A.tcharkhtchi-simulation Of Roto Molding Process

SIMULATION OF ROTATIONAL MOLDING

Abbas TCHARKHTCHI

INTRODUCTION Non-reactive rotational molding

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

Solid

cooling

molten state

Examples: thermoplastics (PE, PP, PA, PC,…)

Solid

REACTIVE ROTATIONAL MOLDING • There are chemical reaction during this processing .

Chemical reactions

Liquid

Solid

or heating

Solid

chemical reactions

liquid

Solid

• Examples: Thermosets, rubbers, polymerization of certain polymers

(PA6) chemical modification of certain polymers,

DIFFERENT STEPS OF SIMULATION Non-reactive rotational molding

Reactive rotational molding - Chemical reactions (crosslinking, polymerization) - Rheology - Flow of liquid mixture

- flow of particles (powder) ? -Sintering - Melting - Rheology - Flow of melted (viscous) polymer - Solidification (crystallization)

Heat transfer

CYCLE TIME 200

T (°C)

C 150

100

D

B

A

E F

50

I

II

III 10

IV 20

V

time (min) 40

30

solid Molten polymer solid+molten polymer

solid

solid+molten polymer

HEAT TRANSFER

HEAT TRANSFER Heating Oven

1.

mold

Polymer molten+solid

air + powder

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 TRANSFER 1 - Convection air of oven / metallic surface of the mold

 ∂T − km   ∂x 2 - Conduction in the thickness of the mold

  = hov / m (Tov − T ) 

∂T  ∂  ∂T  km ρm Cpm  =   ∂x   ∂t  ∂x 

3 - Transmission mold / polymer

 ∂T − km   ∂x

  ∂T  = − k   p   ∂x 

4 - Conduction in the thickness of the molten polymer layer ∂  ∂T   ∂T  ρ P C PP   + ∆H =  k P  ∂x  ∂x   ∂t  5 - Convection polymer / mixture of air and powder

 ∂T − kp  ∂x

  = h pa (T pa − T ) 

RESULTS

Evolutions de Ta pour les trois conditions opératoires choisies. Comparaison des courbes expérimentales et numériques (Tfour = 300 °C, tchauffe = 20, 25 et 30 min).

REACTIVE ROTATIONAL MOLDING

REACTIVE ROTATIONAL MOLDING Rheochemistry and rheokinetic of thermosets during rotational molding

Chemistry

- Cross-linking mechanism - Kinetic models

Rheology

- Evolution of viscosity - Rhelogical models

Fluid Mechanic

- Fluid flow models - Finite elements and SPH

Heat transfer Experimental methods, DSC, IR spectrophotometry, Rheometry

REACTIVE ROTATIONAL MOLDING Cross-linking reaction d [E ] 2 ( ) − = [ E ] 0 [ A ] 0 1 − x × k '+ k ([OH dt

(

]0 + x[ E ] 0 ) + k " [ HX ] ) 500

1

450

taux de conversion 130°C

0,8

400

taux de conversion 140°C

0,7

350

taux de conversion 140°C

0,6

300

Taux de conversion therorique

0,5

250

0,4

200

0,3

150

0,2

100

0,1

50

Viscosité Pa.s

η  x*   =  * η0  x − x 

A + Bα

taux de conversion

Rheology

0,9

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

0

0

0

10

20

30

40 temps /min

50

60

70

80

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

SIMULATION OF FLUID FLOW

A cylinrical mold turning aroude its principal axis

SIMULATION OF FLUID FLOW

A part with more complex geometry

SIMULATION OF FLUID FLOW

Cubic mold in rotomolding condition

NON-REACTIVE ROTATIONAL MOLDING

FORMATION OF DIFFERENT LAYERS Melting + Coalescence Layer by Layer Particle (polymer)

moule

1st layer

Molten Polymer

moule

2nd layer

moule

moule

3th layer

4th layer

FORMATION OF THE FIRST LAYER The following schema shows the mechanism of melting of a particle and its adhesion on the internal surface of the mold. mg

Surface Of the mold

mg

mg

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.

FORMATION OF THE FIRST LAYER

γ

mg

The shear force induced by the weight of particle assures the adhesion between melted particle and the surface of the mold.

F

mg

On the superior part of the mold, the surface tension spreads the melted polymer on the surface

NON-REACTIVE ROTATIONAL MOLDING - Flow of particles (powder) ? -Sintering (coalescence + densification) Polymer support X

1

3

1

2 and 3

4

2

4

Different steps of coalescence de grains 1) initial state 2 and 3) growth 4) final state

t

DIFFERENT MODELS - Frenkel

2

x r

- Kuckzynski - Eshely

- Lontz

3  γ  t 2  η 

=

 x2  1 , 02  r

  

 γt X =  a  ηa0

n

= K (T )t

  

1/ 2

  2 3 x λ =  t 2  r − τ   η0 1 − e  

    t    

x

r

Coalescence of 2 particules

Example: PVDF - Under optical microscope

T = ambiante

t = 80 s

T = 172,8 °C

t = 100 s

t = 20 s

t = 120 s

t = 40 s

t = 140 s

t = 60 s

t =160 s

Example: PVDF

1

2

3

NON-REACTIVE ROTATIONAL MOLDING

- Melting - Rheology - Flow of molten (viscous) polymer - Solidification (crystallization)

CONCLUSION

Reactive rotational molding Reactive rotational molding

Chemical reactions Kinetic model

Heat transfer

Rheology η=f(t)

T=f(t)

η=f(x)

fluid flow model

X: degree of conversion

CONCLUSION

Non-reactive rotational molding Non-reactive rotational molding

Coalescence Kinetic model

Heat transfer

Melting

T=f(t) X: degree of conversion

Formation of layers Densification

Rheology fluid flow model

Cooling

Solidification crystallization