THE DYNAMIC INTERACTION OF THE CUTTING PROCESS, WORKPIECE, AND LATHESSTRUCTURE IN FACING

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 cu tting forces and the cutting conditions are determined. A generalized modal analysis is used to solve the four governing equations in the fr equency domain. It is found that there are four dimensionless quantiti es that couple the equations, the most important being N-o, the ratio of the static stiffness of the workpiece to the translational stiffnes s of the turret. The dimensionless critical depth of cut H-c and corre sponding chatter frequency coefficient Omega(c)(2) are determined as a function of N-o, for two feed rates, several surface speeds, and for two workpiece boundary conditions; cantilevered and clamped-hinged. It is shown that the magnitudes of H-c and Omega(c)(2) are oscillatory a s a function of N-o, and the occurrence of their peak values is propor tional to the surface speed of the workpiece to the fourth power. It i s found that for the parameters selected the effect of the dynamic res ponse of the lathe bed is to increase by 7 percent the values of N-o a t which the peak values of H-c occur. It is also found that the value of the equivalent viscous damping of the system and the magnitude of t he real part of the cutting force coefficient govern the magnitudes of H-c and Omega(c)(2) as a function of N-o.