Using Dimensional Analysis to Build a Better Transfer Function

A key ingredient in designing products that are more robust is a thorough knowledge of the physics of the ideal function of those products and the physics of the failure modes of those products. We refer to the mathematical functions describing this physics as the transfer functions for that product. Dimensional analysis (DA) is a well known, but often overlooked, tool for reducing the number of experiments needed to characterize a physical system. In this paper, we demonstrate how the application of DA can be used to reduce the size of a DOE needed to estimate transfer functions experimentally. Furthermore, the transfer function generated using DOEs with DA tend to be more general than those generated using larger DOEs directly on the design parameters. With ever-increasing competitive pressure and reduced product development time, a tool such as DA, which can dramatically reduce experimental cost, is an incredibly valuable addition to an engineers toolbox.