Mathematical Modelling of Rod-Type Piezo-Electric Transducers for Acoustoelectronic Devices
DOI:
https://doi.org/10.20535/RADAP.2021.86.58-67Keywords:
piezoelectric transducer, acoustoelectronics, mathematical model, electrical signal generatorAbstract
The work is devoted to the peculiarities of the construction and study of mathematical models of rod-type piezoelectric transducers, which are widely used in various acoustoelectronic devices (hydroacoustic means of target detection, ultrasonic non-destructive testing, medical diagnostics, etc.). In contrast to the existing mathematical models of piezoelectric transducers (based on amplitude-phase dependences, resonant piezoelectric transducers, equivalent circuits, etc.), the proposed mathematical model makes it possible to establish a dependence, which is a mathematical description of the acoustic coupling that exists in a solid piezoceramic rod between wave fields on its various areas.
An algorithm for calculating a mathematical model of rod-type piezoelectric transducers is presented and based on the determination of the transformation ratio, which occurs when the inverse piezoelectric effect. Analytical dependencies, which make it possible to determine the electrical impedance and the amplitude value of the potential in the electrical circuit of the piezoelectric transducer, are obtained. It is shown that these dependencies underlie the expression for determining the transformation ratio К(ω, П), which is a mathematical model of a rod piezoelectric transducer. At the same time, the principle of operation of such a transducer provides for the use of longitudinal vibrations in a prismatic rod.
The results of the mathematical modelling are presented on the example of a rod transducer with a square cross-section made of piezoelectric ceramics of the PZT type. The performed comparisons of the calculated and experimentally obtained values of the frequency dependence of the modulus of the transformation ratio of the piezoceramic transducer showed a high convergence between them (the discrepancy between the results of mathematical modelling and the experimentally obtained data for the same value of the operating frequency does not exceed 8.5%).
References
References
Zheng T., Ardolino M., Bacchetti A. & Perona M. (2020). The applications of Industry 4.0 technologies in manufacturing context: a systematic literature review. International Journal of Production Research, Vol. 59, Iss. 6, pp. 1922-1954. DOI: 10.1080/00207543.2020.1824085.
Sanchez-Rojas J. L. (Ed.) (2020). Piezoelectric Transducers: Materials, Devices and Applications. Micromachines, 524 p. DOI: 10.3390/books978-3-03936-857-0.
Vikash Jaiman, Shumaila Akbar (2021). Micro-electromechanical systems technology to improve the performance of various industries: a study. International Journal of Advance Scientific Research and Engineering Trends, Vol. 6, Iss. 3, pp. 176-181. DOI: 10.51319/2456-0774.2021.3.0030.
Petrishchev O. N., Bazilo C. V. (2017). Methodology of Determination of Physical and Mechanical Parameters of Piezoelectric Ceramics. Journal of Nano- and Electronic Physics, Vol. 9, Issue 3, pp. 03022-1–03022-6. DOI: 10.21272/jnep.9(3).03022.
Kudzinovska I. P. (2014). Mathematical modelling of vibrations of round piezoceramic plate taking into account viscoelasticity of material. Visnyk Zaporiz'kogo nacional'nogo universytetu [Bulletin of Zaporizhzhіa National University], No 1, pp. 59–66. [In Ukrainian].
Wu L., Chure M. C., Chen Y. C., Wu K. K., Chen B. H. (2012). Electrode Size and Dimensional Ratio Effect on the Resonant Characteristics of Piezoelectric Ceramic Disk. Ceramic Materials - Progress in Modern Ceramics, Feng Shi, IntechOpen, DOI: 10.5772/38673.
Calas H., Moreno E., Eiras J. A., Vera A., Munoz R., Leija L. (2008). Model for Radial Modes in a Thin Piezoelectric Annular Array. Japanese Journal of Applied Physics, Vol. 47, No. 10, pp. 8057–8064. DOI: 10.1143/JJAP.47.8057.
Bazilo C. V. (2017). Principles of electrical impedance calculating of oscillating piezoceramic disk in the area of medium frequencies. Radio Electronics, Computer Science, Control, No. 4, pp. 15–25. DOI: 10.15588/1607-3274-2017-4-2. [In Ukrainian].
Bezverkhy O., Zinchuk L., Karlash V. (2013). An influence of electric loading on piezoceramic resonators’ vibrations characteristics. Fizy'ko-matematy'chne modelyuvannya ta informacijni texnologiyi [Physical and mathematical modelling and information technology], No. 18, pp. 9–20. [In Ukrainian].
Zubtsov V. I. (2004). Matematicheskaya model' preobrazovatelya staticheskikh mekhanicheskikh napryazhenii vnutri deformiruemykh materialov [Mathematical model of the transducer of static mechanical stresses inside deformable materials]. Inzhenernaya fizika [Engineering Physics], No. 4, pp. 31–36.
