An analytical force model for orthogonal elliptical vibration cutting technique

The elliptical vibration cutting (EVC) technique has been found to be a promising technique for ultraprecision machining of various materials. In each overlapping EVC cycle, the thickness of cut (TOC) of work material, and the tool velocity get continuously varied. These two inherent phenomena, in fact, introduce transient characteristics into its cutting mechanics, which are considered to be different from the one applied for conventional cutting technique. Recently, a few theoretical models have been developed to understand the material removal mechanism with the EVC technique; however, in those studies, the transient phenomena were not considered. In the present research, an analytical force model for the orthogonal EVC process was developed in order to fully understand the EVC mechanism, and to more accurately predict the transient cutting force values. Three important factors: (i) transient TOC, (ii) transient shear angle, and (iii) transition characteristic of friction reversal were investigated and analyzed mainly based on geometric modeling and the Lee and Shaffer's slip-line solution. Mathematical evaluation shows that they may have significant influence on EVC process, and thus on its output performance. In order to validate the proposed force model, a series of low-frequency orthogonal EVC tests were conducted. The experimental transient cutting force values were compared with the predicted values calculated using the proposed model, and they are found to be in a good agreement with each other.