root/branches/maintenance/3.0/Modelica/Mechanics/Translational.mo

Revision 1195, 200.1 kB (checked in by AHaumer, 3 days ago)

solves #103 (2 x reinit) for MSL 2.2.2, 3.0 and 3.0_ImprovedFriction
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1within Modelica.Mechanics;
2package Translational
3  "Library to model 1-dimensional, translational mechanical systems"
4  extends Modelica.Icons.Library2;
5  import SI = Modelica.SIunits;
6  annotation (
7  version="1.1.1", versionDate="2007-11-22",
8    Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{100,
9            100}}), graphics={
10        Line(points={{-84,-73},{66,-73}}, color={0,0,0}),
11        Rectangle(
12          extent={{-81,-22},{-8,-65}},
13          lineColor={0,0,0},
14          fillPattern=FillPattern.Sphere,
15          fillColor={192,192,192}),
16        Line(points={{-8,-43},{-1,-43},{6,-64},{17,-23},{29,-65},{40,-23},{50,-44},
17              {61,-44}}, color={0,0,0}),
18        Line(points={{-59,-73},{-84,-93}}, color={0,0,0}),
19        Line(points={{-11,-73},{-36,-93}}, color={0,0,0}),
20        Line(points={{-34,-73},{-59,-93}}, color={0,0,0}),
21        Line(points={{14,-73},{-11,-93}}, color={0,0,0}),
22        Line(points={{39,-73},{14,-93}}, color={0,0,0}),
23        Line(points={{63,-73},{38,-93}}, color={0,0,0})}),
24                                                        Documentation(info="<html>
25<p>
26This package contains components to model <i>1-dimensional translational
27mechanical</i> systems.
28</p>
29<p>
30The <i>filled</i> and <i>non-filled green squares</i> at the left and
31right side of a component represent <i>mechanical flanges</i>.
32Drawing a line between such squares means that the corresponding
33flanges are <i>rigidly attached</i> to each other. The components of this
34library can be usually connected together in an arbitrary way. E.g. it is
35possible to connect two springs or two sliding masses with inertia directly
36together.
37<p> The only <i>connection restriction</i> is that the Coulomb friction
38elements (e.g. MassWithStopAndFriction) should be only connected
39together provided a compliant element, such as a spring, is in between.
40The reason is that otherwise the frictional force is not uniquely
41defined if the elements are stuck at the same time instant (i.e., there
42does not exist a unique solution) and some simulation systems may not be
43able to handle this situation, since this leads to a singularity during
44simulation. It can only be resolved in a \"clean way\" by combining the
45two connected friction elements into
46one component and resolving the ambiguity of the frictional force in the
47stuck mode.
48</p>
49<p> Another restriction arises if the hard stops in model MassWithStopAndFriction are used, i. e.
50the movement of the mass is limited by a stop at smax or smin.
51<font color=\"#ff0000\"> <b>This requires the states Stop.s and Stop.v</b> </font>. If these states are eliminated during the index reduction
52the model will not work. To avoid this any inertias should be connected via springs
53to the Stop element, other sliding masses, dampers or hydraulic chambers must be avoided. </p>
54<p>
55In the <i>icon</i> of every component an <i>arrow</i> is displayed in grey
56color. This arrow characterizes the coordinate system in which the vectors
57of the component are resolved. It is directed into the positive
58translational direction (in the mathematical sense).
59In the flanges of a component, a coordinate system is rigidly attached
60to the flange. It is called <i>flange frame</i> and is directed in parallel
61to the component coordinate system. As a result, e.g., the positive
62cut-force of a \"left\" flange (flange_a) is directed into the flange, whereas
63the positive cut-force of a \"right\" flange (flange_b) is directed out of the
64flange. A flange is described by a Modelica connector containing
65the following variables:
66</p>
67<pre>
68   Modelica.SIunits.Position s    \"Absolute position of flange\";
69   <b>flow</b> Modelica.SIunits.Force f  \"Cut-force in the flange\";
70</pre>
71 
72<p>
73This library is designed in a fully object oriented way in order that
74components can be connected together in every meaningful combination
75(e.g. direct connection of two springs or two shafts with inertia).
