A fundamental approach to the study of the mechanics of ultrasonic machining

A theoretical investigation into the mechanics of ultrasonic machining is presented in this paper on the following lines: the material removal in ultrasonic machining is due to the periodic hammering by the cutting tool on the workpiece material through rigid spherical abrasive particles. The dislodging of material from the workpiece during machining is due to brittle fracture. No consideration is given to the cavitation erosion and the removal of the material due to the impinging of the flying abrasive particles which are being projected onto the workpiece material by the vibrating tool. Simulating by the principle of elastic waves propagation, the strain energy density distribution in a brittle half space, when a single rigid abrasive grit gives a single ‘half-wave displacement with a cutoff’ to it, is ascertained. The fracture profile due to this is found and the material removal rate is calculated. Maintaining the same amplitude of vibration, the static loads at the abrasive workpiece contacts are calculated, for different sizes of abrasive grits, independently. Finally, the variation of machining rates for constant static loads with the mean diameter of abrasive grains is determined, for the given amplitude and frequency of vibration. The results agree with the experimental observations available in the published literature (Nishimura et al. 1959)