Modelica - Modeling a slider element in OpenModelica

3
votes

Rheological models are usually build using three (or four) basics elements, which are :

  • The spring (existing in Modelica.Mechanics.Translational.Components for example). Its equation is f = c * (s_rel - s_rel0);

  • The damper (dashpot) (also existing in Modelica.Mechanics.Translational.Components). Its equation is f = d * v_rel; for a linear damper, an could be easily modified to model a non-linear damper : f = d * v_rel^(1/n);

  • The slider, not existing (as far as I know) in this library... It's equation is abs(f)<= flim. Unfortunately, I don't really understand how I could write the corresponding Modelica model...

I think this model should extend Modelica.Mechanics.Translational.Interfaces.PartialCompliant, but the problem is that f (the force measured between flange_b and flange_a) should be modified only when it's greater than flim... If the slider extends PartialCompliant, it means that it already follows the equations flange_b.f = f; and flange_a.f = -f; Adding the equation f = if abs(f)>flim then sign(f)*flim else f; gives me an error "An independent subset of the model has imbalanced number of equations and variables", which I couldn't really explain, even if I understand that if abs(f)<=flim, the equation f = f is useless...

Actually, the slider element doesn't generate a new force (just like the spring does, depending on its strain, or just like the damper does, depending on its strain rate). The force is an input for the slider element, which is sometime modified (when this force becomes greater than the limit allowed by the element). That's why I don't really understand if I should define this force as an input or an output....

If you have any suggestion, I would greatly appreciate it ! Thanks

After the first two comments, I decided to add a picture that, I hope, will help you to understand the behaviour I'm trying to model. Different rheological elements On the left, you can see the four elements used to develop rheological models :

  • a : the spring
  • b : the linear damper (dashpot)
  • c : the non-linear damper
  • d : the slider

On the right, you can see the behaviour I'm trying to reproduce : a and b are two associations with springs and c and d are respectively the expected stress / strain curves. I'm trying to model the same behaviour, except that I'm thinking in terms of force and not stress. As i said in the comment to Marco's answer, the curve a reminds me the behaviour of a diode :

  • if the force applied to the component is less than the sliding limit, there is no relative displacement between the two flanges
  • if the force becomes greater than the sliding limit, the force transmitted by the system equals the limit and there is relative displacement between flanges
2
modelicaopenmodelica
In the series connection of figure a. on the right the cut forces of the slider, the spring, and the force source are equal. If the force value of the force source exceeds the value flim there is no solution to the problem. Good numerics must fail at this point with an indication of the problem. If you want to make it work you need something gobbling the superfluous force at the slider. This could be a mass with its inertial force connected to the right end of the slider (or spring). That creates a force-bypass towards the large mass of the inertial system where the slider is also fixed. - Tobias

2 Answers

2
votes

I can't be sure, but I suspect what you are really trying to model here is Coulomb friction (i.e. a constant force that always opposes the direction of motion). If so, there is already a component in the Modelica Standard Library, called MassWithStopAndFriction, that models that (and several other flavors of friction). The wrinkle is that it is bundled with inertia.

If you don't want the inertia effect it might be possible to set the inertia to zero. I suspect that could cause a singularity. One way you might be able to avoid the singularity is to "evaluate" the parameter (at least that is what it is called in Dymola when you set the Evaluate flat to be true in the command line). No promises whether that will work since it is model and tool dependent whether such a simplification can be properly handled.

If Coulomb friction is what you want and you really don't want inertia and the approach above doesn't work, let me know and I think I can create a simple model that will work (so long as you don't have inertia).

1
votes

A few considerations: - The force is not an input and neither an output, but it is just a relation that you add into the component in order to define how the force will be propagated between the two translational flanges of the component. When you deal with acausal connectors I think it is better to think about the degrees of freedom of your component instead of inputs and outputs. In this case you have two connectors and independently at which one of the two frames you will recieve informations about the force, the equation you implement will define how that information will be propagated to the other frame. - I tested this:

model slider
  extends 
    Modelica.Mechanics.Translational.Interfaces.PartialCompliantWithRelativeStates;
  parameter Real flim = 1;
equation 
  f = if abs(f)>flim then sign(f)*flim else f;
end slider;

on Dymola and it works. It is correct modelica code so it should be work also in OpenModelica, I can't think of a reason why it should be seen as an unbalance mathematical model.

I hope this helps,

Marco