within Modelica.Mechanics; package Translational "Library to model 1-dimensional, translational mechanical systems" extends Modelica.Icons.Package; import SI = Modelica.SIunits; package Examples "Demonstration examples of the components of this package" extends Modelica.Icons.ExamplesPackage; model SignConvention "Examples for the used sign conventions." extends Modelica.Icons.Example; Translational.Components.Mass mass1(L=1, s(fixed=true), v(fixed=true), m=1) annotation (Placement( transformation(extent={{40,60},{60,80}}, rotation=0))); Translational.Sources.Force force1 annotation (Placement(transformation(extent={{ -4,60},{16,80}}, rotation=0))); Modelica.Blocks.Sources.Constant constant1(k=1) annotation (Placement(transformation(extent={{ -44,60},{-24,80}}, rotation=0))); Translational.Components.Mass mass2(L=1, s(fixed=true), v(fixed=true), m=1) annotation (Placement( transformation(extent={{40,0},{60,20}}, rotation=0))); Translational.Sources.Force force2 annotation (Placement(transformation(extent={{ -4,20},{16,40}}, rotation=0))); Modelica.Blocks.Sources.Constant constant2(k=1) annotation (Placement(transformation(extent={{ -44,20},{-24,40}}, rotation=0))); Translational.Components.Mass mass3(L=1, s(fixed=true), v(fixed=true), m=1) annotation (Placement( transformation(extent={{-40,-40},{-20,-20}}, rotation=0))); Translational.Sources.Force force3(useSupport=true) annotation (Placement(transformation(extent={{ 20,-40},{0,-20}}, rotation=0))); Modelica.Blocks.Sources.Constant constant3(k=1) annotation (Placement(transformation(extent={{ 60,-40},{40,-20}}, rotation=0))); Translational.Components.Fixed fixed annotation (Placement(transformation(extent={{0,-60},{20,-40}}))); equation connect(constant1.y,force1. f) annotation (Line(points={{-23,70},{-6,70}}, color={0,0,127})); connect(constant2.y,force2. f) annotation (Line(points={{-23,30},{-6,30}}, color={0,0,127})); connect(constant3.y,force3. f) annotation (Line(points={{39,-30},{22,-30}}, color={0,0,127})); connect(force1.flange, mass1.flange_a) annotation (Line( points={{16,70},{40,70}}, color={0,127,0}, smooth=Smooth.None)); connect(force2.flange, mass2.flange_b) annotation (Line( points={{16,30},{70,30},{70,10},{60,10}}, color={0,127,0}, smooth=Smooth.None)); connect(mass3.flange_b, force3.flange) annotation (Line( points={{-20,-30},{0,-30}}, color={0,127,0}, smooth=Smooth.None)); connect(fixed.flange, force3.support) annotation (Line( points={{10,-50},{10,-40}}, color={0,127,0}, smooth=Smooth.None)); annotation (Documentation(info="

If all arrows point in the same direction a positive force results in a positive acceleration a, velocity v and position s.

For a force of 1 N and a mass of 1 Kg this leads to 

        a = 1 m/s2
        v = 1 m/s after 1 s (SlidingMass1.v)
        s = 0.5 m after 1 s (SlidingMass1.s)

The acceleration is not available for plotting.

System 1) and 2) are equivalent. It doesn't matter whether the force pushes at flange_a in system 1 or pulls at flange_b in system 2.

It is of course possible to ignore the arrows and connect the models in an arbitrary way. But then it is hard see in what direction the force acts.

In the third system the two arrows are opposed which means that the force acts in the opposite direction (in the same direction as in the two other examples).

"), Diagram(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{ 100,100}}), graphics={ Text( extent={{-100,80},{-82,60}}, textString="1)", lineColor={0,0,255}), Text( extent={{-100,40},{-82,20}}, textString="2)", lineColor={0,0,255}), Text( extent={{-100,-20},{-82,-40}}, textString="3)", lineColor={0,0,255})}), experiment(StopTime=1.0, Interval=0.001)); end SignConvention; model InitialConditions "Setting of initial conditions" extends Modelica.Icons.Example; Translational.Components.Fixed fixed2( s0=1) annotation (Placement(transformation( extent={{-100,60},{-80,80}}, rotation=0))); Translational.Components.Spring s2( s_rel0=2, c=1e3) annotation (Placement( transformation(extent={{-60,60},{-40,80}}, rotation=0))); Translational.Components.Mass m3( L=3, s(start=4.5, fixed=true), v(fixed=true), m=1) annotation (Placement( transformation(extent={{-20,60},{0,80}}, rotation=0))); Translational.Components.SpringDamper sd2( s_rel0=4, c=111, d=1) annotation (Placement( transformation(extent={{20,60},{40,80}}, rotation=0))); Translational.Components.Mass m4( L=5, s(start=12.5, fixed=true), v(fixed=true), m=1) annotation (Placement( transformation(extent={{60,60},{80,80}}, rotation=0))); Translational.Components.Fixed fixed1( s0=-1) annotation (Placement(transformation( extent={{-100,-20},{-80,0}}, rotation=0))); Translational.Components.Spring s1( s_rel0=1, c=1e3, s_rel(start=1, fixed=true)) annotation (Placement(transformation(extent={{-58,-20}, {-38,0}}, rotation=0))); Translational.Components.Mass m1( L=1, v(fixed=true), m=1) annotation (Placement(transformation( extent={{-20,-20},{0,0}}, rotation=0))); Translational.Components.SpringDamper sd1( s_rel0=1, c=111, s_rel(start=1, fixed=true), v_rel(fixed=true), d=1) annotation (Placement(transformation(extent={{20,-20},{ 40,0}}, rotation=0))); Translational.Components.Mass m2( L=2, m=1) annotation (Placement(transformation( extent={{60,-20},{80,0}}, rotation=0))); equation connect(s2.flange_a, fixed2.flange) annotation (Line( points={{-60,70},{-90,70}}, color={0,127,0}, smooth=Smooth.None)); connect(s1.flange_a, fixed1.flange) annotation (Line( points={{-58,-10},{-90,-10}}, color={0,127,0}, smooth=Smooth.None)); connect(m1.flange_a, s1.flange_b) annotation (Line( points={{-20,-10},{-38,-10}}, color={0,127,0}, smooth=Smooth.None)); connect(sd1.flange_a, m1.flange_b) annotation (Line( points={{20,-10},{0,-10}}, color={0,127,0}, smooth=Smooth.None)); connect(m2.flange_a, sd1.flange_b) annotation (Line( points={{60,-10},{40,-10}}, color={0,127,0}, smooth=Smooth.None)); connect(m4.flange_a, sd2.flange_b) annotation (Line( points={{60,70},{40,70}}, color={0,127,0}, smooth=Smooth.None)); connect(sd2.flange_a, m3.flange_b) annotation (Line( points={{20,70},{0,70}}, color={0,127,0}, smooth=Smooth.None)); connect(m3.flange_a, s2.flange_b) annotation (Line( points={{-20,70},{-40,70}}, color={0,127,0}, smooth=Smooth.None)); annotation ( Documentation(info="

There are several ways to set initial conditions. In the first system the position of the mass m3 was defined by using the modifier s(start=4.5), the position of m4 by s(start=12.5). These positions were chosen such that the system is a rest. To calculate these values start at the left (Fixed1) with a value of 1 m. The spring has an unstretched length of 2 m and m3 an length of 3 m, which leads to 

        1   m (fixed1)
      + 2   m (spring s2)
      + 3/2 m (half of the length of mass m3)
      -------
        4,5 m = s(start = 4.5) for m3
      + 3/2 m (half of the length of mass m3)
      + 4   m (springDamper 2)
      + 5/2 m (half of length of mass m4)
      -------
       12,5 m = s(start = 12.5) for m4

This selection of initial conditions has the effect that Dymola selects those variables (m3.s and m4.s) as state variables. In the second example the length of the springs are given as start values but they cannot be used as state for pure springs (only for the spring/damper combination). In this case the system is not at rest.

"), experiment(StopTime=5.0, Interval=0.001)); end InitialConditions; model WhyArrows "Use of arrows in Mechanics.Translational" extends Modelica.Icons.Example; Translational.Components.Fixed fixed annotation (Placement(transformation(extent={{ -20,20},{0,40}}, rotation=0))); Translational.Components.Rod rod1( L=1) annotation (Placement(transformation(extent={ {-48,20},{-28,40}}, rotation=0))); Translational.Components.Rod rod2( L=1) annotation (Placement(transformation(extent={ {20,20},{40,40}}, rotation=0))); Translational.Components.Rod rod3( L=1) annotation (Placement(transformation(extent={ {-30,58},{-50,78}}, rotation=0))); Translational.Sensors.PositionSensor positionSensor2 annotation (Placement( transformation(extent={{60,20},{80,40}}, rotation=0))); Translational.Sensors.PositionSensor positionSensor1 annotation (Placement( transformation(extent={{-60,20},{-80,40}}, rotation=0))); Translational.Sensors.PositionSensor positionSensor3 annotation (Placement( transformation(extent={{-60,58},{-80,78}}, rotation=0))); Translational.Components.Fixed fixed1( s0=-1.9) annotation (Placement(transformation( extent={{-100,-60},{-80,-40}}, rotation=0))); Translational.Components.Spring spring1( s_rel0=2, c=11) annotation (Placement( transformation(extent={{-80,-60},{-60,-40}}, rotation=0))); Translational.Components.Mass mass1( L=2, s(fixed=true), v(fixed=true), m=1) annotation (Placement( transformation(extent={{-50,-60},{-30,-40}}, rotation=0))); Translational.Components.Fixed fixed2( s0=-1.9) annotation (Placement(transformation( extent={{0,-60},{20,-40}}, rotation=0))); Translational.Components.Spring spring2( s_rel0=2, c=11) annotation (Placement( transformation(extent={{30,-60},{50,-40}}, rotation=0))); Translational.Components.Mass inertia2( L=2, m=1, s(fixed=true), v(fixed=true)) annotation (Placement( transformation(extent={{80,-60},{60,-40}}, rotation=0))); equation connect(spring1.flange_b, mass1.flange_b) annotation (Line(points={{-60,-50}, {-60,-72},{-30,-72},{-30,-50}}, color={0,191,0})); connect(spring2.flange_b, inertia2.flange_b) annotation (Line(points={{50,-50}, {60,-50}}, color={0,191,0})); connect(rod3.flange_b,positionSensor3. flange) annotation (Line( points={{-50,68},{-60,68}}, color={0,127,0}, smooth=Smooth.None)); connect(rod1.flange_a,positionSensor1. flange) annotation (Line( points={{-48,30},{-60,30}}, color={0,127,0}, smooth=Smooth.None)); connect(rod1.flange_b, fixed.flange) annotation (Line( points={{-28,30},{-10,30}}, color={0,127,0}, smooth=Smooth.None)); connect(rod3.flange_a, fixed.flange) annotation (Line( points={{-30,68},{-10,68},{-10,30}}, color={0,127,0}, smooth=Smooth.None)); connect(fixed.flange, rod2.flange_a) annotation (Line( points={{-10,30},{20,30}}, color={0,127,0}, smooth=Smooth.None)); connect(rod2.flange_b,positionSensor2. flange) annotation (Line( points={{40,30},{60,30}}, color={0,127,0}, smooth=Smooth.None)); connect(fixed1.flange,spring1. flange_a) annotation (Line( points={{-90,-50},{-80,-50}}, color={0,127,0}, smooth=Smooth.None)); connect(fixed2.flange,spring2. flange_a) annotation (Line( points={{10,-50},{30,-50}}, color={0,127,0}, smooth=Smooth.None)); annotation ( Documentation(info="

When using the models of the translational sublibrary it is recommended to make sure that all arrows point in the same direction because then all component have the same reference system. In the example the distance from flange_a of Rod1 to flange_b of Rod2 is 2 m. The distance from flange_a of Rod1 to flange_b of Rod3 is also 2 m though it is difficult to see that. Without the arrows it would be almost impossible to notice. That all arrows point in the same direction is a sufficient condition for an easy use of the library. There are cases where horizontally flipped models can be used without problems.

"), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Text( extent={{-84,10},{88,2}}, lineColor={0,0,255}, textString="positionSensor2.s = positionSensor3.s"), Text( extent={{-78,-4},{86,-12}}, lineColor={0,0,255}, textString="positionSensor3.s <>positionSensor1.s"), Text( extent={{-82,-80},{92,-88}}, textString="Both systems are equivalent", lineColor={0,0,255}), Line( points={{-90,-28},{90,-28}}, thickness=0.5, color={0,0,255})}), experiment(StopTime=1.0, Interval=0.001)); end WhyArrows; model Accelerate "Use of model accelerate." extends Modelica.Icons.Example; Translational.Sources.Accelerate accelerate annotation (Placement(transformation( extent={{-40,20},{-20,40}}, rotation=0))); Translational.Components.Mass mass(L=1, m=1) annotation (Placement( transformation(extent={{0,20},{20,40}}, rotation=0))); Modelica.Blocks.Sources.Constant constantAcc(k=1) annotation (Placement(transformation(extent={{-80,20}, {-60,40}}, rotation=0))); equation connect(accelerate.flange, mass.flange_a) annotation (Line( points={{-20,30},{0,30}}, color={0,127,0}, smooth=Smooth.None)); connect(constantAcc.y, accelerate.a_ref) annotation (Line( points={{-59,30},{-42,30}}, color={0,0,127}, smooth=Smooth.None)); annotation (Documentation(info="

Demonstrate usage of component Sources.Accelerate by moving a massing with a predefined acceleration.

"), experiment(StopTime=1.0, Interval=0.001)); end Accelerate; model Damper "Use of damper models." extends Modelica.Icons.Example; Translational.Components.Mass mass1( L=1, s(start=3, fixed=true), v(start=10, fixed=true), m=1) annotation (Placement(transformation(extent={{-80,60},{-60, 80}}, rotation=0))); Translational.Components.Damper damper1( d=25) annotation (Placement(transformation( extent={{-20,60},{0,80}}, rotation=0))); Translational.Components.Fixed fixed1( s0=4.5) annotation (Placement(transformation( extent={{22,60},{42,80}}, rotation=0))); Translational.Components.Mass mass2( L=1, s(start=3, fixed=true), v(start=10, fixed=true), m=1) annotation (Placement(transformation(extent={{-80,0},{-60, 20}}, rotation=0))); Translational.Components.Damper damper2( d=25) annotation (Placement(transformation( extent={{-20,0},{0,20}}, rotation=0))); Translational.Components.Fixed fixed2( s0=4.5) annotation (Placement(transformation( extent={{20,0},{40,20}}, rotation=0))); Translational.Components.Mass mass3( L=1, s(start=3, fixed=true), v(start=10, fixed=true), m=1) annotation (Placement(transformation(extent={{-80,-60},{-60, -40}}, rotation=0))); Translational.Components.Fixed fixed3( s0=4.5) annotation (Placement(transformation( extent={{20,-60},{40,-40}}, rotation=0))); Translational.Components.Spring spring2( s_rel0=1, c=1) annotation (Placement( transformation(extent={{-20,-20},{0,0}}, rotation=0))); Translational.Components.SpringDamper springDamper3( s_rel0=1, d=25, c=1) annotation (Placement( transformation(extent={{-20,-60},{0,-40}}, rotation=0))); equation connect(mass1.flange_b, damper1.flange_a) annotation (Line(points= {{-60,70},{-20,70}}, color={0,191,0})); connect(mass2.flange_b, damper2.flange_a) annotation (Line(points={{-60,10}, {-20,10}}, color={0,191,0})); connect(damper2.flange_b,spring2. flange_b) annotation (Line(points={{0, 10},{0,-10}}, color={0,191,0})); connect(damper2.flange_a,spring2. flange_a) annotation (Line(points={{-20, 10},{-20,-10}}, color={0,191,0})); connect(mass3.flange_b, springDamper3.flange_a) annotation (Line( points={{-60,-50},{-20,-50}}, color={0,191,0})); connect(damper1.flange_b, fixed1.flange) annotation (Line( points={{0,70},{32,70}}, color={0,127,0}, smooth=Smooth.None)); connect(damper2.flange_b, fixed2.flange) annotation (Line( points={{0,10},{30,10}}, color={0,127,0}, smooth=Smooth.None)); connect(springDamper3.flange_b, fixed3.flange) annotation (Line( points={{0,-50},{30,-50}}, color={0,127,0}, smooth=Smooth.None)); annotation (Documentation(info="

Demonstrate usage of damper components in different variants.

"), experiment(StopTime=1.0, Interval=0.001)); end Damper; model Oscillator "Oscillator demonstrates the use of initial conditions." extends Modelica.Icons.Example; Translational.Components.Mass mass1( L=1, s(start=-0.5, fixed=true), v(start=0, fixed=true), m=1) annotation (Placement(transformation(extent={{-20,40},{0, 60}}, rotation=0))); Translational.Components.Spring spring1( s_rel0=1, c=10000) annotation (Placement( transformation(extent={{20,40},{40,60}}, rotation=0))); Translational.Components.Fixed fixed1( s0=1) annotation (Placement(transformation( extent={{60,40},{80,60}}, rotation=0))); Translational.Sources.Force force1 annotation (Placement(transformation(extent={{ -60,40},{-40,60}}, rotation=0))); Modelica.Blocks.Sources.Sine sine1(freqHz=15.9155) annotation (Placement(transformation( extent={{-100,40},{-80,60}}, rotation=0))); Translational.Components.Mass mass2( L=1, s(start=-0.5, fixed=true), v(start=0, fixed=true), m=1) annotation (Placement(transformation(extent={{-20,-60},{0, -40}}, rotation=0))); Translational.Components.Spring spring2( s_rel0=1, c=10000) annotation (Placement( transformation(extent={{20,-60},{40,-40}}, rotation=0))); Translational.Components.Fixed fixed2( s0=1) annotation (Placement(transformation( extent={{60,-60},{80,-40}}, rotation=0))); Translational.Sources.Force force2 annotation (Placement(transformation(extent={{ -60,-60},{-40,-40}}, rotation=0))); Modelica.Blocks.Sources.Sine sine2(freqHz=15.9155) annotation (Placement(transformation( extent={{-100,-60},{-80,-40}}, rotation=0))); Translational.Components.Damper damper1( d=10) annotation (Placement(transformation( extent={{20,-36},{40,-16}}, rotation=0))); equation connect(mass1.flange_b, spring1.flange_a) annotation (Line(points= {{0,50},{20,50}}, color={0,191,0})); connect(spring2.flange_a,damper1. flange_a) annotation (Line(points={{20, -50},{20,-26}}, color={0,191,0})); connect(mass2.flange_b, spring2.flange_a) annotation (Line(points= {{0,-50},{20,-50}}, color={0,191,0})); connect(damper1.flange_b,spring2. flange_b) annotation (Line(points={{40, -26},{40,-50}}, color={0,191,0})); connect(sine1.y,force1. f) annotation (Line(points={{-79,50},{-62,50}}, color={0,0,127})); connect(sine2.y,force2. f) annotation (Line(points={{-79,-50},{-62,-50}}, color={0,0,127})); connect(spring1.flange_b, fixed1.flange) annotation (Line( points={{40,50},{70,50}}, color={0,127,0}, smooth=Smooth.None)); connect(force2.flange, mass2.flange_a) annotation (Line( points={{-40,-50},{-20,-50}}, color={0,127,0}, smooth=Smooth.None)); connect(force1.flange, mass1.flange_a) annotation (Line( points={{-40,50},{-20,50}}, color={0,127,0}, smooth=Smooth.None)); connect(spring2.flange_b, fixed2.flange) annotation (Line( points={{40,-50},{70,-50}}, color={0,127,0}, smooth=Smooth.None)); annotation ( Documentation(info="

A spring - mass system is a mechanical oscillator. If no damping is included and the system is excited at resonance frequency infinite amplitudes will result. The resonant frequency is given by omega_res = sqrt(c / m) with: 

      c spring stiffness
      m mass

To make sure that the system is initially at rest the initial conditions s(start=0) and v(start=0) for the SlidingMass are set. If damping is added the amplitudes are bounded.

