MultiBondLib.Mechanics3DwithImpulses.Contacts

contact models

Information

The models of this package model collisions of spheres and planes.

Name Description

CollisionSpherePlane models the collision between a spheres and a plane

CollisionSphereSphere models the collision between two spheres

NoCollision dummy collision element

Name	Description
CollisionSpherePlane	models the collision between a spheres and a plane
CollisionSphereSphere	models the collision between two spheres
NoCollision	dummy collision element

MultiBondLib.Mechanics3DwithImpulses.Contacts.CollisionSphereSphere

models the collision between two spheres

MultiBondLib.Mechanics3DwithImpulses.Contacts.CollisionSphereSphere

Information

This element models the collision between two spheres surrounding frame a and frame b.

General parameters

The charactisitics of the impact can be set by the parameters:

elasticity: The elasticity coefficient.
muR: The friction coefficient.

The characteristics of the geometry can be set by the parameters:

ra: The radius of the sphere surrounding frame a.
rb: The radius of the sphere surrounding frame b.

Visualization

The element isn't visualized.

Advanced settings

A collision causes three consecutive impulses. The parameter contactDuration determines the timespan between the first and the last impulse. It is usually very small.

The parameter s_small in the advanced menu reduces the stiffness of the friction for slip velocities in the range from zero up to s_small.

Parameters

Name Default Description

ra 1 radius of sphere at frame a [m]

rb 1 radius of sphere at frame b [m]

elasticity 1.0 Elasticity of impuls

muR 0.0 friction coefficient

Advanced

s_small 1e-4 critical length [m]

contactDuration 1e-9 time to handle the impulses

useParameters true use the parameter values.

Name	Default	Description
ra	1	radius of sphere at frame a [m]
rb	1	radius of sphere at frame b [m]
elasticity	1.0	Elasticity of impuls
muR	0.0	friction coefficient
Advanced
s_small	1e-4	critical length [m]
contactDuration	1e-9	time to handle the impulses
useParameters	true	use the parameter values.

Modelica definition

model CollisionSphereSphere 
  "models the collision between two spheres" 
  import SI = Modelica.SIunits;
  Interfaces.IFrame_a frame_a;
  
  parameter SI.Radius ra = 1 "radius of sphere at frame a";
  parameter SI.Radius rb = 1 "radius of sphere at frame b";
  
  parameter SI.Position s_small = 1e-4 "|Advanced||critical length";
  
  parameter Real elasticity = 1.0 "Elasticity of impuls";
  parameter Real muR = 0.0 "friction coefficient";
  
  parameter Real contactDuration =   1e-9 
    "|Advanced||time to handle the impulses";
  
  parameter Boolean useParameters = true "|Advanced||use the parameter values.";
  
  SI.Radius ra_;
  SI.Radius rb_;
  
  Real elasticity_;
  Real muR_;
  
protected 
  SI.Distance r[3];
  Real eR[3];
  Real noteR[3];
  Real eA[3];
  Real eB[3];
  
  Boolean contact;
  Integer seqState;
  Real frictionImpulseTime;
  Real correctionImpulseTime;
  
  SI.Impulse F[3];
  SI.AngularImpulse T[3];
  SI.Velocity vA[3];
  SI.Velocity Vm[3];
  SI.AngularVelocity Wm[3];
  
  SI.Impulse FR;
  SI.Impulse FA0;
  SI.Impulse FB0;
  SI.Velocity VmR0;
  
  SI.Impulse FA1;
  SI.Impulse FB1;
  SI.Impulse FR1;
  SI.Velocity VFricElast[3];
  
  Real eC[3];
  Real noteC[3];
  Real eD[3];
  Real eE[3];
  
  SI.Impulse FD2;
  SI.Impulse FE2;
  SI.Velocity VmC2;
  
  Real[3,3] R_a;
  Real[3,3] R_b;
  
public 
  Modelica.Blocks.Interfaces.BooleanOutput y;
  Interfaces.IFrame_b frame_b;
initial equation 
  contact = false;
  seqState = -1;
  frictionImpulseTime = 0;
  correctionImpulseTime = 0;
  
equation 
  
algorithm 
  when contact then
    contact :=false;
  end when;
  
  when sqrt(r*r) <= (ra_+rb_) then
    contact :=true;
    seqState := 0;
   frictionImpulseTime :=time + contactDuration/2;
  end when;
  
  when (time >= frictionImpulseTime) and (seqState == 0) then
    contact :=true;
    seqState := 1;
    frictionImpulseTime := 0;
    correctionImpulseTime := time + contactDuration/2;
  end when;
  
