<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article"><front><journal-meta><journal-id journal-id-type="publisher-id">JAMP</journal-id><journal-title-group><journal-title>Journal of Applied Mathematics and Physics</journal-title></journal-title-group><issn pub-type="epub">2327-4352</issn><publisher><publisher-name>Scientific Research Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.4236/jamp.2018.61028</article-id><article-id pub-id-type="publisher-id">JAMP-82286</article-id><article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Physics&amp;Mathematics</subject></subj-group></article-categories><title-group><article-title>
 
 
  Development of Deep-Sea Resonant Sandwich Linear Ultrasonic Motor
 
</article-title></title-group><contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Shaopeng</surname><given-names>He</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Shengjun</surname><given-names>Shi</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Weishan</surname><given-names>Chen</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib></contrib-group><aff id="aff1"><addr-line>State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, China</addr-line></aff><pub-date pub-type="epub"><day>05</day><month>01</month><year>2018</year></pub-date><volume>06</volume><issue>01</issue><fpage>296</fpage><lpage>300</lpage><history><date date-type="received"><day>3,</day>	<month>January</month>	<year>2018</year></date><date date-type="rev-recd"><day>28,</day>	<month>January</month>	<year>2018</year>	</date><date date-type="accepted"><day>31,</day>	<month>January</month>	<year>2018</year></date></history><permissions><copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement><copyright-year>2014</copyright-year><license><license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p></license></permissions><abstract><p>
 
 
  
    A deep-sea resonant sandwich linear ultrasonic motor is proposed and designed. We determine the parameter of its structure by finite-element analysis. The piezoelectric actuator adopts compound vibration mode of fifth order bending vibration and second order longitudinal. The mode degeneracy of that is completed. We manufacture the prototype to measure the performance of it. We measure its vibration mode and resonant frequency. The velocity of prototype can reach 264.5 mm/s while the water pressure is 8 MPa and the voltage signal with frequency of 30.30 kHz and voltage amplitude of 150 V. 
  
