Analytical modeling of dynamic forces and surface performance in ultrasonic surface rolling process

Ultrasonic surface rolling process (USRP) improves surface integrity through severe plastic deformation induced by the superposition of high-frequency ultrasonic vibration on a static load. However, accurate quantification of the associated dynamic force remains challenging due to measurement challenges. This study proposes a novel analytical model for dynamic force prediction based on elastoplastic contact mechanics and kinematic analysis. The model accounts for time-dependent indentation depth and supporting forces, revealing that the dynamic force waveform significantly deviates from a simple sinusoidal pattern. Full-cycle explicit finite element simulations validate the proposed model for both elastic and elastoplastic contacts. The framework accurately captures the distinct loading and unloading paths, quantifies residual indentation depth, and evaluates the increase in surface equivalent modulus after processing. Parameter sensitivity analysis indicates that vibration frequency exerts the greatest influence on the dynamic force, followed by amplitude and static load. This approach provides a robust analytical tool for the systematic characterization and effective optimization of dynamic forces in USRP, and simultaneously enables quantitative prediction of residual indentation depth and surface equivalent modulus for surface integrity evaluation.