Modelica.Mechanics.MultiBody.Examples.Loops.Utilities

Information

Package Content

Name	Description
Cylinder	Cylinder with rod and crank of a combustion engine
GasForce	Simple gas force computation for combustion engine
GasForce2	Rough approximation of gas force in a cylinder
CylinderBase	One cylinder with analytic handling of kinematic loop
Cylinder_analytic_CAD	One cylinder with analytic handling of kinematic loop and CAD visualization
EngineV6_analytic	V6 engine with analytic loop handling
Engine1bBase	Model of one cylinder engine with gas force

Modelica.Mechanics.MultiBody.Examples.Loops.Utilities.Cylinder

Parameters

Type	Name	Default	Description
Boolean	animation	true	= true, if animation shall be enabled
Length	cylinderTopPosition	0.42	Length from crank shaft to end of cylinder. [m]
Length	pistonLength	0.1	Length of cylinder [m]
Length	rodLength	0.2	Length of rod [m]
Length	crankLength	0.2	Length of crank shaft in x direction [m]
Length	crankPinOffset	0.1	Offset of crank pin from center axis [m]
Length	crankPinLength	0.1	Offset of crank pin from center axis [m]
Angle	cylinderInclination	0	Inclination of cylinder [rad]
Angle	crankAngleOffset	0	Offset for crank angle [rad]
Length	cylinderLength	cylinderTopPosition - (pisto...	Maximum length of cylinder volume [m]

Connectors

Type	Name	Description
Frame_a	cylinder_a
Frame_a	cylinder_b
Frame_a	crank_a
Frame_a	crank_b

Modelica definition

model Cylinder "Cylinder with rod and crank of a combustion engine"
  import SI = Modelica.SIunits;
  parameter Boolean animation=true "= true, if animation shall be enabled";
  parameter SI.Length cylinderTopPosition=0.42 
    "Length from crank shaft to end of cylinder.";
  parameter SI.Length pistonLength=0.1 "Length of cylinder";
  parameter SI.Length rodLength=0.2 "Length of rod";
  parameter SI.Length crankLength=0.2 "Length of crank shaft in x direction";
  parameter SI.Length crankPinOffset=0.1 "Offset of crank pin from center axis";
  parameter SI.Length crankPinLength=0.1 "Offset of crank pin from center axis";
  parameter SI.Angle cylinderInclination=0 "Inclination of cylinder";
  parameter SI.Angle crankAngleOffset=0 "Offset for crank angle";
  parameter SI.Length cylinderLength=cylinderTopPosition - (pistonLength +
      rodLength - crankPinOffset) "Maximum length of cylinder volume";

