Changeset 1130 for branches/maintenance

Timestamp:

05/25/08 13:11:28 (6 months ago)

Author:

otter

Message:

maintenance/3.0_ImprovedFriction/Modelica:
New, much simplified method without state machine to describe friction in Rotational and Translational library. The efficiency will be usually enhanced because less event iterations. Since no state machine any longer, inconsistent friction states, due to initialization and/or impulses are no longer possible.
Release notes updated.

Location:

branches/maintenance/3.0_ImprovedFriction/Modelica

Files:

• Mechanics/Rotational.mo (modified) (15 diffs)
• Mechanics/Translational.mo (modified) (14 diffs)
• package.mo (modified) (1 diff)

branches/maintenance/3.0_ImprovedFriction/Modelica/Mechanics/Rotational.mo

@@ -669 +669 @@
           smooth=Smooth.None));
     end FirstGrounded;
+
+    model SimpleFriction "Demonstration of BearingFriction element"
+       extends Modelica.Icons.Example;
+
+      Components.Inertia inertia(
+        J=2,
+        phi(fixed=true, start=0),
+        w(fixed=true, start=0))
+        annotation (Placement(transformation(extent={{20,20},{40,40}})));
+      Sources.Torque torque
+        annotation (Placement(transformation(extent={{-20,20},{0,40}})));
+      annotation (Diagram(coordinateSystem(preserveAspectRatio=true, extent={{
+                -100,-100},{100,100}}), graphics));
+      Blocks.Sources.Sine sine(freqHz=2, amplitude=1.5)
+        annotation (Placement(transformation(extent={{-60,20},{-40,40}})));
+      Components.BearingFriction bearingFriction(tau_pos=[0,1; 1,2], peak=1.1)
+        annotation (Placement(transformation(extent={{60,20},{80,40}})));
+    equation
+      connect(torque.flange, inertia.flange_a) annotation (Line(
+          points={{0,30},{20,30}},
+          color={0,0,0},
+          smooth=Smooth.None));
+      connect(sine.y, torque.tau) annotation (Line(
+          points={{-39,30},{-22,30}},
+          color={0,0,127},
+          smooth=Smooth.None));
+      connect(inertia.flange_b, bearingFriction.flange_a) annotation (Line(
+          points={{40,30},{60,30}},
+          color={0,0,0},
+          smooth=Smooth.None));
+    end SimpleFriction;
 
     model Friction "Drive train with clutch and brake"
@@ -2282 +2313 @@
 
       // Friction torque
-      tau = if locked then sa*unitTorque else (if startForward then 
-        Modelica.Math.tempInterpol1(w, tau_pos, 2) else if startBackward then -
-        Modelica.Math.tempInterpol1(-w, tau_pos, 2) else if pre(mode) == Forward then 
-              Modelica.Math.tempInterpol1(w, tau_pos, 2) else -
-        Modelica.Math.tempInterpol1(-w, tau_pos, 2));
+      tau = if mode == Locked then  sa*unitTorque else 
+            if mode == Free then    0 else 
+            if mode == Forward then  Modelica.Math.tempInterpol1( w, tau_pos, 2) else 
+                                    -Modelica.Math.tempInterpol1(-w, tau_pos, 2);
     end BearingFriction;
 
@@ -2366 +2396 @@
               fillPattern=FillPattern.Solid),
             Line(points={{0,90},{80,70},{80,-40},{70,-40}}, color={0,0,127}),
-            Line(points={{0,90},{-80,70},{-80,-40},{-70,-40}}, color={0,0,127}),
+            Line(points={{0,90},{-80,70},{-80,-40},{-70,-40}}, color={0,0,127}), 
+
             Text(
               extent={{-150,-180},{150,-140}},
@@ -2484 +2515 @@
 
