An improved static model for tool deflection in machining of Ti–6Al–4V acetabular shell produced by selective laser melting

Tool deflection during milling operation leads to dimensional error, decreasing surface quality and increasing rejection rate. In this study, tool deflection during the milling of the inner surfaces of Ti–6Al–4V prosthetic acetabular shell produced by selective laser melting (SLM) was modelled. The first purpose of this research is to provide a general static cutting tool deflection model for ball nose cutters where deviation of machine components and tool holder are so small as to be considered negligible. This is because the values of machine component and tool holder deflection were lower than standard tolerances (10 μm) and found to be lower than 1/15 of tool deflection. The second and third objectives of this work involve calculating contact surfaces by determining workpiece and tool geometry and choosing second moment of inertia using a novel cross section method (CSM). Static models for three quasi-analytical methods (QAM) that are simple cantilever beam model (SCBM), two-section model (TWSM) and our three section model (THSM) are presented. THSM showed high accuracy which was validated by 3D finite element method (FEM3D) and experimental measurements. The accuracy of tool deflection calculation using THSM by computing, shank, flute and ball head deflection and also utilizing CSM to determine second moment of inertia showed notable improvements.