 
</p></abstract><kwd-group><kwd>Piezoelectric Actuator</kwd><kwd> Finite-Element Analysis</kwd><kwd> Hybrid Mode</kwd><kwd>  Fluid-Solid Coupling</kwd></kwd-group></article-meta></front><body><sec id="s1"><title>1. Introduction</title><p>Piezoelectric actuator is a kind of new motor which using inverse piezoelectric effect of piezoelectric ceramics [<xref ref-type="bibr" rid="scirp.82286-ref1">1</xref>] [<xref ref-type="bibr" rid="scirp.82286-ref2">2</xref>] [<xref ref-type="bibr" rid="scirp.82286-ref3">3</xref>]. Piezoelectric actuators have advantages of compact structure, high power with small weight, without electromagnetic interference and self-locking by frictional. Piezoelectric actuators are classified into two types: single vibration mode and compound vibration mode [<xref ref-type="bibr" rid="scirp.82286-ref3">3</xref>] [<xref ref-type="bibr" rid="scirp.82286-ref4">4</xref>] [<xref ref-type="bibr" rid="scirp.82286-ref5">5</xref>]. Piezoelectric actuators of compound vibration mode have higher performance than single vibration mode. At present, piezoelectric actuators have been studied by researchers, and they have been applied into many fields of spaceflight, automation and so on [<xref ref-type="bibr" rid="scirp.82286-ref6">6</xref>] [<xref ref-type="bibr" rid="scirp.82286-ref7">7</xref>] [<xref ref-type="bibr" rid="scirp.82286-ref8">8</xref>] [<xref ref-type="bibr" rid="scirp.82286-ref9">9</xref>]. We study the compound vibration mode piezoelectric motor working in deep-sea environment.</p><p>In this study, we design a deep-sea resonant sandwich linear ultrasonic motor and manufacture the prototype to measure its performance. The piezoelectric actuator adopts compound vibration mode of fifth order bending vibration and second order longitudinal. We complete the mode degeneracy by finite element analysis. We design and set up the experimental platform to measure the performance of prototype. The velocity of prototype can reach 264.5 mm/s while the water pressure is 8 MPa and the voltage signal with frequency of 30.30 kHz and voltage amplitude of 150 V. It verifies the simulation result and reaches the experiment objective.</p></sec><sec id="s2"><title>2. Finite Element Analysis</title><p>We select a configuration to build finite element model as show in <xref ref-type="fig" rid="fig1">Figure 1</xref>. This configuration adopts compound vibration mode of five order bending vibration and second order longitudinal vibration. High order bending vibrations and longitudinal vibrations are small affected by deep-sea environment. We complete the mode degeneracy by adjust the parameter of piezoelectric actuator. We obtain the sensitivity of main parameters about resonant frequency as shown in <xref ref-type="fig" rid="fig2">Figure 2</xref>. We determine the final parameters of structure as show in <xref ref-type="table" rid="table1">Table 1</xref>.</p><table-wrap id="table1" ><label><xref ref-type="table" rid="table1">Table 1</xref></label><caption><title> Parameter of structure</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >d</th><th align="center" valign="middle" >l<sub>r</sub></th><th align="center" valign="middle" >t<sub>b</sub></th><th align="center" valign="middle" >t<sub>l</sub></th><th align="center" valign="middle" >t<sub>s</sub></th><th align="center" valign="middle" >w<sub>f</sub></th><th align="center" valign="middle" >l<sub>h</sub></th><th align="center" valign="middle" >l<sub>b</sub></th></tr></thead><tr><td align="center" valign="middle" >35</td><td align="center" valign="middle" >20</td><td align="center" valign="middle" >6</td><td align="center" valign="middle" >6</td><td align="center" valign="middle" >8</td><td align="center" valign="middle" >8.5</td><td align="center" valign="middle" >37.5</td><td align="center" valign="middle" >6</td></tr></tbody></table></table-wrap><p>After it, the finite element model under water is built to obtain the resonant frequency as shown in <xref ref-type="fig" rid="fig3">Figure 3</xref>. We compare the resonant frequency under water with normal resonant frequency, as shown in <xref ref-type="table" rid="table2">Table 2</xref>. It shows water have stronger effect on five order bending vibration than second order longitudinal vibration. We also get many resonant frequencies with different pressure of water as shown in <xref ref-type="table" rid="table3">Table 3</xref>. It shows the pressure almost has no effect on resonant frequency. Finally, we conduct transient analysis to verify feasibility of this piezoelectric actuator.</p><table-wrap id="table2" ><label><xref ref-type="table" rid="table2">Table 2</xref></label><caption><title> Resonant frequency with different environment</title></caption><table><tbody><thead><tr><th align="center" valign="middle" ></th><th align="center" valign="middle" >Resonant frequency in air</th><th align="center" valign="middle" >Resonant frequency in water</th><th align="center" valign="middle" >Differentials</th></tr></thead><tr><td align="center" valign="middle" >bending vibration (kHz)</td><td align="center" valign="middle" >30.730</td><td align="center" valign="middle" >30.214</td><td align="center" valign="middle" >0.516</td></tr><tr><td align="center" valign="middle" >longitudinal vibration (kHz)</td><td align="center" valign="middle" >30.588</td><td align="center" valign="middle" >30.478</td><td align="center" valign="middle" >0.110</td></tr></tbody></table></table-wrap><table-wrap id="table3" ><label><xref ref-type="table" rid="table3">Table 3</xref></label><caption><title> Resonant frequency with different pressure</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >pressure (Mpa)</th><th align="center" valign="middle" >2</th><th align="center" valign="middle" >4</th><th align="center" valign="middle" >8</th><th align="center" valign="middle" >12</th><th align="center" valign="middle" >16</th><th align="center" valign="middle" >20</th></tr></thead><tr><td