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Modeling Pressure Balanced Valve With Spring

Modeling Pressure Balanced Valve With Spring

Modeling Pressure Balanced Valve With Spring

(OP)
I'm having trouble modeling this in excel so i'm sure i'm not getting the equations right. Most of what i have is all linear for instance force pushing the needle up (see image for reference) I have as P1*A1-P2*A1-P3*A2-k*x where the x is 0-1 and it is correlated to the Cv of the needle and seat i have ranging from cv=10 (practically no differential) to cv=.28 (about 5,000 psi differential). P3 is 0 going back to tank. P2 is dependent on the Cv. For simplicity i'm using water and simple cv calculation of Cv=Q(SG/deltaP)1/2. P1 and P2 are being fed from a manual needle and seat holding pressure against a positive displacement pump.

Modeling the single drop is simply application of the Cv equation P1=(Q/Cv)2*SG+P2. However when i try to model the second part i end up with a whole bunch of nothing until the P1 hits 5000 and then the Cv of the second part goes which has gone from 10 to 2 in a gradual form goes to .28 in like 1 step (At this point on manual section i'm incrementing Cv by 0.001 per step, so 0.301, 0.300, 0.299.... etc. I'm using a k of 5000 at 1" for the spring. Please see attached spread sheet for rough idea of where i'm at.

For the second Cv i tried to interpolate it from the range deltaP1-2 0-5000, Cv 10-.28 with .28 being the point at which the spring would be fully compressed and maximum desired drop achieved. I'm trying to model this with some degree of accuracy so i don't have to spend thousands and thousands experimenting with different spring strengths and chamber diameters.

Excel File
https://files.engineering.com/getfile.aspx?folder=...

Image

RE: Modeling Pressure Balanced Valve With Spring

Hello bryansonnier
To get an answer I suggest that instaed of explaining your excel calculation you present in clear text what you try to achieve with your construction. Add what physical conditions/limits you need. We engineers tend to stick to the first practical solution/construction that comes to mind. It could be useful sometimes to lean back and look for modifications or alternatives.

RE: Modeling Pressure Balanced Valve With Spring

Your equation P1*A1-P2*A1-P3*A2-k*x

is missing a couple things - pressure P2 acts on area (A1-A2) not A1, also the spring force can/should include a preload, i.e. Fspring = kx + C.

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