MultiBondLib.Mechanics3D.Forces

Information

There are mainly three types of force elements:

• physical interactions like spring or damper elements
• soft collision models, that include geometric computations
• artificially generated forces

Elements of this package do not create rigid connections and therefore do not close kinematic loops.

Name	Description
Damping	linear damping element
Spring	linear spring element
WorldForce	world force acting on frame
WorldTorque	world torque acting on frame
SoftImpuls_SphereSphere	soft impact between two spheres

MultiBondLib.Mechanics3D.Forces.Damping

Information

The damper generates a counteracting force that is proportional to the relative velocity.

The damping coefficient can be set by the parameter d.

Parameters

Name	Default	Description
d	0	Damping constant [N.s/m]

Modelica definition

model Damping "linear damping element" 
  parameter Real d(
    final unit="N.s/m",
    final min=0) = 0 "Damping constant";
  Interfaces.Frame_a frame_a;
  Interfaces.Frame_b frame_b;
  
  
protected 
  inner Defaults MBG_defaults(n=3);
  Interfaces.Mech2MBG Mech2MBG1;
  Interfaces.MBG2Mech MBG2Mech1;
  Junctions.J0 J0_1(n=3);
  Passive.R R1(R={d}, n=3);
  Junctions.J0 J0_2(n=3);
  Sources.Se Se1(n=3, e0={0});
  Bonds.MultiBond MultiBond8;
  Bonds.MultiBond MultiBond3;
  Bonds.MultiBond MultiBond1;
  Bonds.MultiBond MultiBond2;
  Bonds.MultiBond MultiBond4;
  Bonds.MultiBond MultiBond5;
  Bonds.Utilities.MultiBondTail MultiBondTail2;
  Bonds.Utilities.MultiBondTail MultiBondTail1;
  Bonds.Utilities.MultiBondTail MultiBondTail3;
  Bonds.Utilities.MultiBondTail MultiBondTail4;
  
equation 
  connect(Mech2MBG1.frame_a, frame_a);
  connect(MultiBond1.MultiBondCon2, J0_1.MultiBondCon1);
  connect(MultiBond4.MultiBondCon2,J0_2. MultiBondCon1);
  connect(MultiBond8.MultiBondCon2, J0_2.MultiBondCon3);
  connect(MultiBond8.MultiBondCon1, Se1.MultiBondCon1);
  connect(MultiBond5.MultiBondCon2, J0_2.MultiBondCon2);
  connect(J0_1.MultiBondCon2, MultiBond2.MultiBondCon2);
  connect(MBG2Mech1.frame_b, frame_b);
  connect(MultiBond3.MultiBondCon1, J0_1.MultiBondCon4);
  connect(R1.MultiBondCon1, MultiBond3.MultiBondCon2);
  connect(MultiBond4.MultiBondCon1, Mech2MBG1.MultiBondConRot);
  connect(MultiBond5.MultiBondCon1, MBG2Mech1.MultiBondConRot);
  connect(MultiBond2.MultiBondCon1, MBG2Mech1.MultiBondConTrans);
  connect(MultiBond1.MultiBondCon1, Mech2MBG1.MultiBondConTrans);
end Damping;

MultiBondLib.Mechanics3D.Forces.Spring

Information

The spring generates a counteracting force that is linear dependent on the positional shift.

The spring coefficient can be set by the parameter c. The rest lenght can be specified by the parameter s0.

A spring with a rest length s0 unequal to zero, has a stiff behavior if its length is approaching zero. The parameter s_small in the advanced menu reduces this stiffness for spring lengths ranging from zero up to s_small.