       // friction torque
-      tau = if locked then sa*unitTorque else if free then 0 else cgeo*fn*(if startForward then 
-              Modelica.Math.tempInterpol1(w, mue_pos, 2) else if startBackward then 
-              -Modelica.Math.tempInterpol1(-w, mue_pos, 2) else if pre(mode) ==
-        Forward then Modelica.Math.tempInterpol1(w, mue_pos, 2) else -
-        Modelica.Math.tempInterpol1(-w, mue_pos, 2));
+      tau = if mode == Locked then sa*unitTorque else 
+            if mode == Free then   0 else 
+            cgeo*fn*(if mode==Forward then  Modelica.Math.tempInterpol1( w, mue_pos, 2) else 
+                                           -Modelica.Math.tempInterpol1(-w, mue_pos, 2));
     end Brake;
 
@@ -2665 +2695 @@
 
       // friction torque
-      tau = if locked then sa*unitTorque else if free then 0 else cgeo*fn*(if startForward then 
-              Modelica.Math.tempInterpol1(w_rel, mue_pos, 2) else if 
-        startBackward then -Modelica.Math.tempInterpol1(-w_rel, mue_pos, 2) else 
-        if pre(mode) == Forward then Modelica.Math.tempInterpol1(w_rel, mue_pos,
-        2) else -Modelica.Math.tempInterpol1(-w_rel, mue_pos, 2));
+      tau = if mode == Locked then sa*unitTorque else 
+            if mode == Free then   0 else 
+            cgeo*fn*(if mode==Forward then  Modelica.Math.tempInterpol1( w_rel, mue_pos, 2) else 
+                                           -Modelica.Math.tempInterpol1(-w_rel, mue_pos, 2));
     end Clutch;
 
@@ -2683 +2712 @@
         "Geometry constant containing friction distribution assumption";
       parameter SI.Force fn_max(final min=0, start=1) "Maximum normal force";
-      parameter SI.AngularVelocity w_small=1e10
-        "Relative angular velocity near to zero if jumps due to a reinit(..) of the velocity can occur (set to low value only if such impulses can occur)"
-         annotation(Dialog(tab="Advanced"));
 
       Real u "normalized force input signal (0..1)";
-      SI.Force fn "Normal force (fn=fn_max*inPort.signal)";
-      Boolean startForward
-        "true, if w_rel=0 and start of forward sliding or w_rel > w_small";
-      Boolean locked "true, if w_rel=0 and not sliding";
-      Boolean stuck(final start=false) "w_rel=0 (forward sliding or locked)";
-
+      SI.Force fn "Normal force (fn=fn_max*u)";
+      Boolean locked(start=false) "true, if locked";
+      Boolean free "true, if not active (no friction)";
     protected
       SI.Torque tau0 "Friction torque for w=0 and sliding";
       SI.Torque tau0_max "Maximum friction torque for w=0 and locked";
       Real mue0 "Friction coefficient for w=0 and sliding";
-      Boolean free "true, if frictional element is not active";
       Real sa(final unit="1")
         "path parameter of tau = f(a_rel) Friction characteristic";
+      constant SI.AngularVelocity w_eps = 1e-8
+        "If newFrictionDescription: defines region around zero, where the friction state is determined by acceleration, otherwise by w";
       constant Real eps0=1.0e-4 "Relative hysteresis epsilon";
       SI.Torque tau0_max_low "lowest value for tau0_max";
@@ -2706 +2730 @@
       constant SI.AngularAcceleration unitAngularAcceleration = 1;
       constant SI.Torque unitTorque = 1;
+      Real sa0 = (tau0_max + (tau0_max - tau0))/unitTorque
+        "Value of sa when start of forward sliding at w=0";
     public
       Modelica.Blocks.Interfaces.RealInput f_normalized
@@ -2860 +2886 @@
       tau0_max = if free then tau0_max_low else peak2*tau0;
 
