Title: Mathematical modelling of surface roughness in ultrasonic machining of titanium using Buckingham-Π approach: a review

Authors: Rupinder Singh, J.S. Khamba

Addresses: Department of Mechanical and Production Engineering, G.N.D.E. College, Ludhiana, Punjab 141006, India. ' Department of Mechanical Engineering, Punjabi University, Patiala, Punjab 147004, India

Abstract: In the present study, the fundamental principles of Ultrasonic Machining (USM) and effect of operating parameters on workpiece Surface Roughness (SR) of titanium and its alloys has been reviewed. Along with this outcome of Taguchi-based model has been used for developing a mathematical model of SR using Buckingham|s π-theorem for stationary USM of titanium. Six input parameters namely, tool material, power rating, slurry type, slurry temperature, slurry concentration and slurry grit size were selected to give output in form of SR. This study will provide the main effect of these variables on SR and will shed more light on the SR mechanism in USM of titanium. The comparison of mathematical model with experimental results will serve as further validation of this study.

Keywords: USM; ultrasonic machining; titanium; Buckingham pi theorem; micromodels; dimensional analysis; macro models; surface roughness; mathematical modelling; Taguchi methods; tool materials; power rating; slurry type; slurry temperature; slurry concentration; slurry grit size.

DOI: 10.1504/IJAT.2009.021635

International Journal of Abrasive Technology, 2009 Vol.2 No.1, pp.3 - 24

Published online: 30 Nov 2008 *

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