Curvature effects on circular feed end-milling, part 2: stability analysis

Abstract

The non-periodic delay differential equation (DDE) derived in Ozoegwu et al. (in press) to govern chatter of circular milling is averaged over a single discrete delay to get a periodic DDE that approximates chatter of circular end-milling. Chatter stability analysis of the averaged periodic DDE respectively using both the second order least squares approximated full-discretisation map and the modified full-discretisation map on systems governed by linear force law and nonlinear force law gives that curvature diminishes chatter stability because of its reducing effect on damping. This result is in conformity with the simulation-derived results in Ozoegwu et al. (in press). The destabilising effect of curvature gets stronger with lowering of the spindle speed. It is recommended that experimental validation of effects of curvature on stability of end-milling should be done at low spindle speed range. The observed destabilising effect of curvature on chatter stability increases with fall in natural frequency of the tool thus stiffer tools with more strengthening profiles should be selected for circular milling.