Parametric Study of Bolt Clamping Effect on Resonance Characteristics of Langevin Transducers with Lumped Circuit Models

We recently proposed a numerical model using equivalent circuit models to analyze the resonance characteristics of Langevin transducers and design them in a systematic manner. However, no pre-load torque biased by a metal bolt was considered in the model. Here, a parametric study is, therefore, carried out to reveal how model parameters are adapted to incorporate the pre-compression effect into our existing model. Analytical results are compared with corresponding experimental data, particularly regarding the input electrical impedance and effective electromechanical coupling coefficient for the transducer at resonance modes. The frequency response of input impedance is presented as a function of torque, both theoretically and experimentally. For 10.0 N·m bias, for instance, both resonance and anti-resonance frequencies are calculated as 38.64 kHz and 39.78 kHz, while these are measured as 38.62 kHz and 39.77 kHz by the impedance analyzer. The impedance difference between these cases is 14 Ω at resonance and 9 kΩ at anti-resonance, while the coupling coefficients in both cases become 0.238 and 0.239, respectively. Hence, these test results are closely matched with their theoretical values. Consequently, this study provides a quantitative guideline that specifies the pre-loading condition of bolt clamps with proper parameter settings to predict the intended resonance characteristics of Langevin transducers.