Automated Upgraded Generalized Full-Discretization Method: Application to the Stability Study of a Thin-Walled Milling Process

Abstract

A tensor-based general order full-discretization method which can be automated to preempt all manual case-by-case symbolic analyses associated with chatter stability identification is upgraded with the capacity for model order reduction of elastic thin-walled workpieces. The implemented method is then exploited for studying the sensitivity of the precision of stability lobes of a reduced elastic thin-walled workpiece to arbitrary variation of interpolation order of both the current and delayed regenerative chatter states. The studied system shows almost identical results for unidirectional and bidirectional models. It was further found that within the numerically stable interpolation orders which are usually from 0 to 9, stability lobes are mildly sensitive to the variation of the order of the current state but strongly sensitive to the variation of the order of the delayed state. Though no combination of orders of current and delayed states is seen to outperform the others in all spindle speed ranges, it is recommended to keep the order of the delayed state at 3 while the order of the current state is varied to get the best results. Error surfaces and time-domain simulations were instrumental in the deductions and discussions of results. The programmed method offers potential industrial benefit of making use of stability lobes for precise selection of productive chatter-free process parameters more user-friendly.