"), experiment(StopTime=1.0, Interval=0.001)); end Oscillator; model Sensors "Sensors for translational systems." import Modelica; extends Modelica.Icons.Example; Translational.Sensors.ForceSensor forceSensor annotation (Placement( transformation(extent={{-34,40},{-14,60}}, rotation=0))); Translational.Sensors.SpeedSensor speedSensor1 annotation (Placement( transformation(extent={{40,-40},{60,-20}}, rotation=0))); Translational.Sensors.PositionSensor positionSensor1 annotation (Placement( transformation(extent={{40,0},{60,20}}, rotation=0))); Translational.Sensors.AccSensor accSensor1 annotation (Placement( transformation(extent={{40,-80},{60,-60}}, rotation=0))); Translational.Components.Mass mass(L=1, s(fixed=true), v(fixed=true), m=1) annotation (Placement( transformation(extent={{20,40},{40,60}}, rotation=0))); Translational.Sources.Force force annotation (Placement(transformation(extent={{-64,40}, {-44,60}}, rotation=0))); Modelica.Blocks.Sources.Sine sineForce(amplitude=10, freqHz=4) annotation (Placement( transformation(extent={{-100,40},{-80,60}}, rotation=0))); Translational.Sensors.PositionSensor positionSensor2 annotation (Placement( transformation(extent={{60,40},{80,60}}, rotation=0))); Modelica.Mechanics.Translational.Sensors.MultiSensor multiSensor annotation (Placement(transformation(extent={{-8,40},{12,60}}))); equation connect(sineForce.y, force.f) annotation (Line(points={{-79,50},{-66,50}}, color={0,0,127})); connect(forceSensor.flange_a, force.flange) annotation (Line( points={{-34,50},{-44,50}}, color={0,127,0}, smooth=Smooth.None)); connect(mass.flange_a, positionSensor1.flange) annotation (Line( points={{20,50},{20,10},{40,10}}, color={0,127,0}, smooth=Smooth.None)); connect(mass.flange_a, speedSensor1.flange) annotation (Line( points={{20,50},{20,-30},{40,-30}}, color={0,127,0}, smooth=Smooth.None)); connect(mass.flange_a, accSensor1.flange) annotation (Line( points={{20,50},{20,-70},{40,-70}}, color={0,127,0}, smooth=Smooth.None)); connect(mass.flange_b, positionSensor2.flange) annotation (Line( points={{40,50},{60,50}}, color={0,127,0}, smooth=Smooth.None)); connect(forceSensor.flange_b, multiSensor.flange_a) annotation (Line( points={{-14,50},{-8,50}}, color={0,127,0}, smooth=Smooth.None)); connect(multiSensor.flange_b, mass.flange_a) annotation (Line( points={{12,50},{20,50}}, color={0,127,0}, smooth=Smooth.None)); annotation ( Documentation(info="

These sensors measure 

   force f in N
   position s in m
   velocity v in m/s
   acceleration a in m/s2

The measured velocity and acceleration is independent on the flange the sensor is connected to. The position depends on the flange (flange_a or flange_b) and the length L of the component. Plot PositionSensor1.s, PositionSensor2.s and SlidingMass1.s to see the difference.

"), experiment(StopTime=1.0, Interval=0.001)); end Sensors; model Friction "Use of model Stop" extends Modelica.Icons.Example; Modelica.Mechanics.Translational.Components.MassWithStopAndFriction stop1( L=1, s(fixed=true), v(fixed=true), smax=25, smin=-25, m=1, F_prop=1, F_Coulomb=5, F_Stribeck=10, fexp=2) annotation (Placement(transformation(extent={{20,60}, {40,80}}, rotation=0))); Translational.Sources.Force force annotation (Placement(transformation(extent={{-20,60}, {0,80}}, rotation=0))); Modelica.Blocks.Sources.Sine sineForce(amplitude=25, freqHz=0.25) annotation (Placement( transformation(extent={{-60,60},{-40,80}}, rotation=0))); Modelica.Mechanics.Translational.Components.MassWithStopAndFriction stop2( L=1, smax=0.9, smin=-0.9, F_Coulomb=3, F_Stribeck=5, s(start=0, fixed=true), m=1, F_prop=1, fexp=2, v(start=-5, fixed=true)) annotation (Placement(transformation(extent={{42,-60},{62, -40}}, rotation=0))); Translational.Components.Spring spring(s_rel0=1, c=500) annotation (Placement( transformation(extent={{2,-60},{22,-40}}, rotation=0))); Translational.Components.Fixed fixed2(s0=-1.75) annotation (Placement(transformation( extent={{-40,-60},{-20,-40}}, rotation=0))); Translational.Sources.Force force2 annotation (Placement(transformation(extent={{-22,0}, {-2,20}}, rotation=0))); Components.Mass mass( m=1, L=1, s(fixed=true), v(fixed=true)) annotation (Placement(transformation(extent={{10,0},{30,20}}))); Components.SupportFriction supportFriction(f_pos= Examples.Utilities.GenerateStribeckFrictionTable( F_prop=1, F_Coulomb=5, F_Stribeck=10, fexp=2, v_max=12, nTable=50)) annotation (Placement(transformation(extent={{40,0},{60,20}}))); equation connect(spring.flange_b, stop2.flange_a) annotation (Line(points={{22,-50}, {42,-50}},color={0,191,0})); connect(sineForce.y, force.f) annotation (Line(points={{-39,70},{-22,70}}, color={0,0,127})); connect(spring.flange_a, fixed2.flange) annotation (Line( points={{2,-50},{-30,-50}}, color={0,127,0}, smooth=Smooth.None)); connect(force.flange, stop1.flange_a) annotation (Line( points={{0,70},{20,70}}, color={0,127,0}, smooth=Smooth.None)); connect(force2.flange, mass.flange_a) annotation (Line( points={{-2,10},{10,10}}, color={0,127,0}, smooth=Smooth.None)); connect(mass.flange_b, supportFriction.flange_a) annotation (Line( points={{30,10},{40,10}}, color={0,127,0}, smooth=Smooth.None)); connect(sineForce.y, force2.f) annotation (Line( points={{-39,70},{-30,70},{-30,10},{-24,10}}, color={0,0,127}, smooth=Smooth.None)); annotation ( Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Text( extent={{-100,80},{-80,60}}, textString="1)", lineColor={0,0,255}), Text( extent={{-100,20},{-80,0}}, textString="2)", lineColor={0,0,255}), Text( extent={{-100,-40},{-80,-60}}, lineColor={0,0,255}, textString="3)")}), Documentation(info="
  1. Simulate and then plot stop1.f as a function of stop1.v This gives the Stribeck curve.
  2. The same model is also available by modeling the system with a Mass and a SupportFriction model. The SupportFriction model defines the friction characteristic with a table. The table is constructed with function Examples.Utilities.GenerateStribeckFrictionTable(..) to generate the same friction characteristic as with stop1. The simulation results of stop1 and of model mass are therefore identical.
  3. Model stop2 gives an example for a hard stop. However there can arise some problems with the used modeling approach (use of reinit(..), convergence problems). In this case use the ElastoGap to model a stop (see example Preload).
"), experiment(StopTime=5.0, Interval=0.001)); end Friction; model PreLoad "Preload of a spool using ElastoGap models." extends Modelica.Icons.Example; Translational.Components.ElastoGap innerContactA( c=1000e3, d=250, s_rel0=0.001) annotation (Placement(transformation(extent={{-70,20},{-50,40}}, rotation=0))); Translational.Components.ElastoGap innerContactB( c=1000e3, d=250, s_rel0=0.001) annotation ( Placement( transformation(extent={{50,20},{70,40}}, rotation=0))); Translational.Components.Mass spool( L=0.19, m=0.150, s(start=0.01475, fixed=true), v(fixed=true)) annotation (Placement(transformation(extent={{0,-40}, {40,0}}, rotation=0))); Translational.Components.Fixed fixedLe( s0=-0.0955) annotation (Placement( transformation(extent={{-10,-10},{10,10}}, rotation=270, origin={-80,90}))); Translational.Components.Mass springPlateA( m=10e-3, L=0.002, s(start=-0.093, fixed=true), v(fixed=true)) annotation (Placement(transformation(extent={{-38,60}, {-18,80}}, rotation=0))); Translational.Components.Mass springPlateB( m=10e-3, s(start=-0.06925, fixed=true), L=0.002, v(fixed=true)) annotation ( Placement(transformation(extent={{20,60},{40,80}}, rotation=0))); Translational.Components.Spring spring( c=20e3, s_rel0=0.025) annotation (Placement(transformation(extent={{-10,60},{10,80}},rotation= 0))); Translational.Components.ElastoGap outerContactA( c=1000e3, d=250, s_rel0=0.0015) annotation (Placement(transformation(extent={{-70,60},{-50,80}}, rotation=0))); Translational.Components.ElastoGap outerContactB( c=1000e3, d=250, s_rel0=0.0015) annotation (Placement(transformation(extent={{50,60},{70, 80}}, rotation=0))); Translational.Components.Rod rod1( L=0.007) annotation (Placement(transformation( extent={{-40,30},{-20,50}}, rotation=0))); Translational.Components.Damper friction( d=2500) annotation (Placement( transformation( origin={-80,50}, extent={{-10,-10},{10,10}}, rotation=270))); Translational.Sources.Force force annotation (Placement(transformation(extent={{-38,-30}, {-18,-10}}, rotation=0))); Translational.Components.Rod housing( L=0.0305) annotation (Placement(transformation( extent={{-10,80},{10,100}}, rotation=0))); Translational.Components.Rod rod3( L=0.00575) annotation (Placement(transformation( extent={{-40,-2},{-20,18}}, rotation=0))); Translational.Components.Rod rod4( L=0.00575) annotation (Placement(transformation( extent={{20,-2},{40,18}}, rotation=0))); Translational.Components.Rod rod2( L=0.007) annotation (Placement(transformation( extent={{20,30},{40,50}}, rotation=0))); Modelica.Blocks.Sources.Sine sineForce(amplitude=150, freqHz=0.01) annotation (Placement(transformation(extent={{-78,-30},{-58,-10}}, rotation=0))); equation connect(outerContactA.flange_b,springPlateA. flange_a) annotation (Line( points={{-50,70},{-38,70}}, color={0,191,0})); connect(springPlateA.flange_b,spring. flange_a) annotation (Line(points={{-18,70}, {-18,70},{-10,70}},color={0,191,0})); connect(spring.flange_b,springPlateB. flange_a) annotation (Line(points={{10,70}, {20,70}}, color={0,191,0})); connect(springPlateB.flange_b,outerContactB. flange_a) annotation (Line( points={{40,70},{40,70},{50,70}}, color={0,191,0})); connect(outerContactB.flange_b,housing. flange_b) annotation (Line(points={{70,70}, {70,90},{10,90}}, color={0,191,0})); connect(springPlateA.flange_b,rod1. flange_a) annotation (Line(points={{-18,70}, {-18,52},{-40,52},{-40,40}}, color={0,191,0})); connect(innerContactA.flange_a,rod3. flange_a) annotation (Line(points={{-70,30}, {-80,30},{-80,8},{-40,8}}, color={0,191,0})); connect(innerContactA.flange_b,rod1. flange_b) annotation (Line(points={{-50,30}, {-20,30},{-20,40}}, color={0,191,0})); connect(rod2.flange_a,innerContactB. flange_a) annotation (Line(points={{20,40}, {20,30},{50,30}}, color={0,191,0})); connect(rod4.flange_b,innerContactB. flange_b) annotation (Line(points={{40,8},{ 70,8},{70,30}}, color={0,191,0})); connect(friction.flange_b,rod3. flange_a) annotation (Line(points={{-80,40}, {-80,8},{-40,8}}, color={0,191,0})); connect(rod3.flange_b,rod4. flange_a) annotation (Line(points={{-20,8},{ 20,8}}, color={0,191,0})); connect(rod2.flange_b,springPlateB. flange_a) annotation (Line(points={{40,40}, {40,52},{20,52},{20,70}}, color={0,191,0})); connect(spool.flange_a,rod4. flange_a) annotation (Line(points={{0,-20},{ 0,8},{20,8}}, color={0,191,0})); connect(sineForce.y, force.f) annotation (Line(points={{-57,-20},{-46,-20},{ -40,-20}}, color={0,0,127})); connect(force.flange, spool.flange_a) annotation (Line( points={{-18,-20},{0,-20}}, color={0,127,0}, smooth=Smooth.None)); connect(outerContactA.flange_a, fixedLe.flange) annotation (Line( points={{-70,70},{-80,70},{-80,90}}, color={0,127,0}, smooth=Smooth.None)); connect(housing.flange_a, fixedLe.flange) annotation (Line( points={{-10,90},{-80,90}}, color={0,127,0}, smooth=Smooth.None)); connect(friction.flange_a, fixedLe.flange) annotation (Line( points={{-80,60},{-80,90}}, color={0,127,0}, smooth=Smooth.None)); annotation ( Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Text( extent={{-92,-72},{90,-80}}, textString="positive force => spool moves in positive direction ", lineColor={0,0,255}), Text( extent={{-48,-52},{42,-60}}, textString="Simulate for 100 s", lineColor={0,0,255}), Text( extent={{-100,-62},{88,-70}}, lineColor={0,0,255}, textString="plot spool.s as a function of force.f")}), Documentation(info="

When designing hydraulic valves it is often necessary to hold the spool in a certain position as long as an external force is below a threshold value. If this force exceeds the threshold value a linear relation between force and position is desired. There are designs that need only one spring to accomplish this task. Using the ElastoGap elements this design can be modelled easily. Drawing of spool.




Spool position s as a function of working force f.

"), experiment(StopTime=100, Interval=0.1)); end PreLoad; model ElastoGap "Demonstrate usage of ElastoGap" extends Modelica.Icons.Example; Components.Fixed fixed annotation (Placement(transformation(extent={{-10,-10},{10,10}}))); Components.Rod rod1(L=2) annotation (Placement(transformation(extent={{-40,-10},{-20,10}}))); Components.Rod rod2(L=2) annotation (Placement(transformation(extent={{20,-10},{40,10}}))); Components.SpringDamper springDamper1( c=10, s_rel0=1, s_rel(fixed=false, start=1), d=1.5) annotation (Placement(transformation(extent={{-40,20},{-20,40}}))); Components.SpringDamper springDamper2( c=10, s_rel0=1, s_rel(fixed=false, start=1), d=1.5) annotation (Placement(transformation(extent={{20,20},{40,40}}))); Components.Mass mass1( s(fixed=true, start=2), L=0, m=1, v(fixed=true)) annotation (Placement(transformation(extent={{-10,20},{10,40}}))); Components.ElastoGap elastoGap1( c=10, s_rel(fixed=false, start=1.5), s_rel0=1.5, d=1.5) annotation (Placement(transformation(extent={{-40,-40},{-20,-20}}))); Components.ElastoGap elastoGap2( c=10, s_rel(fixed=false, start=1.5), s_rel0=1.5, d=1.5) annotation (Placement(transformation(extent={{20,-40},{40,-20}}))); Components.Mass mass2( s(fixed=true, start=2), L=0, m=1, v(fixed=true)) annotation (Placement(transformation(extent={{-10,-40},{10,-20}}))); parameter SI.TranslationalDampingConstant d=1.5 "Damping constant"; equation connect(rod1.flange_b, fixed.flange) annotation (Line( points={{-20,0},{0,0}}, color={0,127,0}, smooth=Smooth.None)); connect(fixed.flange, rod2.flange_a) annotation (Line( points={{0,0},{20,0}}, color={0,127,0}, smooth=Smooth.None)); connect(springDamper1.flange_a, rod1.flange_a) annotation (Line( points={{-40,30},{-48,30},{-48,0},{-40,0}}, color={0,127,0}, smooth=Smooth.None)); connect(springDamper2.flange_b, rod2.flange_b) annotation (Line( points={{40,30},{50,30},{50,0},{40,0}}, color={0,127,0}, smooth=Smooth.None)); connect(springDamper1.flange_b, mass1.flange_a) annotation (Line( points={{-20,30},{-10,30}}, color={0,127,0}, smooth=Smooth.None)); connect(mass1.flange_b, springDamper2.flange_a) annotation (Line( points={{10,30},{20,30}}, color={0,127,0}, smooth=Smooth.None)); connect(rod1.flange_a, elastoGap1.flange_a) annotation (Line( points={{-40,0},{-48,0},{-48,-30},{-40,-30}}, color={0,127,0}, smooth=Smooth.None)); connect(rod2.flange_b, elastoGap2.flange_b) annotation (Line( points={{40,0},{50,0},{50,-30},{40,-30}}, color={0,127,0}, smooth=Smooth.None)); connect(elastoGap1.flange_b, mass2.flange_a) annotation (Line( points={{-20,-30},{-10,-30}}, color={0,127,0}, smooth=Smooth.None)); connect(mass2.flange_b, elastoGap2.flange_a) annotation (Line( points={{10,-30},{20,-30}}, color={0,127,0}, smooth=Smooth.None)); annotation ( Documentation(info="

This model demonstrates the effect of ElastoGaps on eigenfrequency:
Plot mass1.s and mass2.s as well as mass1.v and mass2.v

mass1 is moved by both spring forces all the time.
Since elastoGap1 lifts off at s > -0.5 m and elastoGap2 lifts off s < +0.5 m, mass2 moves freely as long as -0.5 m < s < +0.5 m.

"), experiment(StopTime=1.0, Interval=0.01)); end ElastoGap; model Brake "Demonstrate braking of a translational moving mass" extends Modelica.Icons.Example; Modelica.Mechanics.Translational.Components.Brake brake(fn_max=1, useSupport= false) annotation (Placement(transformation(extent={{6,40},{26,20}}))); Modelica.Mechanics.Translational.Components.Mass mass1(m=1, s(fixed=true), v(start=1, fixed=true)) annotation (Placement(transformation(extent={{-34,20},{-14,40}}))); Modelica.Blocks.Sources.Step step(startTime=0.1, height=2) annotation (Placement(transformation(extent={{-10,-10},{10,10}}, rotation=0, origin={-24,-10}))); Modelica.Mechanics.Translational.Components.Brake brake1( fn_max=1, useSupport= true) annotation (Placement(transformation(extent={{6,-60},{26,-40}}))); Modelica.Mechanics.Translational.Components.Mass mass2(m=1, s(fixed=true), v(start=1, fixed=true)) annotation (Placement(transformation(extent={{-34,-60},{-14,-40}}))); Modelica.Mechanics.Translational.Components.Fixed fixed annotation (Placement(transformation(extent={{6,-80},{26,-60}}))); equation connect(mass1.flange_b, brake.flange_a) annotation (Line( points={{-14,30},{6,30}}, color={0,127,0}, smooth=Smooth.None)); connect(step.y, brake.f_normalized) annotation (Line( points={{-13,-10},{16,-10},{16,19}}, color={0,0,127}, smooth=Smooth.None)); connect(mass2.flange_b, brake1.flange_a) annotation (Line( points={{-14,-50},{6,-50}}, color={0,127,0}, smooth=Smooth.None)); connect(step.y, brake1.f_normalized) annotation (Line( points={{-13,-10},{16,-10},{16,-39}}, color={0,0,127}, smooth=Smooth.None)); connect(fixed.flange, brake1.support) annotation (Line( points={{16,-70},{16,-60}}, color={0,127,0}, smooth=Smooth.None)); annotation ( Documentation(info="

This model consists of a mass with an initial velocity of 1 m/s. After 0.1 s, a brake is activated and it is shown that the mass decelerates until it arrives at rest and remains at rest. Two versions of this system are present, one where the brake is implicitly grounded and one where it is explicitly grounded.

