Fuzzy stability analysis of milling processes
During machining, unstable self-excited vibrations known as regenerative chatter can occur when the depth of cut is too large. Chatter causes excessive tool wear or failure and a poor surface finish on the machined workpiece, and so it is desirable to predict, and hence avoid the onset of this instability. Regenerative chatter is a function of empirical cutting coefficients, and the structural dynamics of the machine-tool system. There can be significant uncertainties in the underlying parameters, so that predicted stability limits do not necessarily agree with those found in practice. This makes the chatter problem a good candidate for the development of new or alternative methods to model uncertainty in structural dynamics. In the present study, fuzzy arithmetic techniques are applied to the chatter stability problem. An implementation of fuzzy arithmetic is developed based upon the work of Hanss and Klimke. The arithmetic is then applied to two techniques for predicting milling chatter stability: the classical approach of Altintas, and the time-finite element method of Mann. It is shown that for some cases careful programming can reduce the computational effort to acceptable levels. The resulting fuzzy arithmetic bounds are compared to previously published data, to investigate how uncertainty propagation techniques can insight into chatter predictions. The problem of milling chatter uncertainty is also considered within the framework of Ben-Haim's information-gap theory. It is shown that the numerical approaches can be used to solve process design problems with robustness to the uncertain parameters. © 2008 by the Katholieke Universiteit Leuven Department of Mechanical Engineering All rights reserved.
