Abstract
The stability behaviour of delay differential equations describing chatter instability in machining operations has been studied. A transcendental characteristic equation characterizing the onset of the instability is analysed. It is found that increasing the feed rate increases stable machining regions as the depth of cut is continuously increased near a critical value. Furthermore, the non-linear behaviour occurring when stable machining is lost has been shown to be super- and subcritical bifurcations without the assumption of small time delay between successive tool cuts.
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