Study on the longitudinal–torsional composite vibration of a sectional exponential horn

The longitudinal–torsional composite vibration of a sectional exponential horn was studied theoretically and experimentally. The horn consists of an exponential horn with an untapered rod at its large end. Based on the plane-wave approximation, the resonance frequency equations and other characteristics for the longitudinal and torsional vibrations of the horn were derived and some theoretical curves were given. Since the sound speeds of the longitudinal and torsional vibrations are different in the same material, the longitudinal and torsional vibrations in a horn are generally difficult to resonate at the same resonance frequency. In this paper, to overcome this problem, the cross-sectional radius decay coefficient of the exponential part in the sectional horn, which determines the sound speeds and other performance parameters of the horn, is selected to make the longitudinal and torsional vibrations resonate at the same frequency. By means of this method, the simultaneous resonance of the longitudinal and torsional vibrations in the horn is achieved by choosing the proper value of the radius decay coefficient. Some sectional exponential horns were designed and made, their resonance frequencies were measured, and the vibrational characteristics of the horn under large excitation were observed qualitatively. Experimental results show that the measured resonance frequencies of the horns are in good agreement with the theoretical results, and the measured resonance frequencies of the longitudinal and torsional vibrations are also in good agreement with each other. Therefore the simultaneous resonance of the longitudinal and torsional vibrations in the same horn are achieved both theoretically and experimentally. This kind of sectional exponential horn can be used in ultrasonic machining, ultrasonic drilling, ultrasonic fatigue testing, and other applications which need very large mechanical displacement amplitudes.