Abbas TCHARKHTCHI

SIMULATION OFSIMULATION OF

ROTATIONAL MOLDING ROTATIONAL MOLDING

Non-reactive rotational molding

INTRODUCTIONINTRODUCTION

Reactive rotational molding

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,…)

• 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

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

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

HEAT TRANSFERHEAT TRANSFER

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

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 −=

∂

∂−

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

REACTIVE REACTIVE

ROTATIONAL MOLDINGROTATIONAL MOLDING

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

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

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

A cylinrical mold turning aroude its principal axis

SIMULATION OF FLUID FLOW SIMULATION OF FLUID FLOW

A part with more complex geometry

SIMULATION OF FLUID FLOW SIMULATION OF FLUID FLOW

Cubic mold in rotomolding condition

SIMULATION OF FLUID FLOW SIMULATION OF FLUID FLOW

NONNON--REACTIVE REACTIVE

ROTATIONAL MOLDINGROTATIONAL MOLDING

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

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.

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

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

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

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

Example: PVDFExample: PVDF

1 2 3

NONNON--REACTIVE ROTATIONAL MOLDINGREACTIVE ROTATIONAL MOLDING

- Melting

- Rheology

- Flow of molten (viscous) polymer

- Solidification (crystallization)

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

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