  Modelica.Mechanics.MultiBody.Parts.BodyCylinder Piston(
    diameter=0.1,
    r={0,pistonLength,0},
    color={180,180,180},
    animation=animation);
  Modelica.Mechanics.MultiBody.Parts.BodyBox Rod(
    widthDirection={1,0,0},
    height=0.06,
    color={0,0,200},
    width=0.02,
    r_shape={0,-0.02,0},
    r={0,rodLength,0},
    animation=animation);
  Modelica.Mechanics.MultiBody.Joints.Revolute B2(
    n={1,0,0},
    cylinderLength=0.02,
    animation=animation,
    cylinderDiameter=0.055);
  Modelica.Mechanics.MultiBody.Parts.BodyBox Crank4(
    height=0.05,
    widthDirection={1,0,0},
    width=0.02,
    r={0,-crankPinOffset,0},
    animation=animation);
  Modelica.Mechanics.MultiBody.Parts.BodyCylinder Crank3(
    r_shape={-0.01,0,0},
    length=0.12,
    diameter=0.03,
    r={crankPinLength,0,0},
    color={180,180,180},
    animation=animation);
  Modelica.Mechanics.MultiBody.Parts.BodyCylinder Crank1(
    diameter=0.05,
    r_shape={-0.01,0,0},
    length=0.12,
    r={crankLength - crankPinLength,0,0},
    color={180,180,180},
    animation=animation);
  Modelica.Mechanics.MultiBody.Parts.BodyBox Crank2(
    height=0.05,
    widthDirection={1,0,0},
    width=0.02,
    r={0,crankPinOffset,0},
    animation=animation);
  Joints.RevolutePlanarLoopConstraint B1(
    n={1,0,0},
    cylinderLength=0.02,
    animation=animation,
    cylinderDiameter=0.055);
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation Mid(r={crankPinLength/2,0,0}, animation=
        false);
  Modelica.Mechanics.MultiBody.Joints.Prismatic Cylinder(useAxisFlange=true,
    s(start=-0.3),
    n={0,-1,0},
    boxWidth=0.02);
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation Mounting(r={crankLength,0,0}, animation=
        false);
  Modelica.Mechanics.MultiBody.Parts.FixedRotation CylinderInclination(
    r={crankLength - crankPinLength/2,0,0},
    n_y={0,cos(cylinderInclination),sin(cylinderInclination)},
    animation=false,
    rotationType=Modelica.Mechanics.MultiBody.Types.RotationTypes.TwoAxesVectors);
  Modelica.Mechanics.MultiBody.Parts.FixedRotation CrankAngle1(
    n_y={0,cos(crankAngleOffset),sin(crankAngleOffset)},
    animation=false,
    rotationType=Modelica.Mechanics.MultiBody.Types.RotationTypes.TwoAxesVectors);
  Modelica.Mechanics.MultiBody.Parts.FixedRotation CrankAngle2(
    n_y={0,cos(-crankAngleOffset),sin(-crankAngleOffset)},
    animation=false,
    rotationType=Modelica.Mechanics.MultiBody.Types.RotationTypes.TwoAxesVectors);
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation CylinderTop(r={0,cylinderTopPosition,0},
      animation=false);
  GasForce gasForce(L=cylinderLength, d=0.1);
  Interfaces.Frame_a cylinder_a;
  Interfaces.Frame_a cylinder_b;
  Interfaces.Frame_a crank_a;
  Interfaces.Frame_a crank_b;
equation 
  connect(B1.frame_a, Mid.frame_b);
  connect(Rod.frame_a, B1.frame_b);
  connect(Cylinder.frame_b, Piston.frame_b);
  connect(Crank1.frame_a, CrankAngle1.frame_b);
  connect(B2.frame_a, Piston.frame_a);
  connect(Rod.frame_b, B2.frame_b);
  connect(Crank4.frame_b, CrankAngle2.frame_a);
  connect(Cylinder.support, gasForce.flange_b);
  connect(Cylinder.axis, gasForce.flange_a);
  connect(CylinderInclination.frame_b, CylinderTop.frame_a);
  connect(Crank1.frame_b, Crank2.frame_a);
  connect(Crank3.frame_b, Crank4.frame_a);
  connect(Crank3.frame_a, Crank2.frame_b);
  connect(Crank2.frame_b, Mid.frame_a);
  connect(CylinderTop.frame_b, Cylinder.frame_a);
  connect(CylinderInclination.frame_a, cylinder_a);
  connect(Mounting.frame_a, cylinder_a);
  connect(Mounting.frame_b, cylinder_b);
  connect(CrankAngle1.frame_a, crank_a);
  connect(CrankAngle2.frame_b, crank_b);

end Cylinder;

Modelica.Mechanics.MultiBody.Examples.Loops.Utilities.GasForce

Information

Parameters

Type	Name	Default	Description
Length	L		Length of cylinder [m]
Diameter	d		Diameter of cylinder [m]
Volume	k0	0.01	Volume V = k0 + k1*(1-x), with x = 1 + s_rel/L [m3]
Volume	k1	1	Volume V = k0 + k1*(1-x), with x = 1 + s_rel/L [m3]
HeatCapacity	k	1	Gas constant (p*V = k*T) [J/K]
Initialization
Distance	s_rel.start	0	relative distance (= flange_b.s - flange_a.s) [m]

Connectors

Type	Name	Description
Flange_a	flange_a	Left flange of compliant 1-dim. translational component
Flange_b	flange_b	Right flange of compliant 1-dim. translational component

