Download Study Materials for Rolling Compaction | MATE 460 and more Study notes Materials science in PDF only on Docsity!
INTRODUCTION
Rolling compaction is a widely utilized industrial process by which a material in a powder state is compacted into an agglomerate form. Rolling compaction is most often used as an intermediary step in the overall powder processing. Figure 1 shows a typical powder compaction process
Figure 1 – Typical compaction process
Agglomeration, or the act of collecting in mass, is an important step in powder processing because it improves the ease of powder handling and material flowability, it produces a product with a uniform shape, and allows for very precise mixture control.
Rolling compaction is a simple process, but calculations of the stress states are very complex. Figure 2 shows a typical rolling set up at half symmetry.
Figure 2 – Rolling compaction Schematic
Here we can see some of the processing parameters for rolling compaction as
well as the overall flow direction of the material. ho and hf are the entrance and exit heights respectively, α is the overall contact angle, R is the radius, and Fr and Ft are the radial force and moment acting on the roller respectively.
Another factor that complicates rolling compaction is the use of materials that are not fully dense. A powder, or any porous material, acts differently mechanically than fully dense materials. Because pressure densifies a porous material it yields along a yield locus, which is a function of equivalent stress and pressure and can be seen in Figure 3.
Figure 3 - Yield locus for a fully dense material (left) and a porous material (right)
The material behaves elastically as long as it is contained within the locus, but when the yield conditions hit the yield locus the material flows plastically under conditions for that material, or in other words, it yields by the flow rule for that material.
In order to gain a better understanding of the rolling compaction process, an explicit model has been generated in ABAQUS® for the simulation and parametric study of variables associated with rolling compaction.
MODEL CONSTRUCTION
Powder Green Granules
FormingProcess
Final Compact
CompactionRolling Granulation
Flow
Fr Ft
α
R
ho
hf
θ=
θ=α
ELASTIC (reversible)
tensile compressive^ p
σY (^) YIELD
σ
Fully Dense Materials Porous Materials
ELASTIC (reversible) tensile compressive
YIELD
σ
p
In order to gain a better understanding of the compaction process, a set of ABAQUS® models was created with different processing parameters in order to note the effects of these parameters on the final compact. These models are based on the standard two dimensional rolling compaction model for fully dense materials given in the examples in the ABAQUS® documentation. This model is a 2 Dimensional (2D) half symmetry model.
The model given in the example was one that had a rigid surface acting as a roller with the material moving under the roller and being deformed through this process. A schematic of this can be seen in Figure 4.
Figure 4 – Schematic of the model given in the examples
This model has problems that could lead to exaggerated errors in later calculations. The greatest problem is the severe deformation that the mesh undergoes as it travels through the rollers.
In order to limit the effects of these errors the model was converted from a pure Lagrangian model to a Arbitrary Lagrangian Eulerian (ALE) model. This means that instead of the entire mesh moving through the rollers,
the mesh stays at a constant inflow and out flow points. The material then flows through the mesh therefore allowing the mesh to keep a more consistent shape. This is also coupled with adaptive meshing to keep the elements as close to the equilibrium shape as possible. Figure 5 shows the ALE model schematic.
Figure 5 – ALE mode schematic
The next modification made was making the material a porous material, yielding under the Gurson model for porous materials, and with the parameters used for q 1 , q2 , q3 , being 1, 1, and 1 respectively. The effect of varying the yield parameters of the material was not examined in this study, so all of these parameters are constant throughout the models.
Table 1 is a list of the parameters used in this model. Model Constants Density 7.85E+03 kg/m^ Relative Density 5.00E- Radius 3.00E-01 m Mass Scaling 1.00E+ time 1.50E+00 sec Unless otherwise noted mu 0. Entrance Height 0.02 m Exit Height 0.01 m alpha 22.5 degrees Gap Size 0.01 m Table 1 – Model parameters
that feeds the material through the rollers. Figure 8 show the how much of an effect that friction plays on the compaction process.
VVF vs. Coef of Friction
0.00E+ 5.00E- 1.00E-
1.50E- 2.00E- 2.50E- 3.00E-
3.50E- 4.00E-
4.50E-
0 0.2 0.4 0.6 0.8 1 Coef of Friction
VVF
Figure 8 – VVF dependence on friction
There is a moderate improvement at 0.2, though it takes almost an entire second for the material to reach steady-state and the material only experiences a 15% compaction.
The neutral angle moves farther away from the exit point from the rollers as the friction coefficient rises. This can be seen in Figure 9
Neutral angle vs Coef. of Friction
15
0 0.2 0.4 0.6 0.8 1 Coef. of Friction
Neutral Angle (deg)
Figure 9 – Neutral angle dependence on friction
This is intuitive because as the friction goes up, the material can be more easily accelerated to the same speed as the roller.