Visualization

Parameters

Name	Default	Description
animation	true	animate spring
c	0	Spring constant [N/m]
s0	0	rest length of spring [m]
Advanced
s_small	1e-4	critical Spring length [m]
Animation
if animation = true
width	world3D.defaultForceWidth	Width of spring [m]
coilWidth	width/5	Width of spring coil [m]
numberOfWindings	5	Number of spring windings
color	world3D.defaultForceElementC...	Color of spring

Modelica definition

model Spring "linear spring element" 
  import SI = Modelica.SIunits;
  import MB = Modelica.Mechanics.MultiBody;
  
  Interfaces.Frame_a frame_a;
  Interfaces.Frame_b frame_b;
  
  parameter Boolean animation = true "animate spring";
  
  parameter Real c(
    final unit="N/m",
    final min=0) = 0 "Spring constant";
  
  parameter SI.Position s0 = 0 "rest length of spring";
  parameter SI.Position s_small = 1e-4 "|Advanced||critical Spring length";
  
  parameter SI.Distance width= world3D.defaultForceWidth 
    "|Animation|if animation = true| Width of spring";
  parameter SI.Distance coilWidth=width/5 
    "|Animation|if animation = true| Width of spring coil";
  parameter Integer numberOfWindings=5 
    "|Animation|if animation = true| Number of spring windings";
  parameter MB.Types.Color color= world3D.defaultForceElementColor 
    "|Animation|if animation = true| Color of spring";
  
  SI.Distance s;
  SI.Distance d[3];
  SI.Force f[3];
  
protected 
  outer World3D world3D;
  inner Defaults MBG_defaults(n=3);
  
  Interfaces.MBG2Mech MBG2Mech1;
  Interfaces.Mech2MBG Mech2MBG1;
  
  Junctions.J0 J0_1(n=3);
  Junctions.J0 J0_2(n=3);
  Sources.Se Se1(n=3, e0={0});
  Sources.mSe mSe1(n=3);
  Bonds.MultiBond MultiBond8;
  Bonds.MultiBond MultiBond3;
  Bonds.MultiBond MultiBond1;
  Bonds.MultiBond MultiBond2;
  Bonds.MultiBond MultiBond4;
  Bonds.MultiBond MultiBond5;
  Bonds.Utilities.MultiBondTail MultiBondTail2;
  Bonds.Utilities.MultiBondTail MultiBondTail1;
  Bonds.Utilities.MultiBondTail MultiBondTail3;
  Bonds.Utilities.MultiBondTail MultiBondTail4;
  
  parameter Integer ndim=if world3D.enableAnimation and animation then 1 else 0;
  MB.Visualizers.Advanced.Shape springShape[ndim](
    each shapeType="spring",
    each color=color,
    each length=s,
    each width=width,
    each height=coilWidth,
    each lengthDirection=d,
    each widthDirection={0,0,1},
    each r_shape={0,0,0},
    each r=MBG2Mech1.x,
    each extra=numberOfWindings,
    each R=MB.Frames.Orientation(T=identity(3),w=zeros(3)));
  
equation 
  d = Mech2MBG1.x - MBG2Mech1.x;
  s = sqrt(d*d);
  f = if s >= s_small then c*d - s0*c*(d/s) else c*d - s0*c*(d/s_small);
  mSe1.s = f;
  
  connect(Mech2MBG1.frame_a, frame_a);
  connect(MBG2Mech1.frame_b, frame_b);
  connect(MultiBond1.MultiBondCon2, J0_1.MultiBondCon1);
  connect(MultiBond4.MultiBondCon2,J0_2. MultiBondCon1);
  connect(MultiBond5.MultiBondCon2, J0_2.MultiBondCon2);
  connect(MultiBond3.MultiBondCon2, J0_1.MultiBondCon4);
  connect(mSe1.MultiBondCon1, MultiBond3.MultiBondCon1);
  connect(MultiBond1.MultiBondCon1, Mech2MBG1.MultiBondConTrans);
  connect(MultiBond8.MultiBondCon2, J0_2.MultiBondCon3);
  connect(Se1.MultiBondCon1, MultiBond8.MultiBondCon1);
  connect(MultiBond5.MultiBondCon1, MBG2Mech1.MultiBondConRot);
  connect(MultiBond4.MultiBondCon1, Mech2MBG1.MultiBondConRot);
  connect(MultiBond2.MultiBondCon2, MBG2Mech1.MultiBondConTrans);
  connect(MultiBond2.MultiBondCon1, J0_1.MultiBondCon2);
end Spring;

