1 | within ; |
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2 | package Elevator |
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3 | model Elevator |
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4 | extends Modelica.Icons.Example; |
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5 | parameter Integer nPas = 2 "Number of passengers"; |
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6 | parameter Modelica.SIunits.Mass mPas = 80 "Mass of one passenger"; |
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7 | parameter Modelica.SIunits.Mass mCab = 250 "Mass of cabin"; |
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8 | parameter Modelica.SIunits.Mass mCou = 410 "Mass of counterweight"; |
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9 | parameter Modelica.SIunits.Length DP = 0.8 "Diameter of drive pulley"; |
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10 | parameter Modelica.SIunits.Inertia JP = 15 "Inertia of drive pulley"; |
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11 | parameter Real EtaP = 0.96 "Efficiency of drive pulley"; |
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12 | parameter Real iG = 55 "Ratio of gearbox"; |
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13 | parameter Real EtaG = 0.80 "Efficiency of gearbox"; |
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14 | parameter Modelica.SIunits.Inertia JMG = 0.03 "Inertia of gearbox + motor"; |
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15 | parameter Modelica.SIunits.Velocity vMax = 2 "Max. speed of cabin"; |
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16 | final parameter Modelica.SIunits.Length R2T=(DP/2)/iG |
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17 | "Transmission rotational -> translational"; |
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18 | parameter Modelica.SIunits.Length s0 = 0 "Initial position of cabin"; |
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19 | parameter Modelica.SIunits.Velocity v0 = 0 "Initial velocity of cabin"; |
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20 | Modelica.Blocks.Sources.Trapezoid trapezoid( |
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21 | rising=2.5, |
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22 | width=5, |
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23 | falling=2.5, |
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24 | period=10, |
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25 | nperiod=1, |
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26 | offset=0, |
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27 | startTime=0.5, |
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28 | amplitude=vMax/R2T) |
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29 | annotation (Placement(transformation(extent={{-10,-10},{10,10}}, |
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30 | rotation=0, |
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31 | origin={-60,50}))); |
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32 | Modelica.Mechanics.Rotational.Sources.Speed speed(exact = true) annotation(Placement(transformation(extent = {{-10, -10}, {10, 10}}, rotation=0, origin={-30,50}))); |
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33 | Modelica.Mechanics.Rotational.Components.IdealGear gearBox(ratio=iG, |
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34 | useSupport=false) |
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35 | annotation (Placement(transformation(extent={{-10,40},{10,60}}))); |
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36 | IdealDrivePulley drivePulley(useTranslationalSupport=false, radius=DP/2) |
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37 | annotation (Placement(transformation( |
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38 | extent={{-10,-10},{10,10}}, |
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39 | rotation=270, |
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40 | origin={30,50}))); |
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41 | MassGravitation cabin( |
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42 | s(start=s0), |
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43 | v(start=v0), |
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44 | m=mCab + nPas*mPas) |
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45 | annotation (Placement(transformation(extent={{10,0},{30,20}}))); |
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46 | MassGravitation counterweight(m=mCou) |
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47 | annotation (Placement(transformation(extent={{30,0},{50,20}}))); |
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48 | equation |
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49 | connect(drivePulley.flange_a, cabin.flange) annotation(Line(points={{20,40}, |
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50 | {20,20}}, color = {0, 127, 0})); |
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51 | connect(drivePulley.flange_b, counterweight.flange) annotation(Line(points={{40,40}, |
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52 | {40,20}}, color = {0, 127, 0})); |
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53 | connect(speed.flange, gearBox.flange_a) |
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54 | annotation (Line(points={{-20,50},{-14,50},{-10,50}}, color={0,0,0})); |
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55 | connect(gearBox.flange_b, drivePulley.flange) |
