Hiroki Takahara

The Effect of Multiple Dynamic Absorbers on Regenerative Chatter and Resonance in End Milling Process

The present study investigates the effect of multiple dynamic absorbers on regenerative chatter and resonance caused by forced vibration generated in the end milling operations. Regenerative chatter is caused by the cutting force variation due to the phase difference between the wave left by the previous cutting edge and the wave left by the current one. This phase difference is expressed as the product of the tooth passing period and chatter frequency [1]. The tooth passing period depends on the spindle rotation frequency and the number of teeth. Chatter frequency is related to the natural frequency of the tool and spindle system. If the integral multiple of the spindle rotation frequency approaches to the natural frequency, the phase difference gets smaller and the critical depth of cut at the onset of chatter is increased. Therefore the critical depth of cut varies with the spindle speed and stable cutting conditions are plotted on the chatter stability lobe, which is a chart that represents the boundary between stable and unstable cuts as a function of the spindle speed and the depth of cut. The chatter stability lobe is widely employed to find the axial depth of cut and the spindle speed in which chatter doesn’t occur. Meanwhile, the cutting force variation by the intermittent cutting with an end milling tool causes the forced vibration. The excitation frequency is determined by the spindle rotation frequency and the number of teeth. When the integral multiple of the excitation frequency approaches to the natural frequency of the tool and spindle system, resonance can be caused by the forced vibration. The resonance occurs in the spindle speed resistant to chatter. Therefore, there is a need for a countermeasure against not just the chatter but also the resonance caused by the forced vibration. In the present study, the cutting conditions which can lead to the chatter and the resonance are investigated by the direct numerical integration method. It is made clear that the optimum tuning parameters of the absorbers to maximize the critical depth of cut vary with the spindle speed. Furthermore, a significant suppression effect on the chatter and the resonance by using the absorbers mounted in a rotating collet holder with a spindle is confirmed.Copyright

Countermeasure Against Regenerative and Forced Chatter of Flexible Workpieces in Milling Processs Using Bi-directional Excitation

A novel extended methodology for chatter suppression in milling process by applying external forced vibrations to the workpiece in two orthogonal directions which are the feed and cross-feed directions. Both the regenerative and forced chatter suppression during the milling process of flexible workpieces are investigated. Here, the workpiece is subject to a sinusoidal periodic force in the feed direction to disrupt the regenerative effect. Additionally, to minimize the forced chatter, the workpiece is subject to the periodic excitation force in cross-feed direction. This force is proportional to the magnitude of the estimated cutting force in cross-feed direction and has a phase opposite to the cutting force to minimize the vibration amplitudes. The effectiveness of the proposed method is evaluated numerically and experimentally, for the spindle speed located in both the local minima and local maxima of the stability lobe diagram. The numerical simulations indicate significant suppression effect in terms of vibration amplitudes, resulting in suppression of both the regenerative chatter and the forced chatter. Experiments were conducted by using a workpiece-mounted active stage composed of flexure hinges and driven by piezoelectric actuators. The experimental results agree qualitatively with the numerical simulations. The proposed method indicates a remarkable vibration reduction effect for both regenerative and forced chatters.

Hamiltonian Formulation of the Free Surface and Interface Motions in a Tank (2nd Report, Nonlinear Time History Response Analysis)

This paper deals with nonlinear liquid surface and interfacial wave motions in a tank containing two incompressible irrotational fluids of different densities. In theoretical analysis, the governing equations and canonical form of a system of two fluids with a dynamic free surface and interface are given by applying Hamiltons principle. Moreover, the nonlinear ordinary differential system which governs liquid surface and interfacial wave motions is derived by using Dirichlet-Neumann operators and the generalized Fourier series expansion. Solving these ordinary differential system yields the time histories and the transitions of surface and interfacial wave motions in a rectangular tank. The validly of the theoretical analysis is verified through the experiments. The theoretical results are shown to be in good agreement with the experimental results.