Maximum Spring Constant for 0.5 cm Length Spring: Does Radius Play a Role?

[anubodh]

What is the maximum possible spring constant for a spring ( practically) for a spring of length 0.5 cm?
does it depend on the radius?

 

[mfb]

It does depend on the radius. You can use a solid block of metal, I would not call this a "spring" but it does have a really large spring constant (and the constant is proportional to the area).

 

[AceEngineer]

The max spring rate depends on the geometry and material. Check out belleville springs (washers), a couple in parallel can get real stiff.
http://en.wikipedia.org/wiki/Belleville_washer

AceEngineer

 

[anubodh]

Sir,thanks for your replies but can you tell me specifically that can a 1m spring of radius 1cm have a spring constant of 10^6 or more?

 

[Q_Goest]

Hi anubodh. Can you be more specific? What units are the 10^6? Is that in N-m?

Sounds like you want a 1 cm diameter, 1 m long spring. Is this under compression or under tension? If under compression, such a spring would be more like pushing on a rope. It would buckle almost instantly even if it were a solid rod. You could guide it inside a thick walled tube but ultimately the amount of load you're looking to put on this comes into play. What is the maximum load you're looking for? Please provide units in your responce and a complete description of the spring.

 

[anubodh]

Sir, the units are N-m.I want to store 10^5 joules of energy in 1x1x(100-200) cm3 of space.So, i want to ask that can a spring (that fits in this space) store such amount of energy (which is only possible if it has a spring constant of 10^5 N-m approx).And yes it is under compression.

 

[cjl]

That's likely not going to be possible, at least with a spring - 10^5 joules is a lot of energy to be storing with a spring in that sort of volume. What is your application where you need that kind of energy storage? A battery could definitely store 10⁵ J in that sort of volume - that's only around 4 W-hr.

 

[PhanthomJay]

Now spring constants have units of force/length (N/m in SI) and energy has units of force*length (N-m, or Joules, in SI). I take it you want to store 10^5 J energy in the spring by compressing it? This would be stored as internal potential energy in the spring.

If you consider a solid rod as a spring, which doesn't look like your typical coiled spring but nonetheless behaves in a similar way per Hooke's law, within the elastic and buckling limits, then a solid rod has a spring constant of AE/L, where A is its cross sectional area, E is Youngs Modulus, and L is the length of the rod. Looks like for a 1 cm radius rod, A is 3(10^-4) m^2, E (assume steel) is 2(10^11) N/m^2, and L you specify as 1 m.

If I do the math right, I get a spring constant of 3(2)(10^7) = 6(10^7) N/m. Stiff enough for you? If the rod is only 0.5 m long, your stiffness (spring constant) is double that.

So can a spring have a spring constant greater than 10^6 N/m. Sure!
But can it store 10^5 J of energy? No way! It will have crushed long before that.

 

[AlephZero]

But can it store 10^5 J of energy? No way! It will have crushed long before that.

You can estimate how much volume of material you need to store the energy.

Strain energy = 1/2 x stress x strain x volume = 1/2 x stress² x volume / E.

Taking a fairly conservative elastic stress level of 200 MPa for steel, E = 200 GPa, and energy = 10^5 J, that gives

volume = 10⁵ x 2 x 200 x 10⁹ / (200 x 10⁶)²
= 100 cubic meters.

You were probably hoping your spring would be a bit smaller than that

 

[anubodh]

Can we do this by compressing water. I know the pressure required is very high but by dividing in in 1 cm3 boxes or even smaller, the force required to compress one at a time comes out very low i.e.1000 N.(though the pressure remains high) because the small area.

 

[mfb]

Then you need to find some way to maintain that pressure to store the energy. In principle, you can compress everything, if you maintain the pressure from all sides this allows to store a lot of energy. In practice, the setup will be so large that the total energy density is bad.

10^5J in 200cm^3 gives ~70J/g with the density of iron. A flywheel can manage that as a mechanical energy storage, but it does not fit in a volume of 1cm x 1cm x 200cm.

 

[sophiecentaur]

Can we do this by compressing water. I know the pressure required is very high but by dividing in in 1 cm3 boxes or even smaller, the force required to compress one at a time comes out very low i.e.1000 N.(though the pressure remains high) because the small area.

I don't think it's very fruitful to try to store energy in what is regarded as an 'incompressible medium' The container would be the thing that stored the energy as it stretched, rather than the water.

 

[Q_Goest]

Hi anubodh. In short, there's no way to store that much energy within the dimensions you proposed (a tube 1 cm in diameter and 1 m long).

For something like this, the best way to store 'spring' energy I think is using a pneumatic spring because materials such as steel or liquids such as water won't compress sufficiently. So I did some rough calculations to see if it's even possible. If you initially pressurize a cylinder with a piston to some fairly high pressure (ex: 600 to 1000 MPa)* and if you have some place to put some volume for the gas to be compressed into, preferably one that is at least a few times larger than this 1 cm diameter x 1 m long volume you're suggesting, then you start getting close. But the walls on the cylinder and your storage volume vessel will be thick to say the least, on the order of 1 cm. So yea, you could store that much energy in a volume maybe 10 times larger than what you're envisioning but it would be extremely difficult because you're up against the physical strength of the materials.

*In general industry, there are 'off the shelf' tubing and fittings that can reach these pressures but this is aproximately the limit of the materials that could be used for this kind of set up.