Modelica definition

model GasForce "Simple gas force computation for combustion engine"
  import SI = Modelica.SIunits;

  extends Modelica.Mechanics.Translational.Interfaces.PartialCompliant;
  parameter SI.Length L "Length of cylinder";
  parameter SI.Diameter d "Diameter of cylinder";
  parameter SIunits.Volume k0=0.01 
    "Volume V = k0 + k1*(1-x), with x = 1 + s_rel/L";
  parameter SIunits.Volume k1=1 
    "Volume V = k0 + k1*(1-x), with x = 1 + s_rel/L";
  parameter SIunits.HeatCapacity k=1 "Gas constant (p*V = k*T)";
  constant Real pi=Modelica.Constants.pi;

  // Only for compatibility reasons
  Real x "Normalized position of cylinder";
  Real y "Normalized relative movement (= -s_rel/L)";
  SI.Density dens;
  Modelica.SIunits.Conversions.NonSIunits.Pressure_bar press 
    "cylinder pressure";
  SI.Volume V;
  SI.Temperature T;
  SI.Velocity v_rel;
protected 
  constant SI.Mass unitMass=1;
  Modelica.SIunits.Pressure p;
equation 
  y = -s_rel/L;
  x = 1 + s_rel/L;
  v_rel = der(s_rel);

  press = p/1e5;
  p = (if v_rel < 0 then (if x < 0.987 then 177.4132*x^4 - 287.2189*x^3 +
    151.8252*x^2 - 24.9973*x + 2.4 else 2836360*x^4 - 10569296*x^3 + 14761814
    *x^2 - 9158505*x + 2129670) else (if x > 0.93 then -3929704*x^4 +
    14748765*x^3 - 20747000*x^2 + 12964477*x - 3036495 else 145.930*x^4 -
    131.707*x^3 + 17.3438*x^2 + 17.9272*x + 2.4))*1e5;

  f = -1.0E5*press*pi*d^2/4;

  V = k0 + k1*(1 - x);
  dens = unitMass/V;
  (p/1e5)*V = k*T;
end GasForce;

Modelica.Mechanics.MultiBody.Examples.Loops.Utilities.GasForce2

Information

The gas force in a cylinder is computed as function of the relative distance of the two flanges. It is required that s_rel = flange_b.s - flange_a.s is in the range

    0 ≤ s_rel ≤ L

where the parameter L is the length of the cylinder. If this assumption is not fulfilled, an error occurs.

Extends from Modelica.Mechanics.Translational.Interfaces.PartialCompliant (Compliant connection of two translational 1D flanges).

Parameters

Type	Name	Default	Description
Length	L		Length of cylinder [m]
Length	d		diameter of cylinder [m]
Volume	k0	0.01	Volume V = k0 + k1*(1-x), with x = 1 - s_rel/L [m3]
Volume	k1	1	Volume V = k0 + k1*(1-x), with x = 1 - s_rel/L [m3]
HeatCapacity	k	1	Gas constant (p*V = k*T) [J/K]
Initialization
Distance	s_rel.start	0	relative distance (= flange_b.s - flange_a.s) [m]

Connectors

Type	Name	Description
Flange_a	flange_a	Left flange of compliant 1-dim. translational component
Flange_b	flange_b	Right flange of compliant 1-dim. translational component

Modelica definition

model GasForce2 "Rough approximation of gas force in a cylinder"
  import SI = Modelica.SIunits;

  extends Modelica.Mechanics.Translational.Interfaces.PartialCompliant;
  parameter SI.Length L "Length of cylinder";
  parameter SI.Length d "diameter of cylinder";
  parameter SIunits.Volume k0=0.01 
    "Volume V = k0 + k1*(1-x), with x = 1 - s_rel/L";
  parameter SIunits.Volume k1=1 
    "Volume V = k0 + k1*(1-x), with x = 1 - s_rel/L";
  parameter SIunits.HeatCapacity k=1 "Gas constant (p*V = k*T)";

