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# Need support in hydro calculations

## Need support in hydro calculations

(OP)
Dear Gents,
Currently I am trying to design a hydraulic absorbing system for a small on-board crane. This system consists of a hydraulic cylinder and a bladder accumulator connected in a closed loop via piping.
The work principle is that the cylinder remains extended during normal conditions (max safety working load hanging on the wire statically) while it gets compressed during dynamic overload conditions (i.e. emergency braking)thus this system shall absorb kinetic energy created. The kinetic energy to be absorbed is calculated by 1/2mV^2 and is obviously known.
The cylinder size was chosen mostly by guessing rather than exact calculations. After that we have been evaluating this system by experiments (checking cylinder compression in different per-charge pressure of accumulator and different loads).
What I am trying to do now is an excel sheet which can show us the required cylinder piston diameter, stroke, accumulator size and its per-charge pressure and also it's capacity to absorb kinetic energy so we do not have to evaluate it by tests again and again.

Would appreciate any help...

### RE: Need support in hydro calculations

It's Boyle's law...

P1 x V1 = P2 x V2

Whilst the charge and discharge is slow and therefore isothermal, the above is close enough for what you need.

However, if the charge and subsequent discharge are quick, you will have an adiabatic cycle...in other words, the gas will cool as it expands and you will get different results. The gas will also heat up as it compresses. This heating and cooling makes the gas expand and contract, which will give you more or less absorption depending on the application.

Where the process becomes adiabatic, you need to apply a polytropic exponent to the calculation. The polytropic constant for nitrogen is 1.4

P1 is the pre-charge, which needs to be 90% of the minimum oil pressure to make sure that the acc is always working.

P2 is the minimum hydraulic pressure

V1 is pre-charge volume

V2 is volume of the gas a the highest hydraulic pressure

You can use the same principle to work out any other pressures and volumes that you may want to find.

### RE: Need support in hydro calculations

HPost's methods above are just what I'm doing for a hydraulic accumulator system. That ought to work fine in a lot of situations.

If the system isn't able to reach equilibrium between pressure changes at your accumulator (i.e. if pressure changes really fast or frequently) you may need some more sophisticated methods. These can start looking like surge analysis.

If it were me dealing with some quick changing, or oscillating pressure, I might just call Blacoh or Parker and see if they'll sort it out for me.

### RE: Need support in hydro calculations

(m*v^2)/2 = integral(Force(x)*x,dx) = integral(Pressure(x)*Area*x,dx) where x is the distance. You can have a smaller diameter but longer cylinder or a shorter cylinder with a shorter stroke. Obviously the larger diameter cylinder will stop the load more abruptly. The first design constraint is how far do you want the cylinder to move when absorbing shock?

Don't worry about heat loss if the collision and rebound happen quickly. There isn't enough time for heat to escape the cylinder. Use PV^1.4=K not PV=K.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com

### RE: Need support in hydro calculations

Automotive suspension dampeners transfer fluid displaced by a piston travel from one chamber to another thru a set of valves that absorb energy by creating resistance in the fluid flow. They typically use a floating piston with a small charge of inert gas on one side to maintain a certain level of pressure within the fluid to ensure consistent performance. But not the same as using an accumulator. The single acting cylinder with an accumulator would behave more like a spring than a dampener.

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