About Cut Thickness in Vibration Tracking Cutting

Regenerative chatter is the main cause of vibration in cutting, having a negative impact on the machining process. The paper reviews the fundamental theories of regenerative chatter developed by J. Tlusty and S. A. Tobias et al. and stability analysis methods using feedback control theory presented by N. Merritt. In order to determine more accurately the thickness of the sheared layer during cutting by vibration trace, it is proposed to revise the application of existing formulas and approaches to analytical calculations of cutting dynamics. The authors of the paper highlight a disadvantage existing in these theories associated with the assumption that the vibration level depends on the phase shift between waves on the cutting surface of neighbouring passes. The conducted studies have shown that even in the absence of phase shear, the thickness of the cut layer is not a constant value, and the delay time between neighbouring revolutions does not remain constant, decreasing at each moment of time by the value Δτ. It is also shown that even in the absence of phase shear, the equality of the natural oscillation frequency of the cutter and the oscillation frequency of the chip-forming force creates a condition for resonance, which leads to the occurrence of maximum vibrations. Thus, the study questions the widespread assertion that the absence of phase shear ensures vibration-free cutting.