-      /* 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(stuck) and (sa > tau0_max/unitTorque or pre(startForward) and sa >
-        tau0/unitTorque or w_rel > w_small) or initial() and (w_rel > 0);
-      locked = pre(stuck) and not startForward;
-
-      // acceleration and friction torque
-      a_rel = unitAngularAcceleration* (if locked then 0 else sa - tau0/unitTorque);
-      tau = if locked then sa*unitTorque else (if free then 0 else cgeo*fn*
-        Modelica.Math.tempInterpol1(w_rel, mue_pos, 2));
-
-      // Determine configuration
-      stuck = locked or w_rel <= 0;
+      /* Friction characteristic */
+      locked = if w_rel > w_eps then false else 
+               if sa > tau0_max/unitTorque then false else true;
+
+      a_rel = unitAngularAcceleration*(if locked then 0 else sa - sa0);
+
+      tau = if locked then sa*unitTorque else if free then 0 else 
+                           cgeo*fn*Math.tempInterpol1(w_rel, mue_pos, 2);
     end OneWayClutch;
 
@@ -3001 +3019 @@
       SI.Torque tauLossMin "Torque loss for negative speed";
 
-      Boolean tau_aPos(start=true)
-        "true, if torque of flange_a is not negative";
-      Boolean startForward(start=false) "true, if starting to roll forward";
-      Boolean startBackward(start=false) "true, if starting to roll backward";
-      Boolean locked(start=false) "true, if gear is locked";
+      Boolean tau_aPos(start=true) "true, if torque of flange_a is >= 0";
 
       Boolean ideal "true, if losses are neglected";
 
-      constant Integer Unknown=3 "Value of mode is not known";
-      constant Integer Free=2 "Element is not active";
-      constant Integer Forward=1 "w_a > 0 (forward rolling)";
-      constant Integer Stuck=0
-        "w_a = 0 (forward rolling, locked or backward rolling)";
-      constant Integer Backward=-1 "w_a < 0 (backward rolling)";
-      Integer mode(
-        final min=Backward,
-        final max=Unknown,
-        start=Free,
-        fixed=true);
+      constant Integer Free=2 "Element is not active" annotation(HideResult=true);
+      constant Integer Forward=1 "Forward sliding" annotation(HideResult=true);
+      constant Integer Locked=0 "Locked (no relative motion)" annotation(HideResult=true);
+      constant Integer Backward=-1 "Backward sliding" annotation(HideResult=true);
+      Integer mode(final max=2, final min=-1, start=Free)
+        "Mode of friction element: 2: free, 1: forward sliding, 0: Locked, -1: Backward sliding";
 
       annotation (
@@ -3203 +3212 @@
 
     protected
+      constant SI.AngularVelocity w_eps = 1e-8
+        "Defines region around zero, where the friction state is determined by acceleration, otherwise by w_a";
       constant SI.AngularAcceleration unitAngularAcceleration = 1;
       constant SI.Torque unitTorque = 1;
-      function equal "Compare whether two Real matrices are identical"
-
-        extends Modelica.Icons.Function;
-        input Real A[:, :];
-        input Real B[:, :];
-        input Real eps=Modelica.Constants.eps
-          "two numbers r1, r2 are identical if abs(r1-r2) <= eps";
-        output Boolean result;
-      algorithm
-        result := false;
-        if size(A, 1) == size(B, 1) and size(A, 2) == size(B, 2) then
-          result := true;
-          for i in 1:size(A, 1) loop
-            for j in 1:size(A, 2) loop
-              if abs(A[i, j] - B[i, j]) >= eps then
-                result := false;
-              end if;
-            end for;
-          end for;
-        end if;
-        annotation (Documentation(info="<HTML>
-<p>
-The function call
-</p>
-<pre>     equal(A1, A2);
-</pre>
-<p>
-returns <b>true</b>, if the two Real matrices A1 and A2 have the
-same dimensions and the same elements. Otherwise the function
-returns <b>false</b>. Two elements r1 and r2 of A1 and A2 respectively
-are checked on equality by the test 'eps >= abs(r1-r2)', where 'eps'
-can be provided as third argument of the function (the default is
-Modelica.Constants.eps).
-</p>
-</HTML>"));
-      end equal;
     equation
       assert(abs(ratio) > 0,
         "Error in initialization of LossyGear: ratio may not be zero");
 
