Pneumatic fenders

[mch2qh]

We use big pneumatic fenders for protecting ships and structures when berthing. The example in mind is a 3.3m dia x 6.5m long unit with 20mm thick skin. They skins are aramid reinforced rubber (bit like conveyor belt constrution), flexible but non-elastic. The mid-body is cylindrical and the ends approximate to a very flat eliptical cone.

The problem I have is that a first principles calculation of work done when compressing a pneumatic fender gives values way short (about 60%) of the figures claimed in various manufacturers' catalogues. However, I don't think anyone has actually bothered checking the performance claims in the last 30~40 years!! Everyone else seems to have copied tables from one of the original manufacturers.

So, by a fairly simple geometry check I can estimate the initial and final volumes - typically V2 = 0.6 to 0.7 * V1 when compressed to their "rated" deflection (varies depending on the actual model. Initial pressure is 50kPa on the units in question. They're filled with air so pretty easy to estimate P2, also the energy required to compress. These fenders are typically squashed coaxially between two flat faces (a ship and a berthing frame) and I'm trying to get a reasonably close correlation between the theory and manufacturer claimed values, but typically I'm getting lower energy, pressure and reaction (latter estimated as P2 x footprint area).

So the question is, and given that my thermo is a little rusty, should I be applying adiabatic gas laws or have I missed something fundamental? I should perhaps add that the time to compress the fender is anything from around 10s to 30s depending on size and berthing speed, the reinforced rubber skin is a very good insulator so heat loss in this short time will be pretty low.

Hints, suggestions, tips and anything else pointing me in the right direction really appreciated.

Cheers,
Mike

 

[MintJulep]

When you say "flexible, but non-elastic" I suspect you mean than when you squeeze it parts don't puff out like a balloon, right?

Two things come to mind.

First - the energy required to deform the things is non-trivial - even if they were not pressurized.

Second - it probably behaves like a balloon, at least a little.

 

[mch2qh]

Not really, the skin is a flexible fabric (layers of rubber and fabric mesh). So the fender freely deflects when compressed - the load needed to do this is small compared to the load needed to compress the air. The sides do squash just like a balloon, except owing to the fabrics in the rubber, the ends get a little "wrinkled".

You have to make some assumptions on the end geometry (like the midbody part turns into a rectangular block + a half cylinders running down each side, the "bulge@). Ends are a little more tricky as they're not pure hemispheres but I've got a pretty good model now based on measured dimensions, shape.

So, ignoring loads needed to flex the skin, is there anything fundamentally wrong in my assumption of an adiabatic gas model for this application?

Thanks again!

 

[mch2qh]

My estimates so far have been based on the ISO standard governing pneumatics which are the same as appear in most manufactuer's performance tables. What these companies don't provide is any justification for their values and the sums just aren't adding up.

I've tried adiabatic, polytropic and isotropic cases. I've allowed for hoop and longitudinal extension of skin under claimed pressures, but nothing is a good and consistent match. I understand that the ISO tables were based on measured gauge pressures and rather less consistently measured contact areas from which reaction is calculated and integrated to get the energy. This method (defined in the ISO) falls apart if contact footprint isn't precisely measured and I think this is a major reason theory and practice diverge.

What I'm tasked with is coming up with a working mathematical model that reconciles fairly well with the ISO tables and can then be applied to other cases which the manufacturers aren't otherwise able to provide information for. We'll get around this somehow with a sensitivity analysis but I was hoping that theory and practice would be a bit more consistent.