The calculation of cooling time in injection moulding

Various way available to calculate cooling time in injection mould, the easiest way of course using numerical method, software package like mold flow, C - mold or your own compile numerical method language also available in the market, for detail and specific calculation, i suggest to write your own equation base on the problem, after that write in the programming language and understanding the result for the next optimization.

Why Cooling?

 Plastic industry is one of the world’s fastest growing industries, ranked as one of the few billion-dollar industries. Almost every product that is used in daily life involves the usage of plastic and most of these products can be produced by plastic injection molding method. Injection molding represents the most important process for manufacturing plastic parts. It is suitable for mass-producing products, since raw material can be converted into  a molding by single procedure The plastic injection molding process is a cyclic process.[1]
The cooling phase of the injection moulding process accounts for up to 75% of the overall cycle time. It therefore follows that a reduction in cooling time will in turn reduce the overall cycle time and hence, increase the throughput rate
Experimentally, cooling times are defined as the time taken for the pressure at the primary sensor to return to atmospheric, after the injection of a consecutive shot. The molten polymer cools and solidifies in the mould [2]
The cooling system design was primarily based on the experience of the designer but the development of new
rapid prototyping process makes possible to manufacture very complex channel shapes what makes this empirical
former method inadequate. So the design of the cooling system must be formulated as an optimization problem
The heat-transfer processes which occur in the plastic part and in the mould during the injection moulding of
thermoplastics are rather complex. The situation is one of three-dimensional unsteady-state heat-transfer with a
phase change.

Determining Cooling Time Formula

Ballman and Shusman method, 

they proposed this formula to calculate cooling time for injection mould process

where t is the cooling time in seconds: S is the maximum cavity thickness, mm; alfa is the diffusivity, 0i is the melt temperature at injection, °C; 0w is the mould temperature, °C; and 0e is the ejection temperature, °C, the latter being taken to be the heat deflect temperature (HDT) of the thermoplastic. However, it is recognized that the HDT is not a material constant but is dependent strongly on the processing pressure and sample thickness as well as on the type of material.[3]

Busch, Field and Rosato Method,

they proposed a combination of theoretical and statistical methods to derive the following equation for estimating the cooling time

Wp is part weight and Ncav is the number of cavities of the mould.

Kirch and Menges Method

commonly use in semi crystalline material [5]

J.Z. Liang and J.N. Ness Method

they use new formula base on analytical method,by judicious selection of the representative ejection temperature, the following equation for determining the cooling time of a polymer part in injection moulding can be derived

another formula also variable in many article and journal of material processing, because limited literature that i have, some month a go i also read calculation cooling time method from Professor in Japan and Korea, but, i forget to save those journal.

Which one the best?

i think to find with one the best, we must compare various formula with same temperature of ejection and other parameter we set same, than we compare the result with recommended or actual setting in injection process, of course with same material type.

Reference

[1]. S.H. Tang, Y.M. Kong, S.M. Sapuan, R. Samin, S. Sulaiman, Design and thermal analysis of plastic injection mold, J. Mater. Process. Technol. 171 (2006) 259–267
[2]  A.G. Smith et al,  A computational model for the cooling phase of injection moulding.
[3] C.J. Yu, J.E. Sunderland, Polym. Engng Sci., 32 (1992) 191.
[4] J. Busch, F. Field, Ill, and D. Rosato, Proc. SPE RETEC, Boston, Vol. 1, 1988
[5] G. Wubken and 1. Catic, Kunst~'-Berater