### Title: Development of a mathematical model for the prediction of chip formation instability and its verification by fuzzy logic with genetic algorithm

Authors: Anayet U. Patwari, A.K.M. Nurul Amin, M.H. Istihyaq, Waleed F. Faris

Addresses: Department of Manufacturing and Materials Engineering, College of Engineering, International Islamic University Malaysia, 53100 Kuala Lumpur, Malaysia. ' Department of Manufacturing and Materials Engineering, College of Engineering, International Islamic University Malaysia, 53100 Kuala Lumpur, Malaysia. ' Department of Manufacturing and Materials Engineering, College of Engineering, International Islamic University Malaysia, 53100 Kuala Lumpur, Malaysia. ' Department of Mechanical Engineering, College of Engineering, International Islamic University Malaysia, 53100 Kuala Lumpur, Malaysia

Abstract: Chip morphology and segmentation play a predominant role in determining machinability and chatter during the machining of different materials. At lower cutting speeds the chip is often discontinuous, while it becomes serrated as the cutting speeds are increased. It has been identified that the chip formation process has a discrete nature, associated with the periodic shearing process of the chip during machining of different materials. Apart from the primary serrated teeth, a typical instability of periodic nature, in the form of secondary saw/serrated teeth, which appear at the free edge of the chip, has been identified. Mechanism of formation of these teeth has been studied and the frequency of their formation has been determined. In this paper, a new analytical technique is proposed to predict the frequency of chip formation instability as a function of cutting parameters. In this technique, a mathematical model has been developed between the cutting parameters and the instability frequency of the chip serration based on response surface methodology and the model is verified by fuzzy logic with genetic algorithm.

Keywords: chip formation instability; fuzzy logic; genetic algorithms; response surface methodology; RSM; mathematical modelling; cutting parameters; chip morphology; chip segmentation; machinability; chatter vibration; chip serration.

International Journal of Machining and Machinability of Materials, 2010 Vol.8 No.1/2, pp.38 - 54

Published online: 05 Aug 2010 *