RMS, crest factor, kurtosis and the FFT: what each says about a vibration signal

An accelerometer on a machine produces a long list of numbers. Features are small summaries of that list. Each one answers a different question.

RMS: how strong is the vibration overall?

RMS (root mean square) is the square root of the average of the squared samples. It behaves like an overall energy level. For a pure sine wave, RMS is the amplitude divided by √2.

Peak and crest factor: is it spiky?

Peak is the largest excursion in the window. Crest factor is peak divided by RMS. A pure sine has a crest factor of about 1.41. Short impacts raise the peak much more than the RMS, so the crest factor rises.

Kurtosis: how heavy are the tails?

Kurtosis describes how often extreme values occur compared with a normal (Gaussian) distribution. Spiky signals have high kurtosis. Check the convention a tool uses: many report excess kurtosis (kurtosis minus 3), where a Gaussian signal is close to 0.

FFT: which frequencies are present?

The fast Fourier transform splits the signal into frequencies. On a spindle, lines related to the rotation speed (RPM divided by 60 gives hertz) are a natural thing to look at. The frequency resolution is the sampling rate divided by the number of samples, so a longer window resolves closer frequencies.

Why use several features?

No single number tells the whole story. A steady loud signal and a quiet signal with a few sharp impacts can have similar RMS but very different crest factor and kurtosis. In my thesis prototype, RMS, peak, crest factor, kurtosis and the FFT spectrum were computed for each acquisition.

The vibration playground lets you change mass, stiffness and damping and watch all of these numbers move. It is an illustration with generated signals, not measured data.