"), experiment(StopTime=2.0, Interval=0.001)); end Brake; model HeatLosses "Demonstrate the modeling of heat losses" extends Modelica.Icons.Example; Components.Mass mass1( m=1, s(fixed=true), L=0.1, v(fixed=true)) annotation (Placement(transformation(extent={{-60,20},{-40,40}}))); Components.SpringDamper springDamper( s_rel(fixed=true), v_rel(fixed=true), c=100, d=10, useHeatPort=true) annotation (Placement(transformation(extent={{-30,20},{-10,40}}))); Components.Damper damper(d=10, useHeatPort=true) annotation (Placement(transformation(extent={{-10,10},{10,-10}}, rotation=-90, origin={-60,-10}))); Components.ElastoGap elastoGap( c=100, d=20, s_rel0=-0.02, useHeatPort=true) annotation (Placement(transformation(extent={{-90,-10},{-70,10}}))); Components.Fixed fixed1 annotation (Placement(transformation(extent={{-70,-40},{-50,-20}}))); Sources.Force force annotation (Placement(transformation(extent={{-90,20},{-70,40}}))); Blocks.Sources.Sine sine1(freqHz=1, amplitude=20) annotation (Placement(transformation(extent={{-120,20},{-100,40}}))); Components.Mass mass2( m=1, L=0.1, s(fixed=false), v(fixed=false)) annotation (Placement(transformation(extent={{0,20},{20,40}}))); Components.SupportFriction supportFriction(useHeatPort=true) annotation (Placement(transformation(extent={{30,20},{50,40}}))); Components.Spring spring(c=100, s_rel(fixed=true)) annotation (Placement(transformation(extent={{60,20},{80,40}}))); Components.Mass mass3( m=1, L=0.1, s(fixed=false), v(fixed=true)) annotation (Placement(transformation(extent={{90,20},{110,40}}))); Components.Brake brake(fn_max=10, useHeatPort=true) annotation (Placement(transformation(extent={{120,20},{140,40}}))); Blocks.Sources.Sine sine2(amplitude=10, freqHz=2) annotation (Placement(transformation(extent={{100,50},{120,70}}))); Components.MassWithStopAndFriction massWithStopAndFriction( L=0.1, m=1, F_prop=0.5, F_Coulomb=1, F_Stribeck=2, fexp=2, smin=0, smax=0.4, v(fixed=true), useHeatPort=true) annotation (Placement(transformation(extent={{180,20},{200,40}}))); Thermal.HeatTransfer.Components.Convection convection annotation (Placement(transformation(extent={{-10,-40},{10,-60}}))); Blocks.Sources.Constant const(k=20) annotation (Placement(transformation(extent={{-30,-90},{-10,-70}}))); Thermal.HeatTransfer.Celsius.FixedTemperature TAmbient(T=25) "Ambient temperature" annotation (Placement(transformation(extent={{40,-60},{20,-40}}))); Components.Fixed fixed2 annotation (Placement(transformation(extent={{-120,-10},{-100,10}}))); Components.SpringDamper springDamper1( c=10000, d=1000, useHeatPort=true, s_rel(fixed=true)) annotation (Placement(transformation(extent={{150,20},{170,40}}))); equation connect(mass1.flange_b, springDamper.flange_a) annotation (Line( points={{-40,30},{-30,30}}, color={0,127,0}, smooth=Smooth.None)); connect(sine1.y, force.f) annotation (Line( points={{-99,30},{-92,30}}, color={0,0,127}, smooth=Smooth.None)); connect(force.flange, mass1.flange_a) annotation (Line( points={{-70,30},{-60,30}}, color={0,127,0}, smooth=Smooth.None)); connect(mass1.flange_a, damper.flange_a) annotation (Line( points={{-60,30},{-60,0}}, color={0,127,0}, smooth=Smooth.None)); connect(damper.flange_b, fixed1.flange) annotation (Line( points={{-60,-20},{-60,-30}}, color={0,127,0}, smooth=Smooth.None)); connect(springDamper.flange_b, mass2.flange_a) annotation (Line( points={{-10,30},{0,30}}, color={0,127,0}, smooth=Smooth.None)); connect(mass2.flange_b, supportFriction.flange_a) annotation (Line( points={{20,30},{30,30}}, color={0,127,0}, smooth=Smooth.None)); connect(supportFriction.flange_b, spring.flange_a) annotation (Line( points={{50,30},{60,30}}, color={0,127,0}, smooth=Smooth.None)); connect(spring.flange_b, mass3.flange_a) annotation (Line( points={{80,30},{90,30}}, color={0,127,0}, smooth=Smooth.None)); connect(mass3.flange_b, brake.flange_a) annotation (Line( points={{110,30},{120,30}}, color={0,127,0}, smooth=Smooth.None)); connect(sine2.y, brake.f_normalized) annotation (Line( points={{121,60},{130,60},{130,41}}, color={0,0,127}, smooth=Smooth.None)); connect(elastoGap.flange_b, mass1.flange_a) annotation (Line( points={{-70,0},{-60,0},{-60,30}}, color={0,127,0}, smooth=Smooth.None)); connect(const.y,convection. Gc) annotation (Line( points={{-9,-80},{0,-80},{0,-60}}, color={0,0,127}, smooth=Smooth.None)); connect(TAmbient.port,convection. fluid) annotation (Line( points={{20,-50},{10,-50}}, color={191,0,0}, smooth=Smooth.None)); connect(elastoGap.flange_a, fixed2.flange) annotation (Line( points={{-90,0},{-110,0}}, color={0,127,0}, smooth=Smooth.None)); connect(elastoGap.heatPort, convection.solid) annotation (Line( points={{-90,-10},{-90,-50},{-10,-50}}, color={191,0,0}, smooth=Smooth.None)); connect(damper.heatPort, convection.solid) annotation (Line( points={{-50,0},{-50,-50},{-10,-50}}, color={191,0,0}, smooth=Smooth.None)); connect(springDamper.heatPort, convection.solid) annotation (Line( points={{-30,20},{-30,-50},{-10,-50}}, color={191,0,0}, smooth=Smooth.None)); connect(supportFriction.heatPort, convection.solid) annotation (Line( points={{30,20},{30,0},{-30,0},{-30,-50},{-10,-50}}, color={191,0,0}, smooth=Smooth.None)); connect(brake.heatPort, convection.solid) annotation (Line( points={{120,20},{120,0},{-30,0},{-30,-50},{-10,-50}}, color={191,0,0}, smooth=Smooth.None)); connect(massWithStopAndFriction.heatPort, convection.solid) annotation ( Line( points={{180,20},{180,0},{-30,0},{-30,-50},{-10,-50}}, color={191,0,0}, smooth=Smooth.None)); connect(brake.flange_b, springDamper1.flange_a) annotation (Line( points={{140,30},{150,30}}, color={0,127,0}, smooth=Smooth.None)); connect(springDamper1.flange_b, massWithStopAndFriction.flange_a) annotation (Line( points={{170,30},{180,30}}, color={0,127,0}, smooth=Smooth.None)); connect(springDamper1.heatPort, convection.solid) annotation (Line( points={{150,20},{150,0},{-30,0},{-30,-50},{-10,-50}}, color={191,0,0}, smooth=Smooth.None)); annotation ( Documentation(info="

This model demonstrates how to model the dissipated power of a Translational model, by enabling the heatPort of all components and connecting these heatPorts via a convection element to the environment. The total heat flow generated by the elements and transported to the environment is present in variable convection.fluid.

"), experiment(StopTime=2.0, Interval=0.001), Diagram(coordinateSystem(extent={{-120,-100},{200,100}}, preserveAspectRatio=false))); end HeatLosses; package Utilities "Utility classes used by the Example models" extends Modelica.Icons.UtilitiesPackage; function GenerateStribeckFrictionTable "Generate Stribeck friction table for example Friction for the SupportFriction" extends Modelica.Icons.Function; input Real F_prop(final unit="N.s/m", final min=0) "Velocity dependent friction coefficient"; input Modelica.SIunits.Force F_Coulomb "Constant friction: Coulomb force"; input Modelica.SIunits.Force F_Stribeck "Stribeck effect"; input Real fexp(final unit="s/m", final min=0) "Exponential decay"; input Real v_max "Generate table from v=0 ... v_max"; input Integer nTable(min=2)=100 "Number of table points"; output Real table[nTable,2] "Friction table"; algorithm for i in 1:nTable loop table[i,1] :=v_max*(i - 1)/(nTable - 1); table[i,2] :=F_Coulomb + F_prop*table[i, 1] + F_Stribeck*exp(-fexp*table[i, 1]); end for; annotation (Documentation(info="

Returns a table with the friction characteristic table[nTable,2] = [0, f1; ....; v_max, fn], where the first column is the velocity v in the range 0..v_max and the second column is the friction force according to the Stribeck curve: 

  F_Coulomb + F_prop*v + F_Stribeck*exp(-fexp*v);
")); end GenerateStribeckFrictionTable; annotation (Documentation(info="

Utility models and functions used in the Examples

")); end Utilities; annotation ( Documentation(info="

This package contains example models to demonstrate the usage of the Translational package. Open the models and simulate them according to the provided description in the models.

")); end Examples; package Components "Components for 1D translational mechanical drive trains" extends Modelica.Icons.Package; model Fixed "Fixed flange" parameter SI.Position s0=0 "Fixed offset position of housing"; Interfaces.Flange_b flange annotation (Placement(transformation( origin={0,0}, extent={{-10,10},{10,-10}}, rotation=180))); equation flange.s = s0; annotation ( Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-80,-40},{80,-40}}, color={0,0,0}), Line(points={{80,-40},{40,-80}}, color={0,0,0}), Line(points={{40,-40},{0,-80}}, color={0,0,0}), Line(points={{0,-40},{-40,-80}}, color={0,0,0}), Line(points={{-40,-40},{-80,-80}}, color={0,0,0}), Line(points={{0,-40},{0,-10}}, color={0,0,0}), Text( extent={{-150,-90},{150,-130}}, textString="%name", lineColor={0,0,255})}), Documentation(info="

The flange of a 1D translational mechanical system fixed at an position s0 in the housing. May be used:

")); end Fixed; model Mass "Sliding mass with inertia" parameter SI.Mass m(min=0, start=1) "Mass of the sliding mass"; parameter StateSelect stateSelect=StateSelect.default "Priority to use s and v as states" annotation(Dialog(tab="Advanced")); extends Translational.Interfaces.PartialRigid(L=0,s(start=0, stateSelect=stateSelect)); SI.Velocity v(start=0, stateSelect=stateSelect) "Absolute velocity of component"; SI.Acceleration a(start=0) "Absolute acceleration of component"; equation v = der(s); a = der(v); m*a = flange_a.f + flange_b.f; annotation ( Documentation(info="

Sliding mass with inertia, without friction and two rigidly connected flanges.

The sliding mass has the length L, the position coordinate s is in the middle. Sign convention: A positive force at flange flange_a moves the sliding mass in the positive direction. A negative force at flange flange_a moves the sliding mass to the negative direction.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-100,0},{-55,0}}, color={0,127,0}), Line(points={{55,0},{100,0}}, color={0,127,0}), Rectangle( extent={{-55,-30},{56,30}}, lineColor={0,0,0}, fillPattern=FillPattern.Sphere, fillColor={255,255,255}), Polygon( points={{50,-90},{20,-80},{20,-100},{50,-90}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line(points={{-60,-90},{20,-90}}, color={0,0,0}), Text( extent={{-150,85},{150,45}}, textString="%name", lineColor={0,0,255}), Text( extent={{-150,-45},{150,-75}}, lineColor={0,0,0}, textString="m=%m")}), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-100,0},{-55,0}}, color={0,127,0}), Line(points={{55,0},{100,0}}, color={0,127,0}), Rectangle( extent={{-55,-30},{55,30}}, lineColor={0,0,0}, fillPattern=FillPattern.Sphere, fillColor={255,255,255}), Polygon( points={{50,-90},{20,-80},{20,-100},{50,-90}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line(points={{-60,-90},{20,-90}}, color={0,0,0}), Line(points={{-100,-29},{-100,-61}}, color={0,0,0}), Line(points={{100,-61},{100,-28}}, color={0,0,0}), Line(points={{-98,-60},{98,-60}}, color={0,0,0}), Polygon( points={{-101,-60},{-96,-59},{-96,-61},{-101,-60}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Polygon( points={{100,-60},{95,-61},{95,-59},{100,-60}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Text( extent={{-44,-41},{51,-57}}, textString="Length L", lineColor={0,0,255}), Line(points={{0,30},{0,53}}, color={0,0,0}), Line(points={{-72,40},{1,40}}, color={0,0,0}), Polygon( points={{-7,42},{-7,38},{-1,40},{-7,42}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Text( extent={{-61,53},{-9,42}}, textString="Position s", lineColor={0,0,255})})); end Mass; model Rod "Rod without inertia" extends Translational.Interfaces.PartialRigid; equation 0 = flange_a.f + flange_b.f; annotation ( Documentation(info="

Rod without inertia and two rigidly connected flanges.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-100,0},{-55,0}}, color={0,127,0}), Line(points={{53,0},{99,0}}, color={0,127,0}), Polygon( points={{50,-90},{20,-80},{20,-100},{50,-90}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line(points={{-60,-90},{20,-90}}, color={0,0,0}), Rectangle( extent={{-55,10},{53,-10}}, lineColor={160,160,164}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Text( extent={{-150,80},{150,40}}, textString="%name", lineColor={0,0,255}), Text( extent={{-150,-30},{150,-60}}, lineColor={0,0,0}, textString="L=%L")}), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-100,0},{-55,0}}, color={0,127,0}), Line(points={{54,0},{100,0}}, color={0,127,0}), Polygon( points={{50,-90},{20,-80},{20,-100},{50,-90}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line(points={{-60,-90},{20,-90}}, color={0,0,0}), Rectangle( extent={{-55,3},{53,-4}}, lineColor={160,160,164}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Line(points={{-100,-29},{-100,-61}}, color={0,0,0}), Line(points={{100,-61},{100,-28}}, color={0,0,0}), Line(points={{-98,-60},{98,-60}}, color={0,0,0}), Polygon( points={{-101,-60},{-96,-59},{-96,-61},{-101,-60}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Polygon( points={{100,-60},{95,-61},{95,-59},{100,-60}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Text( extent={{-44,-41},{51,-57}}, textString="Length L", lineColor={0,0,255})})); end Rod; model Spring "Linear 1D translational spring" extends Translational.Interfaces.PartialCompliant; parameter SI.TranslationalSpringConstant c(final min=0, start = 1) "Spring constant"; parameter SI.Distance s_rel0=0 "Unstretched spring length"; equation f = c*(s_rel - s_rel0); annotation ( Documentation(info="

A linear 1D translational spring. The component can be connected either between two sliding masses, or between a sliding mass and the housing (model Fixed), to describe a coupling of the sliding mass with the housing via a spring.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-60,-90},{20,-90}}, color={0,0,0}), Polygon( points={{50,-90},{20,-80},{20,-100},{50,-90}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Text( extent={{-150,90},{150,50}}, textString="%name", lineColor={0,0,255}), Line(points={{-98,0},{-60,0},{-44,-30},{-16,30},{14,-30},{44,30},{ 60,0},{100,0}},color={0,0,0}), Text( extent={{-150,-45},{150,-75}}, lineColor={0,0,0}, textString="c=%c")}), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-100,0},{-100,65}}, color={128,128,128}), Line(points={{100,0},{100,65}}, color={128,128,128}), Line(points={{-100,60},{100,60}}, color={128,128,128}), Polygon( points={{90,63},{100,60},{90,57},{90,63}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Text( extent={{-56,66},{36,81}}, lineColor={0,0,255}, textString="s_rel"), Line(points={{-86,0},{-60,0},{-44,-30},{-16,30},{14,-30},{44,30},{ 60,0},{84,0}}, color={0,0,0})})); end Spring; model Damper "Linear 1D translational damper" extends Translational.Interfaces.PartialCompliantWithRelativeStates; parameter SI.TranslationalDampingConstant d(final min=0, start = 0) "Damping constant"; extends Modelica.Thermal.HeatTransfer.Interfaces.PartialElementaryConditionalHeatPortWithoutT; equation f = d*v_rel; lossPower = f*v_rel; annotation ( Documentation(info="

Linear, velocity dependent damper element. It can be either connected between a sliding mass and the housing (model Fixed), or between two sliding masses.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-90,0},{-60,0}}, color={0,0,0}), Line(points={{-60,-30},{-60,30}}, color={0,0,0}), Line(points={{-60,-30},{60,-30}}, color={0,0,0}), Line(points={{-60,30},{60,30}}, color={0,0,0}), Rectangle( extent={{-60,30},{30,-30}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Line(points={{30,0},{90,0}}, color={0,0,0}), Polygon( points={{50,-90},{20,-80},{20,-100},{50,-90}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line(points={{-60,-90},{20,-90}}, color={0,0,0}), Text( extent={{-150,90},{150,50}}, textString="%name", lineColor={0,0,255}), Text( extent={{-150,-45},{150,-75}}, lineColor={0,0,0}, textString="d=%d"), Line(visible=useHeatPort, points={{-100,-100},{-100,-20},{-14,-20}}, color={191,0,0}, pattern=LinePattern.Dot, smooth=Smooth.None)}), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-90,0},{-60,0}}, color={0,0,0}), Line(points={{-60,-30},{-60,30}}, color={0,0,0}), Line(points={{-60,-30},{60,-30}}, color={0,0,0}), Line(points={{-60,30},{60,30}}, color={0,0,0}), Rectangle( extent={{-60,30},{30,-30}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Line(points={{30,0},{90,0}}, color={0,0,0}), Line(points={{-50,60},{50,60}}, color={128,128,128}), Polygon( points={{50,63},{60,60},{50,57},{50,63}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Text( extent={{-58,68},{42,78}}, lineColor={128,128,128}, textString="der(s_rel)")})); end Damper; model SpringDamper "Linear 1D translational spring and damper in parallel" extends Translational.Interfaces.PartialCompliantWithRelativeStates; parameter SI.TranslationalSpringConstant c(final min=0, start = 1) "Spring constant"; parameter SI.TranslationalDampingConstant d(final min=0, start = 1) "Damping constant"; parameter SI.Position s_rel0=0 "Unstretched spring length"; extends Modelica.Thermal.HeatTransfer.Interfaces.PartialElementaryConditionalHeatPortWithoutT; protected Modelica.SIunits.Force f_c "Spring force"; Modelica.SIunits.Force f_d "Damping force"; equation f_c = c*(s_rel - s_rel0); f_d = d*v_rel; f = f_c + f_d; lossPower = f_d*v_rel; annotation ( Documentation(info="

A spring and damper element connected in parallel. The component can be connected either between two sliding masses to describe the elasticity and damping, or between a sliding mass and the housing (model Fixed), to describe a coupling of the sliding mass with the housing via a spring/damper.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-80,40},{-60,40},{-45,10},{-15,70},{15,10},{45,70},{ 60,40},{80,40}}, color={0,0,0}), Line(points={{-80,40},{-80,-70}}, color={0,0,0}), Line(points={{-80,-70},{-52,-70}}, color={0,0,0}), Rectangle( extent={{-52,-49},{38,-91}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Line(points={{-52,-49},{68,-49}}, color={0,0,0}), Line(points={{-51,-91},{69,-91}}, color={0,0,0}), Line(points={{38,-70},{80,-70}}, color={0,0,0}), Line(points={{80,40},{80,-70}}, color={0,0,0}), Line(points={{-90,0},{-80,0}}, color={0,0,0}), Line(points={{80,0},{90,0}}, color={0,0,0}), Polygon( points={{53,-18},{23,-8},{23,-28},{53,-18}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line(points={{-57,-18},{23,-18}}, color={0,0,0}), Text( extent={{-150,120},{150,80}}, textString="%name", lineColor={0,0,255}), Text( extent={{-150,-135},{150,-165}}, lineColor={0,0,0}, textString="d=%d"), Text( extent={{-150,-100},{150,-130}}, lineColor={0,0,0}, textString="c=%c"), Line(visible=useHeatPort, points={{-100,-100},{-100,-80},{-5,-80}}, color={191,0,0}, pattern=LinePattern.Dot, smooth=Smooth.None)}), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line( points={{-80,32},{-58,32},{-43,2},{-13,62},{17,2},{47,62},{62,32}, {80,32}}, color={0,0,0}, thickness=0.5), Line(points={{-100,31},{-100,96}}, color={128,128,128}), Line(points={{100,29},{100,94}}, color={128,128,128}), Line(points={{-98,82},{100,82}}, color={128,128,128}), Polygon( points={{90,85},{100,82},{90,79},{90,85}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Text( extent={{-63,83},{46,103}}, lineColor={0,0,255}, textString="s_rel"), Rectangle( extent={{-52,-28},{38,-72}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Line(points={{-51,-72},{69,-72}}, color={0,0,0}), Line(points={{-52,-28},{68,-28}}, color={0,0,0}), Line(points={{38,-50},{80,-50}}, color={0,0,0}), Line(points={{-80,-50},{-52,-50}}, color={0,0,0}), Line(points={{-80,32},{-80,-50}}, color={0,0,0}), Line(points={{80,32},{80,-50}}, color={0,0,0}), Line(points={{-90,0},{-80,0}}, color={0,0,0}), Line(points={{90,0},{80,0}}, color={0,0,0})})); end SpringDamper; model ElastoGap "1D translational spring damper combination with gap" extends Modelica.Mechanics.Translational.Interfaces.PartialCompliantWithRelativeStates; parameter SI.TranslationalSpringConstant c(final min=0, start=1) "Spring constant"; parameter SI.TranslationalDampingConstant d(final min=0, start=1) "Damping constant"; parameter SI.Position s_rel0=0 "Unstretched spring length"; parameter Real n(final min=1) = 1 "Exponent of spring force ( f_c = -c*|s_rel-s_rel0|^n )"; extends Modelica.Thermal.HeatTransfer.Interfaces.PartialElementaryConditionalHeatPortWithoutT; /* Please note that initialization might fail due to the nonlinear spring characteristic (spring force is zero for s_rel > s_rel0) if a positive force is acting on the element and no other force balances this force (e.g., when setting both initial velocity and acceleration to 0) */ Boolean contact "=true, if contact, otherwise no contact"; protected Modelica.SIunits.Force f_c "Spring force"; Modelica.SIunits.Force f_d2 "Linear damping force"; Modelica.SIunits.Force f_d "Linear damping force which is limited by spring force (|f_d| <= |f_c|)"; equation // Modify contact force, so that it is only "pushing" and not // "pulling/sticking" and that it is continuous contact = s_rel < s_rel0; f_c = smooth(1, noEvent( if contact then -c*abs(s_rel - s_rel0)^n else 0)); f_d2 = if contact then d*v_rel else 0; f_d = smooth(0, noEvent( if contact then (if f_d2 < f_c then f_c else if f_d2 > -f_c then -f_c else f_d2) else 0)); f = f_c + f_d; lossPower = f_d*v_rel; annotation ( Documentation(info="

This component models a spring damper combination that can lift off. It can be connected between a sliding mass and the housing (model Fixed), to describe the contact of a sliding mass with the housing.

As long as s_rel > s_rel0, no force is exerted (s_rel = flange_b.s - flange_a.s). If s_rel ≤ s_rel0, the contact force is basically computed with a linear spring/damper characteristic. With parameter n≥1 (exponent of spring force), a nonlinear spring force can be modeled: 

   desiredContactForce = c*|s_rel - s_rel0|^n + d*der(s_rel)

Note, Hertzian contact is described by:

The above force law leads to the following difficulties:

  1. If the damper force becomes larger as the spring force and with opposite sign, the contact force would be \"pulling/sticking\" which is unphysical, since during contact only pushing forces can occur.
  2. When contact occurs with a non-zero relative speed (which is the usual situation), the damping force has a non-zero value and therefore the contact force changes discontinuously at s_rel = s_rel0. Again, this is not physical because the force can only change continuously. (Note, this component is not an idealized model where a steep characteristic is approximated by a discontinuity, but it shall model the steep characteristic.)

