Vibration analysis basics: from time signal to spectrum

Vibration analysis basics come down to one idea: a machine's vibration is a sum of periodic and random components, and the spectrum separates them by frequency. An accelerometer on a bearing housing records a time signal, a few seconds of acceleration values. On its own that signal is hard to read. Converted into a spectrum, it becomes a list of frequencies with amplitudes, and many of those frequencies have mechanical names.

This post walks through that conversion step by step, from the sensor to a spectrum you can defend in a maintenance meeting. It is written for engineers who know what a bearing is but have not set up an FFT analyser themselves.

What the time signal already tells you

The time waveform is the raw record: acceleration sampled at fixed intervals. Before any transform, a few statistics already carry useful information. They are cheap to compute and they are the first features most monitoring systems track.

The limitation is obvious once you think about it. RMS rises for unbalance, for looseness, for a damaged bearing and for a neighbouring machine that has just started. It says that something changed, not what. For that you need frequency.

From time signal to spectrum: the FFT in plain terms

For a real signal, the discrete Fourier transform of a block of N samples gives N/2 + 1 frequency lines from 0 Hz to Nyquist; analysers typically display about N/2.56 of them, because the top of the band sits inside the anti-aliasing filter's roll-off. The FFT is simply a fast algorithm for computing the transform. Each line represents a narrow frequency band, and its height shows how much of the signal's energy sits there.

Three relationships define what the spectrum can show:

• Maximum frequency. The Nyquist frequency is half the sample rate. Anything above it folds back into the spectrum as a false peak, which is called aliasing. An analogue anti-aliasing filter must remove it before the converter, and because no filter is perfectly sharp, the usable range ends some way below Nyquist.
• Resolution. The line spacing is the sample rate divided by N, which is the same as one divided by the record length in seconds. A 1-second record gives 1 Hz lines; a 4-second record gives 0.25 Hz lines.
• Trade-off. Doubling the sample rate without doubling N doubles the frequency range and doubles the line spacing, so the resolution becomes twice as coarse. Fine resolution at high frequency needs long records and therefore more data.

A short example makes this concrete. A four-pole motor running at 1,480 rpm turns at about 24.7 Hz. Suppose a neighbouring fan on a different drive runs at 1,500 rpm, or 25.0 Hz, and its vibration reaches your sensor through the frame. The two peaks are about 0.3 Hz apart. A windowed peak spreads over several lines, so you want a line spacing of roughly 0.1 Hz, which means a record of about ten seconds. A one-second capture would merge them into one peak and you would blame the motor for the fan.

Windowing: why the edges of the record matter

The FFT assumes the record repeats forever. If the signal does not contain a whole number of cycles, the end of the record does not join its start, and that discontinuity smears energy across neighbouring lines. This is spectral leakage. As National Instruments puts it in its note on FFTs and windowing, when the number of periods in the acquisition is not an integer, the endpoints are discontinuous.

A window function tapers the record towards zero at both ends to reduce that smearing. The choice matters less than people think, but it does matter:

• Hann (Hanning) is the general-purpose choice for machine vibration. The same NI note says it is satisfactory in 95 percent of cases.
• Flat top gives the most accurate amplitude for a single tone, at the cost of wider peaks. Use it when calibrating or when an amplitude figure is the deliverable.
• Uniform (no window) suits broadband random signals and transient captures that start and end at zero.

Whatever you choose, write it down. Two spectra with different windows are not directly comparable in amplitude.

Units: acceleration, velocity and displacement

Accelerometers measure acceleration, but vibration is often discussed in velocity or displacement. The three are related by integration, and each one emphasises a different part of the spectrum. Acceleration grows with frequency for the same displacement, so it highlights bearing and gear-mesh content in the kilohertz range. Displacement is dominated by low frequencies, which suits shaft movement in sleeve bearings.