Khutornenko S. V., Voeikov A. N., Vasilchuk D. P. (2011). Matematicheskaya model' piezoelektricheskogo rezonatora pri nalichii gradientnogo polya v ploskosti kristallicheskogo elementa [Mathematical model of a piezoelectric resonator in the presence of a gradient field in the plane of the crystal element]. Naukovi praci DonNTU. Seriya: ''Girny'cho-elektromexanichna'' [Scientific works of DonNTU. Series: "Mining and electromechanical"], Vol. 21(189), pp. 168–172.
Shul’ga M. O. Karlash V. L. (2006). An Efficiency of the Electromechanical Energy Transformation at Piezoceramics Constructional Elements Resonant Vibrations. Fizy'ko-matematy'chne modelyuvannya ta informacijni texnologiyi [Physical and mathematical modelling and information technology], No. 3, pp. 225–237. [In Ukrainian].
Shul’ga M. O. Karlash V. L. (2013). Amplitude-phase characteristics of radial vibrations of a thin piezoceramic disk near resonances. Dopovidi Naczional'noyi akademiyi nauk Ukrayiny [Reports of the National Academy of Sciences of Ukraine], No. 9, pp. 80–86. [In Ukrainian].
Petrishchev O. N., Sharapov V. M., Sotula Zh. V., Bazilo K. V. (2015). Principles of calculation of the piezoelectric elements with surfaces partial electrodes covering. Radio Electronics, Computer Science, Control, No. 1, pp. 15–25. DOI: 10.15588/1607-3274-2015-1-2. [In Ukrainian].
Lineykin S., Ben-Yaakov S. (2004). Feedback isolation by piezoelectric transformers: comparison of amplitude to frequency modulation. IEEE 35th Annual IEEE Power Electronics Specialists Conference, Aachen, Germany, pp. 1834–1840. DOI: 10.1109/PESC.2004.1355395.
Peerasaksophol M., Srilomsak S., Laoratanakul P., Kulworawanichpong T. (2011). Design and implementation of ring-dot piezoelectric ballasts for 36-W fluorescent lamps. European Journal of Scientific Research, Vol. 64, No. 2, pp. 189–205.
Ozeri S., Shmilovitz D. (2006). A time domain measurements procedure of piezoelectric transformers equivalent scheme parameters. IEEE International Symposium on Circuits and Systems ISCAS, pp. 2281–2284. DOI: 10.1109/ISCAS.2006.1693076.
Buchacz A., Placzek M., Wrobel A. (2014). Modelling of passive vibration damping using piezoelectric transducers – the mathematical model. Maintenance and reliability, Vol. 16, No. 2, pp. 301–306.
Bazilo C. (2020). Modelling of bimorph piezoelectric elements for biomedical devices. In: Hu Z., Petoukhov S., He M. (eds). Advances in Artificial Systems for Medicine and Education III. Advances in Intelligent Systems and Computing, Vol. 1126. Springer, Cham, pp. 151–160. DOI: 10.1007/978-3-030-39162-1_14.
Bazilo C. V. (2018). Principles and methods of the calculation of transfer characteristics of disk piezoelectric transformers. Radio Electronics, Computer Science, Control, No. 4, pp. 7–22. DOI: 10.15588/1607-3274-2018-4-1. [In Ukrainian].
Petrishchev O. N. (2012). Garmonicheskie kolebaniya piezokeramicheskikh elementov. Chast' 1. Garmonicheskie kolebaniya piezokeramicheskikh elementov v vakuume I metod rezonansa – antirezonansa. [Harmonic vibrations of piezoceramic elements. Part 1. Harmonic vibrations of piezoceramic elements in vacuum and the method of resonance – antiresonance]. Kyiv, Avers Publ., 300 p.
Grinchenko V. T., Ulitko A. F., Shul'ga N. A. (1989). Mekhanika svyazannykh polei v elementakh konstruktsii. T. 5. Elektrouprugost'. [Mechanics of related fields in the elements of constructions. Vol. 5. Electroelasticity]. Kyiv, Naukova Dumka Publ., 280 p. ISBN 5-12-000378-8.
Andriienko O., Bondarenko M., Antonyuk V. (2019). Automated system for controlling the characteristics of microsystem equipment devices. Quality, Standardization, Control: Theory and Practice: XIX International Scientific Studing Conference, pp. 26-28.
Bazilo C., Zagorskis A., Petrishchev O., Bondarenko Y., Zaika V., Petrushko Y. (2017). Modelling of Piezoelectric Transducers for Environmental Monitoring. Proccedings of 10th International Conference ''Environmental Engineering'', Vilnius Gediminas Technical University, Lithuania. DOI: 10.3846/enviro.2017.008.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Максим Олексійович Бондаренко
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
