The FFT (Fast Fourier Transform) in Vibration Analysis

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Portable balancer & Vibration analyzer Balanset-1A

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Vibration sensor

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Optical Sensor (Laser Tachometer)

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Dynamic balancer “Balanset-1A” OEM

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The Fast Fourier Transform (FFT) is a highly efficient mathematical algorithm that transforms a signal from the time domain into the frequency domain. In vibration analysis it converts a raw, complex time waveform — vibration amplitude plotted against time — into a frequency spectrum, amplitude plotted against frequency. This single transformation is the most important and fundamental process in modern machinery diagnostics; without it, a vibration signal is little more than an unreadable squiggle.

1. Definition: What is an FFT?

The FFT is not a measurement but a computation. It is a fast implementation of the Discrete Fourier Transform, exploiting mathematical symmetries to do in milliseconds what would otherwise take far longer, which is why it can run live on a handheld instrument. Its premise, due to Fourier, is that any complex periodic signal can be reconstructed as a sum of simple sine waves at different frequencies and amplitudes. The FFT runs that idea in reverse: hand it a tangled waveform, and it returns the list of sine waves it is built from.

2. Why the FFT is Essential for Diagnostics

A raw time waveform from a running machine is a jumble of many vibrations happening at once, and it is nearly impossible to judge a machine’s health by eye from that trace. The FFT acts like a prism, splitting the complex signal into its individual frequency components. The result is a clear, actionable chart that lets an analyst see:

• What frequencies are present?
• How much energy (amplitude) sits at each frequency?
• What is the relationship between those frequencies — harmonics, sidebands, and the like?

Because different mechanical and electrical faults — unbalance, misalignment, bearing defects, and looseness — each generate vibration at very specific, predictable frequencies, the spectrum provides a direct roadmap to the root cause of a problem. This frequency-domain view is the basis of all spectral analysis.

3. Key Parameters of an FFT Analysis

To acquire a useful spectrum, an analyst sets several parameters on the data collector or software. Get them wrong and a real fault can be missed; get them right and it stands out clearly.

Fmax (Maximum Frequency)

The highest frequency included in the spectrum. It must be set high enough to capture the highest-frequency fault of interest — high-frequency gear mesh or bearing tones, for instance — but not so high that low-frequency detail is wasted. To prevent aliasing, instruments apply an anti-aliasing low-pass filter below the sampling rate before the FFT is computed.

Resolution (Lines of Resolution)

This sets the level of detail — the number of discrete frequency “bins” calculated across the Fmax. More lines (3,200 or 6,400, say) give finer resolution, meaning a greater ability to separate two frequencies that lie close together. High resolution is essential for distinguishing beat frequencies or resolving the closely spaced sidebands in gearbox analysis. Because bin width equals Fmax divided by the number of lines, there is always a trade-off between span and detail; an FFT resolution calculator shows the resulting bin width and acquisition time for any setting, and a Zoom FFT can concentrate all available lines into a narrow band when even finer separation is needed.

Averaging

Because machine vibration fluctuates, a single FFT snapshot can mislead. Averaging acquires several FFTs in quick succession and combines them, suppressing random noise and yielding a far more stable, repeatable spectrum that genuinely represents the machine’s condition.

Windowing

A window function — most commonly the Hanning window — is a mathematical weighting applied to the time data before the transform. It minimises an error called spectral leakage, which would otherwise smear a sharp peak across neighbouring bins and corrupt both its amplitude and its apparent frequency.

4. Interpreting an FFT Spectrum

A trained analyst reads the spectrum by recognising characteristic patterns:

• A large peak at 1× running speed indicates unbalance.
• A large peak at 2× running speed often points to misalignment.
• A long series of harmonics (1×, 2×, 3×, 4×…) is a classic sign of mechanical looseness.
• A high-frequency peak carrying sidebands spaced at running speed is a tell-tale of a gearbox or bearing fault.
• A raised “floor” of broadband noise can indicate cavitation in a pump or general friction.

By comparing the current spectrum against a baseline recorded when the machine was healthy, an analyst can spot changes and diagnose developing problems long before they become critical failures.

5. The FFT in Practical Field Measurement

On a portable instrument the FFT is computed on the spot from the live accelerometer signal. The Balanset-1A, a two-channel field analyser, captures the time waveform and displays its spectrum from roughly 5 Hz to 1000 Hz, so an engineer can read the running-speed peak, its harmonics, and any bearing or gear tones at the machine. Combined with the once-per-revolution tachometer pulse, the same data set supports phase-based balancing, while order analysis can re-reference the spectrum to multiples of running speed on variable-speed machines — turning the FFT from a static chart into the engine of an on-site diagnostic and balancing workflow.

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