Semi-analytical modelling of forces and tool wear in ultrasonic-assisted milling

• Modified Z-map method developed to identify cutter-workpiece engagement in B-UAM. • Ray-triangle intersection algorithm employed for calculating uncut chip thickness. • Experimental calibration of cutting force coefficients and abrasive wear constant. • Tool flank wear progression predicted by experimentally validated flank wear model. The prediction and monitoring of tool wear following machining is crucial for optimising tool performance and resulting workpiece surface quality. Ball-end ultrasonic-assisted milling (B-UAM) has emerged as a promising alternative to conventional cutting operations for processing difficult-to-cut materials, such as titanium alloys, which are widely used in aerospace applications. However, comprehensive models for predicting cutting forces and tool flank wear specific to B-UAM operations remain notably scant in the current literature, hindering process optimisation and widespread adoption. This paper details an innovative modelling framework specifically developed for B-UAM, incorporating a novel combination of a modified Z-map model for characterising cutter-workpiece engagement (CWE) and determining uncut chip thickness (UCT) using servo-rectangular encirclement (SRE) and ray-triangle intersection methods, together with a semi-analytical model for corresponding cutting force prediction. This was further complemented by a tool flank wear prediction model based on an abrasion dominant wear mechanism. Experimental B-UAM trials using Ti-6Al-4V titanium alloy workpieces validated the capability of the proposed models, with predicted force components ( F x , F y and F z ) showing average errors ranging between 8.7%–26.0%, while results from the tool wear model exhibited close correlation to experimental data with an average coefficient of determination ( R 2 ) of 0.973. The research represents the first analytical based modelling approach for B-UAM operations, providing an essential tool for process optimisation and towards facilitating wider industrial adoption of this advanced machining technology.