A friction model incorporating ultrasonic levitation for normal ultrasonic vibration-assisted deep drawing of copper-nickel alloy sheet

To address the high friction issue in the deep drawing process of copper-nickel alloy sheet, a sliding friction test system under normal ultrasonic vibration (NUV) was developed to investigate the frictional behavior between B30 copper-nickel alloy sheet and steel die. A novel friction model incorporating the ultrasonic levitation effect was proposed considering the influence of vibration amplitude ( A ) on the friction coefficient. Specifically, as A increases from 0 to 6.5 μm, the friction coefficient decreases by 65.48%. The model was further integrated into a finite element model accounting for both surface effect (i.e., friction reduction at the die-sheet interface induced by NUV) and volume softening effects (i.e., decrease in material flow stress and plastic deformation resistance caused by NUV) to simulate NUV-assisted deep drawing, so as to predict the thickness distribution of deep-drawn cups. An NUV-assisted deep drawing setup was established and corresponding experiments were conducted to verify the numerical model. Comparisons of the wall thickness distribution of deep-drawn cups between simulations and experiments verified the accuracy of the proposed friction model and numerical simulation, with a maximum absolute relative error of 7.76%.