Simple Mathematical Models for Complex Industrial Processes
For the successful solution of an industrial problem a crucial, but often difficult first step, is to very clearly define the question that needs to be resolved as this will determine the nature of the modelling that is most appropriate. For example, if the aim is to determine an integrated quantity such as the total volumetric flow of paint between two rolls rather than point estimates, such as the velocity distribution of the paint between the rolls, then one would use a simpler model as integrated quantities are usually more robust with respect to model simplification. This and the fact that successful historical manufacturing processes worked because of their inherently robust, and have been made more so through process optimization, explains why simple models are often successful in capturing the essence required for decision making. Nevertheless, though the final model that resolves the matter is often disarmingly simple, the path to its identification is built on the availability of sophisticated mathematical results, knowledge and expertise. The relevance of this is exemplified in this paper using the reverse roll coating of steel and aluminium strip.
KeywordsIndustrial processes Mathematical modelling Roll coating Lubrication theory
The numerical results shown in this paper were obtained with the assistance of Huu-Nhon Huynh.
- 2.Roberts, W.: Cold rolling of steel. Marcel Dekker, New York (1987)Google Scholar
- 3.Landau, L., Levich, B.: Dragging of a liquid by a moving plate. Acta Physiochim. USSR 17, 42–54 (1942)Google Scholar
- 5.Benkreira H., Edwards M.F., Wilkinson M.F.: Roll coating of purely viscous liquids. Chem. Eng. Sci. 36, 429–434 (1981)Google Scholar
- 7.Bissett E.J.: The line contact problem of elastohydrodynamic lubrication i. Asymptotic structure for low speeds. Proc.R. Soc. Lond. 424, 393–407 (1989)Google Scholar