Mathematical modeling of a mountain bike rear shock

[CK328]

Evening all,
I've recently undertaken a project where my roll is to analyse the suspension of a mountain bike. The suspension unit in question is a Rock Shox Monarch RT3. To give a brief summary:

The shock uses compressed air as the spring, the pressure is adjustable via an air valve.
The shock also has a negative spring- a separate air chamber which opposes the main spring and reduces the breakaway force to get the shock moving.
The shock features adjustable compression and rebound dampers.

The first thing is to try and model the air spring. Currently, to find the force on the piston, I'm using F=P*A.
Then I'm using Boyle's law P1*V1=P2*V2 to model the compression.
Since the compression is not isothermal, I've added the adiabatic gas constant gamma.
P1*V1^gamma=P2*V2^gamma.

I want to get a decent Force/Displacement graph for the air spring so my final formula is:
F=P0*A*(V0/(V0-chang in V)^1.4
where P0 is the initial pressure and V0 is the initial volume.

If anyone can offer a more accurate way to model the compression of a gas please let me know!

I also don't really know where to start with modelling the damping forces other than F=cv so anyhelp would be greatly appreciated.

Cheers.

 

[Achy47]

Hello there,

It sounds like you have a very interesting project on your hands! I would approach this problem by first understanding the fundamental principles behind the behavior of gases and springs. In this case, you are dealing with a gas spring, which behaves differently from a mechanical spring.

To accurately model the compression of a gas, you will need to consider the ideal gas law, which takes into account the temperature, pressure, and volume of a gas. This law is represented by the equation PV=nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. By incorporating this law into your model, you can get a more accurate representation of the compression of the air in your shock.

Additionally, you may want to consider the effects of temperature on the gas spring. As the temperature changes, the pressure and volume of the gas will also change, which will affect the overall behavior of the shock. This can be accounted for by using the ideal gas law and also taking into consideration the specific heat capacity of the gas.

In terms of modelling the damping forces, you will need to consider the viscosity of the fluid in your shock. This can be modeled using the Navier-Stokes equation, which takes into account the velocity and density of the fluid. By incorporating this equation into your model, you can get a better understanding of the damping forces acting on the shock.

I hope this helps in your project. Good luck with your research!