Abstract
The dynamic response of mechanical and civil structures subject to high-amplitude vibration is often dangerous and undesirable. Sometimes controlled vibration is desirable as in ultrasonic machining (USM). Ultrasonic machining (USM) is the removal of material by the abrading action of grit-loaded liquid slurry circulating between the workpiece and a tool vibrating perpendicular to the workface at a frequency above the audible range. A high-frequency power source activates a stack of magnetostrictive material, which produces a low-amplitude vibration of the toolholder. This motion is transmitted under light pressure to the slurry, which abrades the workpiece into a conjugate image of the tool form. This can be achieved via passive and active control methods. In this paper, multi-tool techniques are used in the ultrasonic machining via reducing the vibration in the tool holder and providing reasonable amplitudes for the tools represented by the absorbers. The coupling of the tool holder and absorbers simulating ultrasonic cutting process are investigated. This leads to a multi-degree-of-freedom system subject to external and tuned excitation forces. Multiple scale perturbation method is applied to obtain the Solution up to the second order approximation. Different resonance cases are reported and studied numerically. The stability of the system is investigated applying both phase-plane and frequency response techniques. The effects of the different parameters of the absorbers on the system behavior are studied numerically. Comparison with the available published work is reported. (C) 2008 Elsevier Inc. All rights reserved.