Creating a Finite Element Model for Multi-Mass Spring Systems

[Jonny6001]

Hello,

I am interested in trying to created a discretised model of a helical coil spring to investigate spring surge etc, it will be for automotive engine valvetrain application.

I was thinking that I could build up the matrices from the equations of motion and initially discounting the damping term giving 'ma + kx = F' for each mass element.

My issue arises because ideally I would be specifying the displacement of the top mass which is the contact point of the camshaft according to the valve-lift profile, this would also give me the acceleration of the top mass.
I am unsure as to how the force on the elements tie up since I am specifying displacement and acceleration of the mass in contact with the camshaft.

There will also be another possible situation where the spring loses contact with the camshaft and again I'm unsure about how to deal with this.

Any help or ideas for discussion would be greatly appreciated.

 

[Hassan2]

Hi Jonny,

I think the finite element method fit your problem the best. Once you have the "global" matrix, the given displacement of the tip ( or of any number of nodes) is multiplied by the relevant entries of matrix and goes to the right hand side as the "force" term.

Assembling the global matrix is a little challenging though.