Identifying reformulations of mechanical parametric design constraints

Abstract

The complexity of mechanical design is reflected in the complexity of the design constraints which relate functional requirements to design parameters. Reformulations of the design constraints can significantly reduce this complexity. This is accomplished by a transformation to alternative design parameters, such as a critical ratio, a non-dimensional parameter, or a simple difference; e.g. the ratio of surface area to volume for heat transfer loss, the Reynold's number in fluid mechanics, or the velocity difference across a fluid coupling. We have developed a method by which the alternative parameters are chosen for physical significance and for the ability to create a more direct correspondence to functional behavior as determined by measures of serial and block decomposability of the constraints. Rules have been developed for the creation of physically significant new parameters from the algebraic combination of the original parameters. The rules are based on engineering principles and rely on knowledge about what a parameter physically represents rather than other qualities such as dimensions. A computer based system, called EUDOXUS, has been developed to automate this procedure. The system operates on a set of design constraints to produce sets of transformed constraints in terms of alternative design parameters. The method and its implementation have demonstrated successful results for many highly nonlinear and highly coupled parameterized designs from many mechanical engineering domains.