76As a consequence, most models lead to a system of
77differential-algebraic equations of <i>index 3</i> (= constraint
78equations have to be differentiated twice in order to arrive at
79a state space representation) and the Modelica translator or
80the simulator has to cope with this system representation.
81According to our present knowledge, this requires that the
82Modelica translator is able to symbolically differentiate equations
83(otherwise it is e.g. not possible to provide consistent initial
84conditions; even if consistent initial conditions are present, most
85numerical DAE integrators can cope at most with index 2 DAEs).
86</p>
87
88<dl>
89<dt><b>Library Officer</b>
90<dd><a href=\"http://www.robotic.dlr.de/Martin.Otter/\">Martin Otter</a> <br>
91    Deutsches Zentrum f&uuml;r Luft und Raumfahrt e.V. (DLR)<br>
92    Institut f&uuml;r Robotik und Mechatronik (DLR-RM)<br> 
93    Abteilung Systemdynamik und Regelungstechnik<br>
94    Postfach 1116<br>
95    D-82230 Wessling<br>
96    Germany<br>
97    email: <A HREF=\"mailto:Martin.Otter@dlr.de\">Martin.Otter@dlr.de</A><br><br>
98</dl>
99
100<p>
101<b>Contributors to this library:</b>
102</p>
103
104<ul>
105<li> Main author until 2006:<br>
106     Peter Beater <br>
107     Universit&auml;t Paderborn, Abteilung Soest<br>
108     Fachbereich Maschinenbau/Automatisierungstechnik<br>
109     L&uuml;becker Ring 2 <br>
110     D 59494 Soest <br>
111     Germany <br>
112     email: <A HREF=\"mailto:Beater@mailso.uni-paderborn.de\">Beater@mailso.uni-paderborn.de</A><br><br>
113     </li>
114
115<li> <a href=\"http://www.haumer.at/\">Anton Haumer</a><br>
116     Technical Consulting & Electrical Engineering<br>
117     A-3423 St.Andrae-Woerdern, Austria<br>
118     email: <a href=\"mailto:a.haumer@haumer.at\">a.haumer@haumer.at</a><br><br></li>
119
120<li> <a href=\"http://www.robotic.dlr.de/Martin.Otter/\">Martin Otter</a> (DLR-RM)</li>
121</ul>
122
123<p>
124Copyright &copy; 1998-2008, Modelica Association, Anton Haumer and Universit&auml;t Paderborn, FB 12.
125</p>
126<p>
127<i>This Modelica package is <b>free</b> software; it can be redistributed and/or modified
128under the terms of the <b>Modelica license</b>, see the license conditions
129and the accompanying <b>disclaimer</b> 
130<a href=\"Modelica://Modelica.UsersGuide.ModelicaLicense\">here</a>.</i>
131</p><br>
132 
133</HTML>
134", revisions="<html>
135<ul>
136<li><i>Version 1.0 (January 5, 2000)</i>
137       by Peter Beater <br>
138       Realized a first version based on Modelica library Mechanics.Rotational
139       by Martin Otter and an existing Dymola library onedof.lib by Peter Beater.
140       <br>
141<li><i>Version 1.01 (July 18, 2001)</i>
142       by Peter Beater <br>
143       Assert statement added to \"Stop\", small bug fixes in examples.
144       <br>
145</li>
146<li><i>Version 1.1.0 2007-11-16</i>
147       by Anton Haumer<br>
148       Redesign for Modelica 3.0-compliance<br>
149       Added new components acording to Mechanics.Rotational library
150       <br>
151</li>
152</ul>
153</html>"));
154
155  package Examples "Demonstration examples of the components of this package"
156
157    extends Modelica.Icons.Library;
158
159    annotation (
160      Documentation(info="<html>
161<p>
162This package contains example models to demonstrate the usage of the
163Translational package. Open the models and
164simulate them according to the provided description in the models.
165</p>
166 
167</HTML>
168"));
169
170    model SignConvention "Examples for the used sign conventions."
171      extends Modelica.Icons.Example;
172      annotation (Documentation(info="<html>
173<p>
174If all arrows point in the same direction a positive force
175results in a positive acceleration a, velocity v and position s.
