The Dynamic Interaction of the Cutting Process, Workpiece, and Lathe’s Structure in Facing

Abstract

The effects on the onset of chatter by the dynamic interaction of the workpiece and its method of support, the turret, the lathe bed, the cutting forces and the cutting conditions are determined. A generalized modal analysis is used to solve the four governing equations in the frequency domain. It is found that there are four dimensionless quantities that couple the equations, the most important being N0, the ratio of the static stiffness of the workpiece to the translational stiffness of the turret. The dimensionless critical depth of cut Hc and corresponding chatter frequency coefficient Ωc2 are determined as a function of N0 for two feed rates, several surface speeds, and for two workpiece boundary conditions; cantilevered and clamped-hinged. It is shown that the magnitudes of Hc and Ωc2 are oscillatory as a function of N0, and the occurrence of their peak values is proportional to the surface speed of the workpiece to the fourth power. It is found that for the parameters selected the effect of the dynamic response of the lathe bed is to increase by 7 percent the values of N0 at which the peak values of Hc occur. It is also found that the value of the equivalent viscous damping of the system and the magnitude of the real part of the cutting force coefficient govern the magnitudes of Hc and Ωc2 as a function of N0.