In the literature there are several proposals to fix problem (2). Especially, often the following model is used (see, e.g., Lankarani, Nikravesh: Continuous Contact Force Models for Impact Analysis in Multibody Systems, Nonlinear Dynamics 5, pp. 193-207, 1994, pdf-download): 

   f = c*s_rel^n + (d*s_rel^n)*der(s_rel)

However, this and other models proposed in literature violate issue (1), i.e., unphysical pulling forces can occur (if d*der(s_rel) becomes large enough). Note, if the force law is of the form \"f = f_c + f_d\", then a necessary condition is that |f_d| ≤ |f_c|, otherwise (1) and (2) are violated. For this reason, the most simplest approach is used in the ElastoGap model to fix both problems by using this necessary condition in the force law directly. If s_rel0 = 0, the equations are: 

    if s_rel ≥ 0 then
       f = 0;    // contact force
    else
       f_c  = -c*|s_rel|^n;          // contact spring force (Hertzian contact force)
       f_d2 = d*der(s_rel);         // linear contact damper force
       f_d  = if f_d2 <  f_c then  f_c else
              if f_d2 > -f_c then -f_c else f_d2;  // bounded damper force
       f    = f_c + f_d;            // contact force
    end if;

Note, since |f_d| ≤ |f_c|, pulling forces cannot occur and the contact force is always continuous, especially around the start of the penetration at s_rel = s_rel0.

In the next figure, a typical simulation with the ElastoGap model is shown (Examples.ElastoGap) where the different effects are visualized:

  1. Curve 1 (elastoGap1.f) is the unmodified contact force, i.e., the linear spring/damper characteristic. A pulling/sticking force is present at the end of the contact.
  2. Curve 2 (elastoGap2.f) is the contact force, where the force is explicitly set to zero when pulling/sticking occurs. The contact force is discontinuous when contact starts.
  3. Curve 3 (elastoGap3.f) is the ElastoGap model of this library. No discontinuity and no pulling/sticking occurs.

"), Diagram(coordinateSystem( preserveAspectRatio=false, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-100,0},{-50,0}}, color={0,127,0}), Line( points={{-48,34},{-48,-46}}, color={0,0,0}, thickness=1), Line(points={{8,40},{8,2}}, color={0,0,0}), Line(points={{-2,0},{38,0},{38,44},{-2,44}}, color={0,0,0}), Line(points={{38,22},{72,22}}, color={0,0,0}), Line( points={{-12,-38},{-12,20}}, color={0,0,0}, thickness=1), Line(points={{-12,22},{8,22}}, color={0,0,0}), Line(points={{-12,-38},{-2,-38}}, color={0,0,0}), Line(points={{72,0},{100,0}}, color={0,127,0}), Line(points={{72,22},{72,-42}}, color={0,0,0}), Line(points={{-2,-38},{10,-28},{22,-48},{38,-28},{50,-48},{64,-28}, {72,-40}}, color={0,0,0}), Rectangle( extent={{8,44},{38,0}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Text( extent={{-64,-80},{64,-64}}, lineColor={0,0,255}, textString="s_rel"), Line(points={{-100,-29},{-100,-61}}, color={0,0,0}), Line(points={{100,-61},{100,-28}}, color={0,0,0}), Line(points={{-98,-60},{98,-60}}, color={0,0,0}), Polygon( points={{-101,-60},{-96,-59},{-96,-61},{-101,-60}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Polygon( points={{100,-60},{95,-61},{95,-59},{100,-60}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid)}), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-98,0},{-48,0}}, color={0,127,0}), Line( points={{-48,38},{-48,-38}}, color={0,0,0}, thickness=1), Line(points={{8,-10},{8,-48}}, color={0,0,0}), Line(points={{-2,-50},{38,-50},{38,-6},{-2,-6}}, color={0,0,0}), Line(points={{38,-28},{72,-28}}, color={0,0,0}), Line( points={{-12,-38},{-12,36}}, color={0,0,0}, thickness=1), Line(points={{-12,-28},{8,-28}}, color={0,0,0}), Line(points={{-12,24},{-6,24}}, color={0,0,0}), Line(points={{72,0},{98,0}}, color={0,127,0}), Line(points={{72,22},{72,-42}}, color={0,0,0}), Line(points={{-6,24},{6,34},{18,14},{34,34},{46,14},{60,34},{68,22}}, color={0,0,0}), Rectangle( extent={{8,-6},{38,-50}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Line(points={{-52,-70},{28,-70}}, color={0,0,0}), Polygon( points={{58,-70},{28,-60},{28,-80},{58,-70}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Text( extent={{-150,100},{150,60}}, textString="%name", lineColor={0,0,255}, pattern=LinePattern.Dot), Text( extent={{-150,-125},{150,-95}}, lineColor={0,0,0}, textString="c=%c"), Text( extent={{-150,-160},{150,-130}}, lineColor={0,0,0}, textString="d=%d"), Line(points={{68,22},{72,22}}, color={0,0,0}), Line(visible=useHeatPort, points={{-100,-100},{-100,-44},{22,-44},{22,-28}}, color={191,0,0}, pattern=LinePattern.Dot, smooth=Smooth.None)})); end ElastoGap; model SupportFriction "Coulomb friction in support" extends Modelica.Mechanics.Translational.Interfaces.PartialElementaryTwoFlangesAndSupport2; extends Modelica.Thermal.HeatTransfer.Interfaces.PartialElementaryConditionalHeatPortWithoutT; parameter Real f_pos[:, 2]=[0, 1] "[v, f] Positive sliding friction characteristic (v>=0)"; parameter Real peak(final min=1) = 1 "peak*f_pos[1,2] = Maximum friction force for v==0"; extends Translational.Interfaces.PartialFriction; SI.Position s; SI.Force f "Friction force"; SI.Velocity v "Absolute velocity of flange_a and flange_b"; SI.Acceleration a "Absolute acceleration of flange_a and flange_b"; equation // Constant auxiliary variables f0 = Modelica.Math.tempInterpol1(0, f_pos, 2); f0_max = peak*f0; free = false; s = flange_a.s - s_support; flange_a.s = flange_b.s; // velocity and acceleration of flanges v = der(s); a = der(v); v_relfric = v; a_relfric = a; // Friction force flange_a.f + flange_b.f - f = 0; // Friction force f = if locked then sa*unitForce else (if startForward then Modelica.Math.tempInterpol1( v, f_pos, 2) else if startBackward then -Modelica.Math.tempInterpol1(-v, f_pos, 2) else if pre(mode) == Forward then Modelica.Math.tempInterpol1( v, f_pos, 2) else -Modelica.Math.tempInterpol1(-v, f_pos, 2)); lossPower = f*v_relfric; annotation ( Documentation(info="

This element describes Coulomb friction in support, i.e., a frictional force acting between a flange and the housing. The positive sliding friction force \"f\" has to be defined by table \"f_pos\" as function of the absolute velocity \"v\". E.g. 

       v |   f
      ---+-----
       0 |   0
       1 |   2
       2 |   5
       3 |   8

gives the following table: 

   f_pos = [0, 0; 1, 2; 2, 5; 3, 8];

Currently, only linear interpolation in the table is supported. Outside of the table, extrapolation through the last two table entries is used. It is assumed that the negative sliding friction force has the same characteristic with negative values. Friction is modelled in the following way:

When the absolute velocity \"v\" is not zero, the friction force is a function of v and of a constant normal force. This dependency is defined via table f_pos and can be determined by measurements, e.g., by driving the gear with constant velocity and measuring the needed driving force (= friction force).

When the absolute velocity becomes zero, the elements connected by the friction element become stuck, i.e., the absolute position remains constant. In this phase the friction force is calculated from a force balance due to the requirement, that the absolute acceleration shall be zero. The elements begin to slide when the friction force exceeds a threshold value, called the maximum static friction force, computed via: 

   maximum_static_friction = peak * sliding_friction(v=0)  (peak >= 1)

This procedure is implemented in a \"clean\" way by state events and leads to continuous/discrete systems of equations if friction elements are dynamically coupled which have to be solved by appropriate numerical methods. The method is described in:

Otter M., Elmqvist H., and Mattsson S.E. (1999):
Hybrid Modeling in Modelica based on the Synchronous Data Flow Principle. CACSD'99, Aug. 22.-26, Hawaii.

More precise friction models take into account the elasticity of the material when the two elements are \"stuck\", as well as other effects, like hysteresis. This has the advantage that the friction element can be completely described by a differential equation without events. The drawback is that the system becomes stiff (about 10-20 times slower simulation) and that more material constants have to be supplied which requires more sophisticated identification. For more details, see the following references, especially (Armstrong and Canudas de Witt 1996):

Armstrong B. (1991):
Control of Machines with Friction. Kluwer Academic Press, Boston MA.

Armstrong B., and Canudas de Wit C. (1996):
Friction Modeling and Compensation. The Control Handbook, edited by W.S.Levine, CRC Press, pp. 1369-1382.

Canudas de Wit C., Olsson H., Astroem K.J., and Lischinsky P. (1995):
A new model for control of systems with friction. IEEE Transactions on Automatic Control, Vol. 40, No. 3, pp. 419-425.

"), Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Rectangle( extent={{-90,10},{90,-10}}, lineColor={0,127,0}, fillColor={215,215,215}, fillPattern=FillPattern.Solid), Ellipse( extent={{-48,-10},{-28,-30}}, lineColor={95,95,95}, fillPattern=FillPattern.Sphere, fillColor={175,175,175}), Ellipse( extent={{-10,-10},{10,-30}}, lineColor={95,95,95}, fillPattern=FillPattern.Sphere, fillColor={175,175,175}), Ellipse( extent={{30,-10},{50,-30}}, lineColor={95,95,95}, fillPattern=FillPattern.Sphere, fillColor={175,175,175}), Polygon( points={{-60,-30},{60,-30},{60,-12},{80,-12},{80,-50},{-80,-50},{ -80,-12},{-60,-12},{-60,-30}}, lineColor={95,95,95}, fillPattern=FillPattern.Solid, smooth=Smooth.None, fillColor={175,175,175}), Text( extent={{-150,100},{150,60}}, textString="%name", lineColor={0,0,255}), Line(points={{-10,-85},{-5,-80}}, color={0,0,0}), Line(points={{-5,-90},{5,-80}}, color={0,0,0}), Line(points={{-10,-90},{0,-80}}, color={0,0,0}), Line(points={{0,-90},{10,-80}}, color={0,0,0}), Polygon( points={{-60,-50},{-20,-80},{20,-80},{60,-50},{-60,-50}}, lineColor={95,95,95}, smooth=Smooth.None, fillColor={175,175,175}, fillPattern=FillPattern.Solid), Ellipse( extent={{-50,30},{-30,10}}, lineColor={95,95,95}, fillPattern=FillPattern.Sphere, fillColor={175,175,175}), Ellipse( extent={{-10,30},{10,10}}, lineColor={95,95,95}, fillPattern=FillPattern.Sphere, fillColor={175,175,175}), Ellipse( extent={{30,30},{50,10}}, lineColor={95,95,95}, fillPattern=FillPattern.Sphere, fillColor={175,175,175}), Polygon( points={{-60,30},{60,30},{60,12},{80,12},{80,50},{-80,50},{-80,12}, {-60,12},{-60,30}}, lineColor={95,95,95}, fillPattern=FillPattern.Solid, smooth=Smooth.None, fillColor={175,175,175}), Line(visible=useHeatPort, points={{-100,-100},{-100,-20},{0,-20}}, color={191,0,0}, pattern=LinePattern.Dot, smooth=Smooth.None)})); end SupportFriction; model Brake "Brake based on Coulomb friction" extends Modelica.Mechanics.Translational.Interfaces.PartialElementaryTwoFlangesAndSupport2; extends Modelica.Thermal.HeatTransfer.Interfaces.PartialElementaryConditionalHeatPortWithoutT; parameter Real mue_pos[:, 2]=[0, 0.5] "[v, f] Positive sliding friction characteristic (v>=0)"; parameter Real peak(final min=1) = 1 "peak*mue_pos[1,2] = Maximum friction force for v==0"; parameter Real cgeo(final min=0) = 1 "Geometry constant containing friction distribution assumption"; parameter SI.Force fn_max(final min=0, start=1) "Maximum normal force"; extends Translational.Interfaces.PartialFriction; SI.Position s; SI.Force f "Brake friction force"; SI.Velocity v "Absolute velocity of flange_a and flange_b"; SI.Acceleration a "Absolute acceleration of flange_a and flange_b"; Real mue0 "Friction coefficient for v=0 and forward sliding"; SI.Force fn "Normal force (=fn_max*f_normalized)"; // Constant auxiliary variable Modelica.Blocks.Interfaces.RealInput f_normalized "Normalized force signal 0..1 (normal force = fn_max*f_normalized; brake is active if > 0)" annotation (Placement(transformation( origin={0,110}, extent={{20,-20},{-20,20}}, rotation=90))); equation mue0 = Modelica.Math.tempInterpol1(0, mue_pos, 2); s = s_a; s = s_b; // velocity and acceleration of flanges flange_a and flange_b v = der(s); a = der(v); v_relfric = v; a_relfric = a; // Friction force, normal force and friction force for v_rel=0 flange_a.f + flange_b.f - f = 0; fn = fn_max*f_normalized; f0 = mue0*cgeo*fn; f0_max = peak*f0; free = fn <= 0; // Friction force f = if locked then sa*unitForce else if free then 0 else cgeo*fn*(if startForward then Modelica.Math.tempInterpol1( v, mue_pos, 2) else if startBackward then -Modelica.Math.tempInterpol1(-v, mue_pos, 2) else if pre(mode) == Forward then Modelica.Math.tempInterpol1( v, mue_pos, 2) else -Modelica.Math.tempInterpol1(-v, mue_pos, 2)); lossPower = f*v_relfric; annotation ( Documentation(info="

This component models a brake, i.e., a component where a frictional force is acting between the housing and a flange and a controlled normal force presses the flange to the housing in order to increase friction. The normal force fn has to be provided as input signal f_normalized in a normalized form (0 ≤ f_normalized ≤ 1), fn = fn_max*f_normalized, where fn_max has to be provided as parameter. Friction in the brake is modelled in the following way:

When the absolute velocity \"v\" is not zero, the friction force is a function of the velocity dependent friction coefficient mue(v) , of the normal force \"fn\", and of a geometry constant \"cgeo\" which takes into account the geometry of the device and the assumptions on the friction distributions: 

        frictional_force = cgeo * mue(v) * fn

Typical values of coefficients of friction: 

      dry operation   :  mue = 0.2 .. 0.4
      operating in oil:  mue = 0.05 .. 0.1

The positive part of the friction characteristic mue(v), v >= 0, is defined via table mue_pos (first column = v, second column = mue). Currently, only linear interpolation in the table is supported.

When the absolute velocity becomes zero, the elements connected by the friction element become stuck, i.e., the absolute position remains constant. In this phase the friction force is calculated from a force balance due to the requirement, that the absolute acceleration shall be zero. The elements begin to slide when the friction force exceeds a threshold value, called the maximum static friction force, computed via: 

       frictional_force = peak * cgeo * mue(w=0) * fn   (peak >= 1)

This procedure is implemented in a \"clean\" way by state events and leads to continuous/discrete systems of equations if friction elements are dynamically coupled. The method is described in:

Otter M., Elmqvist H., and Mattsson S.E. (1999):
Hybrid Modeling in Modelica based on the Synchronous Data Flow Principle. CACSD'99, Aug. 22.-26, Hawaii.

More precise friction models take into account the elasticity of the material when the two elements are \"stuck\", as well as other effects, like hysteresis. This has the advantage that the friction element can be completely described by a differential equation without events. The drawback is that the system becomes stiff (about 10-20 times slower simulation) and that more material constants have to be supplied which requires more sophisticated identification. For more details, see the following references, especially (Armstrong and Canudas de Witt 1996):

Armstrong B. (1991):
Control of Machines with Friction. Kluwer Academic Press, Boston MA.

Armstrong B., and Canudas de Wit C. (1996):
Friction Modeling and Compensation. The Control Handbook, edited by W.S.Levine, CRC Press, pp. 1369-1382.

Canudas de Wit C., Olsson H., Astroem K.J., and Lischinsky P. (1995):
A new model for control of systems with friction. IEEE Transactions on Automatic Control, Vol. 40, No. 3, pp. 419-425.

"), Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Rectangle( extent={{-90,10},{90,-10}}, lineColor={0,127,0}, fillColor={215,215,215}, fillPattern=FillPattern.Solid), Rectangle( extent={{-20,30},{20,20}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Rectangle( extent={{-20,-20},{20,-30}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Polygon( points={{0,-30},{10,-50},{-10,-50},{0,-30}}, lineColor={0,0,127}, fillColor={0,0,127}, fillPattern=FillPattern.Solid), Polygon( points={{10,50},{-10,50},{0,30},{10,50}}, lineColor={0,0,127}, fillColor={0,0,127}, fillPattern=FillPattern.Solid), Line( points={{0,90},{0,50}}, color={0,0,0}, smooth=Smooth.None), Rectangle( extent={{20,28},{30,22}}, lineColor={175,175,175}, fillColor={175,175,175}, fillPattern=FillPattern.Solid), Rectangle( extent={{20,-22},{30,-28}}, lineColor={175,175,175}, fillColor={175,175,175}, fillPattern=FillPattern.Solid), Rectangle( extent={{30,28},{36,-102}}, lineColor={175,175,175}, fillColor={175,175,175}, fillPattern=FillPattern.Solid), Rectangle( extent={{14,-96},{30,-102}}, lineColor={175,175,175}, fillColor={175,175,175}, fillPattern=FillPattern.Solid), Line( points={{0,-50},{0,-60},{-40,-50},{-40,48},{0,60},{0,90}}, color={0,0,0}, smooth=Smooth.None), Text( extent={{-150,-120},{150,-160}}, textString="%name", lineColor={0,0,255}), Line(visible=useHeatPort, points={{-100,-102},{-100,-16},{0,-16}}, color={191,0,0}, pattern=LinePattern.Dot, smooth=Smooth.None)})); end Brake; model IdealGearR2T "Gearbox transforming rotational into translational motion" extends Modelica.Mechanics.Rotational.Components.IdealGearR2T; annotation (Documentation(info="

Couples rotational and translational motion, like a toothed wheel with a toothed rack, specifying the ratio of rotational / translational motion.

")); end IdealGearR2T; model IdealRollingWheel "Simple 1-dim. model of an ideal rolling wheel without inertia" extends Modelica.Mechanics.Rotational.Components.IdealRollingWheel; annotation (Documentation(info="

Couples rotational and translational motion, like an ideal rolling wheel, specifying the wheel radius.

")); end IdealRollingWheel; model InitializeFlange "Initializes a flange with pre-defined position, speed and acceleration (usually, this is reference data from a control bus)" extends Modelica.Blocks.Icons.Block; parameter Boolean use_s_start = true "= true, if initial position is defined by input s_start, otherwise not initialized"; parameter Boolean use_v_start = true "= true, if initial speed is defined by input v_start, otherwise not initialized"; parameter Boolean use_a_start = true "= true, if initial acceleration is defined by input a_start, otherwise not initialized"; parameter StateSelect stateSelect=StateSelect.default "Priority to use flange angle and speed as states"; Modelica.Blocks.Interfaces.RealInput s_start(unit="m") if use_s_start "Initial position of flange" annotation (Placement(transformation(extent={{-140,40},{-100,80}}, rotation=0))); Modelica.Blocks.Interfaces.RealInput v_start(unit="m/s") if use_v_start "Initial speed of flange" annotation (Placement(transformation(extent={{-140,-20},{-100,20}}, rotation=0))); Modelica.Blocks.Interfaces.RealInput a_start(unit="m/s2") if use_a_start "Initial angular acceleration of flange" annotation (Placement(transformation(extent={{-140,-80},{-100,-40}}, rotation=0))); Interfaces.Flange_b flange "Flange that is initialized" annotation (Placement( transformation(extent={{90,-10},{110,10}}, rotation=0))); Modelica.SIunits.Position s_flange(stateSelect=stateSelect)=flange.s "Flange position"; Modelica.SIunits.Velocity v_flange(stateSelect=stateSelect)= der(s_flange) "= der(s_flange)"; protected encapsulated model Set_s_start "Set s_start" import Modelica; extends Modelica.Blocks.Icons.Block; Modelica.Blocks.Interfaces.RealInput s_start(unit="m") "Start position" annotation (HideResult=true, Placement(transformation(extent={{-140,-20},{ -100,20}}, rotation=0))); Modelica.Mechanics.Translational.Interfaces.Flange_b flange annotation (Placement( transformation(extent={{90,-10},{110,10}}, rotation=0))); initial equation flange.s = s_start; equation flange.f = 0; end Set_s_start; encapsulated model Set_v_start "Set v_start" import Modelica; extends Modelica.Blocks.Icons.Block; Modelica.Blocks.Interfaces.RealInput v_start(unit="m/s") "Start velocity" annotation (HideResult=true, Placement(transformation(extent={{-140,-20},{ -100,20}}, rotation=0))); Modelica.Mechanics.Translational.Interfaces.Flange_b flange annotation (Placement( transformation(extent={{90,-10},{110,10}}, rotation=0))); initial equation der(flange.s) = v_start; equation flange.f = 0; end Set_v_start; encapsulated model Set_a_start "Set a_start" import Modelica; extends Modelica.Blocks.Icons.Block; Modelica.Blocks.Interfaces.RealInput a_start(unit="m/s2") "Start acceleration" annotation (HideResult=true, Placement(transformation(extent={{-140,-20},{ -100,20}}, rotation=0))); Modelica.Mechanics.Translational.Interfaces.Flange_b flange(s(stateSelect=StateSelect.avoid)) annotation (Placement( transformation(extent={{90,-10},{110,10}}, rotation=0))); Modelica.SIunits.Velocity v = der(flange.s) annotation(HideResult=true); initial equation der(v) = a_start; equation flange.f = 0; end Set_a_start; encapsulated model Set_flange_f "Set flange_f to zero" import Modelica; extends Modelica.Blocks.Icons.Block; Modelica.Mechanics.Translational.Interfaces.Flange_b flange annotation (Placement( transformation(extent={{90,-10},{110,10}}, rotation=0))); equation flange.f = 0; end Set_flange_f; protected Set_s_start set_s_start if use_s_start annotation (Placement( transformation(extent={{-20,50},{0,70}}, rotation=0))); Set_v_start set_v_start if use_v_start annotation (Placement(transformation(extent={{-20, -10},{0,10}}, rotation=0))); Set_a_start set_a_start if use_a_start annotation (Placement(transformation(extent={{-20, -70},{0,-50}}, rotation=0))); Set_flange_f set_flange_f annotation (Placement(transformation(extent={ {20,-100},{40,-80}}, rotation=0))); equation connect(set_s_start.flange, flange) annotation (Line( points={{0,60},{60,60},{60,0},{100,0}}, color={0,0,0}, smooth=Smooth.None)); connect(set_v_start.flange, flange) annotation (Line( points={{0,0},{100,0}}, color={0,0,0}, smooth=Smooth.None)); connect(set_a_start.flange, flange) annotation (Line( points={{0,-60},{60,-60},{60,0},{100,0}}, color={0,0,0}, smooth=Smooth.None)); connect(set_flange_f.flange, flange) annotation (Line( points={{40,-90},{60,-90},{60,0},{100,0}}, color={0,0,0}, smooth=Smooth.None)); connect(s_start, set_s_start.s_start) annotation (Line( points={{-120,60},{-22,60}}, color={0,0,127}, smooth=Smooth.None)); connect(v_start, set_v_start.v_start) annotation (Line( points={{-120,0},{-22,0}}, color={0,0,127}, smooth=Smooth.None)); connect(a_start, set_a_start.a_start) annotation (Line( points={{-120,-60},{-22,-60}}, color={0,0,127}, smooth=Smooth.None)); annotation (Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100, -100},{100,100}}), graphics={ Text( extent={{-94,74},{68,46}}, lineColor={0,0,0}, textString="s_start"), Text( extent={{-94,16},{70,-14}}, lineColor={0,0,0}, textString="v_start"), Text( extent={{-94,-46},{66,-74}}, lineColor={0,0,0}, textString="a_start")}), Documentation(info="

This component is used to optionally initialize the position, speed, and/or acceleration of the flange to which this component is connected. Via parameters use_s_start, use_v_start, use_a_start the corresponding input signals s_start, v_start, a_start are conditionally activated. If an input is activated, the corresponding flange property is initialized with the input value at start time.

