Stochhastic chatter theory

Abstract

The machining process on modern machine tools is a dynamic phenomenon having cause-and-effect interaction under stochastic environments. With a steady increase in utilization parameters, intensive vibrations occur, which are termed chatter. This thesis deals with the investigation of chatter, concentrating primarily on evolving an amplitude-domain stability criterion. It has been proposed that the cause of these chattering vibrations lies in the random separation and subsequent collision between the vibrating tool and the workpiece under sustained cutting operation. This results in repeated impulsive loading and a profile-induced forcing function under regeneration in the coincidence frequency zone, and thus in machining chatter. A physical parameter, viz., covariance (coefficient of variation) of chip thickness, has been identified as the parameter governing the threshold of stability. This accounts for an ensemble of engineering variables influencing the onset of chatter. A general equation for stochastic chatter threshold prediction has been evolved as: 1lim\frac{1}{\text{lim}}lim1? where lim\text{lim}lim is the limit depth of cut, rrr is dynamic coupling and process coefficient, and ??\sigma'?? is mean square cross response (displacement) of the system. The concept of impact loading has been verified experimentally and the postulates enunciated for the stochastic theory have been corroborated. It has been observed that either the tool or the workpiece can cause chatter depending on their relative dynamics and interactions. A sure threshold of stochastic chatter is exhibited if the covariance of chip thickness exceeds unity. The theory has been used for predicting stability zones. Stability charts with varying spindle speeds, cutting speed and feed rates have been drawn up. The theory is directly useful for designers and production engineers in grappling with the problems of chatter. This theory enshrines the essential features and salient concepts of most of the existing chatter theories as well as the principles researched by several other investigators, and explains a range of experimental observations reported in literature. The generalization and extension of this theory to dynamic phenomena analogous to chatter in machine tools has been shown to be possible.