/*
  parameter Real k0=0.01;
  parameter Real k1=1;
  parameter Real k=1;
*/
  constant Real pi=Modelica.Constants.pi;
  Real x "Normalized position of cylinder (= 1 - s_rel/L)";
  SI.Density dens;
  Modelica.SIunits.AbsolutePressure press "Cylinder pressure";
  SI.Volume V;
  SI.Temperature T;
  SI.Velocity v_rel;

protected 
  Modelica.SIunits.SpecificHeatCapacity R_air = Modelica.Constants.R/0.0289651159;
equation 
  x = 1 - s_rel/L;
  v_rel = der(s_rel);

  press = 1.0E5*(if v_rel < 0 then (if x < 0.987 then 177.4132*x^4 - 287.2189*x^3 +
    151.8252*x^2 - 24.9973*x + 2.4 else 2836360*x^4 - 10569296*x^3 + 14761814
    *x^2 - 9158505*x + 2129670) else (if x > 0.93 then -3929704*x^4 +
    14748765*x^3 - 20747000*x^2 + 12964477*x - 3036495 else 145.930*x^4 -
    131.707*x^3 + 17.3438*x^2 + 17.9272*x + 2.4));

  f = -press*pi*d^2/4;

  V = k0 + k1*(1 - x);
  dens = press/(R_air*T);
  press*V = k*T;

  assert(s_rel >= -1.e-12, "flange_b.s - flange_a.s (= " + String(s_rel) +
                           ") >= 0 required for GasForce component.\n" +
                           "Most likely, the component has to be flipped.");
  assert(s_rel <= L + 1.e-12, " flange_b.s - flange_a.s (= " + String(s_rel) +
                              " <= L (" + String(L) + ") required for GasForce component.\n" +
                              "Most likely, parameter L is not correct.");
end GasForce2;

Modelica.Mechanics.MultiBody.Examples.Loops.Utilities.CylinderBase

Parameters

Type	Name	Default	Description
Boolean	animation	true	= true, if animation shall be enabled
Length	cylinderTopPosition	0.42	Length from crank shaft to end of cylinder. [m]
Length	crankLength	0.14	Length of crank shaft in x direction [m]
Length	crankPinOffset	0.05	Offset of crank pin from center axis [m]
Length	crankPinLength	0.1	Offset of crank pin from center axis [m]
Angle_deg	cylinderInclination	0	Inclination of cylinder [deg]
Angle_deg	crankAngleOffset	0	Offset for crank angle [deg]
Piston
Length	pistonLength	0.1	Length of cylinder [m]
Length	pistonCenterOfMass	pistonLength/2	Distance from frame_a to center of mass of piston [m]
Mass	pistonMass	6	Mass of piston [kg]
Inertia	pistonInertia_11	0.0088	Inertia 11 of piston with respect to center of mass frame, parallel to frame_a [kg.m2]
Inertia	pistonInertia_22	0.0076	Inertia 22 of piston with respect to center of mass frame, parallel to frame_a [kg.m2]
Inertia	pistonInertia_33	0.0088	Inertia 33 of piston with respect to center of mass frame, parallel to frame_a [kg.m2]
Rod
Length	rodLength	0.175	Length of rod [m]
Length	rodCenterOfMass	rodLength/2	Distance from frame_a to center of mass of piston [m]
Mass	rodMass	1	Mass of rod [kg]
Inertia	rodInertia_11	0.006	Inertia 11 of rod with respect to center of mass frame, parallel to frame_a [kg.m2]
Inertia	rodInertia_22	0.0005	Inertia 22 of rod with respect to center of mass frame, parallel to frame_a [kg.m2]
Inertia	rodInertia_33	0.006	Inertia 33 of rod with respect to center of mass frame, parallel to frame_a [kg.m2]

Connectors

Type	Name	Description
Frame_a	cylinder_a
Frame_a	cylinder_b
Frame_a	crank_a
Frame_a	crank_b

