Abstract: Compound vibration of tool in cutting and welding makes the machining quality of work pieces finer than one-way vibration, and can greatly improve machining efficiency and extend tool life. Cylinder with multiple diagonal slits can change transducer of longitudinal resonance mode into longitudinal-torsional resonance mode outputting. This technique features simple structure, convenient use and high conversion efficiency. The state of plane principal stress in diagonal slits is derived with longitudinal stress wave reflecting principle to diagonal slit. Propagation of principal stress wave in cylinder is studied. The analysis result shows that principal stress wave propagates along helical line, and its sound propagation velocity is derived. The fact is proved that cylinder with multiple diagonal slits exists longitudinal-torsional resonance mode and the resonance frequency explicit expression is given by means of the equivalent circuit. Based on the analysis of ultrasonic vibration features of cylinder with multiple diagonal slits, factors which affect longitudinal-torsional vibration outputting parameter are established. According to the vibration outputting parameter required by the machining, the geometric size of cylinder with multiple diagonal slits can be accurately defined in application. The finite element mode analysis and experiment results agree with the theoretical analysis.

Key words: Diagonal slit, Longitudinal-torsional resonance, Principal stress wave, Screw-propagation, Vibration converter