Predicting the High Torsionality of Stepped Ultrasonic Horn Design in Longitudinal-Torsional Vibration-Assisted Micro Milling Using Finite Element Analysis and Surrogate Models

Longitudinal–torsional ultrasonic vibration-assisted milling has attracted considerable attention because of its ability to improve machining performance, particularly for materials that are difficult to machine. However, due to the complex nonlinear relationships between geometric parameters and dynamic characteristics, including torsionality, resonance frequency, and frequency separation. Conventional design approaches based on iterative finite element analysis (FEA) are computationally expensive and inefficient for extensive parametric studies. This study proposes an integrated FEA–surrogate modeling framework for designing and predicting high-torsionality stepped ultrasonic horns for micromilling applications. The horn geometry was parameterized using slit-related variables, including the number of slits, angle, length, width, and depth. Modal and harmonic response analyses were conducted in ANSYS to determine the resonance frequencies, vibration mode shapes, and torsional characteristics. The resulting dataset was used to develop and compare several predictive models, including multiple linear regression (MLR), Artificial Neural Networks (ANN), Response Surface Methodology (RSM), polynomial regression, kriging, random forest, and XGBoost. The results revealed that slit depth is the dominant parameter governing torsionality, whereas slit width and length have relatively minor effects. Among the evaluated models, Kriging achieved the highest prediction accuracy, whereas ANN demonstrated strong predictive capability (R2 = 0.9346) and substantially out-performed conventional MLR. The proposed framework provides both predictive capability and engineering insight into the influence of slit geometry on the generation of longitudinal–torsional mode generation, enabling more efficient ultrasonic horn design while reducing the reliance on repeated FEA simulations.

Frequency separation; Longitudinal-torsional vibration mode; Stepped horn; Torsionality; Ultrasonic horn

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