176</p>
177For a force of 1 N and a mass of 1 Kg this leads to
178<pre>
179        a = 1 m/s2
180        v = 1 m/s after 1 s (SlidingMass1.v)
181        s = 0.5 m after 1 s (SlidingMass1.s)
182</pre>
183The acceleration is not available for plotting.
184<p>
185</p>
186System 1) and 2) are equivalent. It doesn't matter whether the
187force pushes at flange_a in system 1 or pulls at flange_b in system 2.
188</p><p>
189It is of course possible to ignore the arrows and connect the models
190in an arbitrary way. But then it is hard see in what direction the
191force acts.
192</p><p>
193In the third system the two arrows are opposed which means that the
194force acts in the opposite direction (in the same direction as in
195the two other examples).
196</p>
197 
198</HTML>
199"), Diagram(coordinateSystem(preserveAspectRatio=true,  extent={{-100,-100},{
200                100,100}}), graphics={
201            Text(
202              extent={{-100,80},{-82,60}},
203              textString="1)",
204              lineColor={0,0,255}),
205            Text(
206              extent={{-100,40},{-82,20}},
207              textString="2)",
208              lineColor={0,0,255}),
209            Text(
210              extent={{-100,-20},{-82,-40}},
211              textString="3)",
212              lineColor={0,0,255})}),
213        experiment(StopTime=1));
214      Translational.Components.Mass mass1(L=1,
215        s(fixed=true),
216        v(fixed=true),
217        m=1)                                      annotation (Placement(
218            transformation(extent={{40,60},{60,80}}, rotation=0)));
219      Translational.Sources.Force force1
220                                 annotation (Placement(transformation(extent={{
221                -4,60},{16,80}}, rotation=0)));
222      Modelica.Blocks.Sources.Constant constant1(k=1) 
223                                 annotation (Placement(transformation(extent={{
224                -44,60},{-24,80}}, rotation=0)));
225      Translational.Components.Mass mass2(L=1,
226        s(fixed=true),
227        v(fixed=true),
228        m=1)                                      annotation (Placement(
229            transformation(extent={{40,0},{60,20}}, rotation=0)));
230      Translational.Sources.Force force2
231                                 annotation (Placement(transformation(extent={{
232                -4,20},{16,40}}, rotation=0)));
233      Modelica.Blocks.Sources.Constant constant2(k=1) 
234                                 annotation (Placement(transformation(extent={{
235                -44,20},{-24,40}}, rotation=0)));
236      Translational.Components.Mass mass3(L=1,
237        s(fixed=true),
238        v(fixed=true),
239        m=1)                                      annotation (Placement(
240            transformation(extent={{-40,-40},{-20,-20}}, rotation=0)));
241      Translational.Sources.Force force3(useSupport=true) 
242                                 annotation (Placement(transformation(extent={{
243                20,-40},{0,-20}}, rotation=0)));
244      Modelica.Blocks.Sources.Constant constant3(k=1) 
245                                 annotation (Placement(transformation(extent={{
246                60,-40},{40,-20}}, rotation=0)));
247      Translational.Components.Fixed fixed
248                  annotation (Placement(transformation(extent={{0,-60},{20,-40}})));
249    equation
250      connect(constant1.y,force1. f) annotation (Line(points={{-23,70},{-6,70}},
251            color={0,0,127}));
252      connect(constant2.y,force2. f) annotation (Line(points={{-23,30},{-6,30}},
253            color={0,0,127}));
254      connect(constant3.y,force3. f) annotation (Line(points={{39,-30},{22,-30}},
255            color={0,0,127}));
256      connect(force1.flange, mass1.flange_a)    annotation (Line(
257          points={{16,70},{40,70}},
258          color={0,127,0},
259          smooth=Smooth.None));
260      connect(force2.flange, mass2.flange_b)    annotation (Line(
261          points={{16,30},{70,30},{70,10},{60,10}},
262          color={0,127,0},
263          smooth=Smooth.None));
264      connect(mass3.flange_b, force3.flange)    annotation (Line(
265          points={{-20,-30},{0,-30}},
266          color={0,127,0},
267          smooth=Smooth.None));
268      connect(fixed.flange, force3.support) annotation (Line(
269          points={{10,-50},{10,-40}},
270          color={0,127,0},
271          smooth=Smooth.None));
272    end SignConvention;
273
274    model InitialConditions "Setting of initial conditions"
275
276      extends Modelica.Icons.Example;
277      annotation (
278        Documentation(info="<html> 
279<p>
280There are several ways to set initial conditions.
