simulation of rotational moldingrts2009.mines-albi.fr/s2-reactive_processes/s2-a.tcharkhtchi.pdf ·...
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Abbas TCHARKHTCHI
SIMULATION OFSIMULATION OF
ROTATIONAL MOLDING ROTATIONAL MOLDING
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Non-reactive rotational molding
INTRODUCTIONINTRODUCTION
Reactive rotational molding
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NON-REACTIVE ROTATIONAL MOLDING
There are not any chemical reactions during rotomolding.
The transformation is based essentially on physical state changes
The polymer is as powder (100-500µm)
heating cooling
Solid molten Solidstate
Examples: thermoplastics (PE, PP, PA, PC,…)
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• There are chemical reaction during this processing .
Chemical reactions
Liquid Solid
• Examples: Thermosets, rubbers, polymerization of certain polymers (PA6) chemical modification of certain polymers,
heating chemical reactions
Solid liquid Solid
or
REACTIVE ROTATIONAL MOLDING
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DIFFERENT STEPS OF SIMULATIONDIFFERENT STEPS OF SIMULATION
Non-reactive rotational molding
- flow of particles (powder) ?-Sintering- Melting- Rheology- Flow of melted (viscous) polymer- Solidification (crystallization)
Reactiverotational molding
- Chemical reactions (cross-linking, polymerization)- Rheology - Flow of liquid mixture
Heat transfer
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A
C
B
F50
100
150
200
time (min)
10 20 30 40
T (°C)
D
E
solid
solid+molten polymer
Molten polymer
solid+molten polymer
CYCLE TIMECYCLE TIME
solid
I II III IV V
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HEAT TRANSFERHEAT TRANSFER
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1. Convection air of oven / metallic surface of the mold
2. Conduction in the thickness of the mold
3. Transmission mold / polymer
4. Conduction in the thickness of the molten polymer layer
5. Convection polymer / mixture of air and powder
Oven mold Polymer molten+solid
air + powder
Heating
HEAT TRANSFERHEAT TRANSFER
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1 - Convection air of oven / metallic surface of the mold
2 - Conduction in the thickness of the mold
3 - Transmission mold / polymer
4 - Conduction in the thickness of the molten polymer layer
5 - Convection polymer / mixture of air and powder
HEAT TRANSFERHEAT TRANSFER
( )TThx
Tk ovmovm −=
∂
∂−
/
∂∂
∂∂
=
∂∂
ρxT
kxt
T C mpmm
∂
∂
∂
∂=∆+
∂
∂
x
Tk
xH
t
TC PPPP ρ
∂
∂−=
∂
∂−
x
Tk
x
Tk pm
( )TThx
Tk papap −=
∂
∂−
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Evolutions de Ta pour les trois conditions opératoires choisies. Comparaison des courbes expérimentales et numériques
(Tfour = 300 °C, tchauffe = 20, 25 et 30 min).
RESULTSRESULTS
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REACTIVE REACTIVE
ROTATIONAL MOLDINGROTATIONAL MOLDING
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RheologyRheology Fluid MechanicFluid Mechanic
Rheochemistry and rheokinetic of thermosets during rotational molding
Rheochemistry and rheokinetic of thermosets during rotational molding
- Cross-linking mechanism- Kinetic models
- Evolution of viscosity- Rhelogical models
Experimental methods, DSC, IR spectrophotometry, Rheometry
- Fluid flow models- Finite elements and SPH
ChemistryChemistry
Heat transfer
REACTIVE ROTATIONAL MOLDINGREACTIVE ROTATIONAL MOLDING
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Cross-linking reaction
Rheology
[ ] ( ) [ ]( )( )][]['1][]["
00
2
00HXkExOHkkxAE
dt
Ed+++×−=−
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 10 20 30 40 50 60 70 80
temps /min
tau
x d
e c
on
vers
ion
0
50
100
150
200
250
300
350
400
450
500
Vis
co
sité
Pa.
