Vibration suppression in multi-tool ultrasonic machining to multi-external and parametric excitations

Ultrasonic machining (USM) is of particular interest for the machining of non-conductive, brittle materials such as engineering ceramics. In this paper, a multi-tool technique is used in USM to reduce the vibration in the tool holder and have reasonable amplitude for the tools. This can be done via dynamic absorbers. The coupling of four non-linear oscillators of the tool holder and tools representing ultrasonic cutting process are investigated. This leads to a four-degree-of-freedom system subjected to multi-external and multi-parametric excitation forces. The aim of this work is to control the tool holder behavior at simultaneous primary, sub-harmonic and internal resonance condition. Multiple scale perturbation method is used to obtain the solution up to the second order approximations. The different resonance cases are reported and studied numerically. The stability of the system is investigated by using both phase-plane and frequency response techniques. The effects of the different parameters of the tools on the system behavior are studied numerically. Comparison with the available published work is reported.