-      ideal = equal(lossTable, [0, 1, 1, 0, 0]);
+      ideal = Modelica.Math.Matrices.isEqual(lossTable, [0, 1, 1, 0, 0], Modelica.Constants.eps);
 
       interpolation_result = if ideal then [1, 1, 0, 0] else 
@@ -3275 +3250 @@
       tauLossMin = if tau_aPos then quadrant4 else quadrant3;
 
-      // Determine rolling/stuck mode when w_rel = 0
-      startForward = pre(mode) == Stuck and sa > tauLossMax/unitTorque or initial() and w_a
-         > 0;
-      startBackward = pre(mode) == Stuck and sa < tauLossMin/unitTorque or initial() and w_a
-         < 0;
-      locked = not (ideal or pre(mode) == Forward or startForward or pre(mode)
-         == Backward or startBackward);
-
-      /* Parameterized curve description a_a = f1(sa), tauLoss = f2(sa)
-       In comparison to Modelica.Mechanics.Rotational.FrictionBase it is possible
-       to simplify the following expression as mode == Stuck is assured in case
-       of startForward or startBackward */
-      tauLoss = if ideal then 0 else (if locked then sa*unitTorque else (if (startForward or 
-            pre(mode) == Forward) then tauLossMax else tauLossMin));
-
-      a_a = unitAngularAcceleration*(if locked then 0 else sa - tauLoss/unitTorque);
-
-      /* Finite state machine to fix configuration after the computation above
-       The above equations are only dependent on pre(mode) and not on the actual
-       value of mode. This prevents loops. So mode can be determined in one step. */
-      mode = if ideal then Free else (if (pre(mode) == Forward or startForward)
-         and w_a > 0 then Forward else if (pre(mode) == Backward or startBackward)
-         and w_a < 0 then Backward else Stuck);
+      // Determine mode of friction element
+       mode = if ideal then Free else 
+              if w_a >  w_eps then Forward else 
+              if w_a < -w_eps then Backward else 
+              if sa > tauLossMax/unitTorque then Forward else 
+              if sa < tauLossMin/unitTorque then Backward else Locked;
+
+       tauLoss = if ideal then 0 else 
+                 if mode == Free then 0 else 
+                 if mode == Locked then sa*unitTorque else 
+                 if mode == Forward then tauLossMax else tauLossMin;
+
+       a_a = unitAngularAcceleration*(if mode==Locked then 0 else sa - tauLoss/unitTorque);
     end LossyGear;
 