For example, if \"use_s_start = true\", then flange.s is initialized with the value of the input signal \"s_start\" at the start time.

Additionally, it is optionally possible to define the \"StateSelect\" attribute of the flange position and the flange speed via parameter \"stateSelection\".

This component is especially useful when the initial values of a flange shall be set according to reference signals of a controller that are provided via a signal bus.

")); end InitializeFlange; model MassWithStopAndFriction "Sliding mass with hard stop and Stribeck friction" extends PartialFrictionWithStop; SI.Velocity v(start=0, stateSelect = StateSelect.always) "Absolute velocity of flange_a and flange_b"; SI.Acceleration a(start=0) "Absolute acceleration of flange_a and flange_b"; parameter Modelica.SIunits.Mass m(start=1) "Mass"; parameter Real F_prop(final unit="N.s/m", final min=0, start = 1) "Velocity dependent friction"; parameter Modelica.SIunits.Force F_Coulomb(start=5) "Constant friction: Coulomb force"; parameter Modelica.SIunits.Force F_Stribeck(start=10) "Stribeck effect"; parameter Real fexp(final unit="s/m", final min=0, start = 2) "Exponential decay"; extends Modelica.Thermal.HeatTransfer.Interfaces.PartialElementaryConditionalHeatPortWithoutT; Integer stopped; encapsulated partial model PartialFrictionWithStop "Base model of Coulomb friction elements with stop" import SI = Modelica.SIunits; import Modelica.Mechanics.Translational.Interfaces.PartialRigid; parameter SI.Position smax(start= 25) "Right stop for (right end of) sliding mass"; parameter SI.Position smin(start=-25) "Left stop for (left end of) sliding mass"; parameter SI.Velocity v_small=1e-3 "Relative velocity near to zero (see model info text)" annotation(Dialog(tab="Advanced")); // Equations to define the following variables have to be defined in subclasses SI.Velocity v_relfric "Relative velocity between frictional surfaces"; SI.Acceleration a_relfric "Relative acceleration between frictional surfaces"; SI.Force f "Friction force (positive, if directed in opposite direction of v_rel)"; SI.Force f0 "Friction force for v=0 and forward sliding"; SI.Force f0_max "Maximum friction force for v=0 and locked"; Boolean free "true, if frictional element is not active"; // Equations to define the following variables are given in this class Real sa(unit="1") "Path parameter of friction characteristic f = f(a_relfric)"; Boolean startForward(start=false, fixed=true) "= true, if v_rel=0 and start of forward sliding or v_rel > v_small"; Boolean startBackward(start=false, fixed=true) "= true, if v_rel=0 and start of backward sliding or v_rel < -v_small"; Boolean locked(start=false) "true, if v_rel=0 and not sliding"; extends PartialRigid(s(start=0, stateSelect = StateSelect.always)); constant Integer Unknown=3 "Value of mode is not known"; constant Integer Free=2 "Element is not active"; constant Integer Forward=1 "v_rel > 0 (forward sliding)"; constant Integer Stuck=0 "v_rel = 0 (forward sliding, locked or backward sliding)"; constant Integer Backward=-1 "v_rel < 0 (backward sliding)"; Integer mode( final min=Backward, final max=Unknown, start=Unknown, fixed=true); protected constant SI.Acceleration unitAcceleration = 1 annotation(HideResult=true); constant SI.Force unitForce = 1 annotation(HideResult=true); equation /* Friction characteristic (locked is introduced to help the Modelica translator determining the different structural configurations, if for each configuration special code shall be generated) */ startForward = pre(mode) == Stuck and (sa > f0_max/unitForce and s < (smax - L/2) or pre(startForward) and sa > f0/unitForce and s < (smax - L/2)) or pre(mode) == Backward and v_relfric > v_small or initial() and (v_relfric > 0); startBackward = pre(mode) == Stuck and (sa < -f0_max/unitForce and s > (smin + L/2) or pre(startBackward) and sa < -f0/unitForce and s > (smin + L/2)) or pre(mode) == Forward and v_relfric < -v_small or initial() and (v_relfric < 0); locked = not free and not (pre(mode) == Forward or startForward or pre(mode) == Backward or startBackward); a_relfric/unitAcceleration = if locked then 0 else if free then sa else if startForward then sa - f0_max/unitForce else if startBackward then sa + f0_max/unitForce else if pre(mode) == Forward then sa - f0_max/unitForce else sa + f0_max/unitForce; /* Friction torque has to be defined in a subclass. Example for a clutch: f = if locked then sa else if free then 0 else cgeo*fn*(if startForward then Math.tempInterpol1( v_relfric, mue_pos, 2) else if startBackward then -Math.tempInterpol1(-v_relfric, mue_pos, 2) else if pre(mode) == Forward then Math.tempInterpol1( v_relfric, mue_pos, 2) else -Math.tempInterpol1(-v_relfric, mue_pos, 2)); */ // finite state machine to determine configuration mode = if free then Free else (if (pre(mode) == Forward or pre(mode) == Free or startForward) and v_relfric > 0 and s < (smax - L/2) then Forward else if (pre(mode) == Backward or pre(mode) == Free or startBackward) and v_relfric < 0 and s > (smin + L/2) then Backward else Stuck); annotation (Documentation(info="

Basic model for Coulomb friction that models the stuck phase in a reliable way.
Additionally, a left and right stop are handled.

")); end PartialFrictionWithStop; equation // Constant auxiliary variables f0 = (F_Coulomb + F_Stribeck); f0_max = f0*1.001; free = f0 <= 0 and F_prop <= 0 and s > smin + L/2 and s < smax - L/2; // Velocity and acceleration of flanges v = der(s); a = der(v); v_relfric = v; a_relfric = a; // Equilibrium of forces 0 = flange_a.f + flange_b.f - f - m*der(v); // Friction force f = if locked then sa*unitForce else if free then 0 else (if startForward then F_prop*v + F_Coulomb + F_Stribeck else if startBackward then F_prop*v - F_Coulomb - F_Stribeck else if pre(mode) == Forward then F_prop*v + F_Coulomb + F_Stribeck*exp(-fexp*abs(v)) else F_prop*v - F_Coulomb - F_Stribeck*exp(-fexp*abs(v))); lossPower = f*v_relfric; equation when (initial()) then assert(s > smin + L/2 or s >= smin + L/2 and v >= 0, "Error in initialization of hard stop. (s - L/2) must be >= smin\n"+ "(s=" + String(s) + ", L=" + String(L) + ", smin=" + String(smin) + ")"); assert(s < smax - L/2 or s <= smax - L/2 and v <= 0, "Error in initialization of hard stop. (s + L/2) must be <= smax\n"+ "(s=" + String(s) + ", L=" + String(L) + ", smax=" + String(smax) + ")"); end when; // Define events for hard stops and reinitialize the state variables velocity v and position s stopped = if s <= smin + L/2 then -1 else if s >= smax - L/2 then +1 else 0; when stopped <> 0 then reinit(s, if stopped < 0 then smin + L/2 else smax - L/2); reinit(v, 0); end when; /* Version 1: when not (s < smax - L/2) then reinit(s, smax - L/2); if (not initial() or v>0) then reinit(v, 0); end if; end when; when not (s > smin + L/2) then reinit(s, smin + L/2); if (not initial() or v<0) then reinit(v, 0); end if; end when; Version 2: stopped := if s <= smin + L/2 then -1 else if s >= smax - L/2 then +1 else 0; when (initial()) then assert(s > smin + L/2 or s >= smin + L/2 and v >= 0, "Error in initialization of hard stop. (s - L/2) must be >= smin\n"+ "(s=" + String(s) + ", L=" + String(L) + ", smin=" + String(smin) + ")"); assert(s < smax - L/2 or s <= smax - L/2 and v <= 0, "Error in initialization of hard stop. (s + L/2) must be <= smax\n"+ "(s=" + String(s) + ", L=" + String(L) + ", smax=" + String(smax) + ")"); end when; when stopped <> 0 then reinit(s, if stopped < 0 then smin + L/2 else smax - L/2); if (not initial() or stopped*v>0) then reinit(v, 0); end if; end when; */ annotation ( Documentation(info="

This element describes the Stribeck friction characteristics of a sliding mass, i. e. the frictional force acting between the sliding mass and the support. Included is a hard stop for the position.

The surface is fixed and there is friction between sliding mass and surface. The frictional force f is given for positive velocity v by: 

f = F_Coulomb + F_prop * v + F_Stribeck * exp (-fexp * v)

The distance between the left and the right connector is given by parameter L. The position of the center of gravity, coordinate s, is in the middle between the two flanges.

There are hard stops at smax and smin, i. e. if flange_a.s >= smin and flange_b.s <= xmax the sliding mass can move freely.

When the absolute velocity becomes zero, the sliding mass becomes stuck, i.e., the absolute position remains constant. In this phase the friction force is calculated from a force balance due to the requirement that the absolute acceleration shall be zero. The elements begin to slide when the friction force exceeds a threshold value, called the maximum static friction force, computed via:

   maximum_static_friction =  F_Coulomb + F_Stribeck

This requires the states Stop.s and Stop.v . If these states are eliminated during the index reduction the model will not work. To avoid this any inertias should be connected via springs to the Stop element, other sliding masses, dampers or hydraulic chambers must be avoided.

For more details of the used friction model see the following reference:

Beater P. (1999):
Entwurf hydraulischer Maschinen. Springer Verlag Berlin Heidelberg New York.

The friction model is implemented in a \"clean\" way by state events and leads to continuous/discrete systems of equations which have to be solved by appropriate numerical methods. The method is described in:

Otter M., Elmqvist H., and Mattsson S.E. (1999):
Hybrid Modeling in Modelica based on the Synchronous Data Flow Principle. CACSD'99, Aug. 22.-26, Hawaii.

More precise friction models take into account the elasticity of the material when the two elements are \"stuck\", as well as other effects, like hysteresis. This has the advantage that the friction element can be completely described by a differential equation without events. The drawback is that the system becomes stiff (about 10-20 times slower simulation) and that more material constants have to be supplied which requires more sophisticated identification. For more details, see the following references, especially (Armstrong and Canudas de Witt 1996):

Armstrong B. (1991):
Control of Machines with Friction. Kluwer Academic Press, Boston MA.
Armstrong B., and Canudas de Wit C. (1996):
Friction Modeling and Compensation. The Control Handbook, edited by W.S.Levine, CRC Press, pp. 1369-1382.
Canudas de Wit C., Olsson H., Astroem K.J., and Lischinsky P. (1995):
A new model for control of systems with friction. IEEE Transactions on Automatic Control, Vol. 40, No. 3, pp. 419-425.

Optional heatPort

The dissipated energy is transported in form of heat to the optional heatPort connector that can be enabled via parameter \"useHeatPort\". Independently whether the heatPort is or is not enabled, the dissipated power is defined with variable \"lossPower\". If contact occurs at the hard stops, the lossPower is not correctly modelled at this time instant, because the hard stop would introduce a Dirac impulse in the lossPower due to the discontinuously changing kinetic energy of the mass (lossPower is the derivative of the kinetic energy at the time instant of the impact).

", revisions="

Release Notes:

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Polygon( points={{80,-100},{50,-90},{50,-110},{80,-100}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line(points={{-30,-100},{50,-100}}, color={0,0,0}), Rectangle( extent={{-30,30},{35,-35}}, lineColor={0,0,0}, fillPattern=FillPattern.Sphere, fillColor={255,255,255}), Line(points={{-90,0},{-30,0}}, color={0,127,0}), Rectangle( extent={{-70,-45},{74,-60}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Rectangle( extent={{-63,-15},{-55,-45}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Rectangle( extent={{60,-16},{69,-45}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Line(points={{35,0},{90,0}}, color={0,127,0}), Text( extent={{-150,80},{150,40}}, textString="%name", lineColor={0,0,255}), Line(points={{-50,-90},{-30,-70}}, color={0,0,0}), Line(points={{-30,-70},{30,-70}}, color={0,0,0}), Line(points={{-30,-90},{-10,-70}}, color={0,0,0}), Line(points={{-10,-90},{10,-70}}, color={0,0,0}), Line(points={{10,-90},{30,-70}}, color={0,0,0}), Text( extent={{-150,-110},{150,-140}}, lineColor={0,0,0}, textString="m=%m"), Line(visible=useHeatPort, points={{-100,-100},{-100,-40},{3,-40}}, color={191,0,0}, pattern=LinePattern.Dot, smooth=Smooth.None)}), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Polygon( points={{50,-75},{20,-65},{20,-85},{50,-75}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line(points={{-60,-75},{20,-75}}, color={0,0,0}), Rectangle( extent={{-30,26},{35,-9}}, lineColor={0,0,0}, fillPattern=FillPattern.Sphere, fillColor={255,255,255}), Line(points={{-90,0},{-30,0}}, color={0,127,0}), Line(points={{35,0},{90,0}}, color={0,127,0}), Rectangle( extent={{-68,-14},{76,-29}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Rectangle( extent={{-119,43},{-111,17}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Line( points={{-111,43},{-111,50}}, color={0,0,0}, pattern=LinePattern.Solid, thickness=0.25, arrow={Arrow.None,Arrow.None}), Line( points={{-151,49},{-113,49}}, color={0,0,0}, pattern=LinePattern.Solid, thickness=0.25, arrow={Arrow.None,Arrow.None}), Text( extent={{-149,51},{-126,60}}, textString="s min", lineColor={0,0,255}), Polygon( points={{-121,52},{-111,49},{-121,46},{-121,52}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Rectangle( extent={{124,42},{132,17}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Line( points={{124,39},{124,87}}, color={0,0,0}, pattern=LinePattern.Solid, thickness=0.25, arrow={Arrow.None,Arrow.None}), Line( points={{-19,78},{121,78}}, color={0,0,0}, pattern=LinePattern.Solid, thickness=0.25, arrow={Arrow.None,Arrow.None}), Text( extent={{-17,83},{6,92}}, textString="s max", lineColor={0,0,255}), Polygon( points={{114,81},{124,78},{114,75},{114,81}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Line( points={{5,26},{5,63}}, color={0,0,0}, pattern=LinePattern.Solid, thickness=0.25, arrow={Arrow.None,Arrow.None}), Line( points={{-77,58},{-1,58}}, color={0,0,0}, pattern=LinePattern.Solid, thickness=0.25, arrow={Arrow.None,Arrow.None}), Text( extent={{-75,60},{-38,71}}, textString="Position s", lineColor={0,0,255}), Polygon( points={{-5,61},{5,58},{-5,55},{-5,61}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Line(points={{-100,-10},{-100,-60}}, color={0,0,0}), Line(points={{100,-10},{100,-60}}, color={0,0,0}), Polygon( points={{90,-47},{100,-50},{90,-53},{90,-47}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Polygon( points={{-90,-47},{-90,-53},{-100,-50},{-90,-47}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Line(points={{-90,-50},{92,-50}}, color={0,0,0}), Text( extent={{-11,-46},{26,-36}}, textString="Length L", lineColor={0,0,255})})); end MassWithStopAndFriction; model RelativeStates "Definition of relative state variables" extends Translational.Interfaces.PartialTwoFlanges; parameter StateSelect stateSelect=StateSelect.prefer "Priority to use the relative angle and relative speed as states"; SI.Position s_rel(start=0, stateSelect=StateSelect.prefer) "Relative position used as state variable"; SI.Velocity v_rel(start=0, stateSelect=StateSelect.prefer) "Relative velocity used as state variable"; SI.Acceleration a_rel(start=0) "Relative angular acceleration"; equation s_rel = flange_b.s - flange_a.s; v_rel = der(s_rel); a_rel = der(v_rel); flange_a.f = 0; flange_b.f = 0; annotation ( Documentation(info="

Usually, the absolute position and the absolute velocity of Modelica.Mechanics.Translational.Inertia models are used as state variables. In some circumstances, relative quantities are better suited, e.g., because it may be easier to supply initial values. In such cases, model RelativeStates allows the definition of state variables in the following way:

An example is given in the next figure

\"relativeStates2\"

Here, the relative position and the relative velocity between the two masses are used as state variables. Additionally, the simulator selects either the absolute position and absolute velocity of model mass1 or of model mass2 as state variables.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Ellipse( extent={{-40,40},{40,-40}}, lineColor={0,255,255}, fillColor={0,255,255}, fillPattern=FillPattern.Solid), Text( extent={{-40,40},{40,-40}}, textString="S", lineColor={0,0,255}), Line( points={{-92,0},{-42,0}}, color={0,0,0}, pattern=LinePattern.Dot), Line( points={{40,0},{90,0}}, color={0,0,0}, pattern=LinePattern.Dot), Text( extent={{-150,90},{150,50}}, textString="%name", lineColor={0,0,255})}), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Ellipse( extent={{-40,40},{40,-40}}, lineColor={0,255,255}, fillColor={0,255,255}, fillPattern=FillPattern.Solid), Text( extent={{-40,40},{40,-40}}, textString="S", lineColor={0,0,255}), Line( points={{40,0},{90,0}}, color={0,0,0}, pattern=LinePattern.Dash), Line(points={{-100,-10},{-100,-80}}, color={160,160,164}), Line(points={{100,-10},{100,-80}}, color={160,160,164}), Polygon( points={{80,-65},{80,-55},{100,-60},{80,-65}}, lineColor={160,160,164}, fillColor={160,160,164}, fillPattern=FillPattern.Solid), Line(points={{-100,-60},{80,-60}}, color={160,160,164}), Text( extent={{-30,-70},{30,-90}}, textString="w_rel", lineColor={0,0,255}), Line(points={{-76,80},{-5,80}}, color={128,128,128}), Polygon( points={{14,80},{-6,85},{-6,75},{14,80}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Text( extent={{18,87},{86,74}}, lineColor={128,128,128}, textString="moving direction"), Line( points={{-90,0},{-40,0}}, color={0,0,0}, pattern=LinePattern.Dash)})); end RelativeStates; annotation (Icon(coordinateSystem(preserveAspectRatio = true, extent = {{-100,-100},{100,100}}), graphics = { Rectangle( origin = {11.5,31.183}, lineColor = {64,64,64}, fillColor = {255,255,255}, fillPattern = FillPattern.Sphere, extent = {{-67,-66},{44,-6}})}), Documentation(info="

This package contains basic components 1D mechanical translational drive trains.

")); end Components; package Sensors "Sensors for 1-dim. translational mechanical quantities" extends Modelica.Icons.SensorsPackage; model PositionSensor "Ideal sensor to measure the absolute position" extends Translational.Interfaces.PartialAbsoluteSensor; Modelica.Blocks.Interfaces.RealOutput s(unit="m") "Absolute position of flange as output signal" annotation (Placement(transformation(extent={{100,-11}, {120,9}}, rotation=0), iconTransformation(extent={{100, -10},{120,10}}))); equation s = flange.s; annotation ( Documentation(info="

Measures the absolute position s of a flange in an ideal way and provides the result as output signals (to be further processed with blocks of the Modelica.Blocks library).

