Forced vibrations of two nonlinearly connected solid waveguides under static load

Forced impact oscillations in nonlinearly coupled solid waveguides with nearly equal natural frequencies are examined using the harmonic balance method. A dynamic model is used to describe the process of ultrasonic micro-forging where the material to be worked is considered as a nonlinear connecting-link between the ultrasonic transducer and passive waveguide-reflector. The influence of the material properties (yield stress, stiffness of tool–workpiece contact, striker and blank geometries) and the processing conditions (amplitude of vibration, static compressive force, work rate) on the resonance characteristics of the vibratory system is taken into account. The resonance and antiresonance frequencies, boundaries of response stability, ranges of inphase and antiphase oscillations of impacting waveguides, and some other features of strongly coupled vibrators under impact loading are determined. It is shown also that the largest amplitude of impact oscillations can be attained only if the natural frequency of the ultrasonic transducer exceeds that of the waveguide-reflector. By measuring the dynamic drift in the unfastened ultrasonic unit, it is possible to control, directly in the course of ultrasonic micro-forging, the thickness of the metal workpiece. Calculated data are compared with the experimental results.