Self-Excited Vibrations in a Delay Oscillator: Application to Milling With Simultaneously Engaged Helical Flutes

This paper investigates the stability of a milling process with simultaneously engaged flutes by extending the state-space temporal finite elements method. In contrast to prior works, multiple flute engagement due to both a high depth of cut and a high step-over distance are considered. A particular outcome of this study is the development of a frame work to determine the stability of periodic, piecewise continuous delay differential equations. Another major outcome is the demonstration of different stability behavior at the loss of stability in comparison to prior results. To elaborate more, period doubling regions are shown to appear at relatively high radial immersions when multiple flutes with either a zero or non-zero helix angle are simultaneously cutting.