acceleration. And here a limit kicks in that no setting can get around. It's the sensor mounting, not the instrument's menu, that caps the top frequency. - A stud: up to 10 kHz and beyond. The only option if you're seriously chasing bearings and gear mesh. - An adhesive pad: roughly up to 5–7 kHz. - A two-pole magnet: roughly up to 5 kHz. - A magnet on a flat, ground pad: roughly 1.5–2 kHz. It holds up for the ISO 20816 standard in the band up to 1000 Hz, but for a bearing's envelope spectrum — the processing that pulls the impact rhythm out of the high-frequency band — it's no longer enough. - A handheld probe: 300–500 Hz and poor repeatability. Not usable for a trend. - A sensor on paint or an uneven surface: the mounting's own resonance drops to under 1 kHz, and you get a 'defect' that isn't there. > A classic trap: you take a bearing envelope reading with a magnet and find a 1.8 kHz peak. Remount on a stud, and the peak disappears. That was the magnet's own resonance, landing inside the demodulation band — the very high-frequency band the envelope is built from. Another one: a 412 Hz line that doesn't match any calculated frequency of the machine. At a sampling rate (samples per second) of 5120 Hz and an Fmax of 2000 Hz, through an imperfect anti-aliasing filter — which is supposed to cut off everything above the working band — a 4708 Hz component from a bracket resonance 'folded back' into view. The rule: sampling rate should be no lower than 2.56·Fmax, and a suspicious peak needs to be checked by re-recording at a different Fmax. Sources: [ISO 20816-1:2016](https://www.iso.org/standard/63180.html) · [ISO 13373-3:2015](https://www.iso.org/standard/40840.html) ## Number of lines: how to separate two close peaks The number of lines determines whether you can tell two neighboring frequencies apart or just see one thick hump. Practical rule of thumb: to reliably separate two peaks, make Δf no more than a third of the gap between them. If the peaks sit 0.9 Hz apart, a 1 Hz resolution won't get you anywhere. From there it's just arithmetic, and it's always the same. Work out your target frequencies. Find the smallest gap between them. Divide it by three to get the Δf you need. From Δf and Fmax, get the number of lines; from Δf, get the record length. Only then go to the instrument. A typical worked example. An induction motor at 1480 rpm, 1x = 24.67 Hz. You suspect a broken rotor bar, which produces sidebands — companion lines flanking the main one — around 1x spaced by 2·s·P, where s is slip and P is the number of pole pairs. At 1.3% slip and two pole pairs, the spacing is 1.3 Hz, meaning you need to resolve 24.67 and 23.37 Hz. You need a Δf of about 0.3 Hz and a record no shorter than 3.3 s. A setting of N = 6400 at Fmax = 2000 Hz gives Δf = 0.3125 Hz and T = 3.2 s. You'll see the sidebands. A second worked example, closer to the shop floor. Two fans run in a common duct at 24.5 and 24.9 Hz, there's an audible beat, and it's unclear whose vibration it is. The gap is 0.4 Hz, so Δf needs to be no more than 0.13 Hz, and the record no shorter than 7.5 s. The same story applies to a motor's running frequency sitting near the mains line: 4x at 1486 rpm lands on 99.07 Hz, and twice the mains frequency sits at 100 Hz. The gap is 0.93 Hz, needing a Δf of roughly 0.2–0.3 Hz and a 4–5 s record. Resolution can be raised two ways: lower Fmax or raise N. Both lengthen the record, because T = N / Fmax. There's no way around this — it's a property of the Fourier transform, not stinginess on the instrument maker's part. A compromise that doesn't cost you the overview is the zoom function: it calculates a fine spectrum in a narrow band around the frequency you're interested in, without increasing the total number of lines across the whole spectrum. Useful around a gearbox's mesh frequency, where you need to separate sidebands without losing Fmax across the rest of the spectrum. - The minimum found on instruments: 400 lines. Good only for overall level. - The working setting for a route: 1600 lines. Covers unbalance, misalignment, looseness, blade-pass frequencies. - Fine analysis: 6400–12,800 lines. Sidebands, rotor bars, close frequencies, the mesh zone. - Don't set 6400 everywhere 'just in case': acquisition time quadruples, and the route won't fit in a shift. ## Table: task, Fmax, resolution, what to look at | Task | Fmax | Resolution | What to look at | | --- | --- | --- | --- | | Decide whether balancing is needed | 10x running speed, typically 200–500 Hz | 400–1600 lines, Δf ≈ 0.3–1 Hz | Amplitude and phase of 1x (phase is the vibration's angle relative to the tachometer marker), the ratio of 1x to overall vibration, the height of 2x and 3x | | Assess overall condition under ISO 20816 | 10–1000 Hz band | Coarse is fine; the number matters more than the picture | mm/s RMS and the rise from baseline, not the absolute value