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56 | annotation (Line(points={{10,50},{15,50},{20,50}}, color={0,0,0})); |
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57 | connect(trapezoid.y, speed.w_ref) |
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58 | annotation (Line(points={{-49,50},{-42,50}}, color={0,0,127})); |
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59 | annotation(Diagram(coordinateSystem(preserveAspectRatio = false, extent = {{-100, -100}, {100, 100}})), experiment(StopTime=12, Interval=0.01), |
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60 | Documentation(info="<html> |
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61 | <p> |
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62 | This example of an elevator demonstrates the usage of a <a href=\"modelica://ModelicaAdditions/Mechanics/Rotational/Components/GearConstantEfficiency\">gearbox with constant efficiency</a> and |
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63 | a <a href=\"modelica:/ModelicaAdditions/Mechanics.Rotational/Components/DrivePulleyConstantEfficiency\">drive pulley with constant efficiency</a>. |
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64 | </p> |
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65 | <p> |
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66 | The flange_a of the gearbox is driven by a prescribed speed, flange_b of the gearbox drives the rotational flange of the drive pulley. |
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67 | At the two ends of a rope through translational flanges flange_a and flange_b of the drive pulley the cabin (with passengers) and a counterweight are hanging. |
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68 | </p> |
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69 | <p> |
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70 | Speed rises linearly between 0 and 2.5 seconds from to 2 m/s, then remains constant for 4.5 seconds and during the following 2.5 seconds speed is reduced linearly to 0. |
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71 | This results in lifting the cabin by 14 m and in turn lowering the counterweight by 14 m. |
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72 | </p> |
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73 | </html>"), |
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74 | __Dymola_experimentSetupOutput); |
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75 | end Elevator; |
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76 | |
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77 | model IdealDrivePulley "1-dim. model of ideal drive pulley" |
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78 | import Modelica.Constants.eps; |
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79 | parameter Modelica.SIunits.Distance radius(final min = eps) "Wheel radius"; |
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80 | parameter Boolean useTranslationalSupport = false |
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81 | "= true, if Translational support flange enabled, otherwise implicitly grounded" |
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82 | annotation(Evaluate = true, HideResult = true, choices(checkBox = true)); |
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83 | Modelica.SIunits.Torque tau "Torque at rotational flange"; |
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84 | Modelica.SIunits.Force f_a "Force at translational flange a"; |
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85 | Modelica.SIunits.Force f_b "Force at translational flange b"; |
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86 | Modelica.Mechanics.Rotational.Interfaces.Flange_a flange "Flange of shaft" annotation(Placement(transformation(extent = {{-10, -110}, {10, -90}}, rotation = 0))); |
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87 | Modelica.Mechanics.Translational.Interfaces.Flange_a flange_a annotation(Placement(transformation(extent = {{90, -110}, {110, -90}}), iconTransformation(extent = {{90, -110}, {110, -90}}))); |
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88 | Modelica.Mechanics.Translational.Interfaces.Flange_b flange_b annotation(Placement(transformation(extent = {{90, 110}, {110, 90}}), iconTransformation(extent = {{90, 90}, {110, 110}}))); |
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89 | Modelica.Mechanics.Translational.Interfaces.Support translationalSupport(s = s_support, f = -(f_a + f_b)) if useTranslationalSupport |
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90 | "Translational support of component" annotation(Placement(transformation(extent = {{-110, -10}, {-90, 10}}))); |
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91 | protected |
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92 | Modelica.SIunits.Angle phi "Angle of rotational flange"; |
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93 | Modelica.SIunits.Position s_a |
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94 | "Relative position of translational flange a w.r.t. support"; |
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95 | Modelica.SIunits.Position s_b |
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96 | "Relative position of translational flange b w.r.t. support"; |
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97 | Modelica.SIunits.Position s_support |