MultiBondLib.Mechanics3D.Forces.WorldForce

Information

The force is resolved in the inertial system

Parameters

Name	Default	Description
f[3]	{1,0,0}	world force [N]

Modelica definition

model WorldForce "world force acting on frame" 
  import SI = Modelica.SIunits;
  import MB = Modelica.Mechanics.MultiBody;
  
  Interfaces.Frame_b frame_b;
  
  parameter SI.Force f[3] = {1,0,0} "world force";
  
protected 
  outer World3D world3D;
  inner Defaults MBG_defaults(n=3);
  
  Interfaces.MBG2Mech MBG2Mech1;
  
  Bonds.MultiBond MultiBond1;
  
  Sources.Se Se1(n=3, e0=f);
  
  Sources.Se Se2(n=3, e0={0});
  Bonds.MultiBond MultiBond4;
equation 
  
  connect(MBG2Mech1.frame_b, frame_b);
  connect(MultiBond1.MultiBondCon2, MBG2Mech1.MultiBondConRot);
  connect(Se2.MultiBondCon1, MultiBond1.MultiBondCon1);
  connect(MultiBond4.MultiBondCon2, MBG2Mech1.MultiBondConTrans);
  connect(Se1.MultiBondCon1, MultiBond4.MultiBondCon1);
end WorldForce;

MultiBondLib.Mechanics3D.Forces.WorldTorque

Information

The torque is resolved in the inertial system

Parameters

Name	Default	Description
t[3]	{1,0,0}	world force [N.m]

Modelica definition

model WorldTorque "world torque acting on frame" 
  import SI = Modelica.SIunits;
  import MB = Modelica.Mechanics.MultiBody;
  
  Interfaces.Frame_b frame_b;
  
  parameter SI.Torque t[3] = {1,0,0} "world force";
  
protected 
  outer World3D world3D;
  inner Defaults MBG_defaults(n=3);
  Interfaces.MBG2Mech MBG2Mech1;
  Bonds.MultiBond MultiBond1;
  Sources.Se Se1(e0={0});
  Sources.Se Se2(n=3, e0=t);
  Bonds.MultiBond MultiBond4;
  Passive.mTF_effort mTF_effort1;
  Bonds.MultiBond MultiBond2;
  
equation 
  connect(MBG2Mech1.frame_b, frame_b);
  connect(Se2.MultiBondCon1, MultiBond1.MultiBondCon1);
  connect(MultiBond4.MultiBondCon2, MBG2Mech1.MultiBondConTrans);
  connect(Se1.MultiBondCon1, MultiBond4.MultiBondCon1);
  connect(MultiBond2.MultiBondCon2, MBG2Mech1.MultiBondConRot);
  connect(mTF_effort1.MultiBondCon2, MultiBond2.MultiBondCon1);
  connect(mTF_effort1.MultiBondCon1, MultiBond1.MultiBondCon2);
  connect(mTF_effort1.M, MBG2Mech1.R);
end WorldTorque;

MultiBondLib.Mechanics3D.Forces.SoftImpuls_SphereSphere

Information

The spheres are supposed to suround the two connector with the radii ra and rb.

The collision characteristics can be specified by the coefficients of the virtual spring and damper.