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={Line(points={{-70,0},{-90,0}}, color={0,0,0}), Text( extent={{80,-28},{114,-62}}, lineColor={0,0,0}, textString="s")})); end PositionSensor; model SpeedSensor "Ideal sensor to measure the absolute velocity" extends Translational.Interfaces.PartialAbsoluteSensor; Modelica.Blocks.Interfaces.RealOutput v(unit="m/s") "Absolute velocity of flange as output signal" annotation (Placement(transformation(extent={{100,-10},{120,10}}, rotation=0))); equation v = der(flange.s); annotation ( Documentation(info="

Measures the absolute velocity v of a flange in an ideal way and provides the result as output signals (to be further processed with blocks of the Modelica.Blocks library).

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={Line(points={{-70,0},{-90,0}}, color={0,0,0}), Text( extent={{80,-28},{111,-61}}, lineColor={0,0,0}, textString="v")})); end SpeedSensor; model AccSensor "Ideal sensor to measure the absolute acceleration" extends Translational.Interfaces.PartialAbsoluteSensor; SI.Velocity v "Absolute velocity of flange"; Modelica.Blocks.Interfaces.RealOutput a(unit="m/s2") "Absolute acceleration of flange as output signal" annotation (Placement(transformation(extent={{100,-10},{120,10}}, rotation=0))); equation v = der(flange.s); a = der(v); annotation ( Documentation(info="

Measures the absolute acceleration a of a flange in an ideal way and provides the result as output signals (to be further processed with blocks of the Modelica.Blocks library).

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={Line(points={{-70,0},{-90,0}}, color={0,0,0}), Text( extent={{80,-28},{115,-60}}, lineColor={0,0,0}, textString="a")})); end AccSensor; model RelPositionSensor "Ideal sensor to measure the relative position" extends Translational.Interfaces.PartialRelativeSensor; Modelica.Blocks.Interfaces.RealOutput s_rel(unit="m") "Distance between two flanges (= flange_b.s - flange_a.s) as output signal" annotation (Placement(transformation(extent={{-10,-10}, {10,10}}, rotation=270, origin={0,-110}))); equation s_rel = flange_b.s - flange_a.s; 0 = flange_a.f; annotation ( Documentation(info="

Measures the relative position s of a flange in an ideal way and provides the result as output signals (to be further processed with blocks of the Modelica.Blocks library).

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-70,0},{-90,0}}, color={0,0,0}), Line(points={{70.4,0},{100,0}}, color={0,0,127}), Text( extent={{8,-68},{42,-102}}, lineColor={0,0,0}, textString="s"), Line(points={{0,-99},{0,-60}}, color={0,0,127})})); end RelPositionSensor; model RelSpeedSensor "Ideal sensor to measure the relative speed" extends Translational.Interfaces.PartialRelativeSensor; SI.Position s_rel "Distance between the two flanges (flange_b.s - flange_a.s)"; Modelica.Blocks.Interfaces.RealOutput v_rel(unit="m/s") "Relative velocity between two flanges (= der(flange_b.s) - der(flange_a.s)) as output signal" annotation (Placement(transformation(extent={{-10,-10}, {10,10}}, rotation=270, origin={0,-110}))); equation s_rel = flange_b.s - flange_a.s; v_rel = der(s_rel); 0 = flange_a.f; annotation ( Documentation(info="

Measures the relative speed v of a flange in an ideal way and provides the result as output signals (to be further processed with blocks of the Modelica.Blocks library).

", revisions= "

Release Notes:

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-70,0},{-90,0}}, color={0,0,0}), Line(points={{70.4,0},{100,0}}, color={0,0,127}), Text( extent={{8,-68},{42,-102}}, lineColor={0,0,0}, textString="v"), Line(points={{0,-100},{0,-61}}, color={0,0,127})})); end RelSpeedSensor; model RelAccSensor "Ideal sensor to measure the relative acceleration" extends Translational.Interfaces.PartialRelativeSensor; SI.Position s_rel "Distance between the two flanges (flange_b.s - flange_a.s)"; SI.Velocity v_rel "Relative velocity between the two flanges (der(flange_b.s) - der(flange_a.s))"; Modelica.Blocks.Interfaces.RealOutput a_rel(unit="m/s2") "Relative acceleration between two flanges (= der(v_rel)) as output signal" annotation (Placement(transformation(extent={{-10,-10}, {10,10}}, rotation=270, origin={0,-110}))); equation s_rel = flange_b.s - flange_a.s; v_rel = der(s_rel); a_rel = der(v_rel); 0 = flange_a.f; annotation ( Documentation(info="

Measures the relative acceleration a of a flange in an ideal way and provides the result as output signals (to be further processed with blocks of the Modelica.Blocks library).

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-70,0},{-90,0}}, color={0,0,0}), Line(points={{70.4,0},{100,0}}, color={0,0,127}), Text( extent={{7,-68},{41,-102}}, lineColor={0,0,0}, textString="a"), Line(points={{0,-99},{0,-60}}, color={0,0,127})})); end RelAccSensor; model ForceSensor "Ideal sensor to measure the force between two flanges" extends Translational.Interfaces.PartialRelativeSensor; Modelica.Blocks.Interfaces.RealOutput f(unit="N") "Force in flange_a and flange_b (f = flange_a.f = -flange_b.f) as output signal" annotation (Placement(transformation( origin={-80,-110}, extent={{10,-10},{-10,10}}, rotation=90))); equation flange_a.s = flange_b.s; flange_a.f = f; annotation ( Documentation(info="

Measures the cut-force between two flanges in an ideal way and provides the result as output signal (to be further processed with blocks of the Modelica.Blocks library).

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Text( extent={{-40,-70},{40,-120}}, lineColor={0,0,0}, textString="f"), Line(points={{-70,0},{-90,0}}, color={0,0,0}), Line(points={{70,0},{90,0}}, color={0,0,0}), Line(points={{-80,-100},{-80,0}}, color={0,0,127})})); end ForceSensor; model PowerSensor "Ideal sensor to measure the power between two flanges (= flange_a.f*der(flange_a.s))" extends Translational.Interfaces.PartialRelativeSensor; Modelica.Blocks.Interfaces.RealOutput power(unit="W") "Power in flange flange_a as output signal" annotation (Placement(transformation( origin={-80,-110}, extent={{10,-10},{-10,10}}, rotation=90))); equation flange_a.s = flange_b.s; power = flange_a.f*der(flange_a.s); annotation ( Documentation(info="

Measures the power between two flanges in an ideal way and provides the result as output signal power (to be further processed with blocks of the Modelica.Blocks library).

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Text( extent={{-75,-79},{67,-119}}, lineColor={0,0,0}, textString="power"), Line(points={{-70,0},{-90,0}}, color={0,0,0}), Line(points={{70,0},{90,0}}, color={0,0,0}), Line(points={{-80,-100},{-80,0}}, color={0,0,127})})); end PowerSensor; model MultiSensor "Ideal sensor to measure the absolute velocity, force and power between two flanges" extends Translational.Interfaces.PartialRelativeSensor; Modelica.Blocks.Interfaces.RealOutput power(unit="W") "Power in flange flange_a as output signal" annotation (Placement(transformation( origin={-60,-110}, extent={{10,-10},{-10,10}}, rotation=90))); Modelica.Blocks.Interfaces.RealOutput f(unit="N") "Force in flange_a and flange_b (f = flange_a.f = -flange_b.f) as output signal" annotation (Placement(transformation( extent={{10,-10},{-10,10}}, rotation=90, origin={0,-110}))); Modelica.Blocks.Interfaces.RealOutput v(unit="m/s") "Absolute velocity of flange as output signal as output signal" annotation (Placement(transformation( extent={{-10,-10},{10,10}}, rotation=-90, origin={60,-110}))); equation flange_a.s = flange_b.s; f = flange_a.f; v = der(flange_a.s); power = f*v; annotation ( Documentation(info="

Measures the absolute velocity of a flange_a, the cut-force and power between two flanges in an ideal way and provides the results as output signals v, f and power, respectively.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Text( extent={{-146,-70},{-56,-100}}, lineColor={0,0,0}, textString="power"), Line(points={{-70,0},{-90,0}}, color={0,0,0}), Line(points={{70,0},{90,0}}, color={0,0,0}), Line(points={{-60,-100},{-60,-60}}, color={0,0,127}), Text( extent={{-28,-71},{52,-101}}, lineColor={0,0,0}, textString="f"), Line(points={{0,-100},{0,-60}}, color={0,0,127}), Line(points={{60,-100},{60,-60}}, color={0,0,127}), Text( extent={{60,-70},{114,-101}}, lineColor={0,0,0}, textString="v")})); end MultiSensor; annotation ( Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{100, 100}}), graphics={ Line(points={{-56,-61},{-56,-81}}, color={0,0,0}), Line(points={{-36,-61},{-36,-81}}, color={0,0,0}), Line(points={{-16,-61},{-16,-81}}, color={0,0,0}), Line(points={{4,-61},{4,-81}}, color={0,0,0}), Line(points={{24,-61},{24,-81}}, color={0,0,0}), Line(points={{44,-61},{44,-81}}, color={0,0,0})}), Documentation(info="

This package contains ideal sensor components that provide the connector variables as signals for further processing with the Modelica.Blocks library.

")); end Sensors; package Sources "Sources to drive 1D translational mechanical components" extends Modelica.Icons.SourcesPackage; model Position "Forced movement of a flange according to a reference position" extends Modelica.Mechanics.Translational.Interfaces.PartialElementaryOneFlangeAndSupport2 ( s(stateSelect=if exact then StateSelect.default else StateSelect.prefer)); parameter Boolean exact=false "true/false exact treatment/filtering the input signal"; parameter SI.Frequency f_crit=50 "if exact=false, critical frequency of filter to filter input signal" annotation(Dialog(enable=not exact)); SI.Velocity v(start=0, stateSelect=if exact then StateSelect.default else StateSelect.prefer) "If exact=false, absolute velocity of flange_b else dummy"; SI.Acceleration a(start=0) "If exact=false, absolute acceleration of flange_b else dummy"; Modelica.Blocks.Interfaces.RealInput s_ref(unit="m") "Reference position of flange as input signal" annotation (Placement( transformation(extent={{-140,-20},{-100,20}}, rotation=0))); protected parameter Modelica.SIunits.AngularFrequency w_crit=2*Modelica.Constants.pi*f_crit "Critical frequency"; constant Real af=1.3617 "s coefficient of Bessel filter"; constant Real bf=0.6180 "s*s coefficient of Bessel filter"; initial equation if not exact then s = s_ref; end if; equation if exact then s = s_ref; v = 0; a = 0; else // Filter: a = s_ref*S^2/(1 + (af/w_crit)*S + (bf/w_crit^2)*S^2) v = der(s); a = der(v); a = ((s_ref - s)*w_crit - af*v)*(w_crit/bf); end if; annotation ( Documentation(info="

The input signal s_ref defines the reference position in [m]. Flange flange_b is forced to move relative to the support connector according to this reference motion. According to parameter exact (default = false), this is done in the following way:

  1. exact=true
    The reference position is treated exactly. This is only possible, if the input signal is defined by an analytical function which can be differentiated at least twice. If this prerequisite is fulfilled, the Modelica translator will differentiate the input signal twice in order to compute the reference acceleration of the flange.
  2. exact=false
    The reference position is filtered and the second derivative of the filtered curve is used to compute the reference acceleration of the flange. This second derivative is not computed by numerical differentiation but by an appropriate realization of the filter. For filtering, a second order Bessel filter is used. The critical frequency (also called cut-off frequency) of the filter is defined via parameter f_crit in [Hz]. This value should be selected in such a way that it is higher as the essential low frequencies in the signal.

The input signal can be provided from one of the signal generator blocks of the block library Modelica.Blocks.Sources.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Text( extent={{-56,-36},{-178,-66}}, lineColor={0,0,0}, textString="s_ref"), Rectangle( extent={{-100,20},{100,-20}}, lineColor={0,127,0}, fillColor={215,215,215}, fillPattern=FillPattern.Solid), Text( extent={{150,60},{-150,100}}, textString="%name", lineColor={0,0,255}), Line(points={{0,52},{0,32}}, color={0,0,0}), Line(points={{-29,32},{30,32}}, color={0,0,0}), Line(points={{-30,-32},{30,-32}}, color={0,0,0}), Line(points={{0,-32},{0,-100}}, color={0,0,0}), Line(points={{30,-42},{20,-52}}, color={0,0,0}), Line(points={{30,-32},{10,-52}}, color={0,0,0}), Line(points={{20,-32},{0,-52}}, color={0,0,0}), Line(points={{10,-32},{-10,-52}}, color={0,0,0}), Line(points={{0,-32},{-20,-52}}, color={0,0,0}), Line(points={{-10,-32},{-30,-52}}, color={0,0,0}), Line(points={{-20,-32},{-30,-42}}, color={0,0,0}), Text( extent={{144,-30},{30,-60}}, lineColor={0,0,0}, textString="exact="), Text( extent={{134,-68},{22,-96}}, lineColor={0,0,0}, textString="%exact")})); end Position; model Speed "Forced movement of a flange according to a reference speed" extends Modelica.Mechanics.Translational.Interfaces.PartialElementaryOneFlangeAndSupport2 ( s(start=0, fixed=true, stateSelect=StateSelect.prefer)); parameter Boolean exact=false "true/false exact treatment/filtering the input signal"; parameter SI.Frequency f_crit=50 "if exact=false, critical frequency of filter to filter input signal" annotation(Dialog(enable=not exact)); SI.Velocity v(stateSelect=if exact then StateSelect.default else StateSelect.prefer) "Absolute velocity of flange_b"; SI.Acceleration a "If exact=false, absolute acceleration of flange_b else dummy"; Modelica.Blocks.Interfaces.RealInput v_ref(unit="m/s") "Reference speed of flange as input signal" annotation (Placement( transformation(extent={{-140,-20},{-100,20}}, rotation=0))); protected parameter Modelica.SIunits.AngularFrequency w_crit=2*Modelica.Constants.pi*f_crit "Critical frequency"; initial equation if not exact then v = v_ref; end if; equation v = der(s); if exact then v = v_ref; a = 0; else // Filter: a = v_ref/(1 + (1/w_crit)*s) a = der(v); a = (v_ref - v)*w_crit; end if; annotation ( Documentation(info="

The input signal v_ref defines the reference speed in [m/s]. Flange flange_b is forced to move relative to the support connector according to this reference motion. According to parameter exact (default = false), this is done in the following way:

  1. exact=true
    The reference speed is treated exactly. This is only possible, if the input signal is defined by an analytical function which can be differentiated at least once. If this prerequisite is fulfilled, the Modelica translator will differentiate the input signal once in order to compute the reference acceleration of the flange.
  2. exact=false
    The reference speed is filtered and the first derivative of the filtered curve is used to compute the reference acceleration of the flange. This first derivative is not computed by numerical differentiation but by an appropriate realization of the filter. For filtering, a first order filter is used. The critical frequency (also called cut-off frequency) of the filter is defined via parameter f_crit in [Hz]. This value should be selected in such a way that it is higher as the essential low frequencies in the signal.

The input signal can be provided from one of the signal generator blocks of the block library Modelica.Blocks.Sources.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Text( extent={{-54,-36},{-174,-68}}, lineColor={0,0,0}, textString="v_ref"), Line(points={{-30,-32},{30,-32}}, color={0,0,0}), Line(points={{0,-32},{0,-100}}, color={0,0,0}), Line(points={{30,-42},{20,-52}}, color={0,0,0}), Line(points={{30,-32},{10,-52}}, color={0,0,0}), Line(points={{20,-32},{0,-52}}, color={0,0,0}), Line(points={{10,-32},{-10,-52}}, color={0,0,0}), Line(points={{0,-32},{-20,-52}}, color={0,0,0}), Line(points={{-10,-32},{-30,-52}}, color={0,0,0}), Line(points={{-20,-32},{-30,-42}}, color={0,0,0}), Rectangle( extent={{-100,20},{100,-20}}, lineColor={0,127,0}, fillColor={215,215,215}, fillPattern=FillPattern.Solid), Line(points={{-29,32},{30,32}}, color={0,0,0}), Line(points={{0,52},{0,32}}, color={0,0,0}), Text( extent={{150,60},{-150,100}}, textString="%name", lineColor={0,0,255}), Text( extent={{146,-38},{32,-64}}, lineColor={0,0,0}, textString="exact="), Text( extent={{140,-76},{22,-102}}, lineColor={0,0,0}, textString="%exact")})); end Speed; model Accelerate "Forced movement of a flange according to an acceleration signal" extends Modelica.Mechanics.Translational.Interfaces.PartialElementaryOneFlangeAndSupport2 (s(start=0, fixed=true, stateSelect=StateSelect.prefer)); SI.Velocity v(start=0, fixed=true, stateSelect=StateSelect.prefer) "Absolute velocity of flange_b"; SI.Acceleration a "Absolute acceleration of flange_b"; Modelica.Blocks.Interfaces.RealInput a_ref(unit="m/s2") "Absolute acceleration of flange as input signal" annotation (Placement(transformation(extent={{-140,-20},{-100,20}}, rotation=0))); equation v = der(s); a = der(v); a = a_ref; annotation ( Documentation(info="

The input signal a in [m/s2] moves the 1D translational flange connector flange_b with a predefined acceleration, i.e., the flange is forced to move relative to the support connector with this acceleration. The velocity and the position of the flange are also predefined and are determined by integration of the acceleration.

The acceleration \"a(t)\" can be provided from one of the signal generator blocks of the block library Modelica.Blocks.Source.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Text( extent={{-56,-40},{-166,-68}}, lineColor={0,0,0}, textString="a_ref"), Line(points={{-30,-32},{30,-32}}, color={0,0,0}), Line(points={{0,-32},{0,-100}}, color={0,0,0}), Line(points={{30,-42},{20,-52}}, color={0,0,0}), Line(points={{30,-32},{10,-52}}, color={0,0,0}), Line(points={{20,-32},{0,-52}}, color={0,0,0}), Line(points={{10,-32},{-10,-52}}, color={0,0,0}), Line(points={{0,-32},{-20,-52}}, color={0,0,0}), Line(points={{-10,-32},{-30,-52}}, color={0,0,0}), Line(points={{-20,-32},{-30,-42}}, color={0,0,0}), Rectangle( extent={{-100,20},{100,-20}}, lineColor={0,127,0}, fillColor={215,215,215}, fillPattern=FillPattern.Solid), Line(points={{-29,32},{30,32}}, color={0,0,0}), Line(points={{0,52},{0,32}}, color={0,0,0}), Text( extent={{150,60},{-150,100}}, textString="%name", lineColor={0,0,255})})); end Accelerate; model Move "Forced movement of a flange according to a position, velocity and acceleration signal" extends Modelica.Mechanics.Translational.Interfaces.PartialElementaryOneFlangeAndSupport2; Modelica.Blocks.Interfaces.RealInput u[3] "Position, velocity and acceleration of flange as input signals" annotation (Placement(transformation(extent={{-140,-20},{-100,20}}, rotation=0))); protected function position extends Modelica.Icons.Function; input Real q_qd_qdd[3] "Required values for position, speed, acceleration"; input Real dummy "Just to have one input signal that should be differentiated to avoid possible problems in the Modelica tool (is not used)"; output Real q; algorithm q :=q_qd_qdd[1]; annotation (derivative(noDerivative=q_qd_qdd) = position_der, InlineAfterIndexReduction=true); end position; function position_der extends Modelica.Icons.Function; input Real q_qd_qdd[3] "Required values for position, speed, acceleration"; input Real dummy "Just to have one input signal that should be differentiated to avoid possible problems in the Modelica tool (is not used)"; input Real dummy_der; output Real qd; algorithm qd :=q_qd_qdd[2]; annotation (derivative(noDerivative=q_qd_qdd, order=2) = position_der2, InlineAfterIndexReduction=true); end position_der; function position_der2 extends Modelica.Icons.Function; input Real q_qd_qdd[3] "Required values for position, speed, acceleration"; input Real dummy "Just to have one input signal that should be differentiated to avoid possible problems in the Modelica tool (is not used)"; input Real dummy_der; input Real dummy_der2; output Real qdd; algorithm qdd :=q_qd_qdd[3]; end position_der2; equation s = position(u,time); annotation ( Documentation(info="

Flange flange_b is forced to move relative to the support connector with a predefined motion according to the input signals: 

    u[1]: position of flange
    u[2]: velocity of flange
    u[3]: acceleration of flange

The user has to guarantee that the input signals are consistent to each other, i.e., that u[2] is the derivative of u[1] and that u[3] is the derivative of u. There are, however, also applications where by purpose these conditions do not hold. For example, if only the position dependent terms of a mechanical system shall be calculated, one may provide position = position(t) and set the velocity and the acceleration to zero.

