Abstract

In ultra-precision machining (UPM) of micro-structured functional surfaces (µ-SFS), tool servo dynamic errors (tool servo tracking error and tool servo induced vibration) would deteriorate surface quality as two crucial issues. At the machined surface, the tool servo tracking error manifests as surface fluctuation due to its phase shift, and the tool servo induced vibration presents with periodical patterns. To eliminate or reduce the tool servo dynamic errors, theoretical and experimental results innovatively reveal that: (1) for the mathematical prerequisite the tool path should be at least fourth-order differentiable (snap), and (2) for the physical mechanism the second-order derivative of tool path (required acceleration) should be less than the rated acceleration provided by the tool servo. It is of significance that the study draws up two crucial suggestions on the tool path in UPM of µ-SFS to effectively improve surface quality.