Modelica definition

model CylinderBase 
  "One cylinder with analytic handling of kinematic loop"
  import SI = Modelica.SIunits;
  import Cv = Modelica.SIunits.Conversions;
  parameter Boolean animation=true "= true, if animation shall be enabled";
  parameter SI.Length cylinderTopPosition=0.42 
    "Length from crank shaft to end of cylinder.";
  parameter SI.Length crankLength=0.14 "Length of crank shaft in x direction";
  parameter SI.Length crankPinOffset=0.05 
    "Offset of crank pin from center axis";
  parameter SI.Length crankPinLength=0.1 "Offset of crank pin from center axis";
  parameter Cv.NonSIunits.Angle_deg cylinderInclination=0 
    "Inclination of cylinder";
  parameter Cv.NonSIunits.Angle_deg crankAngleOffset=0 "Offset for crank angle";
  parameter SI.Length pistonLength=0.1 " Length of cylinder";
  parameter SI.Length pistonCenterOfMass=pistonLength/2 
    " Distance from frame_a to center of mass of piston";
  parameter SI.Mass pistonMass(min=0) = 6 " Mass of piston";
  parameter SI.Inertia pistonInertia_11(min=0) = 0.0088 
    " Inertia 11 of piston with respect to center of mass frame, parallel to frame_a";
  parameter SI.Inertia pistonInertia_22(min=0) = 0.0076 
    " Inertia 22 of piston with respect to center of mass frame, parallel to frame_a";
  parameter SI.Inertia pistonInertia_33(min=0) = 0.0088 
    " Inertia 33 of piston with respect to center of mass frame, parallel to frame_a";

  parameter SI.Length rodLength=0.175 " Length of rod";
  parameter SI.Length rodCenterOfMass=rodLength/2 
    " Distance from frame_a to center of mass of piston";
  parameter SI.Mass rodMass(min=0) = 1 " Mass of rod";
  parameter SI.Inertia rodInertia_11(min=0) = 0.006 
    " Inertia 11 of rod with respect to center of mass frame, parallel to frame_a";
  parameter SI.Inertia rodInertia_22(min=0) = 0.0005 
    " Inertia 22 of rod with respect to center of mass frame, parallel to frame_a";
  parameter SI.Inertia rodInertia_33(min=0) = 0.006 
    " Inertia 33 of rod with respect to center of mass frame, parallel to frame_a";
  final parameter SI.Length cylinderLength=cylinderTopPosition - (
      pistonLength + rodLength - crankPinOffset) 
    "Maximum length of cylinder volume";

  Modelica.Mechanics.MultiBody.Parts.FixedTranslation Mid(animation=false, r={crankLength -
        crankPinLength/2,crankPinOffset,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation Mounting(r={crankLength,0,0}, animation=
        false);
  Modelica.Mechanics.MultiBody.Parts.FixedRotation CylinderInclination(
    r={crankLength - crankPinLength/2,0,0},
    animation=false,
    rotationType=Modelica.Mechanics.MultiBody.Types.RotationTypes.RotationAxis,
    n={1,0,0},
    angle=cylinderInclination);
  Modelica.Mechanics.MultiBody.Parts.FixedRotation CrankAngle(
    animation=false,
    rotationType=Modelica.Mechanics.MultiBody.Types.RotationTypes.RotationAxis,
    n={1,0,0},
    angle=crankAngleOffset);
  Joints.Assemblies.JointRRP jointRRP(
    n_a={1,0,0},
    n_b={0,-1,0},
    rRod1_ia={0,rodLength,0},
    animation=false,
    rRod2_ib=-{0,pistonLength,0},
    s_offset=-cylinderTopPosition);
  Modelica.Mechanics.MultiBody.Parts.BodyShape Rod(
    animation=animation,
    r={0,rodLength,0},
    r_CM={0,rodLength/2,0},
    shapeType="2",
    lengthDirection={1,0,0},
    widthDirection={0,0,-1},
    length=rodLength/1.75,
    width=rodLength/1.75,
    height=rodLength/1.75,
    color={155,155,155},
    extra=1,
    r_shape={0,0,0},
    animateSphere=false,
    m=rodMass,
    I_11=rodInertia_11,
    I_22=rodInertia_22,
    I_33=rodInertia_33);
  Modelica.Mechanics.MultiBody.Parts.BodyShape Piston(
    animation=animation,
    r={0,pistonLength,0},
    r_CM={0,pistonLength/2,0},
    shapeType="3",
    length=0.08,
    width=0.08,
    height=0.08,
    extra=1,
    lengthDirection={1,0,0},
    widthDirection={0,0,-1},
    color={180,180,180},
    animateSphere=false,
    m=pistonMass,
    I_11=pistonInertia_11,
    I_22=pistonInertia_22,
    I_33=pistonInertia_33);
  GasForce gasForce(L=cylinderLength, d=0.1);

