VD-01Vibration & Structural Dynamics

Vibration Unit Converter

Displacement, velocity and acceleration at a frequency - peak, RMS and peak-to-peak - on a tripartite nomograph.

Measured quantity

Frequency

3,000 CPM / RPM equivalent

Quantity

Detector

Unit

Amplitude

m/s

Displacement pk-pk

40,510µm

Velocity RMS

4,500mm/s

Acceleration peak

203.9g

Tripartite nomographvelocity peak vs frequency

Constant displacement (µm pk)Constant acceleration (m/s² pk)

Displacement

unit	peak	RMS	pk-pk
µm	20,260	14,320	40,510
mm	20.26	14.32	40.51
mil	797.5	563.9	1,595

Velocity

unit	peak	RMS	pk-pk
mm/s	6,364	4,500	12,730
m/s	6.364	4.5	12.73
in/s	250.5	177.2	501.1

Acceleration

unit	peak	RMS	pk-pk
m/s²	1,999	1,414	3,999
g	203.9	144.2	407.7
mm/s²	1.999e6	1.414e6	3.999e6

§ Theory of operation

Three views of the same motion

For sinusoidal vibration at angular frequency $\omega = 2\pi f$ , displacement, velocity and acceleration are related by simple differentiation:

\begin{aligned} x(t) &= D\,\sin(\omega t) \\ v(t) &= \omega D\,\cos(\omega t) \qquad V = \omega\,D \\ a(t) &= -\omega^2 D\,\sin(\omega t) \qquad A = \omega\,V = \omega^2\,D \end{aligned}

Integration divides by ω; differentiation multiplies by ω. That's why displacement emphasises low frequencies (shaft movement in sleeve bearings, building sway), acceleration emphasises high frequencies (bearing and gear defects), and velocity - roughly proportional to fatigue stress and vibration energy - is the preferred broadband severity measure (ISO 10816 / ISO 20816).

Detectors

\mathit{RMS} = \mathit{peak}\,/\,\sqrt{2} \qquad \text{peak-to-peak} = 2\cdot\mathit{peak} \quad \text{(sine only)}

Proximity probes traditionally report displacement peak-to-peak (µm or mils), velocity is usually RMS (mm/s) in Europe and peak (in/s) in North America, and acceleration is often in g peak. These conversions are exact only for a pure sinusoid; for complex signals, each spectral line must be converted separately.

The tripartite nomograph

Plotting velocity against frequency on log-log axes turns constant displacement and constant acceleration into straight lines with slopes of +1 and −1. Any sinusoidal vibration is a single point on this chart, from which all three amplitudes can be read - the classic way vibration criteria and shock spectra are drawn.