Study on predictive model of cutting force and geometry parameters for oblique elliptical vibration cutting

•An analytical force model of oblique elliptical vibration cutting (EVC) is proposed.•This model is helpful to better understand the mechanism of oblique EVC.•It can be applied to conventional turning and ultrasonic vibration assisted turning.•The predicted results of this model are accurate.

Elliptical vibration cutting (EVC), as one of the promising methods for ultra-precision machining, has aroused many scholars' attention. However, few studies focused on the basic mechanism of oblique EVC. In the present study, an analytical force model of oblique EVC has been developed, which only use the material properties, tool geometry and the physical laws of deformation. The transient thickness of cut and transient shear angle are considered in the proposed model. Based on the analysis of oblique EVC mechanism, the geometric parameters of oblique ultrasonic vibration assisted turning (UVAT) are predicted by this model, which are in good agreement with the experimental results available in the literature. The transient cutting force components of orthogonal EVC are also predicted, results of which are in accord with the experimental results. Thus this model is available to predict the geometry parameters and cutting force of the orthogonal EVC accurately. In addition, the proposed model can also be applied to predict geometric parameters and cutting force components of oblique EVC.