Mechanical work via force/displacement integration with PMX

Force/displacement integration with PMX for measuring measurement work


Mechanical work performed W will be measured by integrating force F over displacements.

(Because the processing is time-discrete, this is actually a summation, however the term integration will still be used here.)

The beginning and end of the integration are determined by measurable events such as fixed displacement or force values or signal edges on a digital input.


Integration over displacement is achieved by first deriving the displacement based on the time, multiplying by F and then integrating with time again:

Example A

Integration over displacement from s1 to s2:

In this case events s=s1 and s=2 determine the beginning and end of the integration. These points on the displacement axis must in any case be reached during the process. Otherwise the beginning or end will not be detected.


Example B

Measuring the maximum value of work. This is useful, for example, if the full scale of the displacement is undetermined or cannot be reached reliably.

Integration begins and ends at the same point on the displacement axis s=s1: W = ∮F(s) * ds.

Work may decrease during the return stroke, for example due to spring relaxation. The maximum value is retained with a Peak block.


Details of the glyphs in example A:


Please note that the Hold block comes before the Peak block in the order of calculations. Thus the edge of Flag_01 first results in the Hold function and then causes the Peak block to be reset.


In example A the Hold block is already reset during the return. If the value needs to be held for longer, the block could for example be reset externally by a digital signal or by an additional Trigger block.


These examples are simply for the purpose of illustration. They cannot be used as the basis for any warranty or liability claims.

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