in isolation from history | | Misalignment, looseness, rubbing | 10–20x running speed, typically 1000 Hz | 1600 lines, Δf ≈ 0.6 Hz | 1x, 2x, 3x, half-orders 0.5x and 1.5x, the noise floor, the axial direction | | Blade-pass frequency, pump or fan hydraulics | 5–10x blade-pass frequency | 1600 lines | The peak at z·1x and its harmonics, a broadband rise under cavitation | | Motor rotor bars, a mains line near 1x | 200–2000 Hz | 6400–12,800 lines, Δf ≤ 0.2–0.3 Hz | Sidebands around 1x spaced by 2·s·P, the line at twice the mains frequency | | Rolling-element bearings, early stage | 5–10 kHz on acceleration, plus an envelope in the 2–10 kHz band | 1600 lines on the envelope | BPFO, BPFI, BSF, FTF (calculated defect frequencies for the outer race, inner race, rolling elements and cage), sideband spacing, crest factor (peak-to-RMS ratio), bearing temperature | | Gear mesh and its sidebands | At least 3·GMF (GMF is the mesh frequency), typically 5–10 kHz | 6400 lines, or zoom around GMF | The mesh frequency and sideband spacing: the spacing equals the running frequency of the defective gear | | Finding resonance, run-up and coast-down (free deceleration after the drive is switched off) | 1x…5x, tied to speed rather than a fixed band | No averaging, a tracking filter, or a coast-down recording | Amplitude and phase of 1x against rotation frequency: a sharp peak and a phase swing of roughly 180° | | A slow-speed unit, 20–100 rpm | 50–200 Hz | Δf ≤ 0.1 Hz, record no shorter than 10 s | Displacement in µm, the low-frequency spectrum, individual impacts in the time waveform | > The table gives you orders of magnitude, not a recipe for your specific machine. Work out the kinematics: the speed of each shaft, the number of blades, the number of teeth, the gear ratios. Settings get chosen after you've calculated the target frequencies, not before. ## Record length and stable speed You buy resolution with seconds, at a fixed exchange rate: Δf = 1 / T. Want 1 Hz? Record for a second. Want 0.1 Hz? Record for ten seconds. No amount of processing gets around this. Which brings up a requirement people forget most often. For all ten seconds, the machine has to hold one operating mode. A working criterion: speed drift over the record shouldn't exceed a quarter of Δf. Otherwise the line smears across two or more adjacent bins (a bin being one line of the frequency grid), its amplitude drops, and you conclude the defect went away. Translated into concrete numbers. A machine at 1500 rpm, you want Δf = 0.125 Hz, an 8 s record. A quarter of Δf is 0.03 Hz, roughly 0.13% of the running frequency, about 2 rpm. Over eight seconds, speed shouldn't drift by more than two rpm. On a constant-load motor, that's achievable; on a variable-frequency drive with a floating load, usually not. There's also a useful reverse signal on site. If the 1x amplitude and phase are drifting by more than 10–15% over the measurement, fine resolution won't help you: the machine is most likely running near resonance. Then change the speed, or, if you can't, change the mounting conditions on the foundation. Balancing in that state is pointless; the influence coefficient will come out unreliable. - [x] Target frequencies and the needed Δf were worked out before the reading, not after. - [x] Checked that speed holds steady over the record: watch the tachometer reading from start to finish, not just once. - [x] The operating mode was fixed: load, speed, temperature. A reading without a recorded mode can't be compared with the previous one. - [x] On a variable-frequency drive, don't chase a fine Δf. There, use order tracking, a tracking filter, or time-synchronous averaging keyed to the tachometer marker — methods that tie the measurement to the actual speed rather than to an absolute frequency scale. - [x] On a slow-speed unit, make peace with a long record in advance. A roll at 60 rpm gives 1x = 1 Hz, and separating 1x, 2x and nearby lines in one second is physically impossible. ## Averaging: how much, and when it hurts Spectrum averaging is needed against random noise. Each averaging pass lowers the noise floor in proportion to the square root of the number of averages: four averages give roughly a twofold improvement, sixteen give a fourfold one. Beyond that, returns drop off faster than acquisition time grows. A working setting for a route: 4 averages. If the shop floor is noisy or the reading is jumping around, set 8–10. 