How to calculate pressure on piston in damper system?

[Logan.Nels]

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

 

[chicopee]

To get the units straight, I use the English system by using the equation F(lbf)= (M(lbm)x A(ft/sec^)) / (Gc (lbm-ft/sec^2-lbf)) whereby Gc=32.2. For your equation (and using the same English units presented in the first paragraph); then Delta P=(lbf/ft^2); Q=(ft^3/sec); Ao= (ft^2); Rho= (lbm/ft^3); (1-Beta^4), Cd and Y are unitless. I am finding out that your Delta P,in your equation, has for unit(lbf) and not (lbf/ft^2).

 

[HPost]

Which way is this damper working?

There is a volume differential to consider, how is the excess oil handle and likewise, how is the make up fluid taken in?

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

 

[btrueblood]

Usually if my numbers look wrong, I've forgotten to convert from mm to m (or mm^2 to m^2), or in. to ft. I always convert flow problems to SI units, to avoid slugs and poundals and similar slimy/mythical creatures, then convert back after the heavy math is done.

 

[PNachtwey]

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?

What you are asking is impossible without knowing what the steady state pressure is to start with. A steady state pressure can be assumed and then changes in pressure on both sides can be calculated. This will result in a differential force equal to the force applied assuming a constant velocity.

I think you are really interested in the differential force since that is what is going to resist the force applied to the piston rod.

If you have a varying F(t) that is applied to the rod, differential equations will be required to do the simulation. If F(t) is constant then you should be able to calculate a constant velocity and pressures.
I don't have time right now to figure this out but for inspiration see this for the simple steady force solution.
Think in terms of a force balance where the sum of forces must be 0 at constant velocity.

https://forum.deltamotion.com/viewtopic.php?f=18&t=497

Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/