Parameters

Name	Default	Description
c	0	Spring constant [N/m]
d	0	Damping constant [N.s/m]
ra	1	radius of sphere at frame a [m]
rb	1	radius of sphere at frame b [m]
Advanced
s_small	1e-4	critical Spring length [m]

Modelica definition

model SoftImpuls_SphereSphere "soft impact between two spheres" 
  import SI = Modelica.SIunits;
  import MB = Modelica.Mechanics.MultiBody;
  
  Interfaces.Frame_a frame_a;
  Interfaces.Frame_b frame_b;
  
  parameter Real c(
    final unit="N/m",
    final min=0) = 0 "Spring constant";
  
  parameter Real d(
    final unit="N.s/m",
    final min=0) = 0 "Damping constant";
  
  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 Spring length";
  
//  parameter Real muR "friction coefficient";
//  parameter SI.Velocity vAdhesion "range of Adhesion";
  
  SI.Distance s;
  SI.Distance r[3];
  Real eR[3];
  SI.Force fI[3];
//  SI.Force fR[3];
//  SI.Velocity deltaV[3];
//  SI.Velocity vR[3];
  
  
protected 
  outer World3D world3D;
protected 
  inner Defaults MBG_defaults(n=3);
  
protected 
  Interfaces.MBG2Mech MBG2Mech1;
  Interfaces.Mech2MBG Mech2MBG1;
  
protected 
  Junctions.J0 J0_1(n=3);
  Junctions.J0 J0_2(n=3);
  Sources.Se Se1(n=3, e0={0});
  Sources.mSe mSe1(n=3);
  Bonds.MultiBond MultiBond8;
  Bonds.MultiBond MultiBond3;
  Bonds.MultiBond MultiBond1;
  Bonds.MultiBond MultiBond2;
  Bonds.MultiBond MultiBond4;
  Bonds.MultiBond MultiBond5;
  Bonds.Utilities.MultiBondTail MultiBondTail2;
  Bonds.Utilities.MultiBondTail MultiBondTail1;
  Bonds.Utilities.MultiBondTail MultiBondTail3;
  Bonds.Utilities.MultiBondTail MultiBondTail4;
  
equation 
  r = Mech2MBG1.x - MBG2Mech1.x;
  s = sqrt(r*r);
  eR = if s >= s_small then r/s else r/s_small;
  fI = if (s-ra-rb) < 0 then c*(s-ra-rb)*eR else zeros(3);
//  deltaV = Mech2MBG1.MultiBondConTrans.f - MBG2Mech1.MultiBondConTrans.f;
//  vR = deltaV - eR*(deltaV*eR);
//  fR = if sqrt(vR*vR) > vAdhesion then sqrt(fI*fI)*muR*vR/sqrt(vR*vR) else 
//            sqrt(fI*fI)*muR*(vR/vAdhesion);
//  mSe1.s = fI+fR;
  mSe1.s = fI;
  
  connect(Mech2MBG1.frame_a, frame_a);
  connect(MBG2Mech1.frame_b, frame_b);
  connect(MultiBond1.MultiBondCon2, J0_1.MultiBondCon1);
  connect(MultiBond4.MultiBondCon2,J0_2. MultiBondCon1);
  connect(MultiBond5.MultiBondCon2, J0_2.MultiBondCon2);
  connect(MultiBond3.MultiBondCon2, J0_1.MultiBondCon4);
  connect(mSe1.MultiBondCon1, MultiBond3.MultiBondCon1);
  connect(MultiBond1.MultiBondCon1, Mech2MBG1.MultiBondConTrans);
  connect(MultiBond8.MultiBondCon2, J0_2.MultiBondCon3);
  connect(Se1.MultiBondCon1, MultiBond8.MultiBondCon1);
  connect(MultiBond5.MultiBondCon1, MBG2Mech1.MultiBondConRot);
  connect(MultiBond4.MultiBondCon1, Mech2MBG1.MultiBondConRot);
  connect(MultiBond2.MultiBondCon2, MBG2Mech1.MultiBondConTrans);
  connect(MultiBond2.MultiBondCon1, J0_1.MultiBondCon2);
end SoftImpuls_SphereSphere;