  Modelica.Mechanics.MultiBody.Parts.FixedTranslation Crank(animation=false, r={crankLength,0,0});
  Interfaces.Frame_a cylinder_a;
  Interfaces.Frame_a cylinder_b;
  Interfaces.Frame_a crank_a;
  Interfaces.Frame_a crank_b;
equation 

  connect(jointRRP.frame_ia, Rod.frame_a);
  connect(Mid.frame_b, jointRRP.frame_a);
  connect(gasForce.flange_a, jointRRP.axis);
  connect(jointRRP.bearing, gasForce.flange_b);
  connect(jointRRP.frame_ib, Piston.frame_b);
  connect(jointRRP.frame_b, CylinderInclination.frame_b);
  connect(CrankAngle.frame_b, Mid.frame_a);
  connect(cylinder_a, CylinderInclination.frame_a);
  connect(cylinder_a, Mounting.frame_a);
  connect(cylinder_b, Mounting.frame_b);
  connect(CrankAngle.frame_a, crank_a);
  connect(crank_a, Crank.frame_a);
  connect(Crank.frame_b, crank_b);
end CylinderBase;

Modelica.Mechanics.MultiBody.Examples.Loops.Utilities.Cylinder_analytic_CAD

Information

Parameters

Type	Name	Default	Description
Boolean	animation	true	= true, if animation shall be enabled
Length	cylinderTopPosition	0.42	Length from crank shaft to end of cylinder. [m]
Length	crankLength	0.14	Length of crank shaft in x direction [m]
Length	crankPinOffset	0.05	Offset of crank pin from center axis [m]
Length	crankPinLength	0.1	Offset of crank pin from center axis [m]
Angle_deg	cylinderInclination	0	Inclination of cylinder [deg]
Angle_deg	crankAngleOffset	0	Offset for crank angle [deg]
Piston
Length	pistonLength	0.1	Length of cylinder [m]
Length	pistonCenterOfMass	pistonLength/2	Distance from frame_a to center of mass of piston [m]
Mass	pistonMass	6	Mass of piston [kg]
Inertia	pistonInertia_11	0.0088	Inertia 11 of piston with respect to center of mass frame, parallel to frame_a [kg.m2]
Inertia	pistonInertia_22	0.0076	Inertia 22 of piston with respect to center of mass frame, parallel to frame_a [kg.m2]
Inertia	pistonInertia_33	0.0088	Inertia 33 of piston with respect to center of mass frame, parallel to frame_a [kg.m2]
Rod
Length	rodLength	0.175	Length of rod [m]
Length	rodCenterOfMass	rodLength/2	Distance from frame_a to center of mass of piston [m]
Mass	rodMass	1	Mass of rod [kg]
Inertia	rodInertia_11	0.006	Inertia 11 of rod with respect to center of mass frame, parallel to frame_a [kg.m2]
Inertia	rodInertia_22	0.0005	Inertia 22 of rod with respect to center of mass frame, parallel to frame_a [kg.m2]
Inertia	rodInertia_33	0.006	Inertia 33 of rod with respect to center of mass frame, parallel to frame_a [kg.m2]

Connectors

Type	Name	Description
Frame_a	cylinder_a
Frame_a	cylinder_b
Frame_a	crank_a
Frame_a	crank_b

Modelica definition

model Cylinder_analytic_CAD 
  "One cylinder with analytic handling of kinematic loop and CAD visualization"
  extends CylinderBase;
  Visualizers.FixedShape CrankShape(
    animation=animation,
    shapeType="1",
    lengthDirection={1,0,0},
    extra=1,
    widthDirection={0,1,0},
    length=crankPinOffset/0.5,
    width=crankPinOffset/0.5,
    height=crankPinOffset/0.5,
    r_shape={crankLength - crankPinLength/2 - 0.002,0,0});
equation 

  connect(CrankShape.frame_a, CrankAngle.frame_b);
end Cylinder_analytic_CAD;

Modelica.Mechanics.MultiBody.Examples.Loops.Utilities.EngineV6_analytic

Parameters

Type	Name	Default	Description
Boolean	animation	true	= true, if animation shall be enabled

