{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T10:48:06Z","timestamp":1779360486194,"version":"3.51.4"},"reference-count":24,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T00:00:00Z","timestamp":1688947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["51877070"],"award-info":[{"award-number":["51877070"]}]},{"name":"National Natural Science Foundation of China","award":["U20A20198"],"award-info":[{"award-number":["U20A20198"]}]},{"name":"National Natural Science Foundation of China","award":["51577048"],"award-info":[{"award-number":["51577048"]}]},{"name":"National Natural Science Foundation of China","award":["E2021208008"],"award-info":[{"award-number":["E2021208008"]}]},{"name":"Natural Science Foundation of Hebei Province of China","award":["51877070"],"award-info":[{"award-number":["51877070"]}]},{"name":"Natural Science Foundation of Hebei Province of China","award":["U20A20198"],"award-info":[{"award-number":["U20A20198"]}]},{"name":"Natural Science Foundation of Hebei Province of China","award":["51577048"],"award-info":[{"award-number":["51577048"]}]},{"name":"Natural Science Foundation of Hebei Province of China","award":["E2021208008"],"award-info":[{"award-number":["E2021208008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In most of the piezoelectric stacked motors studied, the stator usually adopts two compound modes to drive the rotor to do step motion. This design method not only improves the utilization rate of the stator but also improves the torque output to a certain extent and increases the output displacement. In this study, a new type of multi-degree of freedom piezoelectric actuator is proposed for the utilization of a stator. The actuator realizes three compound vibration modes of bending-longitudinal-bending on a single stator, which changes the two compound modes of longitudinal bending and also changes the single motion mode of the stepper motor along a straight line. The rotor is set as a ball to drive it to rotate. The designed motor presents a different driving signal under which the rotor will no longer be accompanied by a return displacement. The finite element method is used to complete the design analysis, and the experimental analysis of the designed motor is carried out after the prototype is made. The multi-degree-of-freedom piezoelectric actuator can achieve a speed of 8.56 mm\/c and a driving load of 1200 g at a voltage of 400 v and a working frequency of 42.7 kHz.<\/jats:p>","DOI":"10.3390\/s23146264","type":"journal-article","created":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T01:58:14Z","timestamp":1689040694000},"page":"6264","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Development and Analysis of Multi-Degree-of-Freedom Piezoelectric Actuator Based on Elephant Trunk Structure"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2383-7607","authenticated-orcid":false,"given":"Zheng","family":"Li","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China"},{"name":"School of Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kaiwen","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haibo","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuetong","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoqiang","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hexu","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1109\/TMECH.2018.2790923","article-title":"Development of a non-resonant piezoelectric motor with nanometer resolution driving ability","volume":"23","author":"Xu","year":"2018","journal-title":"IEEE-ASME Trans. Mechatron."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2188","DOI":"10.1109\/TIE.2016.2626242","article-title":"A frog-shaped linear piezoelectric actuator using first-order longitudinal vibration mode","volume":"64","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"107604","DOI":"10.1016\/j.ijmecsci.2022.107604","article-title":"Transfer matrix modeling and experimental verification of forked piezoelectric actuators","volume":"232","author":"Yu","year":"2022","journal-title":"Int. J. Mech. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2200589","DOI":"10.1002\/adfm.202200589","article-title":"Hybrid-Piezoelectret Based Highly Efficient Ultrasonic Energy Harvester for Implantable Electronics","volume":"32","author":"Wan","year":"2022","journal-title":"Adv. Funct. Mater."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"e2207600","DOI":"10.1002\/smll.202207600","article-title":"Implantable Triboelectric Nanogenerators for Self-Powered Cardiovascular Healthcare","volume":"9","author":"Che","year":"2023","journal-title":"Small"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zeng, Y., Jiang, L., Sun, Y., Yang, Y., Quan, Y., Wei, S., Lu, G., Li, R., Rong, J., and Chen, Y. (2020). 