50% overlap saves time: neighboring records partly reuse the same samples. Worth knowing what averaging doesn't do, before you spend half an hour on it. It doesn't improve frequency resolution. It doesn't remove a steady 50 Hz mains pickup: that pickup is coherent and doesn't average out to zero; it's dealt with through grounding, shielding and cable routing. It doesn't save you from clipping: a clipped signal stays clipped. Now for the harm. Averaging assumes the process is the same across all the records. The moment that isn't true, averaging destroys exactly what you were looking for. ### Linear averaging All records weighted equally. The standard for a routine spectrum on a steady-state machine. This is what a route procedure means when it says '4 averages.' ### Exponential Recent data weighs more. Needed when you're following a changing signal in real time: adjusting speed, loading the machine, watching it warm up. ### Peak hold Captures the maximum across all records. Useful during coast-down and run-up, to catch a resonance peak. No good for an amplitude trend: you'll be comparing random outliers. ### Time-synchronous averaging (TSA) Averaging in the time domain, keyed to the tachometer marker. Anything not synchronous with rotation gets suppressed; only what repeats revolution to revolution survives. This is how 1x and its harmonics are isolated, and how shafts are separated in a multi-stage gearbox. > Where you must not average: an impact, a bump test (finding a structure's natural frequency by striking it), run-up and coast-down, any nonstationary process. In a bump test, you don't average spectra continuously — you average the responses to 3–10 individual triggered impacts. Continuous averaging smears the impulse response into noise, and the natural frequency disappears from the spectrum. And keep the time arithmetic in your head: a record lasts T, multiplied by the number of averages. 6400 lines and 4 averages across fifty route points won't fit in a shift, which is why 1600 is used for the route and 6400 only for suspect points. ## Windows: Hanning, flat top, rectangular The FFT (fast Fourier transform) assumes your record contains a whole number of periods of the signal. In real life that's almost never true — the record cuts off mid-cycle, and you get a discontinuity at the edges. That discontinuity spreads the energy of one honest line into its neighbors. This is called leakage, and it looks like blurred skirts around every peak. A window is a weighting function that smoothly tapers the start and end of the record to zero, so there's no discontinuity. The price is paid either in resolution or in amplitude accuracy. There's no universal window — there are three working options. ### Hanning: the default A reasonable balance between leakage and resolution. Effective line width about 1.5 bins. Understates a single peak's amplitude by up to 16% if the peak falls between grid lines. Use it for all routine steady-state spectra, for trends, and for checking whether 1x dominates. ### Flat top: accurate amplitude Amplitude error is practically zero, but the spectral line comes out wider, about 3.8 bins. Resolution is worse, and close lines merge. Use it when you need to accurately measure the height of one specific line: sensor calibration, checking against a reference, verifying a setpoint. In a normal diagnostic spectrum it just gets in the way. ### Rectangular: no window Best resolution and maximum leakage. Used where the signal itself decays to zero: an impact, a bump test, a transient. Also used with synchronous capture, when a whole number of revolutions fits into the record via the tachometer marker. ### Exponential For a bump test with long decay, when the response doesn't die out before the record ends. Boosts the start and forcibly damps the tail. > Spectra taken with different windows aren't directly comparable by amplitude. Fix the window in the point's procedure together with Fmax, the number of lines and the number of averages, and don't change it between routes. Otherwise a trend you've been building for six months gets reset, and there's almost no way to notice after the fact. ## The time waveform: always look at it A spectrum averages by nature. It honestly tells you which frequencies are present on average, and it hides one-off events. An early-stage bearing defect produces a rare impact once every few shaft revolutions. In the spectrum that impact smears into the noise floor; in the time waveform, you see distinct sharp spikes. So the rule is simple: open the time record before you start interpreting the spectrum. What to look for by eye: individual impulses, repeating bursts, clipped tops, asymmetry between the positive and negative half-cycles, envelope modulation, a rattle on only one half-cycle. Estimate the crest factor — the ratio of peak to RMS. For a clean sine wave it's 1.41; values of 4–5 and up point to an impact-type signal. To keep impacts from getting clipped, you need specific settings, not just the intention to see them. - Look at acceleration, not velocity. Integration essentially acts as a low-pass filter and smooths out short impulses. - Keep the upper bound on acceleration high. An impact a fraction of a millisecond wide needs a sampling rate in the tens of kilohertz. At an Fmax of 500 Hz, you physically won't see