Three-Dimensional DEM Simulations of Bulk Handling by Screw Conveyors

864/JOURNAL OF ENGINEERING MECHANICS/SEPTEMBER2001

JOURNAL OF ENGINEERING MECHANICS /SEPTEMBER 2001/

865

FIG. 1.

Spiral Object in DEM

FIG. 3.Calculation Cycle in DEM

FIG. 2.Unfolded Figure of Spiral Line at r p 22

r =x ϩy (5)͙p p p

y p

Ϫ1

␾=tan (6)

p x p

If r p is within the range between r spin and r spout ,the particle is able to contact the surface of the spiral.

Fig.2shows an unfolded depiction of the spiral line at a distance r p from the z Ј-axis.Assuming the spiral has no thick-ness,the distance between the center of the particle and the spiral surface perpendicular to the spiral surface d is given by

p d =

z Ϫ

␪cos ␾(7)

p p p ͩ

ͪ

2␲

By comparing the distance given by (7)and the particle radius R p ,the contact can be judged between the particle and the spiral object

d

d ՆR =no contact

(8)

p p Also,the normal vector at the contact point is given by sub-stituting r p ,␪p ,and ␾p given by (3)–(6)into (2).

In the same way,contact can be judged between a particle and the edge of the spiral,considering the distance and the direction between a particle and a contact point on the edge.Further,the equations for cylinder objects can be derived with a procedure similar to that described above.

Fig.3is a summary of the DEM logic used in this study,with emphasis on the force-displacement law between particles and screw conveyor components.In the force-displacement law,every particle parameter expressed in global coordinates is transformed into local coordinates based on a spiral or a cylinder object;then,contact with the spiral or the cylinder object is checked,using equations as described above.If the particle contacts the object,forces are applied to the particle expressed in local coordinates,using a force-displacement law.This force is transformed into global coordinates and added to the other contributions,such as contact forces between the other particles and body forces.This process is performed for all particles.For the case in which there is more than one object,as in the present analysis,the process encompasses every object.Of course,the force applied to each object is recorded during this process.Each machine object (e.g.,spiral,cylinders)is driven with prescribed translational and angular velocities,and each particle obeys Newton’s second law of motion.

A linear contact law is used,in which normal and shear forces are proportional to both the overlap at the contact point and to the stiffness.For energy dissipation at a contact hys-teretic damping is introduced,in which normal stiffness on