Acceleration, Velocity and Displacement Conversion (AVD)

A classic problem in vibration measurement is that the sensor output is often not the quantity that has to be assessed. Accelerometers are the easiest to mount and have the widest frequency response, but machine vibration severity is assessed by velocity, and clearance or deformation by displacement. The module separates the choice of sensor from the quantity viewed: any input gives all three.

Why conversion is more than a factor

Integration in the time domain accumulates DC drift, and after a few seconds the displacement curve leaves the screen. Integration in the frequency domain has to handle the low-frequency band where the signal-to-noise ratio is poor: a cut-off set too high removes real low-frequency content, and one set too low lets drift contaminate the whole band. Differentiating velocity or displacement to acceleration amplifies high-frequency noise. The module builds in unit normalization, integration and differentiation, low-frequency suppression and peak spectrum calculation, and runs time- and frequency-domain chains in parallel so they cross-check each other during measurement.

Functions

Screen layout

A left panel contains channel selection (eight check boxes with channel name and unit), independent display units for the three quantities, the high-pass filter switch and cut-off (0 = automatic, with the applied value displayed), statistics, refresh and stay-on-top. The plot area shows the time domain on the left and the frequency domain on the right: acceleration, velocity and displacement from top to bottom, so the share of each frequency component in the three quantities can be compared at a glance.

Wherever the sensor quantity differs from the assessed quantity — which is the usual case — the module applies.

Each quantity has its role, and established assessment practice follows clear physics. This table explains, for example, why acceleration can be normal while displacement exceeds its limit.

The module has three layers — unit normalization, integration and differentiation, and low-frequency drift suppression — with parallel time- and frequency-domain outputs.

Step 1: unit normalization

The source describes internal units of g, m/s and mm, with separate input and display units. As a dimensional conversion, nanometres convert to millimetres by dividing by 1,000,000; feet convert to millimetres by multiplying by 304.8. The source nanometre example is incorrect, and the corresponding software implementation requires confirmation.

Step 2: frequency-domain integration (acceleration → velocity → displacement)

For a harmonic component at nonzero angular frequency ω = 2πf, the magnitudes obey |V| = |A| / ω and |D| = |V| / ω. Waveform reconstruction must retain complex phase: V = A / (jω) and D = V / (jω) under the usual Fourier convention, followed by the inverse transform. DC and unreliable low-frequency content require separate handling. These are mathematical relationships; the software implementation has not been independently validated here.

Step 3: high-pass drift suppression

A high-pass filter precedes the integration chain, so components below the cut-off are not integrated. The cut-off is set manually, or with 0 the instrument sets it automatically at the frequency where the spectrum falls to 2 % of its maximum — below that there is no useful signal and integration only amplifies noise. The lower limit is not below the frequency resolution, and the upper limit is Fs/2.56. The applied cut-off is displayed, so the automatic result can be checked.

Step 4: time-domain differentiation (displacement → velocity → acceleration)

Velocity and displacement inputs use the reverse chain: point-by-point differences at the sampling interval give the rate of change, with zero-displacement boundaries at the ends of the record. The system anti-alias filtering keeps amplified high-frequency noise out of band. All three quantities can therefore be obtained from any one input.

Step 5: peak spectrum

The three spectra are windowed FFT magnitudes restored to physical peak units (g peak, mm/s peak, mm peak) with the window correction factor, using the same window scaling as the main spectrum so values can be compared directly. The DC component can be removed before integration to keep zero drift out of the chain.

Reading the plots

Measured data with sine excitation: channel 1 accelerometer, a steady periodic waveform at about 76 Hz.

These four steps turn reading plots into evidence: the waveform shows the signal is clean, the cross-check shows the conversion is correct, the peak shows the source can be traced and the evaluation basis supports the conclusion.