How to calculate the pressure on a piston in a damper system?

[LogNels]

Hello all,

I'm trying to calculate the pressures exerted back on a piston by a working hydraulic fluid in a damper system. I've attached a drawing of the system and the equations I'm using. Essentially the piston motion is restricted by flow through an orifice. I have data for the flow rates through the orifice and I need to calculate the pressures the piston sees based on that data. My solution is giving me unreasonable results. Am I missing something?

Best Regards,
Logan

 

[JBA]

Your equation for the orifice flow ΔP is correct. Just as a note, if your system fluid is hydraulic oil, then I would expect the fluid expansion factor to be "1".

At the same time, your figure indicates that the orifice discharge fluid pressure is being directly applied to the rod side of the piston where the effective pressure area is the (the piston area - the piston rod area); if that is the case, then:

P piston = (F rod – Dp x (A piston – A rod)) / A piston

As a result, the pressure on the top of the piston will be primarily dependent upon the external load on the piston rod.

 

[JBA]

Since the editing time for my prior last post has expired, this post is to correct an error in the equation presented in that post.

"P piston = (F rod – Dp x (A piston – A rod)) / A piston" should be:

P piston = P1 = (F rod + P2 x (A piston – A rod)) / A piston

 

[LogNels]

Hey JBA,

You brought a good point about accounting for the rod area. I realized my biggest problem was that I was oversimplifying the system model.

Thank you for your help!​

 

[Vijayent]

The pressure can be derived from the orifice flow equation -
Q = A x Cd x (sqrt (2 x Delta P/Density))

P = (0.5 x Density^2) / (Area x Orifice coefficient)

SI Units being used

Q - M^3/sec
P - Pascals
Density - kg/m^3
Area - m^2
Orifice coefficient being dependent on the type of orifice