Definition
FFT (Fast Fourier Transform) converts time-domain vibration signals into frequency-domain spectra to identify bearing faults, imbalance, misalignment, and other characteristic frequencies. Vibration sensors use MEMS or IEPE to collect time-domain data, and edge gateways can perform FFT analysis and then report the spectra or feature values to support predictive maintenance.
Principles and Applications
FFT decomposes discrete time-domain signals into the amplitude and phase of each frequency component. The frequency spectrum has frequency (Hz) on the horizontal axis and amplitude on the vertical axis. Bearing faults (inner race, outer race, roller) appear in the spectrum as characteristic frequencies and their harmonics; imbalance produces 1× rotational frequency peaks; misalignment produces 2× rotational frequency; looseness produces broadband components. The sampling rate needs to meet the Nyquist criterion (≥ 2× the highest frequency of interest), and the number of sampling points affects frequency resolution. Window functions (Hanning, Hamming, etc.) can reduce spectral leakage.
Edge computing implementation
Vibration sensors transmit analog/digital signals to edge gateways or industrial PLCs via IEPE or MEMS interfaces. FFT algorithms (such as ARM CMSIS-DSP, embedded FFT libraries) run on the edge to output frequency spectra or extract features (peak frequency, amplitude, envelope, etc.), which are reported to the cloud platform via MQTT, Modbus, OPC UA. This can reduce raw data upload bandwidth and support real-time fault diagnosis and predictive maintenance.
Record length and frequency resolution
A fast Fourier transform reports the amplitude and phase of each frequency component in one record. The spacing of neighboring points on the frequency axis equals the sample rate divided by the number of points. Separating two frequencies that sit close together needs a longer record, not the same record padded with zeros. Zero-padding only makes the curve look denser. It does not raise the true resolution. The sample rate must be higher than twice the highest frequency of interest. If anti-aliasing is not enough, a higher frequency folds into the low band and looks like a fault peak that is not there. Spectra of acceleration, velocity, and displacement have different shapes. When history curves are compared, the unit and the number of integrations have to be the same.
The conditions are a sensor range that covers the peak, a mounting direction aimed at the vibration to be measured, and a speed that is roughly steady through the record. When speed changes, one line becomes a smear and the characteristic frequency no longer matches the calculated value. An edge device that runs the transform should declare the sample rate, the point count, the window, and the engineering unit. The platform cannot assume every gateway uses the same set. Averaging reduces random fluctuation, and more averages make the result less sensitive to a sudden impact. If impact information is needed, keep the time-domain peak as well. Do not upload only the averaged spectrum.
Windows and a false call from leakage
When the record length is not an integer number of signal periods, line energy leaks into neighboring frequencies. A window reduces the discontinuity at the two ends, leakage falls, and the main lobe widens, so two lines that are close become harder to separate. If the window is never stated, and the width of a peak is taken as the fault bandwidth, the judgment is off. Another mistake is to gate a threshold on the theoretical running-speed frequency when no speed sensor is connected. The running speed drifts with load, the threshold never lines up, a healthy machine is reported faulty, or a fault peak drifts out of a narrow threshold.
A mounting resonance puts a high peak at a fixed frequency that has nothing to do with a calculated bearing frequency. If the peak stays at the same frequency after the measurement point is moved, suspect the mounting, not the bearing. Electrical interference often locks to the supply frequency and its integer multiples and does not follow speed. That is a practical way to separate a mechanical fault from interference. If the DC bias is not removed, the lines near zero frequency are large and an automatic peak search keeps reporting zero frequency. When the upload is only the frequency and amplitude of the largest peak, also say whether the record saturated. A saturated spectrum grows a series of harmonics that look a lot like mechanical looseness. After the point count or the sample rate changes, the old thresholds cannot be reused as they are.
Speed lock and drifting lines
Characteristic frequencies are computed from speed. If speed is not measured, or the speed measured is another shaft, the theoretical line misses the measured peak. A narrow threshold then either alarms forever or never alarms. If speed changes clearly during the record, discard that spectrum or switch to an order-tracking method. Do not put it on the same trend as a steady-speed spectrum. When orders and frequency are mixed, the horizontal-axis unit has to be written down. Otherwise every historical threshold fails after the speed changes.
Saturation manufactures a string of harmonics that look like looseness. A mounting resonance stays at one frequency and does not follow speed. Before naming the fault, look at whether the time waveform is clipped, whether the bias is abnormal, and whether the mounting was just changed. When only the largest peak is uploaded, upload saturation, sample rate, and point count with it, so the platform can compare two results. After the record length changes, retire the old thresholds. An averaged spectrum suits a steady fault. Keep the time-domain peak for an impact. The more averages, the harder an occasional hit is to see.
If anti-aliasing is not enough, content above half the sample rate folds back into the low band. A folded peak does not move with speed the way it should, and it is easy to treat as a new mechanical frequency. Raising the sample rate without raising the anti-alias cutoff leaves the problem in place. A window changes the main-lobe width, so an old peak-width threshold cannot continue after the window changes. Peak heights on an acceleration spectrum and a velocity spectrum cannot be compared directly. Integration lowers the high frequencies and raises the low ones. A reported spectrum should say how far the integration has gone. Sensor saturation, a loose mount, and real looseness can all show harmonics. Telling them apart means going back to the time waveform and the mounting, not naming the fault on the frequency axis alone.