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98 | "Absolute position of translational support flange"; |
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99 | equation |
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100 | if not useTranslationalSupport then |
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101 | s_support = 0; |
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102 | end if; |
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103 | phi = flange.phi; |
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104 | tau = flange.tau; |
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105 | s_a = flange_a.s - s_support; |
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106 | s_b = flange_b.s - s_support; |
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107 | f_a = flange_a.f; |
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108 | f_b = flange_b.f; |
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109 | s_a + s_b = 0; |
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110 | phi * radius = s_a; |
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111 | tau + (f_a - f_b) * radius = 0; |
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112 | annotation(Icon(coordinateSystem(preserveAspectRatio = true, extent = {{-100.0, -100.0}, {100.0, 100.0}}, initialScale = 0.1), graphics={ |
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113 | Rectangle(extent={{-100,-12},{-10,-16}}, lineColor={0,0,0}, fillColor={95,95,95}, |
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114 | fillPattern = FillPattern.Solid), |
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115 | Polygon(points = {{57, -85}, {37, -85}, {-57, 85}, {-37, 85}, {57, -85}}, lineColor = {95, 95, 95}, fillColor = {175, 175, 175}, |
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116 | fillPattern = FillPattern.Forward, origin={5, |
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117 | 53}, rotation = 90), |
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118 | Rectangle(lineColor = {64, 64, 64}, fillColor = {192, 192, 192}, |
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119 | fillPattern = FillPattern.HorizontalCylinder, extent = {{-27, -10}, {27, 10}}, origin = {0, -72}, rotation = 90), |
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120 | Ellipse(lineColor = {64, 64, 64}, fillColor = {255, 255, 255}, |
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121 | fillPattern = FillPattern.HorizontalCylinder, extent = {{-30, -80}, {30, 80}}, origin = {0, -18}, rotation = 90), |
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122 | Rectangle(lineColor = {64, 64, 64}, fillColor = {255, 255, 255}, pattern = LinePattern.None, |
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123 | fillPattern = FillPattern.HorizontalCylinder, extent = {{-16, -80}, {16, 80}}, origin = {0, -4}, rotation = 90), |
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124 | Ellipse(lineColor = {64, 64, 64}, fillColor = {128, 128, 128}, |
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125 | fillPattern = FillPattern.Solid, extent = {{-30, -80}, {30, 80}}, origin = {0, 14}, rotation = 90), |
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126 | Ellipse(lineColor = {64, 64, 64}, fillColor = {192, 192, 192}, |
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127 | fillPattern = FillPattern.HorizontalCylinder, extent = {{-4, -10}, {4, 10}}, origin = {0, 14}, rotation = 90), |
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128 | Text(lineColor={0,0,255}, extent = {{-100, 120}, {100, 140}}, textString = "%name"), |
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129 | Polygon(points = {{-57, -85}, {-37, -85}, {57, 85}, {37, 85}, {-57, -85}}, lineColor = {95, 95, 95}, fillColor = {175, 175, 175}, |
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130 | fillPattern = FillPattern.Backward, origin = {5, -53}, rotation = 90), |
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131 | Line(visible = not useTranslationalSupport, points = {{-10, -10}, {10, 10}}, color = {0, 0, 0}, origin = {-110, -20}, rotation = 270), |
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132 | Line(visible = not useTranslationalSupport, points = {{-10, -10}, {10, 10}}, color = {0, 0, 0}, origin = {-110, 0}, rotation = 270), |
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133 | Line(visible = not useTranslationalSupport, points = {{-10, -10}, {10, 10}}, color = {0, 0, 0}, origin = {-110, 20}, rotation = 270), |
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134 | Line(visible = not useTranslationalSupport, points = {{-10, -10}, {10, 10}}, color = {0, 0, 0}, origin = {-110, 40}, rotation = 270), |
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135 | Line(visible = not useTranslationalSupport, points = {{-30, 0}, {30, 0}}, color = {0, 0, 0}, origin = {-100, 0}, rotation = 270), |
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136 | Rectangle(extent={{-100,16},{-10,12}}, lineColor={0,0,0}, fillColor={95,95,95}, |
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137 | fillPattern = FillPattern.Solid)}), |
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138 | Documentation(info = "<html> |
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139 | <p> |
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140 | This is a simple model of a drive pulley without losses and without inertia.<br> |
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141 | It is assumed that the two rotational flanges flange_a and flange_b are connected by a rope. |