3D-Printing Piezoelectric Composite with Honeycomb Structure for Ultrasonic Devices. Micromachines, 11.","DOI":"10.3390\/mi11080713"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"013002","DOI":"10.1088\/1361-6463\/ac27d2","article-title":"Recent progress in 3D printing piezoelectric materials for biomedical applications","volume":"55","author":"Zeng","year":"2022","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.sna.2018.11.018","article-title":"Development of a resonant type piezoelectric stepping motor using longitudinal and bending hybrid bolt-clamped transducer","volume":"285","author":"Wang","year":"2019","journal-title":"Sens. Actuators A Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3041","DOI":"10.1109\/TIE.2018.2847655","article-title":"A two-DOF ultrasonic motor using a longitudinal\u2013bending hybrid sandwich transducer","volume":"66","author":"Liu","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6762","DOI":"10.1109\/TIE.2019.2937047","article-title":"Piezoelectric motor utilizing an alumina PZT transducer 2020","volume":"67","author":"Wu","year":"2020","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.ijmecsci.2018.11.008","article-title":"Analytical modeling of ultrasonic surface burnishing process: Evaluation of through depth localized strain","volume":"151","author":"Teimouri","year":"2019","journal-title":"Int. J. Mech. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.ijmecsci.2015.09.007","article-title":"Analytical, numerical and experimental study of cutting force during thermally enhanced ultrasonic assisted milling of hardened","volume":"103","author":"Elhami","year":"2015","journal-title":"Int. J. Mech. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.jmapro.2020.06.030","article-title":"Development and performance of a novel ultrasonic vibration plate sonotrode for grinding","volume":"57","author":"Cao","year":"2020","journal-title":"J. Manuf. Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.mechatronics.2016.09.002","article-title":"An I-shape linear piezoelectric actuator using resonant type longitudinal vibration transducers","volume":"40","author":"Liu","year":"2016","journal-title":"Mechatronics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"095016","DOI":"10.1088\/1361-665X\/aa7b4f","article-title":"A novel plate type linear piezoelectric actuator using dual-frequency drive","volume":"26","author":"Liu","year":"2017","journal-title":"Smart Mater. Struct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"108223","DOI":"10.1016\/j.ijmecsci.2023.108223","article-title":"A two-DOF linear ultrasonic motor utilizing the actuating approach of longitudinal-traveling-wave\/bending-standing-wave hybrid excitation","volume":"248","author":"Wu","year":"2023","journal-title":"Int. J. Mech. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.ijmecsci.2022.107662","article-title":"A stick-piezoelectric actuator with high assembly interchangeability","volume":"233","author":"Xu","year":"2022","journal-title":"Int. J. Mech. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.ultras.2020.106216","article-title":"Modal analysis and moving performance of a single-mode linear ultrasonic motor","volume":"108","author":"Yin","year":"2020","journal-title":"Ultrasonics"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.ultras.2022.106717","article-title":"Dynamic modeling and analysis of bundled linear ultrasonic motors with non-ideal driving","volume":"124","author":"Liu","year":"2022","journal-title":"Ultrasonics"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.ijmecsci.2019.06.038","article-title":"Development of a friction model based on oblique cutting theory","volume":"160","author":"Lotfi","year":"2019","journal-title":"Int. J. Mech. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1380","DOI":"10.1177\/1045389X12474354","article-title":"Sextro, Modelling the friction contact in an inertia motor","volume":"24","author":"Hunstig","year":"2013","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"035002","DOI":"10.1063\/1.4867455","article-title":"Design and testing of a novel piezoelectric micro-motor actuated by asymmetrical inertial impact driving principle","volume":"85","author":"Zeng","year":"2014","journal-title":"Rev. Sci. Instrum."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1109\/TASE.2014.2352364","article-title":"Fatikow, Modeling and control of piezo-actuated nano positioning stages: A survey","volume":"13","author":"Gu","year":"2016","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1109\/TUFFC.2011.1905","article-title":"A single vibration mode tubular piezoelectric ultrasonic motor","volume":"58","author":"He","year":"2011","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/14\/6264\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:09:42Z","timestamp":1760126982000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/14\/6264"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,10]]},"references-count":24,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["s23146264"],"URL":"https:\/\/doi.org\/10.3390\/s23146264","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,10]]}}}