Numerical Simulation of Rubber Curing Process with Application to Bladders Manufacture

A large number of polymer products are formed into their final shape by polymerization in

situ

. In particular, mold curing process is the final step in many rubber products manufacturing and determines both the quality of the resulting product as well as productions costs. During this process, important changes in the mechanical properties -e.g. viscosity and modulus- take place, changes which are generally hard to be experimentally characterised. In view of this, a mathematical model is proposed for rubber vulcanisation molding, its strategical value being two fold: from production standpoint, its ability to predict optimal production parameters -the optimal curing time being the most important- and from quality assessment perspective, its capacity of predicting molded part properties.

Following the literature -see, e.g. [

1

]- the mathematical model is built from general mass-energy conservation principles. A series of plausible hypothesis are made in order to simplify the model, which results in a combination of i) the unsteady Fourier’s heat conduction equation -(1)- with a distributed internal heat source, resulting from the reaction -(2), ii) the reaction rate equation -(3)- and iii) closure constitutive equations, for the kinetic constants of the process, namely K

$$ _C^\gamma $$

and

t

inc

:

1

$$ \frac{{\partial \Theta }} {{\partial t}} = div\left( {k \cdot grad\Theta } \right) + \frac{{q'}} {{\rho c_p }}in \Omega for t > 0 $$

2

$$ q' = H_r \frac{{dC}} {{dt}} $$

3

$$ \frac{{dC}} {{dt}} = K_C^{\left( \gamma \right)} \left( {1 - C} \right)^\gamma for t > t_{inc} $$

for

t

>

t

inc

An algorithm is proposed to solve this coupled system. A coupled ODE-implicit in time finite element approximation is proposed and implemented under ALBERTA ([

2

]). After calibration of the computational model, the complete temperature and cross-links concentration is obtained for the typical bladder geometry. Performance results as well as a short discussion on error estimator behaviour are also presented.