# How to design a hemispheric flexible pressure vessel?

Consider a balloon, it is a flexible, expanding pressure vessel made of synthetic rubber. I am trying to design a system that will use hemispheric pockets of neoprene to grip an object, much like the one found in this journal:

H. Choi and M. Koç, 'Design and feasibility tests of a flexible gripper based on inflatable rubber pockets', International Journal of Machine Tools and Manufacture, vol. 46, no. 12-13, pp. 1350-1361, 2006. (Behind a paywall, abstract available here)

Although I am not entirely certain where to start, I am dealing with a high pressure (8 bar) and need to work on a small scale (max radius of 40mm).

Values I have recieved from equations found online suggests thickness values in meters and radius expansion reaching the hundrends of meters.

What equations do I need to calculate a solution?

Are neoprene, latex and chloroprene viable materials to use or should I find alternatives?

Is a hemisphere that best pocket shape I can use?

Additionally, how can I calculate the amount of expansion?

• On first glance, I'll advise you to strongly examine what you plan to use to attach these pockets to the surface. Finding a strong enough material probably won't be as hard as finding a joining method that won't fail. Apr 13 '15 at 3:42
• @TrevorArchibald That's a very valid point. Although I still need a starting point. Apr 13 '15 at 3:45
• This is fully doable. I don't have time to write up the equations right now but this is the same pressure as bicycle tires (although with the outer tire as well and not the inner tube alone). Apr 13 '15 at 10:47

This is fully doable. This is the in the higher range as bicycle tires (although with the outer tire as well and not the inner tube alone).

Alright, here goes:

What equations do I need to calculate a solution?

The pressure in a tube can can be modelled by the following equations:

Hoop Force:

$$\sigma_H = \frac{pr}{t}$$

Axial Force

$$\sigma_A = \frac{pr}{2t}$$

Is a hemisphere that best pocket shape I can use?

That is a design question, although when inflated it should ideally be cylindrical to prevent extra stress. This is a bike tyre picture from Wikipedia:

Are neoprene, latex and chloroprene viable materials to use or should I find alternatives?

Neoprene I imagine will leak air, although slowely. Latex and chloroprene should work. I would suggest that you get bike parts to do this if you are trying to build a prototype.

Additionally, how can I calculate the amount of expansion?

Your system is a little dynamic here so it will get bigger as you fill it with pressure.

• Rewrite the equations above with $\epsilon E$ to replace $\sigma$.

• With a constant pressure and E-modulus you should be able to get the final strain.

Bicycle tires have pressures way below 8 bars. Pressure is a minor issue, look for standard pipes, pipe closures or joints in a hardware shop, HomeDepot etc.