281In the first system the position of the mass m3 was defined
282by using the modifier s(start=4.5), the position of m4 by s(start=12.5).
283These positions were chosen such that the system is a rest. To calculate
284these values start at the left (Fixed1) with a value of 1 m. The spring
285has an unstreched length of 2 m and m3 an length of 3 m, which leads to
286</p>
287 
288<pre>
289        1   m (fixed1)
290      + 2   m (spring s2)
291      + 3/2 m (half of the length of mass m3)
292      -------
293        4,5 m = s(start = 4.5) for m3
294      + 3/2 m (half of the length of mass m3)
295      + 4   m (springDamper 2)
296      + 5/2 m (half of length of mass m4)
297      -------
298       12,5 m = s(start = 12.5) for m4
299</pre>
300 
301<p>
302This selection of initial conditions has the effect that Dymola selects
303those variables (m3.s and m4.s) as state variables.
304In the second example the length of the springs are given as start values
305but they cannot be used as state for pure springs (only for the spring/damper
306combination). In this case the system is not at rest.
307</p>
308 
309<p>
310<IMG SRC=../Images/Translational/Fig.translational.examples.InitialConditions.png> 
311</p>
312 
313 
314</html>
315"),     experiment(StopTime=5),
316        Diagram(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},
317                {100,100}}),
318                        graphics));
319
320      Translational.Components.Fixed fixed2(        s0=1) 
321                                       annotation (Placement(transformation(
322              extent={{-100,60},{-80,80}}, rotation=0)));
323      Translational.Components.Spring s2(        s_rel0=2, c=1e3) 
324                                               annotation (Placement(
325            transformation(extent={{-60,60},{-40,80}}, rotation=0)));
326      Translational.Components.Mass m3(           L=3, s(start=4.5, fixed=true),
327        v(fixed=true),
328        m=1)                                          annotation (Placement(
329            transformation(extent={{-20,60},{0,80}}, rotation=0)));
330      Translational.Components.SpringDamper sd2(        s_rel0=4, c=111,
331        d=1)                                          annotation (Placement(
332            transformation(extent={{20,60},{40,80}}, rotation=0)));
333      Translational.Components.Mass m4(           L=5, s(start=12.5, fixed=true),
334        v(fixed=true),
335        m=1)                                           annotation (Placement(
336            transformation(extent={{60,60},{80,80}}, rotation=0)));
337
338      Translational.Components.Fixed fixed1(        s0=-1) 
339                                        annotation (Placement(transformation(
340              extent={{-100,-20},{-80,0}}, rotation=0)));
341      Translational.Components.Spring s1(
342        s_rel0=1,
343        c=1e3,
344        s_rel(start=1, fixed=true)) 
345                        annotation (Placement(transformation(extent={{-58,-20},
346                {-38,0}}, rotation=0)));
347      Translational.Components.Mass m1(           L=1, v(fixed=true),
348        m=1)                            annotation (Placement(transformation(
349              extent={{-20,-20},{0,0}}, rotation=0)));
350      Translational.Components.SpringDamper sd1(
351        s_rel0=1,
352        c=111,
353        s_rel(start=1, fixed=true),
354        v_rel(fixed=true),
355        d=1)            annotation (Placement(transformation(extent={{20,-20},{
356                40,0}}, rotation=0)));
357      Translational.Components.Mass m2(           L=2, m=1) 
358                                        annotation (Placement(transformation(
359              extent={{60,-20},{80,0}}, rotation=0)));
360    equation
361      connect(s2.flange_a, fixed2.flange) annotation (Line(
362          points={{-60,70},{-90,70}},
363          color={0,127,0},
364          smooth=Smooth.None));
365      connect(s1.flange_a, fixed1.flange) annotation (Line(
366          points={{-58,-10},{-90,-10}},
367          color={0,127,0},
368          smooth=Smooth.None));
369      connect(m1.flange_a, s1.flange_b) annotation (Line(
370          points={{-20,-10},{-38,-10}},
371          color={0,127,0},
372          smooth=Smooth.None));
373      connect(sd1.flange_a, m1.flange_b) annotation (Line(
