## Measure Vibration – Should we use Acceleration, Velocity or Displacement?

When using vibration data, especially in conjunction with modelling systems, the measured data is often needed as an acceleration, as a velocity and as a displacement. Sometimes different analysis groups require the measured signals in a different form. Clearly, it is impractical to measure all three at once even if we could. Physically it is nigh on impossible to put three different types of transducer in the same place.

## How Do I Convert Between Acceleration, Velocity & Displacement?

One of the most searched for and read topics on the Noise & Vibration Measurement Blog is that of converting between measurements of acceleration, velocity and displacement. To help anyone…

## New Version of DATS Out Now – V7.0.23 Released

The latest version of the DATS software is now available. Log in to the Prosig support site to download your copy. The new version, V7.0.23, contains many new features, improvements and bug fixes. Read on to find out a little of what you can expect. (more…)

## Converting Acceleration, Velocity & Displacement

From time to time I meet engineers who are interested in the conversions between acceleration, velocity and displacement. Often, they have measured acceleration, but are interested in displacement or vice versa. Equally, velocity is often used to find acceleration. This article outlines the nature of the conversion between these units and will suggest the preferred method for doing so. .

## Calculating Velocity Or Displacement From Acceleration Time Histories

It is quite straightforward to apply “classical” integration techniques to calculate either a velocity time history from an acceleration time history or the corresponding displacement time history from a velocity time history. The standard method is to calculate the area under the curve of the appropriate trace. If the curve follows a known deterministic function then a numerically exact solution can be found; if it follows a non-deterministic function then an approximate solution can be found by using numerical integration techniques such as rectangular or trapezoidal integration. Measured or digitized data falls in to the latter category. However, if the data contains even a small amount of low frequency or DC offset components then these can often lead to misleading (although numerically correct) results. The problem is not caused by loss of information inherent in the digitisation process; neither is it due to the effects of amplitude or time quantisation; it is in fact a characteristic of integrated trigonometric functions that their amplitudes increase with decreasing frequency.

## Examples Of Event Extraction And Removal

In many cases only significant events, such as bumps or other transients in a signal are of relevance. The objective is to be able to isolate these events in a meaningful manner so that they may be automatically recognised and either removed or extracted for analysis in a structured way.

There are two principle objectives initially: one is to be able to recognise an event and the other is to be able to mark it in some way so that subsequent software is able to operate on the actual event. We must also note that an event has a start and an end; the criterion we use to recognise the start may not necessarily be the same criterion we use to recognise the end. Searches for the start and end points are carried out on a Reference Signal. How the reference signal is formed is discussed in detail later, it includes the original signal, various running statistical measures such as the dynamic RMS, differentiation for slope detection, integration and so on. In many cases the start criterion will be some check on the level achieved by the reference signal. By the time any check level has been detected then it is almost certain that the event started earlier! That is, a pre trigger capability is essential.