Vibration Suppression In Ultrasonic MacHining Using Passive Control : Vibration suppression in ultrasonic cutting represented by non-linear differential equations.

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 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.The ultrasonic machining consists of the tool holder and the absorbers as the tools.The aim of this work is the reduction of the vibrations in the tool holder and have reasonable amplitudes for the tools represented by the multi-absorbers.The proposed technique here allows the USM of multi-shapes at different materials simultaneously.This method improves machine efficiency and saves both machining time and tool holder life.Multiple scale perturbation method is applied to obtain the approximate solutions for the differential equations describing the system.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.