Velocity sits in between and is the usual unit for overall machine condition. Severity guidelines such as ISO 20816-1:2016 evaluate machines on broadband vibration magnitude and on changes in that magnitude, which is why a velocity trend is the first thing most maintenance teams look at. We cover the severity zones themselves in our post on ISO 20816 zones A to D.

One caution on integration: integrating acceleration amplifies low-frequency noise. Most analysers apply a high-pass filter first, often at a few hertz. If a velocity spectrum shows a large ramp towards 0 Hz, that is almost always an integration artefact, not a machine fault.

A practical procedure: from sensor to spectrum

This is the sequence we use when setting up a new measurement point. It is deliberately boring, because spectra go wrong in boring ways.

1. Define the fault frequencies you care about. List shaft speeds, gear meshes, blade-pass frequencies and bearing defect frequencies. Our article on bearing fault frequencies shows how to calculate the last group.
2. Choose the sensor and its mounting. Check the accelerometer's usable band against your highest frequency of interest. A MEMS sensor such as the Analog Devices ADXL1002 is specified at plus or minus 50 g with a 3 dB bandwidth up to 11 kHz (within 5 % up to 4.7 kHz) and a resonance around 21 kHz. Stud or adhesive mounting keeps the mounted resonance high; a magnet lowers it.
3. Set the sample rate. Make it well above twice the highest frequency of interest so the anti-aliasing filter has room to roll off.
4. Set the record length. Pick N so that the line spacing resolves the closest pair of frequencies you need to separate, for example running speed and its sidebands.
5. Apply a window. Hann, unless you have a specific reason.
6. Average. Average several spectra, with 50 percent overlap if the analyser supports it, to reduce random noise. Linear averaging of the power spectrum is the default for stationary machines.
7. Record the operating state. Speed, load and temperature at the time of capture. A spectrum without operating context cannot be compared with next month's.
8. Compare against a baseline. Store the first good spectrum per point and operating state, and judge changes relative to it.

The standard that covers this processing chain in detail is ISO 13373-2:2016, which deals with processing, analysis and presentation of vibration data, including time-domain and frequency-domain analysis and signal enhancement.

Reading a spectrum without fooling yourself

Once the spectrum is clean, interpretation starts with orders: frequencies expressed as multiples of running speed. A peak at 1x running speed often points to unbalance. Strong 2x and axial components are a common sign of misalignment. Many harmonics of running speed with a raised noise floor suggest mechanical looseness. These are heuristics, not rules, and every experienced analyst has a story about a 2x peak that turned out to be something else.

Non-synchronous peaks, those that are not integer multiples of running speed, deserve the most attention. Bearing defect frequencies are non-synchronous by design. So are electrical frequencies tied to line supply, and resonances excited by broadband impacts.

Checklist of common mistakes:

• Comparing spectra taken at different speeds without converting to orders.
• Reading amplitude from a Hann-windowed spectrum as if it were a calibrated tone.
• Treating an aliased peak as real because the anti-aliasing filter was disabled.
• Mounting the sensor on a thin cover plate that has its own resonance.
• Forgetting that a loose or failing sensor also changes the spectrum.

The last point is underrated. A sensor that has partly detached produces a spectrum that can look like looseness in the machine. That is why the sensor itself has to be checked before the spectrum is read, a theme we return to in what multimodal sensing is and why it helps.

How NeuroControls approaches this

Our Vibration Node digitises a single channel at 18 bits and 200 kSPS through an ADAQ4003 converter, with an LTC6373 programmable-gain amplifier ahead of it and an ADI ADXL1002 accelerometer. That gives generous headroom above the sensor's band, so the anti-aliasing filter can do its job without eating into the frequencies that matter. Every stream is time-stamped on the hub, and the node flags signal health and dropouts with every segment, so a gap is visible in the record.

Spectra and time-domain features feed the models our engineers train on customer data, from anomaly detection to fault classification and severity grading. The Machine Health Kit combines the Vibration Node with an Acoustic Node on one hub, and the condition monitoring solution page describes how the pieces fit together. If you are planning a first measurement campaign, our notes on models and validation are a good next read.