Equivalent circuit solution to mechanical parallel structure for considering prestressed bolt in Tonpilz transducer

Purpose This study aims to present an improved equivalent circuit solution to the Tonpilz transducer with including the prestressed bolt, which is sometimes omitted in the common equivalent circuit model because the mechanical parallel structure caused by the bolt brings trouble in the analogy to the equivalent circuit. Design/methodology/approach The proposed solution includes the equivalent circuit representation and its matching impedance matrix form. In the Tonpilz transducer, the parallel structure shaped by the bolt and piezoelectric stack divides the force and continues the vibration from the head and tail. The equivalent transformation between the mechanical connection in parallel and the electrical connection in series is the derivation of the equivalent circuit. Therefore, the mechanical behavior of the transducer system can be evaluated by the way of the network circuit and the effect of the bolt on the Tonpilz transducer can be studied. Findings The corresponding simulations indicate the equivalent circuit model considering the bolt gives more accurate evaluation of the Tonpilz transducer. The bolt should not be omitted in the model. The bolt with different diameter can cause the different mechanical change and the different electroacoustic performance of the transducer. The larger diameter of the bolt will result in the higher resonance frequency and the lower conductance of the transducer. The test results of the transducer prototype agree with the improved equivalent circuit simulations well. The effectiveness of the proposed solution has been testified. Originality/value This study solves the problem about the equivalent circuit analogy of the bolt in the Tonpilz transducer. The proposed equivalent circuit representation continues the consistency with the common equivalent circuit model and makes the model more complete. This solution improves the accuracy to simulate the Tonpilz transducer.