Connectors

Type	Name	Description
Flange_b	flange_b
Frame_a	frame_a

Modelica definition

model EngineV6_analytic "V6 engine with analytic loop handling"
  import SI = Modelica.SIunits;
  parameter Boolean animation=true "= true, if animation shall be enabled";
  replaceable model Cylinder = Cylinder_analytic_CAD constrainedby CylinderBase
    "Cylinder type";

  Cylinder cylinder1(
    crankAngleOffset=-30,
    cylinderInclination=-30,
    animation=animation);
  Cylinder cylinder2(
    crankAngleOffset=90,
    cylinderInclination=30,
    animation=animation);
  Cylinder cylinder3(
    cylinderInclination=-30,
    animation=animation,
    crankAngleOffset=210);
  Cylinder cylinder4(
    cylinderInclination=30,
    animation=animation,
    crankAngleOffset=210);
  Cylinder cylinder5(
    cylinderInclination=-30,
    animation=animation,
    crankAngleOffset=90);
  Cylinder cylinder6(
    cylinderInclination=30,
    animation=animation,
    crankAngleOffset=-30);
  Joints.Revolute bearing(useAxisFlange=true,
    n={1,0,0},
    cylinderLength=0.02,
    cylinderDiameter=0.06,
    animation=true);
  Parts.BodyShape crank(
    animation=false,
    r_CM={6*0.1/2,0,0},
    I_22=1.e-5,
    I_33=1.e-5,
    m=6*30,
    I_11=0.1);
  Modelica.Mechanics.Rotational.Interfaces.Flange_b flange_b;
  Interfaces.Frame_a frame_a;
equation 
  connect(cylinder1.crank_b, cylinder2.crank_a);
  connect(cylinder2.cylinder_a, cylinder1.cylinder_b);
  connect(cylinder3.cylinder_a, cylinder2.cylinder_b);
  connect(cylinder3.crank_a, cylinder2.crank_b);
  connect(cylinder3.cylinder_b, cylinder4.cylinder_a);
  connect(cylinder3.crank_b, cylinder4.crank_a);
  connect(cylinder4.cylinder_b, cylinder5.cylinder_a);
  connect(cylinder4.crank_b, cylinder5.crank_a);
  connect(cylinder5.cylinder_b, cylinder6.cylinder_a);
  connect(cylinder5.crank_b, cylinder6.crank_a);
  connect(bearing.frame_b, crank.frame_a);
  connect(crank.frame_b, cylinder1.crank_a);
  connect(bearing.axis, flange_b);
  connect(frame_a, bearing.frame_a);
  connect(bearing.frame_a, cylinder1.cylinder_a);
end EngineV6_analytic;

Modelica.Mechanics.MultiBody.Examples.Loops.Utilities.Engine1bBase

Information

This is a model of the mechanical part of one cylinder of an engine. The combustion is not modelled. The "inertia" component at the lower left part is the output inertia of the engine driving the gearbox. The angular velocity of the output inertia has a start value of 10 rad/s in order to demonstrate the movement of the engine.

The engine is modeled solely by revolute and prismatic joints. Since this results in a planar loop there is the well known difficulty that the cut-forces perpendicular to the loop cannot be uniquely computed, as well as the cut-torques within the plane. This ambiguity is resolved by using the option planarCutJoint in the Advanced menu of one revolute joint in every planar loop (here: joint B1). This option sets the cut-force in direction of the axis of rotation, as well as the cut-torques perpendicular to the axis of rotation at this joint to zero and makes the problem mathematically well-formed.

An animation of this example is shown in the figure below.

Extends from Modelica.Icons.Example (Icon for an example model).