The input signals can be provided from one of the signal generator blocks of the block library Modelica.Blocks.Sources.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Text( extent={{-192,-38},{-32,-70}}, lineColor={0,0,0}, textString="s,v,a"), Line(points={{-30,-32},{30,-32}}, color={0,0,0}), Line(points={{0,-32},{0,-100}}, color={0,0,0}), Line(points={{30,-42},{20,-52}}, color={0,0,0}), Line(points={{30,-32},{10,-52}}, color={0,0,0}), Line(points={{20,-32},{0,-52}}, color={0,0,0}), Line(points={{10,-32},{-10,-52}}, color={0,0,0}), Line(points={{0,-32},{-20,-52}}, color={0,0,0}), Line(points={{-10,-32},{-30,-52}}, color={0,0,0}), Line(points={{-20,-32},{-30,-42}}, color={0,0,0}), Rectangle( extent={{-100,20},{100,-20}}, lineColor={0,127,0}, fillColor={215,215,215}, fillPattern=FillPattern.Solid), Line(points={{0,52},{0,32}}, color={0,0,0}), Line(points={{-29,32},{30,32}}, color={0,0,0}), Text( extent={{150,60},{-150,100}}, textString="%name", lineColor={0,0,255})})); end Move; model Force "External force acting on a drive train element as input signal" extends Modelica.Mechanics.Translational.Interfaces.PartialElementaryOneFlangeAndSupport2; Modelica.Blocks.Interfaces.RealInput f(unit="N") "Driving force as input signal" annotation (Placement(transformation( extent={{-140,-20},{-100,20}}, rotation=0))); equation flange.f = -f; annotation ( Documentation(info="

The input signal \"f\" in [N] characterizes an external force which acts (with positive sign) at a flange, i.e., the component connected to the flange is driven by force f.

Input signal f can be provided from one of the signal generator blocks of Modelica.Blocks.Source.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Polygon( points={{-100,10},{20,10},{20,41},{90,0},{20,-41},{20,-10},{-100, -10},{-100,10}}, lineColor={0,127,0}, fillColor={215,215,215}, fillPattern=FillPattern.Solid), Text( extent={{-150,-32},{-80,-62}}, lineColor={0,0,0}, textString="f"), Text( extent={{-150,90},{150,50}}, textString="%name", lineColor={0,0,255}), Line(points={{-30,-60},{30,-60}}, color={0,0,0}), Line(points={{0,-60},{0,-101}}, color={0,0,0}), Line(points={{-30,-80},{-10,-60}}, color={0,0,0}), Line(points={{-10,-80},{10,-60}}, color={0,0,0}), Line(points={{10,-80},{30,-60}}, color={0,0,0}), Polygon( points={{-61,-50},{-30,-40},{-30,-60},{-61,-50}}, lineColor={0,0,0}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line(points={{-31,-50},{50,-50}}, color={0,0,0}), Line(points={{-50,-80},{-30,-60}}, color={0,0,0})})); end Force; model Force2 "Input signal acting as torque on two flanges" extends Translational.Interfaces.PartialTwoFlanges; Modelica.Blocks.Interfaces.RealInput f(unit="N") "Driving force as input signal" annotation (Placement(transformation( extent={{-20,-20},{20,20}}, rotation=270, origin={0,60}), iconTransformation( extent={{-20,-20},{20,20}}, rotation=270, origin={0,40}))); equation flange_a.f = f; flange_b.f = -f; annotation ( Documentation(info="

The input signal \"f\" in [N] characterizes an external force which acts (with positive sign) at both flanges, i.e., the components connected to these flanges are driven by force f.

Input signal s can be provided from one of the signal generator blocks of Modelica.Blocks.Source.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Text( extent={{-150,-40},{150,-80}}, textString="%name", lineColor={0,0,255}), Polygon( points={{90,0},{60,-30},{60,-10},{10,-10},{10,10},{60,10},{60,31}, {90,0}}, lineColor={0,127,0}, smooth=Smooth.None, fillColor={215,215,215}, fillPattern=FillPattern.Solid), Polygon( points={{-90,0},{-60,30},{-60,10},{-10,10},{-10,-10},{-60,-10},{-60, -30},{-90,0}}, lineColor={0,127,0}, smooth=Smooth.None, fillColor={215,215,215}, fillPattern=FillPattern.Solid)})); end Force2; model LinearSpeedDependentForce "Linear dependency of force versus speed" extends Modelica.Mechanics.Translational.Interfaces.PartialForce; parameter Modelica.SIunits.Force f_nominal "Nominal force (if negative, force is acting as load)"; parameter Boolean ForceDirection=true "Same direction of force in both directions of movement"; parameter Modelica.SIunits.Velocity v_nominal(min=Modelica.Constants.eps) "Nominal speed"; Modelica.SIunits.Velocity v "Velocity of flange with respect to support (= der(s))"; equation v = der(s); if ForceDirection then f = -f_nominal*abs(v/v_nominal); else f = -f_nominal*(v/v_nominal); end if; annotation (Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100, -100},{100,100}}), graphics={Line(points={{-100,-100},{100,100}}, color={0,0,255})}), Documentation(info="

Model of force, linearly dependent on velocity of flange.
Parameter ForceDirection chooses whether direction of force is the same in both directions of movement or not.

")); end LinearSpeedDependentForce; model QuadraticSpeedDependentForce "Quadratic dependency of force versus speed" extends Modelica.Mechanics.Translational.Interfaces.PartialForce; parameter Modelica.SIunits.Force f_nominal "Nominal force (if negative, force is acting as load)"; parameter Boolean ForceDirection=true "Same direction of force in both directions of movement"; parameter Modelica.SIunits.Velocity v_nominal(min=Modelica.Constants.eps) "Nominal speed"; Modelica.SIunits.Velocity v "Velocity of flange with respect to support (= der(s))"; equation v = der(s); if ForceDirection then f = -f_nominal*(v/v_nominal)^2; else f = -f_nominal*smooth(1, if v >= 0 then (v/v_nominal)^2 else -(v/v_nominal)^2); end if; annotation (Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-100,-100},{-80,-98},{-60,-92},{-40,-82},{-20,-68},{0,-50},{20,-28},{40,-2},{60,28},{80,62},{100,100}}, color={0,0,127}, smooth=Smooth.Bezier)}),Documentation(info="

Model of force, quadratic dependent on velocity of flange.
Parameter ForceDirection chooses whether direction of force is the same in both directions of movement or not.

")); end QuadraticSpeedDependentForce; model ConstantForce "Constant force, not dependent on speed" extends Modelica.Mechanics.Translational.Interfaces.PartialForce; parameter Modelica.SIunits.Force f_constant "Nominal force (if negative, force is acting as load)"; equation f = -f_constant; annotation (Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100, -100},{100,100}}), graphics={Line(points={{-100,0},{98,0}}, color={0,0,255}), Text( extent={{-118,58},{126,34}}, lineColor={0,0,0}, textString="%f_constant")}), Documentation(info="

Model of constant force, not dependent on velocity of flange.
Positive force acts accelerating.

")); end ConstantForce; model ConstantSpeed "Constant speed, not dependent on force" extends Modelica.Mechanics.Translational.Interfaces.PartialForce; parameter Modelica.SIunits.Velocity v_fixed "Fixed speed (if negative, force is acting as load)"; Modelica.SIunits.Velocity v "Velocity of flange with respect to support (= der(s))"; equation v = der(s); v = v_fixed; annotation (Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100, -100},{100,100}}), graphics={Line(points={{0,-100},{0,100}}, color={0,0,255}), Text( extent={{-120,60},{124,36}}, lineColor={0,0,0}, textString="%v_fixed")}), Documentation(info="

Model of fixed velocity of flange, not dependent on force.

")); end ConstantSpeed; model ForceStep "Constant force, not dependent on speed" extends Modelica.Mechanics.Translational.Interfaces.PartialForce; parameter Modelica.SIunits.Force stepForce(start=1) "Height of force step (if negative, force is acting as load)"; parameter Modelica.SIunits.Force offsetForce(start=0) "Offset of force"; parameter Modelica.SIunits.Time startTime=0 "Force = offset for time < startTime"; equation f = -offsetForce - (if time < startTime then 0 else stepForce); annotation (Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100, -100},{100,100}}), graphics={Line(points={{-80,-60},{0,-60},{0, 60},{80,60}}, color={0,0,255}), Text( extent={{0,-40},{100,-60}}, lineColor={0,0,0}, textString="time")}), Documentation(info="

Model of a force step at time .
Positive force acts accelerating.

")); end ForceStep; annotation ( Documentation(info="

This package contains ideal sources to drive 1D mechanical translational drive trains.

")); end Sources; package Interfaces "Interfaces for 1-dim. translational mechanical components" extends Modelica.Icons.InterfacesPackage; connector Flange_a "(left) 1D translational flange (flange axis directed INTO cut plane, e. g. from left to right)" SI.Position s "Absolute position of flange"; flow SI.Force f "Cut force directed into flange"; annotation(defaultComponentName = "flange_a", Documentation(info="

This is a flange for 1D translational mechanical systems. In the cut plane of the flange a unit vector n, called flange axis, is defined which is directed INTO the cut plane, i. e. from left to right. All vectors in the cut plane are resolved with respect to this unit vector. E.g. force f characterizes a vector which is directed in the direction of n with value equal to f. When this flange is connected to other 1D translational flanges, this means that the axes vectors of the connected flanges are identical.

The following variables are transported through this connector: 

  s: Absolute position of the flange in [m]. A positive translation
     means that the flange is translated along the flange axis.
  f: Cut-force in direction of the flange axis in [N].
"), Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{ 100,100}}), graphics={Rectangle( extent={{-100,-100},{100,100}}, lineColor={0,127,0}, fillColor={0,127,0}, fillPattern=FillPattern.Solid)}), Diagram(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100}, {100,100}}), graphics={Rectangle( extent={{-40,-40},{40,40}}, lineColor={0,127,0}, fillColor={0,127,0}, fillPattern=FillPattern.Solid), Text( extent={{-160,110},{40,50}}, lineColor={0,127,0}, textString="%name")})); end Flange_a; connector Flange_b "(right) 1D translational flange (flange axis directed OUT OF cut plane)" SI.Position s "Absolute position of flange"; flow SI.Force f "Cut force directed into flange"; annotation(defaultComponentName = "flange_b", Documentation(info="

This is a flange for 1D translational mechanical systems. In the cut plane of the flange a unit vector n, called flange axis, is defined which is directed OUT OF the cut plane. All vectors in the cut plane are resolved with respect to this unit vector. E.g. force f characterizes a vector which is directed in the direction of n with value equal to f. When this flange is connected to other 1D translational flanges, this means that the axes vectors of the connected flanges are identical.

The following variables are transported through this connector: 

  s: Absolute position of the flange in [m]. A positive translation
     means that the flange is translated along the flange axis.
  f: Cut-force in direction of the flange axis in [N].
"), Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Rectangle( extent={{-100,-100},{100,100}}, lineColor={0,127,0}, fillColor={255,255,255}, fillPattern=FillPattern.Solid)}), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={Rectangle( extent={{-40,-40},{40,40}}, lineColor={0,127,0}, fillColor={255,255,255}, fillPattern=FillPattern.Solid), Text( extent={{-40,110},{160,50}}, lineColor={0,127,0}, textString="%name")})); end Flange_b; connector Support "Support/housing 1D translational flange" SI.Position s "Absolute position of flange"; flow SI.Force f "Cut force directed into flange"; annotation (Diagram(coordinateSystem(preserveAspectRatio=true, extent={{-100, -100},{100,100}}), graphics={ Rectangle( extent={{-60,60},{60,-60}}, fillColor={175,175,175}, fillPattern=FillPattern.Solid, pattern=LinePattern.None), Text( extent={{-160,110},{40,50}}, lineColor={0,127,0}, textString="%name"), Rectangle( extent={{-40,-40},{40,40}}, lineColor={0,127,0}, fillColor={0,127,0}, fillPattern=FillPattern.Solid)}), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={Rectangle( extent={{-150,150},{150,-150}}, fillColor={175,175,175}, fillPattern=FillPattern.Solid, pattern=LinePattern.None), Rectangle( extent={{-90,-90},{90,90}}, lineColor={0,127,0}, fillColor={0,127,0}, fillPattern=FillPattern.Solid)}), Documentation(info="

This is a connector for 1-dim. rotational mechanical systems and models the support or housing of a shaft. The following variables are defined in this connector:

s

Absolute position of the support/housing in [m]

f

Reaction force in the support/housing in [N]


The support connector is usually defined as conditional connector. It is most convenient to utilize it

")); end Support; model InternalSupport "Adapter model to utilize conditional support connector" input SI.Force f "External support force (must be computed via force balance in model where InternalSupport is used; = flange.f)"; SI.Position s "External support position (= flange.s)"; Flange_a flange "Internal support flange (must be connected to the conditional support connector for useSupport=true and to conditional fixed model for useSupport=false)" annotation (Placement(transformation(extent={{-10,-10},{10,10}}))); equation flange.f = f; flange.s = s; annotation ( Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={Text( extent={{-200,80},{200,40}}, lineColor={0,0,255}, textString="%name"), Rectangle( extent={{-20,20},{20,-20}}, lineColor={0,127,0}, fillColor={175,175,175}, fillPattern=FillPattern.Solid)}), Documentation(info="

This is an adapter model to utilize a conditional support connector in an elementary component, i.e., where the component equations are defined textually:

Variable f is defined as input and must be provided when using this component as a modifier (computed via a force balance in the model where InternalSupport is used). Usually, model InternalSupport is utilized via the partial models:

PartialElementaryOneFlangeAndSupport,
PartialElementaryTwoFlangesAndSupport,
PartialElementaryRotationalToTranslational.

Note, the support position can always be accessed as internalSupport.s, and the support force can always be accessed as internalSupport.f.

")); end InternalSupport; partial model PartialTwoFlanges "Component with two translational 1D flanges" Flange_a flange_a "(left) driving flange (flange axis directed in to cut plane, e. g. from left to right)" annotation (Placement(transformation(extent={{-110,-10},{-90,10}}, rotation=0))); Flange_b flange_b "(right) driven flange (flange axis directed out of cut plane)" annotation (Placement(transformation(extent={{90,-10},{110,10}}, rotation=0))); annotation ( Documentation(info="

This is a 1D translational component with two flanges. It is used e.g., to built up parts of a drive train consisting of several base components.

")); end PartialTwoFlanges; partial model PartialOneFlangeAndSupport "Partial model for a component with one translational 1-dim. shaft flange and a support used for graphical modeling, i.e., the model is build up by drag-and-drop from elementary components" parameter Boolean useSupport=false "= true, if support flange enabled, otherwise implicitly grounded" annotation(Evaluate=true, HideResult=true, choices(checkBox=true)); Flange_b flange "Flange of component" annotation (Placement(transformation(extent={{90,-10},{110,10}}, rotation=0))); Support support if useSupport "Support/housing of component" annotation (Placement(transformation(extent={{-10,-110},{10,-90}}))); protected Support internalSupport "Internal support/housing of component (either connected to support, if useSupport=true, or connected to fixed, if useSupport=false)" annotation (Placement(transformation(extent={{-3,-83},{3,-77}}))); Components.Fixed fixed if not useSupport "Fixed support/housing, if not useSupport" annotation (Placement(transformation(extent={{10,-94},{30,-74}}))); equation connect(fixed.flange, internalSupport) annotation (Line( points={{20,-84},{20,-80},{0,-80}}, color={0,127,0}, smooth=Smooth.None)); connect(internalSupport, support) annotation (Line( points={{0,-80},{0,-100}}, pattern=LinePattern.None, smooth=Smooth.None)); annotation ( Documentation(info="

This is a 1-dim. translational component with one flange and a support/housing. It is used e.g., to build up parts of a drive train graphically consisting of several components.

If useSupport=true, the support connector is conditionally enabled and needs to be connected.
If useSupport=false, the support connector is conditionally disabled and instead the component is internally fixed to ground.

"), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={Text( extent={{-38,-98},{-6,-96}}, lineColor={95,95,95}, textString="(if useSupport)"), Text( extent={{21,-95},{61,-96}}, lineColor={95,95,95}, textString="(if not useSupport)")}), Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{ 100,100}}), graphics={ Line( visible=not useSupport, points={{-50,-120},{-30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-120},{-10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-10,-120},{10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{10,-120},{30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-100},{30,-100}}, color={0,0,0})})); end PartialOneFlangeAndSupport; partial model PartialTwoFlangesAndSupport "Partial model for a component with two translational 1-dim. shaft flanges and a support used for graphical modeling, i.e., the model is build up by drag-and-drop from elementary components" parameter Boolean useSupport=false "= true, if support flange enabled, otherwise implicitly grounded" annotation(Evaluate=true, HideResult=true, choices(checkBox=true)); Flange_a flange_a "Flange of left end" annotation (Placement(transformation(extent={{-110,-10}, {-90,10}}, rotation=0))); Flange_b flange_b "Flange of right end" annotation (Placement(transformation(extent={{90,-10},{110,10}}, rotation=0))); Support support if useSupport "Support/housing of component" annotation (Placement(transformation(extent={{-10,-110},{10,-90}}))); protected Support internalSupport "Internal support/housing of component (either connected to support, if useSupport=true, or connected to fixed, if useSupport=false)" annotation (Placement(transformation(extent={{-3,-83},{3,-77}}))); Components.Fixed fixed if not useSupport "Fixed support/housing, if not useSupport" annotation (Placement(transformation(extent={{10,-97},{30,-77}}))); equation connect(fixed.flange, internalSupport) annotation (Line( points={{20,-87},{20,-80},{0,-80}}, color={0,127,0}, smooth=Smooth.None)); connect(internalSupport, support) annotation (Line( points={{0,-80},{0,-100}}, pattern=LinePattern.None, smooth=Smooth.None)); annotation ( Documentation(info="

This is a 1-dim. translational component with two flanges and a support/housing. It is used e.g., to build up parts of a drive train graphically consisting of several components.

If useSupport=true, the support connector is conditionally enabled and needs to be connected.
If useSupport=false, the support connector is conditionally disabled and instead the component is internally fixed to ground.

"), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={Text( extent={{-38,-98},{-6,-96}}, lineColor={95,95,95}, textString="(if useSupport)"), Text( extent={{24,-97},{64,-98}}, lineColor={95,95,95}, textString="(if not useSupport)")}), Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{ 100,100}}), graphics={ Line( visible=not useSupport, points={{-50,-120},{-30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-120},{-10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-10,-120},{10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{10,-120},{30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-100},{30,-100}}, color={0,0,0})})); end PartialTwoFlangesAndSupport; partial model PartialRigid "Rigid connection of two translational 1D flanges" SI.Position s "Absolute position of center of component (s = flange_a.s + L/2 = flange_b.s - L/2)"; parameter SI.Length L(start=0) "Length of component, from left flange to right flange (= flange_b.s - flange_a.s)"; Flange_a flange_a "Left flange of translational component" annotation (Placement(transformation(extent={{-110,-10},{-90,10}}, rotation=0))); Flange_b flange_b "Right flange of translational component" annotation (Placement(transformation(extent={{90,-10},{110,10}}, rotation=0))); equation flange_a.s = s - L/2; flange_b.s = s + L/2; annotation ( Documentation(info="

This is a 1-dim. translational component with two rigidly connected flanges. The fixed distance between the left and the right flange is defined by parameter \"L\". The forces at the right and left flange can be different. It is used e.g., to built up sliding masses.

")); end PartialRigid; partial model PartialCompliant "Compliant connection of two translational 1D flanges" Flange_a flange_a "Left flange of compliant 1-dim. translational component" annotation (Placement(transformation(extent={{-110,-10},{-90,10}}, rotation=0))); Flange_b flange_b "Right flange of compliant 1-dim. translational component" annotation (Placement(transformation(extent={{90,-10},{110,10}}, rotation=0))); SI.Position s_rel(start=0) "Relative distance (= flange_b.s - flange_a.s)"; SI.Force f "Force between flanges (positive in direction of flange axis R)"; equation s_rel = flange_b.s - flange_a.s; flange_b.f = f; flange_a.f = -f; annotation ( Documentation(info="

This is a 1D translational component with a compliant connection of two translational 1D flanges where inertial effects between the two flanges are not included. The absolute value of the force at the left and the right flange is the same. It is used to built up springs, dampers etc.

"), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={Polygon( points={{50,-90},{20,-80},{20,-100},{50,-90}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line(points={{-60,-90},{20,-90}}, color={0,0,0})})); end PartialCompliant; partial model PartialCompliantWithRelativeStates "Base model for the compliant connection of two translational 1-dim. shaft flanges where the relative position and relative velocities are used as states" parameter StateSelect stateSelect=StateSelect.prefer "Priority to use phi_rel and w_rel as states" annotation(HideResult=true, Dialog(tab="Advanced")); parameter SI.Distance s_nominal=1e-4 "Nominal value of s_rel (used for scaling)" annotation(Dialog(tab="Advanced")); SI.Position s_rel(start=0, stateSelect=stateSelect, nominal=s_nominal) "Relative distance (= flange_b.s - flange_a.s)"; SI.Velocity v_rel(start=0, stateSelect=stateSelect) "Relative velocity (= der(s_rel))"; SI.Force f "Forces between flanges (= flange_b.f)"; Translational.Interfaces.Flange_a flange_a "Left flange of compliant 1-dim. translational component" annotation (Placement(transformation(extent={{-110,-10},{-90,10}}, rotation=0))); Translational.Interfaces.Flange_b flange_b "Right flange of compliant 1-dim. translational component" annotation (Placement(transformation(extent={{90,-10},{110,10}}, rotation=0))); equation s_rel = flange_b.s - flange_a.s; v_rel = der(s_rel); flange_b.f = f; flange_a.f = -f; annotation ( Documentation(info="

This is a 1-dim. translational component with a compliant connection of two translational 1-dim. flanges where inertial effects between the two flanges are neglected. The basic assumption is that the cut-forces of the two flanges sum-up to zero, i.e., they have the same absolute value but opposite sign: flange_a.f + flange_b.f = 0. This base class is used to built up force elements such as springs, dampers, friction.

