# Re: Modelling Hydraulic Systems

"Tim Wescott" <tim@xxxxxxxxxxxxxxxx> wrote in message
news:c-mdndibEqhD2j3bnZ2dnUVZ_j6dnZ2d@xxxxxxxxxxxxxxx
:I was about to respond to a comment by Peter in the PIDD thread, then I
: realized it'd hijack the thread. So...
:
: Peter mentioned in his response that a hydraulic system can be modeled as
: a mass between two springs. I'll believe that -- but what's the
: underlying physics? Where does the 'spring' come from -- is there an
: accumulator somewhere (springiness in a pneumatic system I can understand,
: but not a hydraulic)?

See
ftp://ftp.deltacompsys.com/public/PDF/SpringEffectEffBulkModl.pdf

The oil on either side of the piston are the 'spring'. Oil compresses, so
does water. The bulk modulus of oil is about 200,000 psi under ideal
conditions. This value will drop if there is air in the oil.

Here is a thread that show the effect of compressing oil.
http://www.patchn.com/SMF/index.php?topic=612.0

When I get serious I use a system of non-linear differential equations. We
have 20Sim for that.

What changes in the model as you change the
: actuator -- the position of the endpoint of one or another of the springs,
: the spring constants, what?
You can see that the natural frequency changes depending on where the piston
is. The natural frequncy is lowest close to the middle of the stroke.
:
: Finally, if there's a web page that details the workings of the sort of
: hydraulic system you're talking about, with the plumbing, the actuators
: (spool valves, right? Whatever a 'spool valve' is?)
Actually, servo valves. The idea is to have the flow proportional to the
control signal but this also depends on the pressure drop across the valve.

and any other things
: that are pertinent to the control of such systems, I'd be interested in
This is a big topic. Jack Johnson has some books on hydraulic motion
control but they are written from a more academic point of view.

I will try to find some good websites.. We have some stuff on our website
but it is mostly marketing.

Peter Nachtwey

.

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