Study on torsional vibration characteristics of conical horn

The realization of torsional vibration by conical horn has more valuable application in project than by exponential horn and stepped horn. The wave equation of torsional wave propagating in the conical horn is analyzed based on one-dimensional wave theory, and the obtained wave equation is a standard Bessel equation. The frequency equation of the conical horn with torsional vibration is deduced on the basis of wave equation and boundary conditions. Then the mathematical expressions of nodal point and transformation ratio are given. The numerical example shows that mathematical expressions describe the acoustic characteristics of the conical horn with torsional vibration accurately. This study could provide theoretical as well as practical values for the conical horn applied in ultrasonic torsional machining.