374          points={{20,-10},{0,-10}},
375          color={0,127,0},
376          smooth=Smooth.None));
377      connect(m2.flange_a, sd1.flange_b) annotation (Line(
378          points={{60,-10},{40,-10}},
379          color={0,127,0},
380          smooth=Smooth.None));
381      connect(m4.flange_a, sd2.flange_b) annotation (Line(
382          points={{60,70},{40,70}},
383          color={0,127,0},
384          smooth=Smooth.None));
385      connect(sd2.flange_a, m3.flange_b) annotation (Line(
386          points={{20,70},{0,70}},
387          color={0,127,0},
388          smooth=Smooth.None));
389      connect(m3.flange_a, s2.flange_b) annotation (Line(
390          points={{-20,70},{-40,70}},
391          color={0,127,0},
392          smooth=Smooth.None));
393    end InitialConditions;
394
395    model WhyArrows "Use of arrows in Mechanics.Translational"
396
397      extends Modelica.Icons.Example;
398      annotation (
399        Documentation(info="<html>
400<p>
401When using the models of the translational sublibrary
402it is recommended to make sure that all arrows point in
403the same direction because then all component have the
404same reference system.
405In the example the distance from flange_a of Rod1 to flange_b
406of Rod2 is 2 m. The distance from flange_a of Rod1 to flange_b
407of Rod3 is also 2 m though it is difficult to see that. Without
408the arrows it would be almost impossible to notice.
409That all arrows point in the same direction is a sufficient
410condition for an easy use of the library. There are cases
411where horizontally flipped models can be used without
412problems.
413</p>
414</html>
415"),     Diagram(coordinateSystem(
416            preserveAspectRatio=true,
417            extent={{-100,-100},{100,100}},
418            grid={2,2}), graphics={
419            Text(
420              extent={{-80,14},{90,0}},
421              lineColor={0,0,255},
422              textString="positionSensor2.s = positionSensor3.s"),
423            Text(
424              extent={{-84,4},{88,-16}},
425              lineColor={0,0,255},
426              textString="positionSensor3.s <>positionSensor1.s"),
427            Text(
428              extent={{-82,-80},{94,-92}},
429              textString="Both systems are equivalent",
430              lineColor={0,0,255}),
431            Line(
432              points={{-90,-28},{90,-28}},
433              thickness=0.5,
434              color={0,0,255})}),
435        experiment(StopTime=1));
436
437      Translational.Components.Fixed fixed
438                                 annotation (Placement(transformation(extent={{
439                -20,20},{0,40}}, rotation=0)));
440      Translational.Components.Rod rod1(        L=1) 
441                                  annotation (Placement(transformation(extent={
442                {-48,20},{-28,40}}, rotation=0)));
443      Translational.Components.Rod rod2(        L=1) 
444                                  annotation (Placement(transformation(extent={
445                {20,20},{40,40}}, rotation=0)));
446      Translational.Components.Rod rod3(        L=1) 
447                                  annotation (Placement(transformation(extent={
448                {-30,58},{-50,78}}, rotation=0)));
449      Translational.Sensors.PositionSensor positionSensor2 annotation (Placement(
450            transformation(extent={{60,20},{80,40}}, rotation=0)));
451      Translational.Sensors.PositionSensor positionSensor1 annotation (Placement(
452            transformation(extent={{-60,20},{-80,40}}, rotation=0)));
453      Translational.Sensors.PositionSensor positionSensor3 annotation (Placement(
454            transformation(extent={{-60,58},{-80,78}}, rotation=0)));
455      Translational.Components.Fixed fixed1(        s0=-1.9) 
456                                          annotation (Placement(transformation(
457              extent={{-100,-60},{-80,-40}}, rotation=0)));
458      Translational.Components.Spring spring1(        s_rel0=2, c=11) 
459                                                   annotation (Placement(
460            transformation(extent={{-80,-60},{-60,-40}}, rotation=0)));
461      Translational.Components.Mass mass1(
462        L=2,
463        s(fixed=true),
464        v(fixed=true),
