A predictive model and process investigation for ultrasonic strengthening of thread root considering initial surface roughness

The ultrasonic surface rolling process (USRP) reduces surface roughness at the thread root, thereby improving the fatigue performance of bolts. Compared with experimental approaches, USRP simulation using finite element methods offers reduced cost and rapid prediction of results. However, initial surface roughness of the workpiece has rarely been incorporated into existing USRP simulation studies. In this study, the Weierstrass–Mandelbrot (W–M) fractal function is superimposed onto the radial coordinates of the thread section based on fractal theory. A finite element model that accounts for considering the initial surface roughness of the thread root is established using Matlab, and a USRP finite element model of the thread root is established based on Hertz contact theory. Three process parameters, namely static pressure, ultrasonic amplitude, and rolling times, are considered for simulation-based analysis and prediction of post-USRP surface roughness. The results show that the proposed model, incorporating initial surface roughness, achieves average prediction error of 4.90% relative to experimental measurements. By contrast, the conventional model that neglects initial surface roughness exhibits a substantially higher error of 33.35%, demonstrating the significant effect of initial surface roughness on prediction accuracy.