Design and Implementation of Elliptical Ultrasonic Vibrational Piezoelectric Transducer

PurposeElliptical ultrasonic vibration is an essential auxiliary method for reducing milling forces and temperatures during machining processes. Rapidly determining the optimal geometric parameters of elliptical ultrasonic transducers for achieving effective vibration is of paramount significance.MethodsThis paper introduces a geometric modeling method for elliptical ultrasonic vibration piezoelectric transducers based on transfer matrice and convolutional neural network (CNN). The method employs the transfer matrix method to establish a composite beam bending vibration model of the transducer and constructs a dataset of the electromechanical coupling coefficient (ke\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_e$$\end{document}) for the piezoelectric ceramic in the X-direction (X-PZT), which corresponds to the transducer model parameters, including the length of the tail mass, the length of the X-PZT, and the length and diameter of the horn. CNN trained the dataset to obtain the ke\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_e$$\end{document} objective function. The Non-Dominated Sorting Genetic Algorithm (NSGA) is used to find the optimal solution for the objective function.ResultsThe results indicate that this method efficiently attains the optimal 2nd-order bending vibration ke value of the transducer to be 21.7%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} , with a corresponding ke\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_e$$\end{document} value of 22.6%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} achieved through finite element simulation, resulting in an error of 0.9%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}. Furthermore, field displacement (Amp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_{mp}$$\end{document}) and impedance model (|Z|) curves for various transducer bending vibrations were obtained, demonstrating that the error associated with the 2nd-order theoretical analyses and finite element simulation results is less than that of the 1st-order, with the maximum error in the 2nd-order ke\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_e$$\end{document} not surpassing 4.5%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}.ConclusionDesign and implementation of an elliptical ultrasonic vibrational transducer were carried out based on the theoretical and simulation studies. The effectiveness of the theoretical model and simulations was experimentally validated through impedance analysis.