@@ -3579 +3544 @@
               fillColor={192,192,192}),
             Polygon(
-              points={{-60,10},{-60,20},{-40,40},{-40,-40},{-60,-20},{-60,10}},
+              points={{-60,10},{-60,20},{-40,40},{-40,-40},{-60,-20},{-60,10}}, 
+
               lineColor={0,0,0},
               fillPattern=FillPattern.HorizontalCylinder,
@@ -6236 +6202 @@
 </p>
 </html>"));
-      // parameter SI.AngularVelocity w_small=1 "Relative angular velocity near to zero (see model info text)";
-      parameter SI.AngularVelocity w_small=1.0e10
-        "Relative angular velocity near to zero if jumps due to a reinit(..) of the velocity can occur (set to low value only if such impulses can occur)"
-         annotation(Dialog(tab="Advanced"));
+
     // Equations to define the following variables have to be defined in subclasses
       SI.AngularVelocity w_relfric
@@ -6250 +6213 @@
       SI.Torque tau0_max "Maximum friction torque for w=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(final unit="1")
         "Path parameter of friction characteristic tau = f(a_relfric)";
-      Boolean startForward(start=false, fixed=true)
-        "true, if w_rel=0 and start of forward sliding";
-      Boolean startBackward(start=false, fixed=true)
-        "true, if w_rel=0 and start of backward sliding";
-      Boolean locked(start=false) "true, if w_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 "w_rel > 0 (forward sliding)";
-      constant Integer Stuck=0
-        "w_rel = 0 (forward sliding, locked or backward sliding)";
-      constant Integer Backward=-1 "w_rel < 0 (backward sliding)";
-      Integer mode(
-        final min=Backward,
-        final max=Unknown,
-        start=Unknown, fixed=true);
+
+      constant Integer Free=2 "Element is not active" annotation(HideResult=true);
+      constant Integer Forward=1 "Forward sliding" annotation(HideResult=true);
+      constant Integer Locked=0 "Locked (no relative motion)" annotation(HideResult=true);
+      constant Integer Backward=-1 "Backward sliding" annotation(HideResult=true);
+      Integer mode(final max=2, final min=-1, start=Free)
+        "Mode of friction element: 2: free, 1: forward sliding, 0: Locked, -1: Backward sliding";
+
     protected
+      constant SI.AngularVelocity w_eps = 1e-8
+        "If newFrictionDescription: defines region around zero, where the friction state is determined by acceleration, otherwise by w";
       constant SI.AngularAcceleration unitAngularAcceleration = 1 annotation(HideResult=true);
       constant SI.Torque unitTorque = 1 annotation(HideResult=true);
@@ -6274 +6233 @@
         "Value of sa when start of forward sliding at w=0";
     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 >  tau0_max/unitTorque or 
-        pre(mode) == Backward and w_relfric >  w_small or initial() and w_relfric > 0;
-      startBackward = pre(mode) == Stuck and sa < -tau0_max/unitTorque or 
-        pre(mode) == Forward  and w_relfric < -w_small or initial() and w_relfric < 0;
-      locked = not free and 
-        not (pre(mode) == Forward or startForward or pre(mode) == Backward or startBackward);
-      a_relfric/unitAngularAcceleration = if locked then               0 else 
-                                          if free then                 sa else 
-                                          if startForward then         sa - sa0 else 
-                                          if startBackward then        sa + sa0 else 
-                                          if pre(mode) == Forward then sa - sa0 else 
-                                                                       sa + sa0;
-    /* Friction torque has to be defined in a subclass. Example for a clutch:
-   tau = if locked then sa else 
-         if free then   0 else 
-         cgeo*fn*(if startForward then          Math.tempInterpol1( w_relfric, mue_pos, 2) else
-                  if startBackward then        -Math.tempInterpol1(-w_relfric, mue_pos, 2) else
-                  if pre(mode) == Forward then  Math.tempInterpol1( w_relfric, mue_pos, 2) else 
-                                               -Math.tempInterpol1(-w_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 w_relfric > 0 then 
-           Forward else 
-         if (pre(mode) == Backward or pre(mode) == Free or startBackward) and w_relfric < 0 then 
-           Backward else 
-           Stuck);
+       mode = if free then Free else 
+              if w_relfric >  w_eps then Forward else 
+              if w_relfric < -w_eps then Backward else 
+              if sa > tau0_max/unitTorque then Forward else 
+              if sa < -tau0_max/unitTorque then Backward else Locked;
+
+       a_relfric = unitAngularAcceleration*(if mode == Locked then  0 else 
+                                            if mode == Free then    sa else 
+                                            if mode == Forward then sa - sa0 else sa + sa0);
+
+       /* Friction torque has to be defined in a subclass. Example for a clutch:
+      tau = if mode == Locked then sa*unitTorque else 
+            if mode == Free   then 0 else 
+            cgeo*fn*(if mode==Forward then  Math.tempInterpol1(w_relfric, mue_pos, 2)
+                                      else -Math.tempInterpol1(-w_relfric, mue_pos, 2));
+   */
     end PartialFriction;
 

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

@@ -898 +898 @@
             Text(
               extent={{-98,-68},{102,-94}},
-              textString="positive force => spool moves in positive direction ",
+              textString="positive force => spool moves in positive direction ", 
+
               lineColor={0,0,255}),
             Text(
@@ -1990 +1991 @@
 
     // 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));
+       f = if mode == Locked then  sa*unitForce else 
+           if mode == Free then      0 else 
+           if mode == Forward then  Math.tempInterpol1( v, f_pos, 2) else 
+                                   -Math.tempInterpol1(-v, f_pos, 2);
+
     end SupportFriction;
 
