Frequency shift in drilling due to margin engagement

Drill chatter degrades hole roundness, hole size, and tool life. This wastes time and money in tools, scrap, and hole rework. Chatter prediction in milling and turning has shown significant benefit to industry; however, researchers have been unable to accurately predict chatter in drilling applications. In the past, the drill, including the chisel edge, was modeled as either a fixed-fixed or fixed-pinned beam (Tekinalp, O., and Ulsoy, A. G., 1989, "Modeling and Finite Element Analysis of Drill Bit Vibrations" ASME J. Eng. Indust. 111, pp. 148-154), but more recent research (Dilley, D. N., Bayly, P. V., and Schaut, A. J., 2005, "Effects of the Chisel Edge on the Chatter Frequency in Drilling" J. Sound Vib., 281, pp. 423-428) has shown that a fixed-embedded model using springs improves frequency matching. The effects of the drill margins on dynamics have not been studied. The fixed-fixed or fixed-pinned model will be shown to be inappropriate for modeling the effects of margin engagement, while the spring-end boundary condition can better approximate the frequency increase observed experimentally as the drill margins engage deeper into the hole. In addition, the shifted frequency is well below the frequency found from an analytical fixed-fixed or fixed-pinned beam. Evidence that the margins cause the frequency shift is seen in three-dimensional waterfall plots that show this shift for pilot hole drilling (in which the margins are engaged), but not for tube drilling (in which margins are not engaged).