the impact's shape. - Record no fewer than 4–6 shaft revolutions. At 1500 rpm that's 0.25 s, though in practice people take 1–2 s; on a 60 rpm roll, you need about 6 s. - Check the input for saturation. Flat-topped peaks mean clipping: RMS reads low, and false harmonics that don't exist on the machine appear in the spectrum. - Mount the sensor rigidly and consistently. A jumpy high-frequency peak more often turns out to be a mounting resonance than a machine defect. - Tie the record to rotation. Revolution-start markers on the graph immediately show how many impacts occur per revolution, which is what tells a bearing apart from rubbing. ## Units and integration: where to look at what The same motion is described by three parameters, linked through frequency: v = ω·d, a = ω·v. From this follows which parameter is informative in which part of the spectrum. Displacement in µm — low frequencies, roughly up to 10 Hz: slow-speed units, clearances, relative shaft motion in a sleeve bearing. Vibration velocity in mm/s — the main working quantity in the 10–1000 Hz band: unbalance, misalignment, looseness, rubbing, and it's exactly what ISO 20816 states its criteria in. Acceleration in g or m/s² — everything above a kilohertz: bearings, gear mesh, the envelope spectrum. Integration inside the instrument isn't free. It boosts low frequencies, so sensor noise and a slow drift at 0.5–2 Hz turn into a characteristic 'hump' at the left edge of the spectrum and inflate the RMS reading. It's cured with a high-pass filter, but with care: a cutoff at 10 Hz will throw out a slow-speed machine's subharmonic (a component below running frequency) along with the noise. Differentiation does the opposite and inflates high-frequency noise. One last note on units, the thing two engineers with two instruments argue about. Don't convert RMS to peak 'for convenience': 4.5 mm/s RMS corresponds to 6.4 mm/s peak and 12.8 mm/s peak-to-peak only for a clean sine wave. If the standard is stated in RMS, report RMS. The discrepancy between true RMS and an analog detector on a non-sinusoidal signal can reach 20–30%, with both instruments working correctly. > The measurement band has to match the band the standard is written in. The Balanset-1A measures vibration-velocity RMS in the 5–200 Hz band. That's more than enough, with margin, for running-speed defects and balancing. But if acceptance is based on a figure in the 10–1000 Hz band, record in the report which band you actually measured in, and don't pass one number off as the other. ## Settings for balancing versus settings for diagnostics Let's separate two different jobs that often get mixed up. Balancing doesn't need fine resolution. It needs repeatability. You're working with one line, the running-speed one, and what matters is its amplitude and phase relative to the tachometer marker. Working setup: Fmax around ten times the running frequency, 400–1600 lines, a Hanning window, stable speed, the same mounting and the same direction on every run. If the 1x phase wanders by more than 10–15° between two identical runs, the influence coefficient will come out as garbage, and no increase in the number of lines will fix that. Diagnostics needs something else: a wide band on acceleration, a stud mount, an envelope spectrum, fine resolution applied precisely, only where you've already worked out which two lines you're separating. It takes longer, needs a different mount, and a different level of expertise. Let's be direct about where our instrument's boundary lies. The Balanset-1A gives vibration-velocity RMS of 0.02–80 mm/s in the 5–200 Hz band, speeds from 100 to 100,000 rpm, phase accuracy of ±1°, simultaneous two-channel acquisition, an FFT spectrum, a time waveform with revolution markers and a record length of 1, 5, 10, 15 or 20 s, harmonic analysis keyed to the tachometer marker, and coast-down recording. That's enough to decide 'balance or not,' compare two bearing housings, find a resonance from a coast-down, balance in one or two planes, and check the result. For hunting pitting on a bearing raceway, you need an analyzer with a high-frequency path and an envelope, and we won't claim otherwise. AXILINE's engineers design and build Balanset instruments and use them for field balancing themselves. If there's no time to sort out the settings, we come out with our own instrument, mount the sensors on your bearings, take a spectrum and the 1x vector, and tell you plainly whether it's unbalance or not. If you'd rather collect your own data, the instrument can be yours to keep: two accelerometers, a laser phase and speed sensor, a two-channel USB module with preamplifiers, integrators and an ADC, and Windows software with a polar diagram, splitting the weight across fixed positions, drilling calculation, saved influence coefficients, trim balancing, tolerance calculation by grade G under ISO 21940-11, and