Modelica definition

partial model Engine1bBase 
  "Model of one cylinder engine with gas force"
  import SI = Modelica.SIunits;
  extends Modelica.Icons.Example;
  Modelica.Mechanics.MultiBody.Parts.BodyCylinder Piston(diameter=0.1, r={0,-0.1,0});
  Modelica.Mechanics.MultiBody.Parts.BodyBox Rod2(
    widthDirection={1,0,0},
    width=0.02,
    height=0.06,
    color={0,0,200},
    r={0,0.2,0});
  Modelica.Mechanics.MultiBody.Joints.Revolute Bearing(useAxisFlange=true,
    n={1,0,0},
    cylinderLength=0.02,
    cylinderDiameter=0.05);
  inner Modelica.Mechanics.MultiBody.World world;
  Modelica.Mechanics.Rotational.Components.Inertia Inertia(
    stateSelect=StateSelect.always,
    J=0.1,
    w(fixed=true),
    phi(
      fixed=true,
      start=0.001,
      displayUnit="rad"));
  Modelica.Mechanics.MultiBody.Parts.BodyBox Crank4(
    height=0.05,
    widthDirection={1,0,0},
    width=0.02,
    r={0,-0.1,0});
  Modelica.Mechanics.MultiBody.Parts.BodyCylinder Crank3(r={0.1,0,0}, diameter=0.03);
  Modelica.Mechanics.MultiBody.Parts.BodyCylinder Crank1(diameter=0.05, r={0.1,0,0});
  Modelica.Mechanics.MultiBody.Parts.BodyBox Crank2(
    height=0.05,
    widthDirection={1,0,0},
    width=0.02,
    r={0,0.1,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation Mid(r={0.05,0,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation cylPosition(                 animation=false, r={0.15,
        0.55,0});
  Utilities.GasForce2 gasForce(        d=0.1, L=0.35);
equation 
  connect(world.frame_b, Bearing.frame_a);
  connect(Crank2.frame_a, Crank1.frame_b);
  connect(Crank2.frame_b, Crank3.frame_a);
  connect(Bearing.frame_b, Crank1.frame_a);
  connect(world.frame_b, cylPosition.frame_a);
  connect(Crank3.frame_b, Crank4.frame_a);
  connect(Inertia.flange_b, Bearing.axis);
  connect(Mid.frame_a, Crank2.frame_b);
end Engine1bBase;

Modelica.Mechanics.MultiBody.Examples.Loops.Utilities.EngineV6_analytic.Cylinder

Parameters

Type	Name	Default	Description
Boolean	animation	true	= true, if animation shall be enabled
Length	cylinderTopPosition	0.42	Length from crank shaft to end of cylinder. [m]
Length	crankLength	0.14	Length of crank shaft in x direction [m]
Length	crankPinOffset	0.05	Offset of crank pin from center axis [m]
Length	crankPinLength	0.1	Offset of crank pin from center axis [m]
Angle_deg	cylinderInclination	0	Inclination of cylinder [deg]
Angle_deg	crankAngleOffset	0	Offset for crank angle [deg]
Piston
Length	pistonLength	0.1	Length of cylinder [m]
Length	pistonCenterOfMass	pistonLength/2	Distance from frame_a to center of mass of piston [m]
Mass	pistonMass	6	Mass of piston [kg]
Inertia	pistonInertia_11	0.0088	Inertia 11 of piston with respect to center of mass frame, parallel to frame_a [kg.m2]
Inertia	pistonInertia_22	0.0076	Inertia 22 of piston with respect to center of mass frame, parallel to frame_a [kg.m2]
Inertia	pistonInertia_33	0.0088	Inertia 33 of piston with respect to center of mass frame, parallel to frame_a [kg.m2]
Rod
Length	rodLength	0.175	Length of rod [m]
Length	rodCenterOfMass	rodLength/2	Distance from frame_a to center of mass of piston [m]
Mass	rodMass	1	Mass of rod [kg]
Inertia	rodInertia_11	0.006	Inertia 11 of rod with respect to center of mass frame, parallel to frame_a [kg.m2]
Inertia	rodInertia_22	0.0005	Inertia 22 of rod with respect to center of mass frame, parallel to frame_a [kg.m2]
Inertia	rodInertia_33	0.006	Inertia 33 of rod with respect to center of mass frame, parallel to frame_a [kg.m2]

Connectors

Type	Name	Description
Frame_a	cylinder_a
Frame_a	cylinder_b
Frame_a	crank_a
Frame_a	crank_b

Modelica definition

replaceable model Cylinder = Cylinder_analytic_CAD constrainedby CylinderBase 
  "Cylinder type";