Development of chatter threshold boundary for milling of metals

This study reports on a novel experimental method for the prediction of chatter based on the chaos theory. The variation of Poincaré sections of the reconstructed phase space attractor is able to identify the transition of the milling system from a stable to an unstable condition, continuously during the milling process. Two mathematical tools are used to measure the variation of Poincaré sections they being; image correlation and a designed regression model. Image correlation uses Poincaré sections as a pattern and the computation of Pearson’s coefficient assists to develop a chatter threshold boundary.
Titanium is the main material in this research, as chatter is more applicable during cutting of titanium due to its specific mechanical properties. Moreover, the method is used in detection of chatter during milling of stainless steel and aluminum in order to demonstrate the method can detect chatter during cutting of other metals. The new method can be used to detect chatter on-line, as it is independent of the cutting parameters and dynamics of the milling process, and can be integrated in the cutting machines. The method does not need expensive equipment and complex process, so it can be easily used in normal production workshop environment.
A regression model computes the trend of changes in the Poincaré sections and gives a numerical output value to define the boundary between the stable and unstable state of the milling process. These mathematical tools can be used in expert software to monitor the milling process on-line and detect the onset of chatter.