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

Dongxi Lv; Chun Yan; Gang Chen; Dong Liu; Xiaofei Wu; Yingdan Zhu

doi:10.1016/j.ultras.2019.106006

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

Ultrasonics. 2020 Feb:101:106006. doi: 10.1016/j.ultras.2019.106006. Epub 2019 Sep 11.

Authors

Dongxi Lv¹, Chun Yan¹, Gang Chen¹, Dong Liu¹, Xiaofei Wu¹, Yingdan Zhu²

Affiliations

¹ Institute of Advanced Manufacturing Technology, Ningbo Institute of Material Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, PR China.
² Institute of Advanced Manufacturing Technology, Ningbo Institute of Material Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, PR China; Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, PR China. Electronic address: y.zhu@nimte.ac.cn.

PMID: 31550623
DOI: 10.1016/j.ultras.2019.106006

Abstract

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.

Keywords: Cutting force; Glass BK7; Probability statistics; Rotary ultrasonic machining; Theoretical model.