Mathematical Model for Chip Serration Frequency in Turning of Stainless Steel with Magnetic Damping from Bottom of Tool Shank

Abstract

Chatter, a violent and often unpredictable relative oscillatory motion between the tool and work-piece, is a serious concern in turning operations. Its occurrence is usually associated with a loud monotonous sound and usually results in increased surface roughness, reduced material removal rates, shortened tool life, and damaged machine-tool bearings. The established theories for chatter are very limited in scope and are often contradicted by empirical evidences. Therefore, chatter avoidance in the past has relied on inefficient techniques like limiting material removal rates or expensive setups such as actuators and ultrasonic vibration damping systems. However, a deeper investigation into chatter formation reveals that chip morphology and segmentation play a significant role during the incidence of chatter. The novel Resonance theory of chatter combines the concept of mode coupling of the machining setup and serrated chip formation, to explain and predict chatter. To validate the postulates of this theory, models for chip serration frequency are essential. At the same time, a reliable and economical chatter control method is required. With this goal, the current research work has developed an empirical mathematical model of chip serration frequency in turning of stainless steel AISI 304 using Response Surface Methodology (RSM). Also, it investigated the influence of damping provided by magnetic field from a permanent ferrite magnet placed beneath the tool shank. The developed chip serration model is in good accord with the experimental data, demonstrating that the empirical model could be used for further chip morphology and chatter analyses.