# Pneumatic cylinder force output and impact energy

I'm designing a little tester for a project which uses a pneumatic cylinder. The pneumatic cylinder's purpose is to apply an impact on a hard surface to test for deflection of the surface. When I looked around catalogs, the pneumatic cylinders have a theoretical force output, for example 3,016 N at 0.6 MPa with an extension speed of 0.8 m/s and a stroke length of 300 mm (preliminary selection although I'm not too sure).

1. How do I calculate the impact energy upon collision with the hard surface, with this information I currently have? There is going to be an amount of impact energy that I need to achieve.

2. I understand that when it comes to energy, the formula to use is $\frac{1}{2} mv^2$. What should the mass be? Is it the mass of the cylinder or whatever is placed on the piston rod end (I intend to put some kind of bumper at the end)?

3. Are "impulse forces" something I should be looking at?

I can't move on to select and appropriately sized pneumatic cylinder for my tester until I understand how to calculate the force output and impact energy.

It's not an easy problem, there are a few things going on at the same time here. Most obviously, the piston has kinetic energy from being accelerated through the bore, which gets transferred to the test item upon impact. This can be calculated from $E_{KE}=\frac{1}{2}mv^2$, as you stated. What's not as obvious is the additional energy transferred to the surface by the piston if it's still being pushed by compressed air during the impact. The total energy delivered by the piston can be hard to calculate, so you might be better off trying to measure it instead. Or, maybe use calculations to get in the ball park then confirm with experiment.

You could launch an object vertically with the piston and measure it's maximum height, or use a pendulum. The change in potential energy of either will be the energy transferred by the piston. Use the formula $E=mg\Delta h$ to calculate the delivered energy.

Also, depending on your application, the time interval over which the impact occurs could be important. Materials behave differently under different rates of strain; armor is tested differently than structural steel, for example. You'll want to verify that the piston impacts the surface at a speed representative of your final application.

In general pneumatics are quite precise when it comes to force but modeling energy in this context brings in a lot of additional unknowns which make be difficult to measure.

The most common method of impact testing is to use an impactor fixed to a pendulum as it's fairly easy to determine the kinetic energy at the lowest point in the swing directly from the initial gravitational potential energy and this gives a very repeatable test.

It's also important to bear in mind that, even when you measure kinetic energy that doesn't really give you a general material property which you can extrapolate from in the same way as something like tensile strength as strain rate is usually a very important factor in impact behavior so the priority is usually to simulate the real world conditions you are interested in as closely as possible.

If you need to use a pneumatic system for some operational reason then the most useful approach may be to treat it as an air spring.