Afternoon STW,

I’m undertaking a project as part of a group and have elected to cover the suspension analysis of a monarch RT3 debonair.

I’m trying to generate a Force/Displacement diagram for the shock, but I’m struggling to work out the most accurate way to model it, so any help would be greatly appreciated.

From the ideal gas law, PV=nRT so to model the shock with adiabatic, isothermal compression it is possible to use Boyle’s Law:

P1V1=P2V2

i.e. volume is inversely proportional to pressure.

Obviously the air spring does not compress at constant temperature, so I’ve added the adiabatic gas constant to the equation which as far as I can tell, accounts for the temperature changes.

This leaves me with:

P1V1^1.4=P1V2^1.4

Which I then combined with F=P*A and did some rearranging of sorts, so to work out the force of the air on the piston for any given position in the stroke:

F=(Area of piston head)x(initial pressure)x(Initial Volume/(Initial Volume-Change in Volume)^1.4)

Is this a reasonable way to model the air spring or is there a better formula someone can direct me towards?

I plan to use this method to model the force of the positive spring and negative spring independently and subtract the negative from the positive.

I’m likely to have to estimate the actual dimensions of the shock too so if anyone had any technical data for a monarch shock it would be very handy!

I’ll also probably have a go at trying to model the dampers and including the static friction for the final graph but I haven’t got that far yet.

Thanks in advance for any info!

I think modelling gas compression adiabatically would be my starting point (PV^gamma = constant).

And you could obviously rearrange your Force equation to be in terms of stroke which would probably be useful.

Your damping terms will then be proportional to derivative of stroke or derivative of stroke squared or otherwise (constant coulomb etc).

This will all be quasi-static so will likely miss some dynamic effects but likely small. You could go crazy and do full equation of motion with masses as well for inertia effects on pistons etc…

Don’t have any dimensional data. If I were you I’d be buying a scrap shock to strip and measure. Or if the project could afford it (or blag if educational) a working shock as well to put on a shock dyno to validate your model.

Enjoy 🙂

Your force/displacement graph will change depending on the velocity because of damping, so you will need to produce a range.

Check out this paper http://www.mech-ing.com/journal/Archive/2010/4-5/1.Mashini/75_gavriloski.mtm10.pdf seems to be pretty on it in terms of air spring modelling.

This forum post, https://www.physicsforums.com/threads/air-spring-stiffness-calculation.520833/ also provides a non-linear equation which looks more sensible than simply using adiabatic compression, particularly as you would be assuming instantaneous compression/expansion which isn’t always the case.

If you google it there is also quite a bit on rolling lobe stuff for trucks which are just air springs, I am sure you can find something on them.

Would you not need to take friction into account too, or would you assume zero?