Optimization in castings—An overview of relevant computational technologies and future challenges

Abstract

The manufacture of defect-free components at low cost and high productivity is as important to the casting industry today as it was 30 years ago. In the past, experience was gained either by using a “trial and error” method or by undertaking expensive experiments. Many “dos” and “don’ts” have evolved in the casting process over a period of time. However, the important ones that come to mind are so fundamental that they challenge the “academic mind” to think all over again. The rules proposed by Professor John Campbell^[1] are classic examples. The message is simple: mathematical complexity in computer models needs to go hand in hand with the rules derived from “first principles.” In the field of optimization, a variety of methods have been proposed over a period of years. At the start of optimization study, the foundryman’s first choice is to use simple but well-established methods such as the use of orthogonal arrays for optimal design of process conditions or the famous “inscribed” or Heuvers’ circle method^[2] for optimal feeding design. The computer simulation software has been based on a variety of computational methods ranging from geometric reasoning techniques (the famous Chvorinov rule and its variants)^{[11,13,15,29–31]} to solving complex partial differential equations using one of the numerical methods. Optimization methods based on solving partial differential methods was an active area of research in the mid-1990s.^[6–10,17] This article reviews a variety of optimization methods including—probably for the first time—geometric reasoning methods. The contribution from various computational methodologies is highlighted with particular emphasis on characterizing “objective functions” and “constraints.” The article also raises some of the challenging issues that the optimization community is facing today for solving casting problems and reports on our recent work on linking geometric reasoning techniques with the finite element method (FEM) and other data mining tools to achieve computationally efficient optimal design of casting processes.