Shape and dimensions projection of ultrasonic vibrations concentrators by computer

Abstract

Oscillations of the tool during ultrasonic machining, realized by a high-frequency current, are transformed through an oscillation system into mechanical vibrations with an amplitude suitable for machining. To increase the longitudinal vibration amplitude of the tool, ultrasonic amplifiers and concentrators are used. Amplitude amplification is achieved by changing the cross-section and shape of the concentrator. The basic shapes of concentrators used in production practice are cylindrical in steps, tapered, exponential, and conical. This paper presents problems related to the computer-aided calculation of ultrasonic vibration concentrators. Calculations are based on the laws of sonic waves propagating through solid bodies and solving differential equations for the basic shapes of concentrators. Due to the changes in the shape of concentrators and cross-section, many complex equations arise. Without computer assistance, solving these equations would be extremely time-consuming and imprecise. The developed program system, which is based on the interaction between the computer and the user, provides the opportunity to design the shape and dimensions of ultrasonic concentrators, select the most suitable type for specific conditions, and calculate all the parameters necessary for manufacturing.