Analysis of ultrasonic vibro-impact systems with equivalent circuits and the harmonic balance method

Vibro-impacts are essential for many ultrasonic applications like ultrasonic welding or ultrasonic motors. These systems are described with a piezoelectric equivalent circuit, that is extended by an impact and a static deflection. As long as the movement of the system is mainly sinusoidal, the method of harmonic balance gives a good approximation of the vibration behaviour. It is known, that the mounting situation has a great influence on the characteristic of a vibro impact system. Therefore the analytical solution of the equivalent circuit is given and discussed for a constant pressing force, a constant gap and an arbitrary foundation stiffness. It turns out that, the dependency of static and harmonic deflection gives a good explanation and deeper understanding of vibro-impact systems. Finally the model is compared to measurements with a constant pressing force.