Advances in manufacturing analysis: fractal theory in modern manufacturing

A review of the applications of fractal theory in modern manufacturing is presented in this chapter. A brief conceptual foundation, typical examples, and methods of computing fractals are summarized. The most common methods of computing fractal dimensions include box-counting, area-based measurements, and fractional Brownian motion (fBm) methods and have been briefly discussed along with the proposed improvements in the literature. It is noted that there are concerted efforts to improve on the known methods to enhance their accuracy and application in various fields. Finally, applications of fractals in thin films, laser processing, machining, and friction stir processes/welding are illustrated based on the published data. It is derived that fractal analysis is important in (1) understanding the growth of structures during different manufacturing processes (and parameters) and (2) developing fractal-like structures for enhanced performance in various engineering applications. Directions for future research and applications of fractal theory in manufacturing and their potentials are described in respective sections of the chapter. The chapter is a useful resource for academic and industry in studying, developing, and manufacturing of fractal-like engineering components and the interrelationships among the manufacturing process, parameters, and fractal characteristics of the engineering product.