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1.2 OPTIMIZATION TECHNIQUES IN
MOULDING
In the literature, various optimization procedures have
been used but all focused on the same objectives. Tang
et al. [4] used an optimization process to obtain a
uniform temperature distribution in the part which gives
the smallest gradient and the minimal cooling time.
Huang [5] tried to obtain uniform temperature
distribution in the part and high production efficiency i.e
a minimal cooling time. Lin [6] summarized the
objectives of the mould designer in 3 facts. Cool the part
the most uniformly, achieve a desired mould temperature
so that the next part can be injected and minimize the
cycle time.
The optimal cooling system configuration is a
compromise between uniformity and cycle time. Indeed
the longer the distance between the mould surface cavity
and the cooling channels is, the higher the uniformity of
the temperature distribution will be [6]. Inversely, the
shorter the distance is, the faster the heat is removed
from the polymer. However non uniform temperatures at
the mould surface can lead to defects in the part. The
control parameters to get these objectives are then the
location and the size of the channels, the coolant fluid
flow rate and the fluid temperature.
Two kinds of methodology are employed. The first one
consists in finding the optimal location of the channels in
order to minimize an objective function [4][7]. The
second approach is based on a conformal cooling line.
Lin [6] defines a cooling line representing the envelop of
the part where the cooling channels are located. Optimal
conditions (location on the cooling and size of the
channels) are searched on this cooling line. Xu et al. [8]
go further and cut the part in cooling cells and perform
the optimization on each cooling cell.
1.3 COMPUTATIONAL ALGORITHMS
To compute the solution, numerical methods are needed.
The heat transfer analysis is performed either by
boundary elements [7] or finite elements method [4].
The main advantage of the first one is that the number of
unknowns to be computed is lower than with finite
elements. Only the boundaries of the problem are
meshed hence the time spent to compute the solution is
shorter than with finite elements. However this method
only provides results on the boundaries of the problem.
In this study a finite element method is preferred because
temperatures history inside the part is needed to
formulate the optimal problem.
To compute optimal parameters which minimize the
objective function Tang et al. [4] use the Powell’s
conjugate direction search method. Mathey et al. [7] use
the Sequential Quadratic Programming which is a
method based on gradients. It can be found not only
deterministic methods but also evolutionary methods.
Huang et al. [5] use a genetic algorithm to reach the
solution. This last kind of algorithm is very time
consuming because it tries a lot of range of solution. In
practice time spent for mould design must be minimized
hence a deterministic method (conjugate gradient) which Based on a morphological analysis of the part, two
surfaces
1
Γ and
3
Γ are introduced respectively as the
erosion and the dilation (cooling line) of the part (Figure
1). The boundary condition of the heat conduction
problem along the cooling line
3
Γ is a third kind
condition with infinite temperatures fixed as fluid
temperatures. The optimization consists in finding these
fluid temperatures. Using a cooling line prevents to
choose the number and size of cooling channels before
optimization is carried out. This represents an important