@@ -2179 +2180 @@
       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));
+    // friction force
+      f = if mode == Locked then  sa*unitForce else 
+          if mode == Free then 0 else 
+          cgeo*fn*(if mode == Forward then  Math.tempInterpol1( v, mue_pos, 2) else 
+                                           -Math.tempInterpol1(-v, mue_pos, 2));
     end Brake;
 
@@ -2627 +2626 @@
               textString="Length L",
               lineColor={0,0,255})}));
+
     encapsulated partial model PartialFrictionWithStop
         "Base model of Coulomb friction elements with stop"
@@ -2658 +2658 @@
       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);
+
+      constant Integer Free=2 "Element is not active" annotation(HideResult=true);
+      constant Integer Forward=1 "Forward sliding" annotation(HideResult=true);
+      constant Integer Locked=0 "Locked (no relative motion)" annotation(HideResult=true);
+      constant Integer Backward=-1 "Backward sliding" annotation(HideResult=true);
+      Integer mode(final max=2, final min=-1, start=Free)
+          "Mode of friction element: 2: free, 1: forward sliding, 0: Locked, -1: Backward sliding";
       protected
+      constant SI.Velocity v_eps = 1e-8
+          "If newFrictionDescription: defines region around zero, where the friction state is determined by acceleration, otherwise by v";
       constant SI.Acceleration unitAcceleration = 1 annotation(HideResult=true);
       constant SI.Force unitForce = 1 annotation(HideResult=true);
@@ -2680 +2675 @@
           "Value of sa when start of forward sliding at w=0";
     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(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(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 - sa0 else 
-                                   if startBackward then        sa + sa0 else 
-                                   if pre(mode) == Forward then sa - sa0 else 
-                                                                sa + sa0;
-    /* 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);
+    /* Friction characteristic */
+       mode = if free then Free else 
+              if v_relfric >  v_eps and s < (smax - L/2) then Forward else 
+              if v_relfric < -v_eps and s > (smin + L/2) then Backward else 
+              if sa >  f0_max/unitForce and s < (smax - L/2) then Forward else 
+              if sa < -f0_max/unitForce and s > (smin + L/2) then Backward else Locked;
+
+       a_relfric = unitAcceleration*(if mode == Locked then  0 else 
+                                     if mode == Free then    sa else 
+                                     if mode == Forward then sa - sa0 else sa + sa0);
     end PartialFrictionWithStop;
+
     equation
       // Constant auxiliary variables
@@ -2718 +2692 @@
       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);
@@ -2723 +2698 @@
       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)));
+       f = if mode == Locked then  sa*unitForce else 
+           if mode == Free then    0 else 
+           if 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));
+
     // Define events for hard stops and reinitiliaze the state variables velocity v and position s
     algorithm
@@ -3561 +3537 @@
             preserveAspectRatio=true,
             extent={{-100,-100},{100,100}},
-            grid={1,1}), graphics={Line(points={{-70,0},{-90,0}}, color={0,0,0}),
+            grid={1,1}), graphics={Line(points={{-70,0},{-90,0}}, color={0,0,0}), 
               Text(
               extent={{80,-28},{114,-62}},
@@ -3593 +3569 @@
             preserveAspectRatio=true,
             extent={{-100,-100},{100,100}},
-            grid={1,1}), graphics={Line(points={{-70,0},{-90,0}}, color={0,0,0}),
+            grid={1,1}), graphics={Line(points={{-70,0},{-90,0}}, color={0,0,0}), 
               Text(
               extent={{80,-28},{111,-61}},
@@ -3627 +3603 @@
             preserveAspectRatio=true,
             extent={{-100,-100},{100,100}},
-            grid={1,1}), graphics={Line(points={{-70,0},{-90,0}}, color={0,0,0}),
+            grid={1,1}), graphics={Line(points={{-70,0},{-90,0}}, color={0,0,0}), 
               Text(
               extent={{80,-28},{115,-60}},
@@ -4681 +4657 @@
 </html>