Thermoforming

A/C Taimoor, A/C Salman, A/C

Waqar

Theoretical Background:

First

of all, thermoforming is a process in which a sheet is first heated and then

molded into a required mold shape. Here we will see what is the background

process, means that how certain inputs are varying and how are they changing,

because in software (Ansys) we are just giving the inputs not the formulas or

the relations by which they are varying.

·

Before

polydata there is geometry as well as meshing, but these donot involve any

formulas.

·

In

polydata we create some tasks as well as their sub tasks and we have to create

mold as well

Velocity or Force Driven:

In polyflow, when we define a

contact we do it with the help of penalty technique. In this way we define the

fluid velocity and wall velocity are related by the condition (in normal

direction) which involves the penalty co-efficient k, i-e,

fn=-k(v-vwall).n

Similarly, we can use this equation

for the tangential direction but we have to take the slip co-efficient into

account, i-e

fs=-Fslip(vs-vs,wall)

We have

seen how the contact force is applied, now here we have some selection of

whether we want our problem to be velocity imposed or force driven. If our

problem is velocity imposed we can use the above mentioned equations but if it

is force driven then we have to solve the corresponding momentum equation,

Fm+Ff =Ma

·

Fm

= force applied on mold

·

Ff = resistance from the fluid

·

a = acceleration of the mold

·

M=mass

of the moving part

Now here

is the question that why we use this equation? It is because we want to define

a limit for the maximum displacement, because when the deformation increases

shear force and hence the motion of the mold is decreased. So if displacement

tends to increase beyond its limit its motion is stopped. That’s why maximum

displacement is calculated.

Isothermal or non-isothermal:

If our simulation is isothermal then

the conditions (thermal boundary conditions) are same before and after the

contact but if our simulation is non-isothermal then the flow conditions are

not the same before and after the contact,i-e

Q=a(T-Tmold)

where ‘a’ is convective co-efficient

·

similarly

the viscosity changes with change in temperature as shown by the following

graph.

Constant viscosity and strain

dependent viscosity:

Most of the times we take constant

viscosity for shell models but sometimes it is more desirable to take viscosity

in terms of local strain. For this case the fluid constitutive equation is

written as follows:

T=2?(?)D

In

simple traction experiment, we, at constant stretching velocity, stretch the

sample of initial length L0 and record the tensile stress as a

function of deformation. After some manipulation we can take viscosity as a

ratio of stress to strain rate.

?*

= V0/(L0+?L)

?

=exp(?*0t)

?(?)=

?0+a ?2+bexp(-((?-

?p)/ ?w)2)

Typical Viscosity Curve Exhibiting Strain

Hardening

Typical

Viscosity Curve Described with the Smooth Ramp Function

·

Now

how postprocessor things are calculated.

Mass of the blown

product:

mblown=?A?hdA

·

?=density

of the parison

·

h=layer

thickness

·

A=surface

area

Permeability of the

blown product:

Permeability is important to be calculated in the

packing of pharmaceuticals where moisture content is important.

p= ? /h

·

?

is permeability co-efficient

·

h

is local thickness