Author:  Huu-Danh Tran, Thu-Quy Le, Ngoc-Pi Vu, and Thanh-Cuong Pham

Place posted: Processes 2026, 14, 1451

Post time: 2026

Abstract: This study investigates ultrasonic vibration-assisted (UV) CNC milling of hardened 90CrSi steel cylindrical surfaces, with emphasis on ultrasonic horn design, experimental analysis, and multi-objective optimization of machining parameters, addressing the need for an inte- grated framework combining system design, experimental validation, and multi-objective optimization. A quarter-wavelength ultrasonic horn was designed and experimentally validated to operate at a frequency of 20 kHz. By adjusting the horn–workpiece system, stable vibration amplitudes were achieved to enable effective ultrasonic-assisted milling of cylindrical surfaces. Milling experiments based on a Box–Behnken design were conducted to examine the effects of vibration amplitude, cutting speed, feed rate, and radial depth of cut on material removal rate (MRR) and surface roughness (Ra). Surrogate models using response surface methodology (RSM) and Gaussian process regression (GPR) were developed to predict machining performance. A GPR-assisted NSGA-II algorithm was then applied to simultaneously maximize MRR and minimize Ra, resulting in a well-defined Pareto front that reveals the trade-off between machining productivity and surface quality.
Furthermore, an AHP-based decision-making approach was employed to select preferred machining conditions from the Pareto-optimal solutions. The GPR models demonstrated high predictive accuracy (R2 > 0.98), and validation experiments confirmed the reliability of the predicted optimal results, with deviations below 5%. In addition, a comparative anal- ysis between ultrasonic-assisted and conventional milling showed that MRR increased by 10.81–40.17%, Ra decreased by 27.11–44.44%, and cutting force was reduced by 14.2–42.65%, providing direct experimental evidence of improved machinability. The results demon- strate that the proposed integrated framework provides an effective strategy for optimizing ultrasonic vibration-assisted milling processes and improving the machinability of hard- ened 90CrSi cylindrical surfaces. Overall, the proposed framework provides a practical and cost-effective strategy for enhancing machining performance and offers a robust approach for multi-objective optimization of ultrasonic vibration-assisted milling processes.

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