The difference to base class \"PartialCompliant\" is that the relative distance and the relative velocity are defined as preferred states. The reason is that for a large class of drive trains, the absolute position is quickly increasing during operation. Numerically, it is better to use relative distances between drive train components because they remain in a limited size. For this reason, StateSelect.prefer is set for the relative distance of this component.

In order to improve the numerics, a nominal value for the relative distance should be set, since drive train distances are in a small order and then step size control of the integrator is practically switched off for such a variable. A default nominal value of s_nominal = 1e-4 is defined. This nominal value might also be computed from other values, such as \"s_nominal = f_nominal / c\" for a spring, if f_nominal and c have more meaningful values for the user.

")); end PartialCompliantWithRelativeStates; partial model PartialElementaryOneFlangeAndSupport "Obsolete partial model. Use PartialElementaryOneFlangeAndSupport2." extends Modelica.Icons.ObsoleteModel; parameter Boolean useSupport=false "= true, if support flange enabled, otherwise implicitly grounded" annotation(Evaluate=true, HideResult=true, choices(checkBox=true)); Modelica.SIunits.Length s "Distance between flange and support (= flange.s - support.s)"; Flange_b flange "Flange of component" annotation (Placement(transformation(extent={{90,-10},{110,10}}, rotation=0))); protected InternalSupport internalSupport(f=-flange.f) "Internal support/housing of component as a model with connector flange (flange is either connected to support, if useSupport=true, or connected to fixed, if useSupport=false)" annotation (Placement(transformation(extent={{-10,-90},{10,-70}}))); Components.Fixed fixed if not useSupport "Fixed support/housing, if not useSupport" annotation (Placement(transformation(extent={{10,-97},{30,-77}}))); public Support support if useSupport "Support/housing of component" annotation (Placement(transformation(extent={{-10,-110},{10,-90}}))); equation s = flange.s - internalSupport.s; connect(internalSupport.flange, support) annotation (Line( points={{0,-80},{0,-100}}, color={0,127,0}, smooth=Smooth.None)); connect(fixed.flange, internalSupport.flange) annotation (Line( points={{20,-87},{20,-80},{0,-80}}, color={0,127,0}, smooth=Smooth.None)); annotation ( Documentation(info="

This is a 1-dim. translational component with one flange and a support/housing. It is used to build up elementary components of a drive train with equations in the text layer.

If useSupport=true, the support connector is conditionally enabled and needs to be connected.
If useSupport=false, the support connector is conditionally disabled and instead the component is internally fixed to ground.

"), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={Text( extent={{-38,-98},{-6,-96}}, lineColor={95,95,95}, textString="(if useSupport)"), Text( extent={{24,-97},{64,-98}}, lineColor={95,95,95}, textString="(if not useSupport)")}), Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{ 100,100}}), graphics={ Line( visible=not useSupport, points={{-50,-120},{-30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-120},{-10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-10,-120},{10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{10,-120},{30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-100},{30,-100}}, color={0,0,0})})); end PartialElementaryOneFlangeAndSupport; partial model PartialElementaryOneFlangeAndSupport2 "Partial model for a component with one translational 1-dim. shaft flange and a support used for textual modeling, i.e., for elementary models" parameter Boolean useSupport=false "= true, if support flange enabled, otherwise implicitly grounded" annotation(Evaluate=true, HideResult=true, choices(checkBox=true)); Modelica.SIunits.Length s "Distance between flange and support (= flange.s - support.s)"; Flange_b flange "Flange of component" annotation (Placement(transformation(extent={{90,-10},{110,10}}, rotation=0))); Support support(s=s_support, f=-flange.f) if useSupport "Support/housing of component" annotation (Placement(transformation(extent={{-10,-110},{10,-90}}))); protected Modelica.SIunits.Length s_support "Absolute position of support flange"; equation s = flange.s - s_support; if not useSupport then s_support = 0; end if; annotation ( Documentation(info="

This is a 1-dim. translational component with one flange and a support/housing. It is used to build up elementary components of a drive train with equations in the text layer.

If useSupport=true, the support connector is conditionally enabled and needs to be connected.
If useSupport=false, the support connector is conditionally disabled and instead the component is internally fixed to ground.

"), Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{ 100,100}}), graphics={ Line( visible=not useSupport, points={{-50,-120},{-30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-120},{-10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-10,-120},{10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{10,-120},{30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-100},{30,-100}}, color={0,0,0})})); end PartialElementaryOneFlangeAndSupport2; partial model PartialElementaryTwoFlangesAndSupport "Obsolete partial model. Use PartialElementaryTwoFlangesAndSupport2." extends Modelica.Icons.ObsoleteModel; parameter Boolean useSupport=false "= true, if support flange enabled, otherwise implicitly grounded" annotation(Evaluate=true, HideResult=true, choices(checkBox=true)); Flange_a flange_a "Flange of left shaft" annotation (Placement(transformation(extent={{-110,-10},{-90,10}}, rotation=0))); Flange_b flange_b "Flange of right shaft" annotation (Placement(transformation(extent={{90,-10},{110,10}}, rotation=0))); Modelica.SIunits.Length s_a "Distance between left flange and support"; Modelica.SIunits.Length s_b "Distance between right flange and support"; protected InternalSupport internalSupport(f=-flange_a.f - flange_b.f) "Internal support/housing of component as a model with connector flange (flange is either connected to support, if useSupport=true, or connected to fixed, if useSupport=false)" annotation (Placement(transformation(extent={{-10,-90},{10,-70}}))); Components.Fixed fixed if not useSupport "Fixed support/housing, if not useSupport" annotation (Placement(transformation(extent={{10,-97},{30,-77}}))); public Support support if useSupport "Support/housing of component" annotation (Placement(transformation(extent={{-10,-110},{10,-90}}))); equation s_a = flange_a.s - internalSupport.s; s_b = flange_b.s - internalSupport.s; connect(internalSupport.flange, support) annotation (Line( points={{0,-80},{0,-100}}, color={0,127,0}, smooth=Smooth.None)); connect(fixed.flange, internalSupport.flange) annotation (Line( points={{20,-87},{20,-80},{0,-80}}, color={0,127,0}, smooth=Smooth.None)); annotation (Documentation(info="

This is a 1-dim. translational component with two flanges and an additional support. It is used e.g., to build up elementary ideal gear components. The component contains the force balance, i.e., the sum of the forces of the connectors is zero (therefore, components that are based on PartialGear cannot have a mass). The support connector needs to be connected to avoid the unphysical behavior that the support force is required to be zero (= the default value, if the connector is not connected).

"), Diagram(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100}, {100,100}}), graphics={Text( extent={{-38,-98},{-6,-96}}, lineColor={95,95,95}, textString="(if useSupport)"), Text( extent={{24,-97},{64,-98}}, lineColor={95,95,95}, textString="(if not useSupport)")}), Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{ 100,100}}), graphics={ Line( visible=not useSupport, points={{-50,-120},{-30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-120},{-10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-10,-120},{10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{10,-120},{30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-100},{30,-100}}, color={0,0,0})})); end PartialElementaryTwoFlangesAndSupport; partial model PartialElementaryTwoFlangesAndSupport2 "Partial model for a component with one translational 1-dim. shaft flange and a support used for textual modeling, i.e., for elementary models" parameter Boolean useSupport=false "= true, if support flange enabled, otherwise implicitly grounded" annotation(Evaluate=true, HideResult=true, choices(checkBox=true)); Flange_a flange_a "Flange of left shaft" annotation (Placement(transformation(extent={{-110,-10},{-90,10}}, rotation=0))); Flange_b flange_b "Flange of right shaft" annotation (Placement(transformation(extent={{90,-10},{110,10}}, rotation=0))); Support support(s=s_support, f = -flange_a.f - flange_b.f) if useSupport "Support/housing of component" annotation (Placement(transformation(extent={{-10,-110},{10,-90}}))); Modelica.SIunits.Length s_a "Distance between left flange and support"; Modelica.SIunits.Length s_b "Distance between right flange and support"; protected Modelica.SIunits.Length s_support "Absolute position of support flange"; equation s_a = flange_a.s - s_support; s_b = flange_b.s - s_support; if not useSupport then s_support = 0; end if; annotation (Documentation(info="

This is a 1-dim. translational component with two flanges and an additional support. It is used e.g., to build up elementary ideal gear components. The component contains the force balance, i.e., the sum of the forces of the connectors is zero (therefore, components that are based on PartialGear cannot have a mass). The support connector needs to be connected to avoid the unphysical behavior that the support force is required to be zero (= the default value, if the connector is not connected).

"), Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{ 100,100}}), graphics={ Line( visible=not useSupport, points={{-50,-120},{-30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-120},{-10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-10,-120},{10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{10,-120},{30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-100},{30,-100}}, color={0,0,0})})); end PartialElementaryTwoFlangesAndSupport2; partial model PartialElementaryRotationalToTranslational "Partial model to transform rotational into translational motion" extends Modelica.Mechanics.Rotational.Interfaces.PartialElementaryRotationalToTranslational; annotation (Documentation(info="

This is a 1-dim. rotational component with

This model is used to build up elementary components of a drive train transforming rotational into translational motion with equations in the text layer.

If useSupportR=true, the rotational support connector is conditionally enabled and needs to be connected.

If useSupportR=false, the rotational support connector is conditionally disabled and instead the rotational part is internally fixed to ground.

If useSupportT=true, the translational support connector is conditionally enabled and needs to be connected.

If useSupportT=false, the translational support connector is conditionally disabled and instead the translational part is internally fixed to ground.

")); end PartialElementaryRotationalToTranslational; partial model PartialForce "Partial model of a force acting at the flange (accelerates the flange)" extends PartialElementaryOneFlangeAndSupport2; Modelica.SIunits.Force f "Accelerating force acting at flange (= flange.f)"; equation f = flange.f; annotation ( Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{100, 100}}), graphics={ Rectangle( extent={{-96,96},{96,-96}}, lineColor={255,255,255}, fillColor={255,255,255}, fillPattern=FillPattern.Solid), Line(points={{0,-60},{0,-100}}, color={0,0,0}), Text( extent={{-150,140},{150,100}}, lineColor={0,0,255}, textString="%name"), Line(points={{-78,80},{51,80}}, color={0,0,0}), Polygon( points={{81,80},{51,90},{51,70},{81,80}}, lineColor={0,0,0}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line(points={{-52,-60},{77,-60}}, color={0,0,0}), Polygon( points={{-82,-60},{-51,-50},{-51,-70},{-82,-60}}, lineColor={0,0,0}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line( visible=not useSupport, points={{-50,-120},{-30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-120},{-10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-10,-120},{10,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{10,-120},{30,-100}}, color={0,0,0}), Line( visible=not useSupport, points={{-30,-100},{30,-100}}, color={0,0,0})}), Documentation(info="

Partial model of force that accelerates the flange.

If useSupport=true, the support connector is conditionally enabled and needs to be connected.
If useSupport=false, the support connector is conditionally disabled and instead the component is internally fixed to ground.

")); end PartialForce; partial model PartialAbsoluteSensor "Device to measure a single absolute flange variable" extends Modelica.Icons.TranslationalSensor; Interfaces.Flange_a flange "Flange to be measured (flange axis directed in to cut plane, e. g. from left to right)" annotation (Placement(transformation(extent={{-110,-10},{-90,10}}, rotation=0))); equation 0 = flange.f; annotation ( Documentation(info="

This is the superclass of a 1D translational component with one flange and one output signal in order to measure an absolute kinematic quantity in the flange and to provide the measured signal as output signal for further processing with the Modelica.Blocks blocks.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-100,-90},{-20,-90}}, color={0,0,0}), Polygon( points={{10,-90},{-20,-80},{-20,-100},{10,-90}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line(points={{-70,0},{-90,0}}, color={0,0,0}), Line(points={{70,0},{100,0}}, color={0,0,127}), Text( extent={{-150,80},{150,40}}, textString="%name", lineColor={0,0,255})})); end PartialAbsoluteSensor; partial model PartialRelativeSensor "Device to measure a single relative variable between two flanges" extends Modelica.Icons.TranslationalSensor; Interfaces.Flange_a flange_a "(left) driving flange (flange axis directed in to cut plane, e. g. from left to right)" annotation (Placement(transformation(extent={{-110,-10},{-90,10}}, rotation=0))); Interfaces.Flange_b flange_b "(right) driven flange (flange axis directed out of cut plane)" annotation (Placement(transformation(extent={{90,-10},{110,10}}, rotation=0))); equation 0 = flange_a.f + flange_b.f; annotation ( Documentation(info="

This is a superclass for 1D translational components with two rigidly connected flanges and one output signal in order to measure relative kinematic quantities between the two flanges or the cut-force in the flange and to provide the measured signal as output signal for further processing with the Modelica.Blocks blocks.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}), graphics={ Line(points={{-51,34},{29,34}}, color={0,0,0}), Polygon( points={{59,34},{29,44},{29,24},{59,34}}, lineColor={0,0,0}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Line(points={{-70,0},{-90,0}}, color={0,0,0}), Line(points={{70,0},{90,0}}, color={0,0,0}), Text( extent={{-150,100},{150,60}}, textString="%name", lineColor={0,0,255})})); end PartialRelativeSensor; partial model PartialFriction "Base model of Coulomb friction elements" //extends Translational.Interfaces.PartialRigid; parameter SI.Velocity v_small=1e-3 "Relative velocity near to zero (see model info text)" annotation(Dialog(tab="Advanced")); // Equations to define the following variables have to be defined in subclasses SI.Velocity v_relfric "Relative velocity between frictional surfaces"; SI.Acceleration a_relfric "Relative acceleration between frictional surfaces"; //SI.Force f "Friction force (positive, if directed in opposite direction of v_rel)"; SI.Force f0 "Friction force for v=0 and forward sliding"; SI.Force f0_max "Maximum friction force for v=0 and locked"; Boolean free "true, if frictional element is not active"; // Equations to define the following variables are given in this class Real sa(unit="1") "Path parameter of friction characteristic f = f(a_relfric)"; Boolean startForward(start=false, fixed=true) "true, if v_rel=0 and start of forward sliding"; Boolean startBackward(start=false, fixed=true) "true, if v_rel=0 and start of backward sliding"; Boolean locked(start=false) "true, if v_rel=0 and not sliding"; constant Integer Unknown=3 "Value of mode is not known"; constant Integer Free=2 "Element is not active"; constant Integer Forward=1 "v_rel > 0 (forward sliding)"; constant Integer Stuck=0 "v_rel = 0 (forward sliding, locked or backward sliding)"; constant Integer Backward=-1 "v_rel < 0 (backward sliding)"; Integer mode( final min=Backward, final max=Unknown, start=Unknown, fixed=true); protected constant SI.Acceleration unitAcceleration = 1 annotation(HideResult=true); constant SI.Force unitForce = 1 annotation(HideResult=true); equation /* Friction characteristic (locked is introduced to help the Modelica translator determining the different structural configurations, if for each configuration special code shall be generated) */ startForward = pre(mode) == Stuck and (sa > f0_max/unitForce or pre(startForward) and sa > f0/unitForce) or pre(mode) == Backward and v_relfric > v_small or initial() and (v_relfric > 0); startBackward = pre(mode) == Stuck and (sa < -f0_max/unitForce or pre( startBackward) and sa < -f0/unitForce) or pre(mode) == Forward and v_relfric < -v_small or initial() and (v_relfric < 0); locked = not free and not (pre(mode) == Forward or startForward or pre( mode) == Backward or startBackward); a_relfric/unitAcceleration = if locked then 0 else if free then sa else if startForward then sa - f0_max/unitForce else if startBackward then sa + f0_max/unitForce else if pre(mode) == Forward then sa - f0_max/unitForce else sa + f0_max/unitForce; /* Friction torque has to be defined in a subclass. Example for a clutch: f = if locked then sa else if free then 0 else cgeo*fn*(if startForward then Math.tempInterpol1( v_relfric, mue_pos, 2) else if startBackward then -Math.tempInterpol1(-v_relfric, mue_pos, 2) else if pre(mode) == Forward then Math.tempInterpol1( v_relfric, mue_pos, 2) else -Math.tempInterpol1(-v_relfric, mue_pos, 2)); */ // finite state machine to determine configuration mode = if free then Free else (if (pre(mode) == Forward or pre(mode) == Free or startForward) and v_relfric > 0 then Forward else if (pre(mode) == Backward or pre(mode) == Free or startBackward) and v_relfric < 0 then Backward else Stuck); annotation (Documentation(info="

Basic model for Coulomb friction that models the stuck phase in a reliable way.

")); end PartialFriction; annotation (Documentation(info="

This package contains connectors and partial models for 1-dim. translational mechanical components. The components of this package can only be used as basic building elements for models.

")); end Interfaces; annotation ( Icon(coordinateSystem(preserveAspectRatio = true, extent = {{-100,-100},{100,100}}), graphics = { Line( origin = {14,53}, points = {{-84,-73},{66,-73}}), Rectangle( origin = {14,53}, lineColor = {64,64,64}, fillColor = {192,192,192}, fillPattern = FillPattern.Sphere, extent = {{-81,-65},{-8,-22}}),Line(visible = true, origin = {14,53}, points = {{-8,-43},{-1,-43},{6,-64},{17,-23},{29,-65},{40,-23},{50,-44},{61,-44}}), Line( origin = {14,53}, points = {{-59,-73},{-84,-93}}), Line( origin = {14,53}, points = {{-11,-73},{-36,-93}}), Line( origin = {14,53}, points = {{-34,-73},{-59,-93}}), Line( origin = {14,53}, points = {{14,-73},{-11,-93}}), Line( origin = {14,53}, points = {{39,-73},{14,-93}}), Line( origin = {14,53}, points = {{63,-73},{38,-93}})}), Documentation(info="

This package contains components to model 1-dimensional translational mechanical systems.

The filled and non-filled green squares at the left and right side of a component represent mechanical flanges. Drawing a line between such squares means that the corresponding flanges are rigidly attached to each other. The components of this library can be usually connected together in an arbitrary way. E.g. it is possible to connect two springs or two sliding masses with inertia directly together.

The only connection restriction is that the Coulomb friction elements (e.g., MassWithStopAndFriction) should be only connected together provided a compliant element, such as a spring, is in between. The reason is that otherwise the frictional force is not uniquely defined if the elements are stuck at the same time instant (i.e., there does not exist a unique solution) and some simulation systems may not be able to handle this situation, since this leads to a singularity during simulation. It can only be resolved in a \"clean way\" by combining the two connected friction elements into one component and resolving the ambiguity of the frictional force in the stuck mode.

Another restriction arises if the hard stops in model MassWithStopAndFriction are used, i. e. the movement of the mass is limited by a stop at smax or smin. This requires the states Stop.s and Stop.v . If these states are eliminated during the index reduction the model will not work. To avoid this any inertias should be connected via springs to the Stop element, other sliding masses, dampers or hydraulic chambers must be avoided.

In the icon of every component an arrow is displayed in grey color. This arrow characterizes the coordinate system in which the vectors of the component are resolved. It is directed into the positive translational direction (in the mathematical sense). In the flanges of a component, a coordinate system is rigidly attached to the flange. It is called flange frame and is directed in parallel to the component coordinate system. As a result, e.g., the positive cut-force of a \"left\" flange (flange_a) is directed into the flange, whereas the positive cut-force of a \"right\" flange (flange_b) is directed out of the flange. A flange is described by a Modelica connector containing the following variables: 

   Modelica.SIunits.Position s    \"Absolute position of flange\";
   flow Modelica.SIunits.Force f  \"Cut-force in the flange\";

This library is designed in a fully object oriented way in order that components can be connected together in every meaningful combination (e.g., direct connection of two springs or two shafts with inertia). As a consequence, most models lead to a system of differential-algebraic equations of index 3 (= constraint equations have to be differentiated twice in order to arrive at a state space representation) and the Modelica translator or the simulator has to cope with this system representation. According to our present knowledge, this requires that the Modelica translator is able to symbolically differentiate equations (otherwise it is e.g., not possible to provide consistent initial conditions; even if consistent initial conditions are present, most numerical DAE integrators can cope at most with index 2 DAEs).

In version 3.2 of the Modelica Standard Library, all dissipative components of the Translational library got an optional heatPort connector to which the dissipated energy is transported in form of heat. This connector is enabled via parameter \"useHeatPort\". If the heatPort connector is enabled, it must be connected, and if it is not enabled, it must not be connected. Independently, whether the heatPort is enabled or not, the dissipated power is available from the new variable \"lossPower\" (which is positive if heat is flowing out of the heatPort). For an example, see Examples.HeatLosses.

Library Officer
Martin Otter
Deutsches Zentrum für Luft und Raumfahrt e.V. (DLR)
Institut für Robotik und Mechatronik (DLR-RM)
Abteilung Systemdynamik und Regelungstechnik
Postfach 1116
D-82230 Wessling
Germany
email: Martin.Otter@dlr.de

Contributors to this library:

Copyright © 1998-2013, Modelica Association, Anton Haumer and Universität Paderborn, FB 12.

This Modelica package is free software and the use is completely at your own risk; it can be redistributed and/or modified under the terms of the Modelica License 2. For license conditions (including the disclaimer of warranty) see Modelica.UsersGuide.ModelicaLicense2 or visit https://www.modelica.org/licenses/ModelicaLicense2.

", revisions=" ")); end Translational;