Grey–Taguchi multi-response optimization of residual stress and compressive layer depth in ultrasonic rolling of Ti-6Al-4V

Ultrasonic surface rolling (USR) is an effective surface treatment technique for improving the fatigue performance of metallic components through the introduction of compressive residual stress (CRS) and subsurface strengthening.However, simultaneous optimization of CRS magnitude and compressive layer depth in Ti-6Al-4V remains challenging because of the complex elastic-plastic behavior induced by coupled static and ultrasonic dynamic loading.In this study, an integrated analytical-statistical framework combining Hertzian contact theory, energybased dynamic impact analysis, and Grey-Taguchi multi-response optimization was developed to optimize the USR process parameters.The proposed analytical model was validated against experimental data reported in the literature and showed satisfactory agreement in predicting the residual stress distribution and compressive layer depth.Parametric analysis and ANOVA results indicate that vibration amplitude is the most influential factor (37.82%), followed by ultrasonic frequency and static load, whereas ball diameter has a comparatively minor effect.The predicted optimal parameter combination was identified as A = 10 μm, S = 460 N, F = 25 kHz, and D = 10 mm.Under these conditions, the maximum compressive residual stress and compressive layer depth reached approximately -711.8 MPa and 278 μm, respectively.The proposed framework provides both physical insight and practical guidance for the optimization of ultrasonic surface rolling parameters in Ti-6Al-4V components.