  when (time >= correctionImpulseTime) and (seqState == 1) then
    contact :=true;
    seqState := 2;
    correctionImpulseTime := 0;
  end when;
  
equation 
  if useParameters then
    ra_ = ra;
    rb_ = rb;
    elasticity_ = elasticity;
    muR_ = muR;
  end if;
  
  r = frame_b.P.x- frame_a.P.x;
  when contact and (seqState == 0) then
    eR = r/sqrt(r*r);
    noteR = if abs(eR[1]) > 0.1 then {0,1,0} else (if abs(eR[2])
       > 0.1 then {0,0,1} else {1,0,0});
    eA = cross(eR, noteR)/sqrt(cross(eR, noteR)*cross(eR, noteR));
    eB = cross(eA, eR);
  end when;
  
  when contact then
    vA = (pre(frame_b.P.v)+cross(transpose(R_b)*pre(frame_b.P.w),-eR*rb_)) -
         (pre(frame_a.P.v)+cross(transpose(R_a)*pre(frame_a.P.w),eR*ra_));
    R_a = frame_a.P.R;
    R_b = frame_b.P.R;
    
  end when;
  
  when contact then
    T = zeros(3);
  end when;
  
  when contact then
    FR = F*eR;
  end when;
  
  when contact and (seqState == 0) then
    VmR0 = (1-elasticity_)*(vA*eR)/2;
    FA0 = 0;
    FB0 = 0;
  end when;
  
  when contact and (seqState == 1) then
    FR1 = 0;
    FA1 = -muR_*abs(pre(FR))*((vA/sqrt(vA*vA))*eA);
    FB1 = -muR_*abs(pre(FR))*((vA/sqrt(vA*vA))*eB);
    VFricElast[1] = if sign(vA[1])*Vm[1] >= abs(vA[1]/2) then 0 else Vm[1]- (vA[1]/2);
    VFricElast[2] = if sign(vA[2])*Vm[2] >= abs(vA[2]/2) then 0 else Vm[2]- (vA[2]/2);
    VFricElast[3] = if sign(vA[3])*Vm[3] >= abs(vA[3]/2) then 0 else Vm[3]- (vA[3]/2);
  end when;
  
  when contact and (seqState == 2) and (pre(VFricElast)*pre(VFricElast) > 0) then
    eC = if pre(VFricElast)*pre(VFricElast) < s_small^2 then {1,0,0} else 
          pre(VFricElast)/sqrt(pre(VFricElast)*pre(VFricElast));
    noteC = if abs(eC[1]) > 0.1 then {0,1,0} else (if abs(eC[2])
       > 0.1 then {0,0,1} else {1,0,0});
    eD = cross(eC, noteC)/sqrt(cross(eC, noteC)*cross(eC, noteC));
    eE = cross(eD, eC);
    
    VmC2 = sqrt(pre(VFricElast)*pre(VFricElast));
    FD2 = 0;
    FE2 = 0;
  end when;
  
  if contact then
    if (seqState == 0) then
      Vm*eR = VmR0;
      F*eA = FA0;
      F*eB = FB0;
   else
       if (seqState == 1) then
         F*eR = FR1;
         F*eA = FA1;
         F*eB = FB1;
     else
        if (seqState == 2) and (pre(VFricElast)*pre(VFricElast) > 0) then
          Vm*eC = VmC2;
          F*eD = FD2;
          F*eE = FE2;
        else
          F = zeros(3);
        end if;
     end if;
   end if;
  else
    F = zeros(3);
  end if;
  
  y = contact;
  
//  Vm = frame_b.Vm - frame_a.Vm;
  
  Vm = (frame_b.Vm+cross(transpose(R_b)*frame_b.Wm,-eR*rb_)) -
       (frame_a.Vm+cross(transpose(R_a)*frame_a.Wm,eR*ra_));
  F = -frame_b.F;
  F = frame_a.F;
  
  Wm = frame_b.Wm - frame_a.Wm;//actually incorrect but ok because Wm is of no relevance
//  T = -frame_b.T; //actually incorrect but ok because T=0;
//  T = frame_a.T; //actually incorrect but ok because T=0;
  T+R_b*cross(-eR*rb_,F) = -frame_b.T; //actually incorrect but ok because T=0;
  T+R_a*cross(eR*ra_,F) = frame_a.T; //actually incorrect but ok because T=0;
  
  frame_a.f = zeros(3);
  frame_a.t = zeros(3);
  frame_b.f = zeros(3);
  frame_b.t = zeros(3);
  
end CollisionSphereSphere;

MultiBondLib.Mechanics3DwithImpulses.Contacts.CollisionSpherePlane

models the collision between a spheres and a plane

MultiBondLib.Mechanics3DwithImpulses.Contacts.CollisionSpherePlane

Information

This element models the collision between a sphere surrounding frame a and a plane throughgoing frame b.

