An analytical method to optimize residual stress in the ultrasonic rolling of titanium alloys Ti6Al4V

Ultrasonic rolling is an effective surface enhancement technique for titanium alloys because it introduces beneficial compressive residual stresses that improve fatigue resistance and service durability. In many aerospace and high-performance engineering applications, both the magnitude and penetration depth of the compressive residual stress field play critical roles in determining long-term structural reliability and resistance to crack initiation and propagation. However, the complex elastic-plastic deformation behavior induced by coupled static and ultrasonic loading makes accurate prediction and simultaneous optimization of these characteristics challenging. This study develops a unified analytical framework for simultaneously predicting and optimizing compressive residual stress magnitude and compressive layer depth during ultrasonic rolling of Ti6Al4V alloy. The proposed approach combines Hertzian contact mechanics, elastic-plastic deformation theory, and response surface methodology to systematically investigate the effects of static load, vibration amplitude, ultrasonic frequency, and rolling ball radius on residual stress evolution and hardened layer development. The analytical predictions were validated through comparison with experimentally reported residual stress profiles under different ultrasonic rolling conditions. The validation results demonstrate reasonable agreement between the analytical predictions and experimental observations in terms of residual stress distribution, peak compressive stress magnitude, and penetration depth. The parametric analysis indicates that static load and vibration amplitude exert dominant influences on residual stress evolution and compressive layer formation. The proposed framework provides a computationally efficient and physically interpretable methodology for analyzing and optimizing ultrasonic rolling parameters for Ti6Al4V alloy.