Closed-Form Time-Domain Solutions of Arbitrary-DOF Forced Vibrations and of Surface Location Error for General-Helix Cylindrical Milling Tools

BackgroundPeriodic cutting forces are inevitably generated during milling processes and the associated forced vibrations leave behind an imprint called surface location error (SLE) on machined parts causing tolerance concerns. Numerical prediction of SLE is extensively demonstrated in literature.PurposeHowever, closed-form models are unarguably preferred over numerical and surrogate models when available due to higher effectiveness and accuracy for design analysis. The few existing closed-form models of forced vibrations and SLE are limited to 1 and 2-DOF systems excited by 1 or 2-dimensional cutting forces (feed and feed-normal directions) for the conventional fixed-helix angle shape even though variable helix angle is a common technical possibility.ResultsThis work proposes a closed-form solution that is based on the more realistic 3-dimensional cutting force for the forced vibrations and SLE of arbitrary-DOF milling excited by arbitrary variable helix angle tools. The validity of the proposed model is checked with comparisons to numerical cases of flexible cutting tools (lumped-mass model) and thin-walled workpieces (continuum/finite element model) drawn from literature.ConclusionTo demonstrate the potential application of the model in SLE suppression without compromising productivity, an optimization problem is formulated and solved for selecting helix angles, and almost complete suppression of SLE is recorded for the illustrative case.