an archive for reports. Consulting support is included. - [x] Fmax set 'with margin' at ten times over: resolution went ten times coarser, and close lines merged into one peak. - [x] Fmax changed, number of lines left at default: Δf came out different, and the new spectrum isn't comparable with the old one. - [x] Settings change between routes: the spectrum trend gets reset, and detecting that after the fact is nearly impossible. - [x] A fine Δf set on a machine with a variable-frequency drive: speed drifts over the record, lines smear, amplitudes drop. - [x] Flat top left on for a routine spectrum: close lines merge, sidebands can't be read. - [x] Hanning applied to a bump test: the impulse response is suppressed, the natural frequency doesn't show up. - [x] Averaging left on during coast-down or an impact test: the event you're looking for gets averaged into noise. - [x] A magnet instead of a stud at an Fmax of 10 kHz: a mounting resonance sits inside the demodulation band and looks like a defect. - [x] Input not checked for saturation: peaks clipped, RMS reads low, false harmonics in the spectrum. - [x] Only the spectrum opened, the time waveform never looked at: rare bearing impacts missed. - [x] Mode not recorded: load, speed and temperature unknown, the reading can't be compared with the previous one. - [x] Measurement band doesn't match the band the standard is stated in. Sources: [ISO 20816-1:2016](https://www.iso.org/standard/63180.html) · [ISO 21940-11:2016](https://www.iso.org/standard/54074.html) · [ISO 13373-3:2015](https://www.iso.org/standard/40840.html) · [Balanset-1A operation manual](https://vibromera.eu/balanset-1a-operation-manual/) · [Balanset-1A manufacturer specification](https://vibromera.eu/product/balanset-1/) ## Frequently asked questions **What Fmax should I set if I just want to know whether balancing is needed?** Take roughly ten times the running frequency. For a machine at 1500 rpm that's an Fmax around 250 Hz, and at 1600 lines you'll get a Δf of about 0.16 Hz with a record of about 6 s. You need to see three things: whether 1x dominates, how much overall vibration exceeds 1x, and whether there's a noticeable 2x and 3x. Separately, take an overall-vibration reading in whatever band your standard is stated in. There's no point going into the kilohertz range at this stage — you'll only lose resolution and pick up high-frequency noise. **1600 lines or 6400: how do I choose without doing the math?** You can't choose without the math, and that's not nitpicking. The number of lines is set by which two frequencies you're separating. Work out your target frequencies from the kinematics, find the narrowest gap, divide it by three, and that gives you the Δf you need. From there, N = Fmax / Δf. If there's no gap smaller than a hertz in your task, 1600 lines is enough. In practice: 1600 across the whole route, 6400 and up only on the point that raised a flag. **Can I just add more averages instead of increasing the number of lines?** No. Averaging lowers the noise floor and stabilizes the amplitude; it doesn't change frequency resolution at all. Two peaks that fall into one line stay one peak even after a hundred averages. Resolution only comes from a smaller Δf — meaning a lower Fmax, more lines, or zoom, and all of that costs record time. **What window should I use for a bump test?** Rectangular, if the response decays fully within the record, or exponential, if the tail doesn't fit. Hanning distorts a bump test: it suppresses the start of the record, which is exactly where the impact's energy sits. And don't turn on continuous averaging — average the responses to 3–10 individual triggered impacts, or the impulse, along with the natural frequency you're looking for, will disappear into noise. **Why do two instruments at the same point show different mm/s readings?** Most often it's different settings, not a faulty instrument. Check, in order: the measurement band, the detector type (true RMS versus an analog detector — the discrepancy on a non-sinusoidal signal can reach 20–30%), the units and representation (RMS, peak, peak-to-peak), the sensor's direction and mounting point, the mounting method, and whether a high-pass filter is engaged after integration. Until these six items match, the numbers can't be compared. **Are the Balanset-1A's settings enough for bearing diagnostics?** For deciding 'is this unbalance or something else,' yes: you see overall vibration and 1x side by side, an FFT spectrum, a time waveform with revolution markers, and a coast-down recording to check for resonance. For early rolling-element bearing diagnostics, no. Vibration-velocity RMS here is measured in the 5–200 Hz band, while emerging bearing defects show up in acceleration in roughly the 2–10 kHz band and in the envelope spectrum. That job needs an analyzer with a high-frequency path and a stud mount.