Mechanistic prediction for cutting force in rotary ultrasonic machining of BK7 glass based on probability statistics

Material removal in rotary ultrasonic machining (RUM) of hard-brittle material is an abnormal complicated process, which involves the combination effects of the numerous abrasive grains with the random distributions in the dimensions and penetration depths. These stochastic characteristics result in the evident differences in the extrusion loading between the material and each individual grain, and their aggregate effects serve to significantly affect the cutting force of the diamond tool. However, few mechanistic prediction models of the cutting force have incorporated in the random distribution features of the abrasive grains, restricting the current optimization methods for the reduction of the cutting force during the formal RUM process. Giving consideration to the abrasive processing kinematics and their distribution features on the tool end-face, the number of the effective grains together with their penetration depths was calculated utilizing the probability statistics. Subsequently, the novel theoretical model of the cutting force was established by incorporating the gaussian distribution characteristics of the grain size and their penetration depths. Afterward, the confirmatory experiments were performed for the validation of the proposed cutting force model, revealing that the predicted results were accordant well with the experimental measurements. Furthermore, it was found that the number of the active abrasive grains accounted for 2.972% of the total number on the tool end-face at the specific processing parameters. Additionally, the mechanistic predictions of the developed model represented that the cutting force depicting an irregular decreasing trend with the grain dimension increasing, which was attributed to the coupling effects between the grain size and their number.