As the industry seeks better quality and efficiency, multitasking machine tools are becoming increasingly popular owing to their ability to create complex parts in one setup. Turn-milling, a type of multi-axis machining, combines milling and turning processes to remove material through simultaneous rotations of the cutter and workpiece with the translational feed of the tool. While turn-milling can be advantageous for large parts made of hard-to-cut materials, it also offers challenges in terms of surface form errors and process stability. Because tool eccentricity and workpiece rotation lead to more complexity in process mechanics and dynamics, traditional milling stability models cannot predict the stability of turn-milling processes. This study presents a mathematical model based on process mechanics and dynamics by incorporating the unique characteristics of the orthogonal turn-milling process to avoid self-excited chatter vibrations. A novel approach was employed to model time-varying delays considering the simultaneous rotation of the tool and workpiece. Stability analysis of the system was performed in both the semi-discrete time and frequency domains. The effects of eccentricity and workpiece speed on stability diagrams were demonstrated and validated through experiments. The results show that the tool eccentricity and workpiece speed alter the engagement geometry and delay in the regeneration mechanism, respectively, leading to significant stability diagram alterations. The proposed approach offers a comprehensive framework for the stability of orthogonal turn-milling and guidance for the selection of process conditions to achieve stable cuts with enhanced productivity.

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