Nine technical papers were presented on 29 April at the 1997 SPE ANTEC in Toronto. Six of the nine papers dealt with certain aspects of the rotational molding heating and cooling process. Nearly every one of these began with words of this type: Rotational molding is a simple process for making hollow plastic objects. Of course, it isn’t, at least insofar as predicting cycle times goes. As it turns out, it appears that we are still lacking an adequate technical description of the process of heating tumbling powder in a clamshell. This technical minute focuses on the importance of heating and cooling models.

Powder Bed Motion

As seen through a glass mold, there seem to be three general types of powder flow in a rotating system. Static bed flow implies that all the powder particles are static relative to one another. The mold surface simply slides against the static bed. This implies that the friction between the mold surface and the powder particles is substantially less than the internal friction between particles. Steady – state circulating bed flow implies that the opposite is true. The friction between the mold surface and the powder particles is much greater than the internal friction between particles and there is steady-state bulk flow within the bed, causing the bed to be fully mixed or turned by the rotating mold surface. Avalanche flow is an intermediate flow situation, where the friction between the mold surface and the powder particles is sufficient to allow the bed to intermittently move with the mold surface. However, when a certain bed height is achieved, the bed structure collapses and a major portion of the powder flows across the remaining static bed. Thus, avalanche flow is an intermittent stick-slip process.

Heating Model Building and the Choice of Bed Motion

Avalanche flow is considered too complex for most model builders. Circulating bed flow was used in the very earliest model [Rao and Throne]. It was coupled with a simple first – order mold temperature response to the isothermal oven temperature, and a penetration model for transient heat conduction into the circulating bed. Heat transfer from the mold to the cavity air was ignored. The powder was assumed to stick to the mold surface when it reached its tack temperature. The thermal diffusivity of the powder was assumed to be constant, as was that of the polymer melt. There was no correction for latent heat of fusion of the polymer. The model seemed to predict heating cycle time. Sometime later, the circulating bed flow model was replaced with a static bed model and the arithmetic reworked, with apparently better results [Throne].

Recent models have used the static bed model [Crawford and colleagues, Vlachopolous and colleagues, Gogos et al, and Bawiskar and White], with many relaxations of the early model limitations. The Crawford model is currently available from Ferry Industries, Inc., Stow OH, as ROTOSOFT ™. The arithmetic becomes substantially easier with the static bed. For example, it can be assumed that the bed properties are only temperature – dependent and not density – dependent. Since there is no friction between the static powder bed and the rotating mold, and subsequently the tacky polymer stuck to the mold, there is no shear layer at the static – moving interface. As a result, the effect of rotation is ignored. In certain cases, the powder bed is assumed to be of rectangular shape, with one side in contact with the mold surface and the other three sides exposed to hot cavity air [Attaran et al]. In other cases, the bed is assumed to be infinitely planar with the mold surface. As a result, one surface contacts the mold and the other the hot cavity air. Most recent models include latent heat of fusion, and the mathematics become more difficult, since it is now necessary to track the time- and position-dependent interfacial boundary between powder and liquid. Although the shape has been modeled recently in non-simple coordinates, it is apparent that planar, Cartesian coordinates work fine for most mold geometries [Gogos et al]. Although remarkable agreement has been reported between experiment and theory [Xu and Crawford], it is unclear how values for certain experimental parameters, such as heat transfer coefficients from oven air to mold and mold to cavity air, were determined. Recent experimental [Nugent] and theoretical work [Gogos et al] supports the very early assumption that whether or not the mold contains powder, it heats at essentially the same rate, and that rate can be predicted by a simple first-order equation in which the only hard-to-measure parameter is the heat transfer coefficient between the oven air and the outer mold surface. So far, the densification effect on thermal properties of the sintering polymer stuck on the mold surface has been neglected.

Cooling Model Building

It is apparent that the arithmetic of cooling is easier than that of heating. It is assumed that the polymer is of uniform thickness and is stuck on the mold surface. The only complexity is the location of the time – and – position – dependent liquid – solid thermal interface. The arithmetic easily demonstrates the effect of applying various cooling techniques at various times in the cooling process.


Even though the static bed model is probably wrong, it seems to work satisfactorily for the heating portion of the cycle time. As a result, there seems little reason to expend energy developing the more complex circulation models. However, it is interesting to note that even though part wall thickness – dependent cycle time is a direct drop – out from the models, experimental data can be rather closely predicted by simple transient heat conduction into a slab:

Cycle Time
After Tack prop. [Final Part Wall Thickness]2

Jim Throne 30 April 1997

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