465        m=1)                                      annotation (Placement(
466            transformation(extent={{-50,-60},{-30,-40}}, rotation=0)));
467      Translational.Components.Fixed fixed2(        s0=-1.9) 
468                                          annotation (Placement(transformation(
469              extent={{0,-60},{20,-40}}, rotation=0)));
470      Translational.Components.Spring spring2(        s_rel0=2, c=11) 
471                                                   annotation (Placement(
472            transformation(extent={{30,-60},{50,-40}}, rotation=0)));
473      Translational.Components.Mass inertia2(           L=2,
474        m=1,
475        s(fixed=true),
476        v(fixed=true))                            annotation (Placement(
477            transformation(extent={{80,-60},{60,-40}}, rotation=0)));
478    equation
479      connect(spring1.flange_b, mass1.flange_b)        annotation (Line(points={{-60,-50},
480              {-60,-72},{-30,-72},{-30,-50}},            color={0,191,0}));
481      connect(spring2.flange_b, inertia2.flange_b)     annotation (Line(points={{50,-50},
482              {60,-50}},           color={0,191,0}));
483      connect(rod3.flange_b,positionSensor3. flange) annotation (Line(
484          points={{-50,68},{-60,68}},
485          color={0,127,0},
486          smooth=Smooth.None));
487      connect(rod1.flange_a,positionSensor1. flange) annotation (Line(
488          points={{-48,30},{-60,30}},
489          color={0,127,0},
490          smooth=Smooth.None));
491      connect(rod1.flange_b, fixed.flange)  annotation (Line(
492          points={{-28,30},{-10,30}},
493          color={0,127,0},
494          smooth=Smooth.None));
495      connect(rod3.flange_a, fixed.flange)  annotation (Line(
496          points={{-30,68},{-10,68},{-10,30}},
497          color={0,127,0},
498          smooth=Smooth.None));
499      connect(fixed.flange, rod2.flange_a)  annotation (Line(
500          points={{-10,30},{20,30}},
501          color={0,127,0},
502          smooth=Smooth.None));
503      connect(rod2.flange_b,positionSensor2. flange) annotation (Line(
504          points={{40,30},{60,30}},
505          color={0,127,0},
506          smooth=Smooth.None));
507      connect(fixed1.flange,spring1. flange_a) annotation (Line(
508          points={{-90,-50},{-80,-50}},
509          color={0,127,0},
510          smooth=Smooth.None));
511      connect(fixed2.flange,spring2. flange_a) annotation (Line(
512          points={{10,-50},{30,-50}},
513          color={0,127,0},
514          smooth=Smooth.None));
515    end WhyArrows;
516
517    model Accelerate "Use of model accelerate."
518
519      extends Modelica.Icons.Example;
520      Translational.Sources.Accelerate accelerate
521                                           annotation (Placement(transformation(
522              extent={{-40,20},{-20,40}}, rotation=0)));
523      Translational.Components.Mass mass(L=1, m=1) 
524                                                  annotation (Placement(
525            transformation(extent={{0,20},{20,40}},  rotation=0)));
526      Modelica.Blocks.Sources.Constant constantAcc(k=1) 
527                                                 annotation (Placement(transformation(extent={{-80,20},
528                {-60,40}},          rotation=0)));
529      annotation (Documentation(info="<html>
530<p>
531Demonstrate usage of component Sources.Accelerate by moving a massing
532with a predefined acceleration.
533</p>
534</html>"), Diagram(coordinateSystem(preserveAspectRatio=true,  extent={{-100,
535                -100},{100,100}}),
536                   graphics),
537        experiment(StopTime=1));
538    equation
539      connect(accelerate.flange, mass.flange_a)    annotation (Line(
540          points={{-20,30},{0,30}},
541          color={0,127,0},
542          smooth=Smooth.None));
543      connect(constantAcc.y, accelerate.a_ref) annotation (Line(
544          points={{-59,30},{-42,30}},
545          color={0,0,127},
546          smooth=Smooth.None));
547    end Accelerate;
548
549    model Damper "Use of damper models."
550
551      extends Modelica.Icons.Example;
552      annotation (Documentation(info="<html>
553<p>
554Demonstrate usage of damper components in different variants.
555</p>
556</html>"),
557