Enhancing surface quality in ultrasonic vibration-assisted micro-milling of bone: A combined RSM-PSO approach and sensitivity analysis

This study presents a novel approach to optimizing surface roughness in ultrasonic vibration-assisted micro-milling (UVAMM) of cortical bone by integrating Response Surface Methodology (RSM) with Particle Swarm Optimization (PSO), complemented by global sensitivity analysis using Sobol indices. Unlike prior studies that focus on conventional bone machining or single-variable optimization, this research provides a multi-parametric and data-driven framework specifically tailored to address the anisotropic nature of bone tissue. Experiments were performed on bovine bone, a validated analog to human cortical bone, using key input variables such as spindle speed, feed rate, depth of cut, tool diameter, and ultrasonic vibration amplitude. A Central Composite Design (CCD) structured the experiments, with RSM-derived regression models optimized via PSO to identify parameter combinations minimizing surface roughness (Ra). Key findings include optimal parameter ranges: for the x -axis, spindle speed of 950 rpm, feed rate of 22 mm/min, tool diameter of 1.14 mm, depth of cut of 0.25 mm, and ultrasonic amplitude of 27 µm; for the y -axis, spindle speed of 950 rpm, feed rate of 22 mm/min, tool diameter of 1.30 mm, depth of cut of 0.50 mm, and ultrasonic amplitude of 26 µm, achieving surface roughness values of 0.30 µm ( x -axis) and 0.50 µm ( y -axis) with prediction errors under 7%. Sobol-based sensitivity analysis revealed direction-dependent (anisotropic) behavior in bone machining, underscoring the clinical relevance of cutting direction with respect to osteonal alignment. By providing a robust optimization-sensitivity framework tailored to the biomechanical complexity of bone, this work offers practical and innovative insights for enhancing surface integrity, precision, and osteointegration in orthopedic and dental procedures.