Purpose Elliptical 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. Methods This 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 (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1717_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$k_e$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>e</mi> </msub> </math></EquationSource> </InlineEquation>) 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 <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1717_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$k_e$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>e</mi> </msub> </math></EquationSource> </InlineEquation> objective function. The Non-Dominated Sorting Genetic Algorithm (NSGA) is used to find the optimal solution for the objective function. Results The results indicate that this method efficiently attains the optimal 2nd-order bending vibration ke value of the transducer to be 21.7<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1717_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\%$</EquationSource> <EquationSource Format="MATHML"><math> <mo>%</mo> </math></EquationSource> </InlineEquation> , with a corresponding <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1717_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$k_e$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>e</mi> </msub> </math></EquationSource> </InlineEquation> value of 22.6<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1717_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\%$</EquationSource> <EquationSource Format="MATHML"><math> <mo>%</mo> </math></EquationSource> </InlineEquation> achieved through finite element simulation, resulting in an error of 0.9<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1717_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\%$</EquationSource> <EquationSource Format="MATHML"><math> <mo>%</mo> </math></EquationSource> </InlineEquation>. Furthermore, field displacement (<InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1717_Article_IEq8.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">$A_{mp}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mrow> <mi mathvariant="italic">mp</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>) 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 <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1717_Article_IEq9.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$k_e$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>e</mi> </msub> </math></EquationSource> </InlineEquation> not surpassing 4.5<InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1717_Article_IEq10.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\%$</EquationSource> <EquationSource Format="MATHML"><math> <mo>%</mo> </math></EquationSource> </InlineEquation>. Conclusion Design 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.

Design and Implementation of Elliptical Ultrasonic Vibrational Piezoelectric Transducer

期刊论文
发表日期：

2025年1月13日

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Zhizhong Wu,
Zhao Zhang,
Deguang Wu,
Yuanhang Chen,
Fan Hu,
Chenxin Guo,
Lijun Tang

摘要

Purpose

Elliptical 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.

Methods

This 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 ( $k_e$ $k_{e}$ ) 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 $k_e$ $k_{e}$ objective function. The Non-Dominated Sorting Genetic Algorithm (NSGA) is used to find the optimal solution for the objective function.

Results

The results indicate that this method efficiently attains the optimal 2nd-order bending vibration ke value of the transducer to be 21.7 $\%$ $%$ , with a corresponding $k_e$ $k_{e}$ value of 22.6 $\%$ $%$ achieved through finite element simulation, resulting in an error of 0.9 $\%$ $%$ . Furthermore, field displacement ( $A_{mp}$ $A_{mp}$ ) 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 $k_e$ $k_{e}$ not surpassing 4.5 $\%$ $%$ .

Conclusion

Design 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.