As an essential characteristic of air-coupled transducers, electrical impedance can provide valuable information for quality control during manufacturing of transducers. It is also found feasible to directly read the optimal operating frequency from the impedance plots when the resonance is independent of the others. However, the spurious resonance emerges when two neighboring resonances are closely spaced, resulting in distorted impedance and ambiguous optimal operating frequency. In this paper, the electrical impedance of air-coupled transducers with spurious resonance is modeled using the Butterworth–Van Dyke (BVD) equivalent circuit. Then model-based sensitivity analysis is performed to evaluate the mutual interference between adjacent resonances. Based on the analysis results, the prestress method is proposed to regulate and suppress the spurious resonance by adjusting the equivalent parameters of the BVD model. Experimental study was carried out on the response of the electrical impedance and the vibration velocity of the transducer with spurious resonance to pre-tightening force. The results show that the spurious resonance disappeared when the pre-tightening force was initially loaded. Moreover, the vibration velocity of two main resonance peaks increases about 45.6% and 33.9% as the pre-tightening torque increases to 0.25 N∙m. Hence it is validated that the proposed prestress method is efficient to suppress the spurious resonance and improve the transducers performance.
Electrical impedance is an essential parameter for characterizing the performance of transducers during manufacturing and application phases. The conventional method to model the electrical impedance is based on Butterworth-Van Dyke (BVD) model with constant equivalent parameters, which is valid only in the neighborhood of resonance frequency. In this study, we present a method for modelling the electrical impedance over broadband featuring an improved BVD model with frequency-dependent equivalent parameters. In order to obtain frequency-dependent parameters from the measured impedance, estimation is performed in a constrained piecewise and stepwise manner. Firstly, a concise calculation method to obtain initial values of equivalent parameters is presented. Then, the original impedance is equally divided into multiple segments and the resonant segments containing the resonant frequencies are located. New impedance data is reconstructed with one of non-resonant segments and the resonant segments. Finally, with the initial values refined by genetic algorithm (GA), equivalent parameters are obtained from the reconstructed impedance based on GA. The estimation results are assigned to the central frequency point of the non-resonant segment. A new segment is generated by shifting the last non-resonant segment one frequency interval, and data reconstruction and estimation process are repeated till all parameters at each frequency are gained. Frequency-dependent parameters are obtained by the combination of a series of constant parameters at each frequency. The proposed method is verified with good accuracy in modelling of electrical impedance and transmitting response of broadband air-coupled transducer used for gas flow measurement which are difficult to be accurately modelled by the traditional method.
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