General parameters

The charactisitics of the impact can be set by the parameters:

elasticity: The elasticity coefficient.
muR: The friction coefficient.

The characteristics of the geometry can be set by the parameters:

ra: The sphere radius.
Nb: normal vector of the plane, pointing from inside to outside.

Visualization

The element isn't visualized.

Advanced settings

A collision causes three consecutive impulses. The parameter contactDuration determines the timespan between the first and the last impulse. It is usually very small.

The parameter s_small in the advanced menu reduces the stiffness of the friction for slip velocities in the range from zero up to s_small.

Parameters

Name Default Description

ra 1 radius of sphere at frame a [m]

Nb[3] {0,1,0} normal vector of plane [m]

elasticity 1.0 Elasticity of impuls

muR 0.0 friction coefficient

Advanced

s_small 1e-4 critical length [m]

contactDuration 1e-9 time to handle the impulses

Name	Default	Description
ra	1	radius of sphere at frame a [m]
Nb[3]	{0,1,0}	normal vector of plane [m]
elasticity	1.0	Elasticity of impuls
muR	0.0	friction coefficient
Advanced
s_small	1e-4	critical length [m]
contactDuration	1e-9	time to handle the impulses

Modelica definition

model CollisionSpherePlane 
  "models the collision between a spheres and a plane" 
  import SI = Modelica.SIunits;
  Interfaces.IFrame_a frame_a;
  
  parameter SI.Radius ra = 1 "radius of sphere at frame a";
  parameter SI.Radius Nb[3] = {0,1,0} "normal vector of plane";
  
  parameter SI.Position s_small = 1e-4 "|Advanced||critical length";
  
  parameter Real elasticity = 1.0 "Elasticity of impuls";
  parameter Real muR = 0.0 "friction coefficient";
  
  parameter Real contactDuration =   1e-9 
    "|Advanced||time to handle the impulses";
  
protected 
  SI.Distance d;
  Real eR[3];
  Real noteR[3];
  Real eA[3];
  Real eB[3];
  
  Boolean contact;
  Integer seqState;
  Real frictionImpulseTime;
  Real correctionImpulseTime;
  
  SI.Impulse F[3];
  SI.AngularImpulse T[3];
  SI.Velocity vA[3];
  SI.Velocity Vm[3];
  SI.AngularVelocity Wm[3];
  
  SI.Impulse FR;
  SI.Impulse FA0;
  SI.Impulse FB0;
  SI.Velocity VmR0;
  
  SI.Impulse FA1;
  SI.Impulse FB1;
  SI.Impulse FR1;
  SI.Velocity VFricElast[3];
  
  Real eC[3];
  Real noteC[3];
  Real eD[3];
  Real eE[3];
  
  SI.Impulse FD2;
  SI.Impulse FE2;
  SI.Velocity VmC2;
  
  Real[3,3] R_a;
  Real[3,3] R_b;
  
public 
  Modelica.Blocks.Interfaces.BooleanOutput y;
  Interfaces.IFrame_b frame_b;
initial equation 
  contact = false;
  seqState = -1;
  frictionImpulseTime = 0;
  correctionImpulseTime = 0;
  
equation 
  
algorithm 
  when contact then
    contact :=false;
  end when;
  
  when d <= ra then
    contact :=true;
    seqState := 0;
    frictionImpulseTime :=time + contactDuration/2;
  end when;
  
  when (time >= frictionImpulseTime) and (seqState == 0) then
    contact :=true;
    seqState := 1;
    frictionImpulseTime := 0;
    correctionImpulseTime := time + contactDuration/2;
  end when;
  
  when (time >= correctionImpulseTime) and (seqState == 1) then
    contact :=true;
    seqState := 2;
    correctionImpulseTime := 0;
  end when;
  
equation 
  d = (frame_a.P.x- frame_b.P.x)*(transpose(frame_b.P.R)*Nb);
  
  when contact and (seqState == 0) then
    eR = transpose(R_b)*Nb/sqrt(Nb*Nb);
    noteR = if abs(eR[1]) > 0.1 then {0,1,0} else (if abs(eR[2])
       > 0.1 then {0,0,1} else {1,0,0});
    eA = cross(eR, noteR)/sqrt(cross(eR, noteR)*cross(eR, noteR));
    eB = cross(eA, eR);
  end when;
  
