REGARDING SOME FUNDAMENTAL ASPECTS OF DESIGN AND DEVELOPMENT OF BESSEL ULTRASONIC CONCENTRATORS USED IN NONCONVENTIONAL MACHINING

Abstract

In the category of nonconventional machining, the use of concentrated energy from ultrasonic mechanical oscillations has long been a practical solution for efficient technological utilization. This work comprehensively develops and addresses an algorithm for sizing circular cross-section ultrasonic concentrators determined by Bessel functions. Bessel functions are canonical solutions to the Bessel differential equation in cylindrical coordinates, as they appear in Laplace's equation or in spherical coordinates derived from Helmholtz's equation. In industrial applications, optimizing process parameters such as vibration amplitude, amplification factor, and mechanical stress in the concentrator is of interest.