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.

Improving surface roughness in turning using optimal control of tool's radial position

“…The long and slender workpieces in turning can be modeled using distributed-parameter approach [5,21,22] or lumped-parameter approach [23][24][25]. Workpieces with small length to diameter ratio posses' very high rigidity and their structural dynamics can be ignored.…”

Modeling and Control of Cutter Vibration in the Presence of Random Distribution of Microhardness of Workpiece and Nonlinear Cutting Forces in Lathe Process

“…Therefore, the magnitude of the sample mean variance σ 2 s is a compromise between these two terms. In fact, (17) serves as a mathematical model to predict values of the sample mean variance under different cutting parameter settings.…”

“…where μ a is the mean of the population distribution of hardness and the variance of the sample hardness means is given by (17).…”

“…(2) The two parameters μ s and σ 2 s of the normal distribution fully describe the characteristics of the random excitation system. (3) The variation level of the dynamic cutting force represented by σ 2 s , is directly affected by the variation of the cutting parameters; see (17).…”

“…The mechanistic modeling methods view the machining process as a combination of the chip load/cutting force relationship, cutting-tool geometry, machining conditions, and tool/work-piece displacement due to cutting forces. The workpiece dynamic behavior is constructed using either the distributed-parameter [17] or the lumped-parameter approaches [18]. Few researchers investigated the dynamic effect of the tool holder.…”