Calculating Spring Constant of Compressed Air | Pneumatic Springs

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The discussion focuses on calculating the spring constant of compressed air in pneumatic springs, emphasizing that the relationship between pressure, volume, and temperature is governed by Boyle's law. As volume decreases, pressure increases, leading to a non-constant force response that deviates from Hooke's Law. The force required to compress the air can be estimated using the bulk modulus, with the formula linking pressure change to volume change. The derived elastic constant for the cylinder is influenced by both the material properties and the geometry of the system. Overall, understanding these relationships allows for predicting the force needed for specific displacements in pneumatic applications.
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How do you calculate the spring constant of compressed air? I know force = k * integral(dx). How do you relate volume to the force?
 
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it is not a constant
 
pressure, volume and temperature are all related with a single formula
as volume goes down, pressure goes up, hence the non-constant comment from Curl
 
But you can say that, if the temperature is constant, the pressure times the volume is constant (Boyle's law). So, if the piston of the gas strut is in a certain position (corresponding to a certain volume) for a certain load plus atmospheric pressure, it will go to half that volume if the total load is doubled.
Starting with 1 atmosphere in the unloaded strut, if the area of the cylinder is A (in m2), then the force to compress it to half that volume (twice atmospheric pressure) will be about 10e4A N.

It doesn't follow Hooke's Law, of course, but you can predict the force needed for a given displacement. Actually, because of the Law involved, you can measure a bigger range of forces using an 'air spring' than a steel coiled one.
 
You can estimate it by using the bulk modulus.
If you have a gas of volume V and want to compress it by \Delta V, you need an increase of pressure
\Delta p = -B \frac{\Delta V}{V}
B can be found for both isothermal or adiabatic processes and for air is of the order of 10^{-5} Pa.
If you apply this to a cylinder of length L and area A,
then
\Delta p = F A
and
\frac{\Delta V}{V}=\frac{\Delta L}{L}
Then
\frac{F}{\Delta L}=- \frac{B A}{L}
and assuming a constant B for small compressions, you could say that the term on the right hand side is the elastic constant of the cylinder.
It depends on the geometry too, not only on the properties of the material. Same as for a real spring.
 
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