  when contact then
    vA = (pre(frame_b.P.v)+cross(transpose(R_b)*pre(frame_b.P.w),zeros(3))) -
         (pre(frame_a.P.v)+cross(transpose(R_a)*pre(frame_a.P.w),-eR*ra));
    R_a = frame_a.P.R;
    R_b = frame_b.P.R;
  end when;
  
  when contact then
    T = zeros(3);
  end when;
  
  when contact then
    FR = F*eR;
  end when;
  
  when contact and (seqState == 0) then
    VmR0 = (1-elasticity)*(vA*eR)/2;
    FA0 = 0;
    FB0 = 0;
  end when;
  
  when contact and (seqState == 1) then
    FR1 = 0;
    FA1 = -muR*abs(pre(FR))*((vA/sqrt(vA*vA))*eA);
    FB1 = -muR*abs(pre(FR))*((vA/sqrt(vA*vA))*eB);
    VFricElast[1] = if sign(vA[1])*Vm[1] >= abs(vA[1]/2) then 0 else Vm[1]- (vA[1]/2);
    VFricElast[2] = if sign(vA[2])*Vm[2] >= abs(vA[2]/2) then 0 else Vm[2]- (vA[2]/2);
    VFricElast[3] = if sign(vA[3])*Vm[3] >= abs(vA[3]/2) then 0 else Vm[3]- (vA[3]/2);
  end when;
  
  when contact and (seqState == 2) and (pre(VFricElast)*pre(VFricElast) > 0) then
    eC = if pre(VFricElast)*pre(VFricElast) < s_small^2 then {1,0,0} else 
          pre(VFricElast)/sqrt(pre(VFricElast)*pre(VFricElast));
    noteC = if abs(eC[1]) > 0.1 then {0,1,0} else (if abs(eC[2])
       > 0.1 then {0,0,1} else {1,0,0});
    eD = cross(eC, noteC)/sqrt(cross(eC, noteC)*cross(eC, noteC));
    eE = cross(eD, eC);
    
    VmC2 = sqrt(pre(VFricElast)*pre(VFricElast));
    FD2 = 0;
    FE2 = 0;
  end when;
  
  if contact then
    if (seqState == 0) then
      Vm*eR = VmR0;
      F*eA = FA0;
      F*eB = FB0;
   else
       if (seqState == 1) then
         F*eR = FR1;
         F*eA = FA1;
         F*eB = FB1;
     else
        if (seqState == 2) and (pre(VFricElast)*pre(VFricElast) > 0) then
          Vm*eC = VmC2;
          F*eD = FD2;
          F*eE = FE2;
        else
          F = zeros(3);
        end if;
     end if;
   end if;
  else
    F = zeros(3);
  end if;
  
  y = contact;
  
//  Vm = frame_b.Vm - frame_a.Vm;
  
  Vm = (frame_b.Vm+cross(transpose(R_b)*frame_b.Wm,zeros(3))) -
       (frame_a.Vm+cross(transpose(R_a)*frame_a.Wm,-eR*ra));
  F = -frame_b.F;
  F = frame_a.F;
  
  Wm = frame_b.Wm - frame_a.Wm;//actually incorrect but ok because Wm is of no relevance
//  T = -frame_b.T; //actually incorrect but ok because T=0;
//  T = frame_a.T; //actually incorrect but ok because T=0;
  T+R_b*cross(zeros(3),F) = -frame_b.T; //actually incorrect but ok because T=0;
  T+R_a*cross(-eR*ra,F) = frame_a.T; //actually incorrect but ok because T=0;
  
  frame_a.f = zeros(3);
  frame_a.t = zeros(3);
  frame_b.f = zeros(3);
  frame_b.t = zeros(3);
  
end CollisionSpherePlane;

MultiBondLib.Mechanics3DwithImpulses.Contacts.NoCollision

dummy collision element

MultiBondLib.Mechanics3DwithImpulses.Contacts.NoCollision

Information

This is a dummy elements that models no collision at all. The contact signal is always false. The force and torque impulses ar always zero.

Modelica definition

model NoCollision "dummy collision element" 
  import SI = Modelica.SIunits;
  Interfaces.IFrame_a frame_a;
  
public 
  Modelica.Blocks.Interfaces.BooleanOutput y;
  Interfaces.IFrame_b frame_b;
equation 
  y = false;
  
  zeros(3) = -frame_b.F;
  zeros(3) = frame_a.F;
  
  zeros(3) = -frame_b.T;
  zeros(3) = frame_a.T;
  
  frame_a.f = zeros(3);
  frame_a.t = zeros(3);
  frame_b.f = zeros(3);
  frame_b.t = zeros(3);
  
end NoCollision;

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