modeling multi-body Coulomb static friction in Modelica language

multibody_Coulomb_static_friction.mo

model multibody_Coulomb_static_friction

//constants
  parameter Real muk=1.0;
  parameter Real mus=1.3;
  parameter Real m1=1.0;
  parameter Real m2=2.0;
  parameter Real m3=3.0;
  parameter Real Fn12=1.0;
  parameter Real Fn23=2.0;
  /*
  to solve the warning: 
  Translation Warning [multibody_Coulomb_static_friction: 43:3-47:9]: In component , in relation V1 == V2, == on Real numbers is only allowed inside functions. 
  based on this post: https://openmodelica.org/forum/default-topic/2263-openmodelica-translation-warning
  */
  parameter Real absTol = 1e-10;    

//variables
  Real X1, X2, X3, V1, V2, V3, A1, A2, A3, F1, F2, F3, Ff12, Ff23;
  
initial equation

  X1=0;
  X2=0;
  X3=0;

  V1=0;
  V2=0;
  V3=-1;

equation

  F1=sin(5*time);
  F2=2*sin(7*time);
  F3=3*sin(11*time);

  V1=der(X1);
  V2=der(X2);
  V3=der(X3);
  
  A1=der(V1);
  A2=der(V2);
  A3=der(V3);

  m1*A1=F1-Ff12;
  m2*A2=F2+Ff12-Ff23;
  m3*A3=F3+Ff23;
  
  if (abs(V1 - V2) < absTol) and (abs(m1*A1-F1)<mus*Fn12) and (abs(m2*A2-F2+Ff23)<mus*Fn12) then 
    A1=A2; 
  else
    Ff12=muk*Fn12*sign(V1-V2); 
  end if;
  
  if (abs(V3 - V2) < absTol) and (abs(m3*A3-F3)<mus*Fn23) and (abs(m2*A2-F2-Ff12)<mus*Fn23) then
    A3=A2; 
  else 
    Ff23=muk*Fn23*sign(V2-V3); 
  end if;
  
end multibody_Coulomb_static_friction;

Have a look at modelica/ModelicaStandardLibrary#1778 and the proposed Tutorial2015.BaseComponents.Friction.IdealDryFriction.