Редактирование: Integrating Rotational Degree Of Freedom in EDEM

==Task==
Understand - how rotational [[DOF]] are integrated inside EDEM. For this: prepare simulation which could be compared with analytics. <br>
For this:
# Prepare factory that creates particles
# Prepare contact model which describes the rule of interaction
# Prepare EDEM simulation
# Measure something and compare it to analytic
==Who we are==
* [[Степанов Алексей]] (responsible for contact model)
* [[Дзенушко Дайнис]] (responsible for factory and EDEM simulation)

==Factory==
We create 2 particles on a distance 0.1m and rotated at an angle of 5-15 () degrees;<br>
These particles are of 2 types "small" and a "big" one; Big particle has identity matrix as rotation matrix; Small particle is rotated using rotation matrix <br>
Particles's velocity and angular velocity equals to zero;<br>
Y and Z coordinates are the same (0.5,0.5); Only X is different (0.45 for "big" and 0.55 for "small");<br>
*For small particle:<br>
double OrientAngle = pi/12; // angle between particles in Radians<br>
orientation[0] = 1.0;	    // Rotating particle. X axis.<br>
orientation[4] = cos(OrientAngle);<br>
orientation[5] = -sin(OrientAngle);<br>
orientation[7] = sin(OrientAngle);<br>
orientation[8] = cos(OrientAngle);<br>

==Contact Model==
In our project we used simple contact modal.<br>
calculatedElem2AdditionalTorqueX =  1.0 * (elem1Orientation[7] * elem2Orientation[4] + elem2Orientation[5] * elem1Orientation[4] );

==EDEM simulation==
===Globals:===
Interaction: Particle to particle<br>
Model: our contact model<br>
No gravity<br>
There are two materials "material" and "material_2" with different density for "material" 1000 for "material_2" 1.7e+05 <br>
Restitution: 0.5<br>
No static and rolling friction<br>
===Particles:===
We create particles of 2 types;"big" with big moment of inertia (100kgm2 X-axis) and "small"(0.000285kgm2 X-axis);Both particles are made of 2 surfaces placed along Z-axis on a distance of 2 particle radius
==Measures==
We measured the period of oscillation<br>
===Analytics===
<math>T = 2\pi\sqrt{\frac{C}{\theta}} = 0.106</math>
===Integration===
We measured period using the Graph of angular velocity and got the result <br>
<math>T = 0.082</math>
==Results==
So we got the result that is different to the analytic;<br>
Then we wrote small programm on C# that integrates the equalation in a simple way and got the result<br> 
<math>T = 0.106</math><br>
We checked all in EDEM simulation; Changing parameters of particles, roll stiffness didn't gave any difference the results stayed different to analytic.
==Additional Measures==
We chacked translational kinetic and potentional energy and they really equals to zero<br>
Graph of Rotational Kinetic energy
<gallery widths=580px heights=350px perrow = 1>
Файл:EDEM_Kin_Energy.jpg
</gallery>
@@ Строка 24: / Строка 24: @@
 ==Contact Model==
-In our project we used simple contact model.<br>
+In our project we used simple contact modal.<br>
-All central forces we made zero. Also we made zero all torques except torque, which operates on a "small" particle. <br>
+calculatedElem2AdditionalTorqueX =  1.0 * (elem1Orientation[7] * elem2Orientation[4] + elem2Orientation[5] * elem1Orientation[4] );
-calculatedElem2AdditionalTorqueX =  1.0 * (elem1Orientation[7] * elem2Orientation[4] + elem2Orientation[5] * elem1Orientation[4] ); <br>
-In this formula С = 1.0
 ==EDEM simulation==
@@ Строка 57: / Строка 55: @@
 Файл:EDEM_Kin_Energy.jpg
 </gallery>
-As we can see the maximum of Kinetic energy is conserving. This graph was extended to 100 seconds(~1220 period)<br>
-and conservation of Rotational Kinetic energy was prooved. Time step ~9.75e-07s.
-[[Category: Студенческие проекты]]
-[[Category: Механика дискретных сред]]
-[[Category: Программирование]]