The clamping force varies along a similarly predictable path, and as reaches its maximum as the material approaches
full density. Figure 10 shows this, note that the force is negative because it points down.
Normalize Clamping Force vs. Coef of Friction
-3.50E+
-3.00E+
-2.50E+
-2.00E+
-1.50E+
-1.00E+
-5.00E-
0.00E+ 0 0.2 0.4 0.6 0.8 1
Coef of Friction
Clamping Force/yeild
stress/area
Figure 10 – Clamping force dependence on friction.
The torque exhibits similar behavior as seen in Figure 11.
Normalize Torque vs. Coef of Friction
0.00E+
5.00E-
1.00E-
1.50E-
2.00E-
2.50E-
3.00E-
3.50E-
4.00E-
0 0.2 0.4 0.6 0.8 1 Coef of Friction
Torque/yeild stress/area
Figure 11 – Torque dependence on friction.
Gap Size
Gap size is a key factor in the compaction of the material. The values for gap size that were studied are 0.005, 0.01, 0.035, 0.06, 0.11 meters. Anything above 0.01 did not fully compact across the cross section of the green body. This is seen in Figure 12.
(a)
(b)
(c) Figure 12 – Variation in porosity across the cross section for a) GS=0.035m, b) GS=0.06m, and c) GS=0.11m
As seen in the above figure, only the outside edge of the compact reaches its final density. So the data for these compactions are irrelevant and inaccurate.
Contact Angle
The contact angle also plays an important role in the compaction of the powders as the contact angle determines the pressure imparted on the compact. Figure 13 shows this relationship between the contact angle and the neutral angle.
Neutral Angle vs. Contact Angle
0 5 10 15 20 25 30 35 Neutral Angle (deg)
Contact Angle (deg)
Figure 13 – Neutral angle dependence on contact angle.
Because there is a greater amount of material flowing through the rollers, The porosity is expected to go down as the contact angle increases, which is shown in Figure 14.
VVF vs. Contact Angle
0.00E+
5.00E-
1.00E-
1.50E-
2.00E-
2.50E-
0 5 10 15 20 25 30 35 Contact Angle (deg)
VVF
Figure 14 – Contact angle dependence of VVF
The clamping force and torque is also representative of the increasing density of the compact.
CONCLUSIONS
The rolling compaction process depends greatly on the friction between the rollers and the material. If the friction between the rollers and the material is not great enough, the material cannot be taken into the rollers. This results in the extrusion of the material with little to no compaction of the powder. This can be seen in Figure 15.
BASIC MODEL
*HEADING
ABAQUS/Explicit (Analytical rigid surfaces) (HOURGLASS=STIFFNESS) Contact Angle 22.5deg Radius 0.3m Friction 0. h0=0.033m *RESTART,WRITE,NUM=
******************Bottom *NODE 1, 0.1, 0. 8001, 0.1, 0. 26, 0., 0. 8026, 0., 0. 66, -0.114798, 0. 8066, -0.114798, 0. 101, -0.2, 0. 8101, -0.2, 0. ********************Roll *NODE, NSET=ROLL 9999, 0., 0. **NODE **10200, 0., 0. **10001,-0.3, 0. *******************Generate Bottome lIne *NGEN,NSET=NBOTTOM 1,26, *NGEN,NSET=NBOTTOM 26,66, *NGEN,NSET=NBOTTOM 66,101, *******************GENERATE TOP LINE *NGEN,NSET=NTOP 8001,8026, *NGEN,NSET=NTOP, LINE=C 8026,8066,1, *NGEN,NSET=NTOP 8066,8101, *******************GENERATE BACK/FRONT/FLOW LINES *NGEN,NSET=NBACK 101,8101, *NGEN,NSET=NFRONT 1,8001, *NSET,NSET=NINFLOW
272.02E06,0.
308.53E06,0.
337.37E06,0.
361.58E06,0.
382.65E06,0.
401.42E06,0.
418.42E06,0.
434.01E06,0.
448.45E06,1.
*DENSITY
7.85E3,
*POROUS METAL PLASTICITY,RELATIVE DENSITY=.
******************INITIAL CONDITIONS
*INITIAL CONDITIONS,TYPE=VELOCITY
BAR,1,0.
******************CONTACT CONDITIONS
*SURFACE,NAME=INFLOW,REGION TYPE=EULERIAN
EINFLOW, S
*SURFACE,NAME=OUTFLOW,REGION TYPE=EULERIAN
EOUTFLOW, S
*SURFACE,TYPE=ELEMENT,NAME=SURF
ETOP,S
*SURFACE, TYPE=SEGMENTS,NAME=SROLLER
START, 0., 0.
