Cyclic shear angle for lamellar chip formation in ultra-precision machining

Shear angle is classically considered constant. In the study, a series of straight orthogonal cutting tests of ultra-precision machining revealed that shear angle cyclically evolved with each lamellar chip formation, i.e. cyclic shear angle. It grew up from an initial shear angle of 0° to a final shear angle 90°-α (α: tool rake angle) and underwent a series of transient shear angles like classical shear angles and a critical shear angle. The critical shear angle is the sum of the half of the tool rake angle and the characteristic shear angle determined by material anisotropy without the friction effect. Moreover, a new model was developed. Further, a series of face turning tests of ultra-precision machining verified that the cyclic shear angle was the intrinsic mechanism of cyclic cutting forces and lamellar chip formation to induce twin-peak high-frequency multimode diamond-tool-tip vibration. Significantly, the study draws up an understanding of shear angle for the discrepancy among the classical models.