s
taux de conversion 130°C
taux de conversion 140°C
taux de conversion 140°C
Taux de conversion therorique
point de gel à 150°C
Point de gel à 140°C
Point de gel à 130°C
viscosité à 130°C 1Hz
viscositéà 140°C 1Hz
Viscosité à 150°C 1Hz
α
η
ηBA
xx
x+
−=
*
*
0
REACTIVE ROTATIONAL MOLDINGREACTIVE ROTATIONAL MOLDING
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SIMULATION (SPH METHOD)SIMULATION (SPH METHOD)
SPH is a Lagragian method for simulation of fluid flow. In this method the material at macroscopic scale is considered as a group of particles of masse mi, rate vi avec other properties like pressure, pi, temperature, Ti, internal
energy Ui, entropy Si,…
• Central function
• Smoothing length
• Conservation of
quantity of mouvement
• Conservation
of energy• Equation of state
• Density
• Schema of integration
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A cylinrical mold turning aroude its principal axis
SIMULATION OF FLUID FLOW SIMULATION OF FLUID FLOW
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A part with more complex geometry
SIMULATION OF FLUID FLOW SIMULATION OF FLUID FLOW
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Cubic mold in rotomolding condition
SIMULATION OF FLUID FLOW SIMULATION OF FLUID FLOW
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NONNON--REACTIVE REACTIVE
ROTATIONAL MOLDINGROTATIONAL MOLDING
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Melting + Coalescence
moule moule
moule moule
1st layer 2nd layer
3th layer 4th layer
Particle (polymer) Molten Polymer
FORMATION OF DIFFERENT LAYERSFORMATION OF DIFFERENT LAYERS
Layer by Layer
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mg mg mgSurfaceOf the mold
The following schema shows the mechanism of melting of a particle and its adhesion on the internal surface of the
mold.
FORMATION OF THE FIRST LAYERFORMATION OF THE FIRST LAYER
The particles fall on the bottom of the mold, will be melted
progressively and spread on the internal surface. This spreading depends on the force of gravity and the surface
tension.
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mg
γ
mg
F
The shear force induced by the weight of particle assures the adhesion between melted particle and the surface of the mold.
On the superior part of the mold, the surface tension spreads the melted polymer on the surface
FORMATION OF THE FIRST LAYERFORMATION OF THE FIRST LAYER
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NONNON--REACTIVE ROTATIONAL MOLDINGREACTIVE ROTATIONAL MOLDING
- Flow of particles (powder) ?-Sintering (coalescence + densification)
1 2
3 4
Polymer
support
Different steps of coalescence de grains 1) initial state2 and 3) growth4) final state
X
t
1 2 and 3 4
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DIFFERENT MODELSDIFFERENT MODELS
- Frenkel
Coalescence of 2 particules
xr
t r
x
ηγ
=2
32
( ) t TKr
xn
=
021
2
,
- Kuckzynski
2/1
0
=
a
t
a
X
η
γ- Eshely
t
er
xt
−η
λ=
τ−
12
3
0
2- Lontz
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t = 20 s t = 40 s t = 60 s
t = 80 s t = 100 s
T = 172,8 °CT = ambiante
t = 140 s t =160 st = 120 s
Example: PVDFExample: PVDF
- Under optical microscope
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Example: PVDFExample: PVDF
1 2 3
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NONNON--REACTIVE ROTATIONAL MOLDINGREACTIVE ROTATIONAL MOLDING
- Melting
- Rheology
- Flow of molten (viscous) polymer
- Solidification (crystallization)
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CONCLUSIONCONCLUSIONReactive rotational molding
Reactive rotational molding
Heat transfer
T=f(t)
Rheologyη=f(t)
Chemical reactions
Kinetic model
η=f(x) X: degree of conversion
fluid flow model
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CONCLUSIONCONCLUSIONNon-reactive rotational molding
Non-reactive rotational molding
Heat transfer
T=f(t)
MeltingCoalescence
Kinetic model
Formation oflayers
fluid flow model
Solidificationcrystallization
Cooling
Densification Rheology
X: degree of conversion