## Gravity term in simple 2 DOF quarter car model?

Hello all

I am trying to derive a quarter car model that i can use Simulink to analyse. The model is 2 DOF and consists of 1 sprung and 1 unsprung mass, suspension spring and damping co-effs, and tyre spring and damping co-effs. Positive is taken as upwards, compression is also taken as positive. There is also a road displacement input to allow for modelling bump response etc. at a later date, but this is set to 0 currently. Overall a fairly standard QCM setup.

My question is regarding gravity as one of the forces on the model. Most models ive seen dont seem to include an explicit weight force, they simply use m*a = ƩF where ƩF sums the forces acting on the unsprung and sprung masses due to the dampers and springs. On my model i have added a weight component for the sprung (Ms*g) and unsprung (Mu*g) masses which acts downwards.

Can anyone tell me if i am adding this weight component unecessarily? I seem to be getting very high frequency vibration in the model and can't tell if this is due to the added weight force. Or am i going about things correctly and simply using unrealistic values for the spring, damping co-effs etc.?

 The weight is actually compensated by the initial displacement of the spring, so the two forces canceled each other's out throughout the masses' motions. See equation (1) and (2) on this page for more info.
 The point that jack action is making is that the gravity force need not be included if you measure deflections from the static equilibrium position (under gravity loading). This means that the gravity effects have already been incorporated into the model. This works just find for the simple linear model. This does not work if you want to use a more accurate, nonlinear model of the suspension system, in which case you simply need to include all forces in your model. You may wish to again re-linearize about the equilibrium point, but that is an additional step.

## Gravity term in simple 2 DOF quarter car model?

I'm beginning to wonder if the problem lies with the setup of the simulink model. Even if i don't need the gravity component it still doesn't seem to explain the extremely high frequency vibration im seeing.

I've realised i've set my position and velocity integrator blocks' initial conditions to 0, i assume this means the masses are starting out on the ground plane. This would explain why the vibration is so severe at the start of the simulation, but i would expect the dampers to do their job and damp this oscillation out. This is not what im seeing, the large velocities and accelerations of the masses seem to remain constant for a significant amount of time...

Not really sure if its possible to diagnose without a diagram of the model...

 Tags dampers, quarter-car, springs, suspension