Predicting the Displacement Gain from the Mechanical Quality Factor in Ultrasonic Transducers

Abstract

The displacement gain is the most important performance parameter for power ultrasonic transducers typically used for welding or cutting: it controls the proportional relationship between the displacement of the tool and the voltage or current input to the transducer, a key process parameter. However, due to the aging effects of the PZT piezoceramics typically used in these transducers, and other variables such as gradual preload loss or tool clamp wear, this displacement gain can drift over time causing a shift in process, and loss of machine-to-machine portability in mass production environments. The “re-calibration” of the displacement gain usually involves a time consuming procedure of standardized controlled tests, and/or measurements using an expensive device such as a laser vibrometer. However, elementary engineering vibrations theory asserts that the displacement gain should be proportional to the static displacement (i.e., 0Hz or DC) and the mechanical quality factor Qm at resonance, derived from a simple Bode plot, which is already familiar to most transducer designers. This research investigates the methods for obtaining the mechanical quality factor from Bode plots (e.g., constant current or constant voltage sweeps), and ring-down techniques using logarithmic decrement, based on their predictability for determining the displacement gain via the static displacement. The investigation focuses solely on welding transducers for semiconductor wire bonding which employ common hard PZT4 or PZT8 piezoelectric materials. Several other metrics are investigated such as impedance, capacitance and electro-mechanical coupling factor. The experimental and theoretical research methods include Bode plots, equivalent circuits, mechanical analogies and scanning laser vibrometry.