Investigation of the machinability of commercially pure titanium in ultrasonic machining using graph theory and matrix method

Abstract

Any type of machining operation is well influenced by the machinability of work material under processing. This work proposes a graph theory and matrix method based technique for the assessment of machinability of titanium in ultrasonic machining. Identification of various machining attributes along with their relative importance has been considered and analyzed by developing a mathematical function by employing graph theory and matrix method. An attribute digraph is developed, which provides a visual illustration of considered attributes with their relative interactions. This digraph is further represented by using matrix expression. A permanent machinability index for all the experimental runs is also obtained from matrix form demonstration based on attribute digraph. The combination of all the attributes for any machining operation makes this method quite versatile. The results reveal that an experimental run having the combination consisting tool material of titanium, grit size of 500, and power supply of 300 W yields optimized results for machinability.