CIRCL, -0.3, 0.31 , 0., 0.
*RIGID BODY, REF NODE=9999,
ANALYTICAL SURFACE=SROLLER
**SURFACE,TYPE=ELEMENT,NAME=SROLLER
**EROLLER,SNEG
**RIGID BODY,ELSET=EROLLER,REF NODE=
****************BOUNDARY CONDITIONS
*STEP
**define the all time needed in the step *DYNAMIC,EXPLICIT ,1. *FIXED MASS SCALING,FACTOR=100000,ELSET=METAL ** *BOUNDARY NBOTTOM,2, 9999,1, ** *BOUNDARY,TYPE=VELOCITY
****************SURFACE INTERACTIONS
*SURFACE INTERACTION,NAME=FRICT
*FRICTION
*CONTACT PAIR,INTERACTION=FRICT
SURF1,SROLLER
*OUTPUT, FIELD, TIME MARKS=YES, NUMBER INTERVAL=
*ELEMENT OUTPUT,ELSET=METAL
PEEQ, VVF, S
*NODE OUTPUT,NSET=BAR
U,
*CONTACT OUTPUT
CSTRESS,
*OUTPUT, HIST, FREQ=
*ENERGY OUTPUT, VAR=PRESELECT
*NODE OUTPUT, NSET=NBACK
V,
*NODE OUTPUT, NSET=ROLL
U, RF
*OUTPUT, FIELD, TIME MARKS=YES, NUMBER INTERVAL=
*ELEMENT OUTPUT,ELSET=METAL
PEEQ, VVF, S
*NODE OUTPUT,NSET=BAR
U,
*ADAPTIVE MESH, ELSET=METAL,CONTROLS=ADAPT
*ADAPTIVE MESH CONTROLS, NAME=ADAPT
*ADAPTIVE MESH CONSTRAINT, TYPE=DISPLACEMENT
NINFLOW, 1,1, 0.
NOUTFLOW,1,1,0.
*END STEP
*NSET,NSET=NOUTFLOW
NFRONT
******************GENERATE ROLLER/BAR NODES
*NFILL,NSET=BAR
NBOTTOM,NTOP,8,
**NGEN, NSET=NROLLER, LINE=C
*****************GENERATE ELEMENTS
*ELEMENT,TYPE=CPE4R,ELSET=METAL
*ELGEN,ELSET=METAL
****(master element,# of rows,increment of node, increment of element, # elements in row, increment of nodes in row, increment of element) *ELSET,ELSET=ETOP,GEN 7001,7100, *ELSET,ELSET=EBOTTOM,GEN 1,100, *ELSET,ELSET=EBACK,GEN 100,7100, *ELSET,ELSET=EFRONT,GEN 1,7001, *****************FLOW ELEMENTS *ELSET,ELSET=EINFLOW EBACK *ELSET,ELSET=EOUTFLOW EFRONT *****************ROLLER ELEMENTS **ELEMENT, TYPE=R2D2,ELSET=EROLLER **10001,10001, **ELGEN,ELSET=EROLLER **10001,199,1,
*****************MATERIAL PROPERTIES *SOLID SECTION,ELSET=METAL,MAT=C15,CONTROL=B 1., *SECTION CONTROLS, HOURGLASS=STIFFNESS, NAME=B
*MATERIAL,NAME=C *ELASTIC 1.5E11,. *PLASTIC 168.72E06, 219.33E06,0. 272.02E06,0.
308.53E06,0.
337.37E06,0.
361.58E06,0.
382.65E06,0.
401.42E06,0.
418.42E06,0.
434.01E06,0.
448.45E06,1.
*DENSITY
7.85E3,
*POROUS METAL PLASTICITY,RELATIVE DENSITY=.
******************INITIAL CONDITIONS
*INITIAL CONDITIONS,TYPE=VELOCITY
BAR,1,0.
******************CONTACT CONDITIONS
*SURFACE,NAME=INFLOW,REGION TYPE=EULERIAN
EINFLOW, S
*SURFACE,NAME=OUTFLOW,REGION TYPE=EULERIAN
EOUTFLOW, S
*SURFACE,TYPE=ELEMENT,NAME=SURF
ETOP,S
*SURFACE, TYPE=SEGMENTS,NAME=SROLLER
START, 0., 0.
CIRCL, -0.3, 0.31 , 0., 0.
