Chatter stability of the robotic milling process involving the influences of low frequency vibrations in three directions

Existing regenerative chatter models orienting for the robotic milling processes only considered the structure mode-induced low frequency vibrations in the $XY$ plane. This article experimentally reports that obvious $Z$-directional low frequency vibrations exist in robotic milling processes with weakly rigid postures, and they can cause multi-cutting phenomenon. Just because of this phenomenon, obvious axial tool-workpiece separation and over-cut phenomena are experimentally observed. This confirms that besides the low frequency vibrations in the $XY$ plane, those in relation to the $Z$ direction also greatly affect the stability of the robotic milling process. Hence, a comprehensive dynamic model is systematically established to couple the influences of the low frequency vibrations in relation to both $XY$ plane and $Z$ direction of the robotic milling process. The low frequency vibrations in relation to the three directions are quantitatively characterized, and then combined to analyze the radial and axial tool-workpiece separations. For the convenience of study, the tool-workpiece engagement region along the axial depth of cut is divided into a static cutting region and a dynamic cutting region. It is theoretically clarified that the axial over-cut phenomenon (AOCP) leads to an obvious stepped shape of the dynamic cutting region. The multiple delay items, which are redistributed by the complex tool-workpiece engagement states, are derived and then integrated to establish the dynamic governing equation. Subsequently, the principle for obtaining stability lobe diagrams (SLDs) of the robotic milling processes is formulated. A series of robotic milling experiments under different weakly rigid postures confirm that the proposed model can give good prediction accuracy of SLDs.