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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Transient Behavior of Extruders
by
Rajath Mudalamane, Dr. David I. Bigio
University of Maryland at College Park
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
INTRODUCTION: Research goals
• STAGE-I: Robust screw design- ‘Minimize variations/fluctuations in the process by using the inherent damping nature of transient behavior of extruders’
• STAGE-II: Unsteady state extrusion process ‘Design for the manufacture of materials with engineered variations in quality (based on performance requirements of the material)’
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Research goals contd
Knowledge of transient behavior of extruders
Experimental observations [1,2,3,4,5,6,7]
Extrusion Extrusion ProcessProcess
QN
Temperatures
d1 d2
d3
d4
?
Theoretical modeling
[8,9,10]
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
INTRODUCTION: Schematic of an Extruder
FEEDER
MELTING
PARTIALLY FILLED, MELT CONVEYING
MIXINGDIE PRESSURE GENERATION
Downstream Processing
•Feeder Dynamics
•Feed stock variations
•Bed instability
•Die flow instability: Spurt flow, shark skin surface roughness
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
INTRODUCTION: Disturbance rejecting characterisics of partly filled extruders
0
50
100
150
200
250
0 20 40 60 80 100 120Time (s)
Pre
ssur
e (p
si)
2 lb/hr7 lb/hr9 lb/hr11 lb/hr
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Introduction contd.
Qin
Qout
Qin
Qout
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Transient model: Extruder Geometry
Kneading block / restrictive element
Starved region Fill length (Lf)
Filled region
Conveying section
FLOW DIRECTION
Control Volume (dotted lines)
H
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Flow into Control Volume, supplied by starved regions
outin QQ
(1)
Apply law of conservation of mass to control volume:
Rate of change of accumulation of material in Control Volume
= -
Flow out of Control Volume driven by pressurization in filled region
=
Macroscopic material balance
Modified White et al approach
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
flstf QQ
dt
dV
• Vf - volume in the filled region
• Qst - flow in the starved regions
• Qfl - flow in the filled region
• Lf - length of the filled region
• – Fill fraction in starved region
flstf QQ
dt
dLWH )1(
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
drag
fst
fflfstf
Q
tLQWH
geometrytLQtLQ
dt
tdL
),(1
rheology,,,rheology,,
L is the total length of the extruder section and L= Lst+Lf
tLfdt
tdLf
f ,)(
For a given geometry and fluid:
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Simulation results: Step response
0.0
0.2
0.4
0.6
0.8
1.0
1.2
8 8.5 9 9.5 10Time (s)
Feed
Output
Pressure
Fill length
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Frequency response
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Sinusoidal disturbance in feedrate
T=0.01s
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.70 8.75 8.80 8.85Time (s)
Flo
wra
te (
cc/s
)
Feed
Output
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Sinusoidal disturbance in feedrate
T=1s
6.06.26.46.66.87.07.27.47.67.88.0
6 8 10 12 14 16Time (s)
Flo
wra
te (
cc/s
)
Feed
Output
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Effect of fill level in extruder
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
7 7.5 8 8.5 9 9.5 10 10.5 11 11.5
time (s)
Flo
wra
tes
(cc/
s)
Feed10%30%50%80%
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Effect of Depth
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25 30 35 40 45
Time (s)
Flo
w r
ate
(cc/
s)
FeedRoot diameter =0.9"0.8"0.7"0.7",80%df
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Step change in screw speed
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
0 0.5 1 1.5 2Time (s)
Fill
leng
th (
cm)
5
5.5
6
6.5
7
7.5
8
8.5
9
Flow
rate
(cc
/s)
Fill length
OutputFlowrate
Screw Speed changed from 300 to 250 rpm at t=0sInput Flowrate constant
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Sinusoidal disturbance in N
6.94E-06
6.96E-06
6.98E-06
7.00E-06
7.02E-06
7.04E-06
7.06E-06
7.08E-06
0 2 4 6 8 10 12Time
Out
put
flow
rate
(cu
bic
met
ers/
s)
T=1s
T=2s
T=4s
T=10s
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Conclusions
• Critical Frequency:– All higher frequencies are damped out and lower
frequencies experience little damping– Function of Screw geometry and operating conditions
• Critical frequency decreases with increasing fill level and vice versa
• Self-leveling response by output rate to changes in screw speed
• Screw speed CAN be used to control output rate with limitations on frequency
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Bibliography1. Tadmor, Z., Klein, I., Van
Nostrand Reinhold Co., N.Y., 1976.
2. White, F.M.,’Viscous Flow’, McGraw-Hill, 1997.
3. Bird, B.S., Stewart, Lightfoot, ‘Transport Phenomena’, McGraw-Hill, 1986
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
8. White, J.L. and Kim, E.K., SPE ANTEC, 2000.
9. White, J.L. and Kim, E.K., Poly. Eng. & Sci., Vol. 41, n 2, 2001.
10. Rauwendaal, C., ‘Polymer Extrusion’, Hanser, 1994.
11. Booy, M.L., Poly. Eng. & Sci., Vol. 20, 1980.
Bibliography (contd.)
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
INTRODUCTION contd.
0
20
40
60
80
100
120
140
160
180
200
0 50 100 150 200Time (s)
Pre
ssur
e (p
si)
2-5lb/hr2-7lb/hr2-9lb/hr