*RIGID BODY, REF NODE=9999,
ANALYTICAL SURFACE=SROLLER
**SURFACE,TYPE=ELEMENT,NAME=SROLLER
**EROLLER,SNEG
**RIGID BODY,ELSET=EROLLER,REF NODE=
****************BOUNDARY CONDITIONS
*STEP
**define the all time needed in the step *DYNAMIC,EXPLICIT ,2. *FIXED MASS SCALING,FACTOR=100000,ELSET=METAL ** *BOUNDARY NBOTTOM,2, 9999,1, ** *BOUNDARY,TYPE=VELOCITY 9999,6,6,0.
CONTACT ANGLE = 15º
*HEADING
ABAQUS/Explicit (Analytical rigid surfaces) (HOURGLASS=STIFFNESS) Contact Angle 15deg Radius 0.3m Friction 0. h0=0.020m *RESTART,WRITE,NUM=
******************Bottom *NODE 1, 0.1, 0. 8001, 0.1, 0. 26, 0., 0. 8026, 0., 0. 56, -0.077607253, 0. 8056, -0.077607253, 0. 101, -0.2, 0. 8101, -0.2, 0. ********************Roll *NODE, NSET=ROLL 9999, 0., 0. **NODE **10200, 0., 0. **10001,-0.3, 0. *******************Generate Bottome lIne *NGEN,NSET=NBOTTOM 1,26, *NGEN,NSET=NBOTTOM 26,56, *NGEN,NSET=NBOTTOM 56,101, *******************GENERATE TOP LINE *NGEN,NSET=NTOP 8001,8026, *NGEN,NSET=NTOP, LINE=C 8026,8056,1, *NGEN,NSET=NTOP 8056,8101, *******************GENERATE BACK/FRONT/FLOW LINES *NGEN,NSET=NBACK 101,8101, *NGEN,NSET=NFRONT 1,8001, *NSET,NSET=NINFLOW NBACK
*NSET,NSET=NOUTFLOW
NFRONT
******************GENERATE ROLLER/BAR NODES
*NFILL,NSET=BAR
NBOTTOM,NTOP,8,
**NGEN, NSET=NROLLER, LINE=C
*****************GENERATE ELEMENTS
*ELEMENT,TYPE=CPE4R,ELSET=METAL
*ELGEN,ELSET=METAL
****(master element,# of rows,increment of node, increment of element, # elements in row, increment of nodes in row, increment of element) *ELSET,ELSET=ETOP,GEN 7001,7100, *ELSET,ELSET=EBOTTOM,GEN 1,100, *ELSET,ELSET=EBACK,GEN 100,7100, *ELSET,ELSET=EFRONT,GEN 1,7001, *****************FLOW ELEMENTS *ELSET,ELSET=EINFLOW EBACK *ELSET,ELSET=EOUTFLOW EFRONT *****************ROLLER ELEMENTS **ELEMENT, TYPE=R2D2,ELSET=EROLLER **10001,10001, **ELGEN,ELSET=EROLLER **10001,199,1,
*****************MATERIAL PROPERTIES *SOLID SECTION,ELSET=METAL,MAT=C15,CONTROL=B 1., *SECTION CONTROLS, HOURGLASS=STIFFNESS, NAME=B
*MATERIAL,NAME=C *ELASTIC 1.5E11,. *PLASTIC 168.72E06, 219.33E06,0. 272.02E06,0.
****************SURFACE INTERACTIONS
*SURFACE INTERACTION,NAME=FRICT
*FRICTION
*CONTACT PAIR,INTERACTION=FRICT
SURF1,SROLLER
*OUTPUT, FIELD, TIME MARKS=YES, NUMBER INTERVAL=
*ELEMENT OUTPUT,ELSET=METAL
PEEQ, VVF, S
*NODE OUTPUT,NSET=BAR
U,
*CONTACT OUTPUT
CSTRESS,
*OUTPUT, HIST, FREQ=
*ENERGY OUTPUT, VAR=PRESELECT
*NODE OUTPUT, NSET=NBACK
V,
*NODE OUTPUT, NSET=ROLL
U, RF
*OUTPUT, FIELD, TIME MARKS=YES, NUMBER INTERVAL=
*ELEMENT OUTPUT,ELSET=METAL
PEEQ, VVF, S
*NODE OUTPUT,NSET=BAR
U,
*ADAPTIVE MESH, ELSET=METAL,CONTROLS=ADAPT
*ADAPTIVE MESH CONTROLS, NAME=ADAPT
*ADAPTIVE MESH CONSTRAINT, TYPE=DISPLACEMENT
NINFLOW, 1,1, 0.
NOUTFLOW,1,1,0.
*END STEP
