{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T10:54:15Z","timestamp":1784026455603,"version":"3.55.0"},"reference-count":28,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2022,11,7]],"date-time":"2022-11-07T00:00:00Z","timestamp":1667779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Projects of Science and Technology Plan of Zhejiang Province","award":["2021C01144"],"award-info":[{"award-number":["2021C01144"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This research focuses on the load characteristics of piezoelectric transducers in the process of longitudinal vibration ultrasonic welding. We are primarily interested in the impedance characteristics of the piezoelectric transducer during loading, which is studied by leveraging the equivalent circuit theory of piezoelectric transducers. Specifically, we propose a cross-value mapping method. This method can well map the load change in ultrasonic welding to the impedance change, aiming to obtain an equivalent model of impedance and load. The least-squares strategy is used for parameter identification during data fitting. Extensive simulations and physical experiments are conducted to verify the proposed model. As a result, we can empirically find that the result from our model agrees with the impedance characteristics from the real-life data measured by the impedance meter, indicating its potential for real practice in controller research and transducer design.<\/jats:p>","DOI":"10.3390\/s22218576","type":"journal-article","created":{"date-parts":[[2022,11,8]],"date-time":"2022-11-08T08:17:12Z","timestamp":1667895432000},"page":"8576","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Analysis of Ultrasonic Machining Characteristics under Dynamic Load"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0749-8441","authenticated-orcid":false,"given":"Zhangping","family":"Chen","sequence":"first","affiliation":[{"name":"School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5225-5855","authenticated-orcid":false,"given":"Xinghong","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shixing","family":"Chen","sequence":"additional","affiliation":[{"name":"Zhejiang Best Optoelectronic Co., Ltd., Jiaxing 314009, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Honghuan","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pengfei","family":"Ni","sequence":"additional","affiliation":[{"name":"Zhejiang Jiakang Electronics Co., Ltd., Jiaxing 314001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Micus, S., Haupt, M., and Gresser, G.T. (2021). Automatic Joining of Electrical Components to Smart Textiles by Ultrasonic Soldering. Sensors, 21.","DOI":"10.3390\/s21020545"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"014302","DOI":"10.1088\/1674-1056\/abc7aa","article-title":"High-resolution bone microstructure imaging based on ultrasonic frequency-domain full-waveform inversion","volume":"30","author":"Li","year":"2021","journal-title":"Chin. Phys. B"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1109\/TBME.2018.2856930","article-title":"A Novel Synchronous Micro Motor for Intravascular Ultrasound Imaging","volume":"66","author":"Peng","year":"2019","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1526","DOI":"10.1109\/TIM.2004.834072","article-title":"A system for high-resolution, nondestructive, ultrasonic imaging of weld grains","volume":"53","author":"Schuster","year":"2004","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Shi, L., Jia, L., Liu, C., Sun, C., Liu, S., and Wu, G. (2022). A Miniaturized Ultrasonic Sugar Concentration Detection System Based on Piezoelectric Micromachined Ultrasonic Transducers. IEEE Trans. Instrum. Meas., 71.","DOI":"10.1109\/TIM.2022.3185650"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1007\/s11837-012-0266-8","article-title":"Ultrasonic Welding of Wires and Cables","volume":"64","author":"Heinz","year":"2012","journal-title":"JOM"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Shaikh, U.F., Das, A., Barai, A., and Masters, I. (2019, January 3\u20134). Electro-Thermo-Mechanical Behaviours of Laser Joints for Electric Vehicle Battery Interconnects. Proceedings of the 2019 Electric Vehicles International Conference (EV), Bucharest, Romania.","DOI":"10.1109\/EV.2019.8892972"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.jmatprotec.2014.09.020","article-title":"Enhanced welding efficiency in laser welding of highly reflective pure copper","volume":"216","author":"Chen","year":"2015","journal-title":"J. Mater. Process. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"117691","DOI":"10.1016\/j.jmatprotec.2022.117691","article-title":"Review of the advancements in aluminum and copper ultrasonic welding in electric vehicles and superconductor applications","volume":"307","author":"Shin","year":"2022","journal-title":"J. Mater. Process. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"103594","DOI":"10.1016\/j.ijmachtools.2020.103594","article-title":"Review of ultrasonic vibration-assisted machining in advanced materials","volume":"156","author":"Yang","year":"2020","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"954","DOI":"10.1016\/j.jmatprotec.2008.03.006","article-title":"Direct welding of different metals used ultrasonic vibration","volume":"209","author":"Matsuoka","year":"2009","journal-title":"J. Mater. Process. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"107375","DOI":"10.1016\/j.ijmecsci.2022.107375","article-title":"Material removal and surface generation in longitudinal-torsional ultrasonic assisted milling","volume":"227","author":"Qin","year":"2022","journal-title":"Int. J. Mech. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Long, Z.L., Zou, J.J., Zhao, S., Sun, W.D., and Sun, Z.D. (2016, January 21\u201324). Numerical modeling and vibration control of transducer in ultrasonically assisted machining. Proceedings of the 2016 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA), Xi\u2019an, China.","DOI":"10.1109\/SPAWDA.2016.7830006"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1007\/s00170-019-04654-6","article-title":"Influence of force load on the stability of ultrasonic longitudinal\u2013torsional composite drilling system","volume":"106","author":"Zhao","year":"2020","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.ultras.2004.07.008","article-title":"Load characteristics of high power sandwich piezoelectric ultrasonic transducers","volume":"43","author":"Lin","year":"2005","journal-title":"Ultrasonics"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wei, X., Yang, Y., Yao, W., and Zhang, L. (2017). PSpice Modeling of a Sandwich Piezoelectric Ceramic Ultrasonic Transducer in Longitudinal Vibration. Sensors, 17.","DOI":"10.3390\/s17102253"},{"key":"ref_17","first-page":"46","article-title":"Characteristics of piezoelectric ultrasonic transducer with electric load modifying frequency","volume":"53","author":"Wang","year":"2017","journal-title":"J. Mech. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zhang, J.G., Long, Z.L., Ma, W.J., Hu, G.H., and Li, Y.M. (2019). Electromechanical Dynamics Model of Ultrasonic Transducer in Ultrasonic Machining Based on Equivalent Circuit Approach. Sensors, 19.","DOI":"10.3390\/s19061405"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"990","DOI":"10.1109\/TUFFC.2012.2284","article-title":"Theoretical modeling and equivalent electric circuit of a bimorph piezoelectric micromachined ultrasonic transducer","volume":"59","author":"Sammoura","year":"2012","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Meng, X., and Lin, S. (2019). Analysis of a Cascaded Piezoelectric Ultrasonic Transducer with Three Sets of Piezoelectric Ceramic Stacks. Sensors, 19.","DOI":"10.3390\/s19030580"},{"key":"ref_21","first-page":"10","article-title":"Influence of the Load on the Characteristics of Ultrasonic Machining Acoustic Systems","volume":"48","author":"Zhe","year":"2012","journal-title":"Aviat. Precis. Manuf. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1109\/TCPMT.2018.2829164","article-title":"Impedance Modeling of Ultrasonic Transducers Used in Heavy Aluminum Wire Bonding","volume":"8","author":"Long","year":"2018","journal-title":"IEEE Trans. Compon. Packag. Manuf. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.ultras.2019.05.005","article-title":"The effects of thermo-mechanical load on the vibrational characteristics of ultrasonic vibration system","volume":"98","author":"Zhao","year":"2019","journal-title":"Ultrasonics"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1016\/j.ultras.2011.01.002","article-title":"Dynamic modeling of thickness-mode piezoelectric transducer using the block diagram approach","volume":"51","author":"Wang","year":"2011","journal-title":"Ultrasonics"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhang, K., Dong, L., and Zhu, Y. (2021, January 19\u201321). Research on output characteristics of piezoelectric energy harvester with different circuit load. Proceedings of the 2021 IEEE 4th International Conference on Automation, Electronics and Electrical Engineering (AUTEEE), Shenyang, China.","DOI":"10.1109\/AUTEEE52864.2021.9668770"},{"key":"ref_26","first-page":"2304","article-title":"Design of High-Frequency Ultrasonic Transducers with Flexure Decoupling Flanges for Thermosonic Bonding","volume":"63","author":"Wang","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"201","DOI":"10.3813\/AAA.918603","article-title":"Coupled Vibration Analysis for a Composite Cylindrical Piezoelectric Ultrasonic Transducer","volume":"99","author":"Zhang","year":"2013","journal-title":"Acta Acust. United Acust."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5380","DOI":"10.1109\/TIE.2011.2130490","article-title":"Design and Implementation of a Rectangular-Type Contactless Transformer","volume":"58","author":"Kim","year":"2011","journal-title":"IEEE Trans. Ind. Electron."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/21\/8576\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:12:03Z","timestamp":1760145123000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/21\/8576"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,7]]},"references-count":28,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["s22218576"],"URL":"https:\/\/doi.org\/10.3390\/s22218576","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,7]]}}}