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142 | The rope moving into flange_a moves out from flange b.<br> |
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143 | The relationship between the rotational flange and the two translational flanges flange_a and flange_b is defined by: |
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144 | </p> |
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145 | <pre> |
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146 | flange_a.s + flange_b.s = 0; |
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147 | flange.phi*radius = flange_a.s; |
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148 | flange.tau + (flange_a.f - flange_b.f)*radius = 0; |
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149 | </pre> |
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150 | <p> |
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151 | Note, there is a balance between torque and the difference of forces * radius, a rotational support is not present.<br> |
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152 | The sum of the two forces appears at the optional translational support. |
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153 | </p> |
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154 | </html>")); |
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155 | end IdealDrivePulley; |
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156 | |
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157 | model MassGravitation "Mass with gravitational force" |
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158 | parameter Modelica.SIunits.Mass m(final min = 0) "Mass"; |
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159 | parameter Modelica.SIunits.Acceleration g = Modelica.Constants.g_n |
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160 | "Gravitation"; |
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161 | Modelica.SIunits.Position s(start = 0) "Position of flange"; |
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162 | Modelica.SIunits.Velocity v(start = 0) "Velocity of flange"; |
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163 | Modelica.SIunits.Acceleration a(start = 0) "Acceleration of flange"; |
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164 | Modelica.Mechanics.Translational.Interfaces.Flange_a flange annotation(Placement(transformation(extent = {{-10, 110}, {10, 90}}))); |
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165 | equation |
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166 | s = flange.s; |
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167 | v = der(s); |
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168 | a = der(v); |
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169 | m * a = flange.f - m * g; |
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170 | annotation(Icon(coordinateSystem(preserveAspectRatio = false), graphics={ |
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171 | Rectangle(extent = {{-55, -30}, {55, 30}}, lineColor = {0, 0, 0}, |
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172 | fillPattern = FillPattern.Sphere, fillColor = {255, 255, 255}, origin = {0, 25}, rotation = 90), |
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173 | Line(points = {{2.62459e-031, -4.28629e-015}, {20, 0}}, color = {0, 127, 0}, origin = {0, 80}, rotation = 90), |
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174 | Text(extent = {{-100, 20}, {100, -20}}, lineColor={0,0,255}, origin = {-80, 0}, rotation = 90, textString = "%name"), |
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175 | Text(extent = {{-100, 10}, {100, -10}}, lineColor={0,0,255}, origin = {90, 0}, rotation = 90, textString = "m=%m"), |
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176 | Line(points = {{-70, -7.71773e-015}, {60, 0}}, color = {0, 0, 0}, origin = {60, -10}, rotation = 90), |
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177 | Polygon(points = {{15, 0}, {-15, 10}, {-15, -10}, {15, 0}}, lineColor = {0, 0, 0}, fillColor = {128, 128, 128}, |
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178 | fillPattern = FillPattern.Solid, origin = {60, 65}, rotation = 90), |
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179 | Polygon(points = {{-10, -30}, {10, -30}, {10, -60}, {20, -60}, {0, -80}, {-20, -60}, {-10, -60}, {-10, -30}}, lineColor = {0, 127, 0}, fillColor = {0, 127, 0}, |
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180 | fillPattern = FillPattern.Solid)}), |
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181 | Diagram(coordinateSystem(preserveAspectRatio = false)), Documentation(info = "<html> |
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182 | <p> |
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183 | This is a simple model of a mass either hanging on a rope or lying on an eleveating platform.<br> |
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184 | Both inertia and gravitional force is modelled. |
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185 | </p> |
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186 | </html>")); |
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187 | end MassGravitation; |
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188 | annotation (uses(Modelica(version="3.2.1"))); |
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189 | end Elevator; |
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