align="center" valign="middle" >bending vibration (kHz)</td><td align="center" valign="middle" >30.201</td><td align="center" valign="middle" >30.178</td><td align="center" valign="middle" >30.156</td><td align="center" valign="middle" >30.132</td><td align="center" valign="middle" >30.109</td><td align="center" valign="middle" >30.088</td></tr><tr><td align="center" valign="middle" >longitudinal vibration (kHz)</td><td align="center" valign="middle" >30.474</td><td align="center" valign="middle" >30.470</td><td align="center" valign="middle" >30.464</td><td align="center" valign="middle" >30.456</td><td align="center" valign="middle" >30.450</td><td align="center" valign="middle" >30.445</td></tr></tbody></table></table-wrap></sec><sec id="s3"><title>3. Experimental Study</title><p>We manufacture the prototype to measure the performance of this piezoelectric actuator, as shown in <xref ref-type="fig" rid="fig4">Figure 4</xref>. After it, we used the scanning laser Doppler vibrometer (PSV-400-M2, Polytec, Germany) to measure its vibration mode and the resonant frequency, as shown in the <xref ref-type="fig" rid="fig5">Figure 5</xref> and <xref ref-type="fig" rid="fig6">Figure 6</xref>. We can know the vibration mode and the resonant frequency is almost coincident with the simulation. We think the fabrication error contribute on the little different.</p><p>When the prototype is placed in the deep sea high pressure simulation system, we use precision impedance analyzer to measure impedance characteristic of prototype and obtain the resonant frequency, as shown in <xref ref-type="fig" rid="fig6">Figure 6</xref>. It has a little reducing compare with the normal environment, which shows correspondence with simulation result. Finally, the velocity of prototype reaches 264.5 mm/s while the water pressure is 8 MPa and the voltage signal with frequency of 30.30 kHz and voltage amplitude of 150 V.</p></sec><sec id="s4"><title>4. Conclusion</title><p>In this study, we design and study a deep-sea resonant sandwich linear piezoelectric actuator. We complete the mode degeneracy of fifth order bending vibration and second order longitudinal vibration. We manufacture the prototype and measure its performance. The measuring result verifies the simulation result. Finally, prototype’s velocity reaches 264.5 mm/s while the water pressure is 8 MPa and the voltage signal with frequency of 30.30 kHz and voltage amplitude of 150 V.</p></sec><sec id="s5"><title>Acknowledgements</title><p>This project is supported by the National Natural Science Foundation of China (No. 51575124).</p></sec><sec id="s6"><title>Cite this paper</title><p>He, S.P., Shi, S.J. and Chen, W.S. (2018) Development of Deep-Sea Resonant Sandwich Linear Ultrasonic Motor. Journal of Applied Mathematics and Physics, 6, 296-300. https://doi.org/10.4236/jamp.2018.61028</p></sec></body><back><ref-list><title>References</title><ref id="scirp.82286-ref1"><label>1</label><mixed-citation publication-type="other" xlink:type="simple">Smithmaitrie, P., Suybangdum, P., Laoratanakul, P. and Muensit, N. (2012) Design and Performance Testing of an Ultrasonic Linear Motor with Dual Piezoelectric Actuators. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2012. https://doi.org/10.1109/TUFFC.2012.2289</mixed-citation></ref><ref id="scirp.82286-ref2"><label>2</label><mixed-citation publication-type="other" xlink:type="simple">Zhakypov, Z., Golubovic, E., Uzunovic, T. and Sabanovic, A. (2013) Piezoelectric Motor Driver: Design and Evaluation. IEEE Control Conference, 2013.</mixed-citation></ref><ref id="scirp.82286-ref3"><label>3</label><mixed-citation publication-type="other" xlink:type="simple">Vyshnevsky, O., Kovalev, S. and Wischnewskiy, W. (2005) A Novel, Single-Mode Piezoceramic Plate Actuator for Ultrasonic Linear Motors. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 52, 2047-2053. 
https://doi.org/10.1109/TUFFC.2005.1561674</mixed-citation></ref><ref id="scirp.82286-ref4"><label>4</label><mixed-citation publication-type="other" xlink:type="simple">Yokoyama, K., Tamura, H. and Masuda, K. (2013) Single-Phase Drive Ultrasonic Linear Motor Using a Linked Twin Square Plate Vibrator. Japanese Journal of Applied Physics, 52, 07HE03. https://doi.org/10.7567/JJAP.52.07HE03</mixed-citation></ref><ref id="scirp.82286-ref5"><label>5</label><mixed-citation publication-type="other" xlink:type="simple">Spanner, K. and Koc, B. (2016) Piezoelectric Motors, an Overview. Actuators, 5, No. 1. https://doi.org/10.3390/act5010006</mixed-citation></ref><ref id="scirp.82286-ref6"><label>6</label><mixed-citation publication-type="other" xlink:type="simple">Shi, Y.L., Li, Y.B. and Zhao, C.S. (2011) A New Type Butterfly-Shaped Transducer Linear Ultrasonic Motor. Journal of Intelligent Material Systems and Structures, 2011, 1045389X11404955.</mixed-citation></ref><ref id="scirp.82286-ref7"><label>7</label><mixed-citation publication-type="other" xlink:type="simple">Shi, Y.L., Zhao, C.S. and Huang, W.Q. (2010) Linear Ultrasonic Motor with Wheel-Shaped Stator. Sensors and Actuators A: Physical, 161, 205-209. 
https://doi.org/10.1016/j.sna.2010.05.009</mixed-citation></ref><ref id="scirp.82286-ref8"><label>8</label><mixed-citation publication-type="other" xlink:type="simple">Cheol-Ho, Y., Ishii, T. and Nakamura, K. (2001) A High Power Ultrasonic Linear Motor Using a Longitudinal and Bending Hybrid Bolt-Clamped Langevin Type Transducer. Japanese Journal of Applied Physics, 40, 3773. 
https://doi.org/10.1143/JJAP.40.3773</mixed-citation></ref><ref id="scirp.82286-ref9"><label>9</label><mixed-citation publication-type="other" xlink:type="simple">Asumi, K., Fukunaga, R. and Fujimura, T. (2009) High Speed, High Resolution Ultrasonic Linear Motor Using V-Shape Two Bolt-Clamped Langevin-Type Transducers. Acoustical Science and Technology, 30, 180-186. 
https://doi.org/10.1250/ast.30.180</mixed-citation></ref></ref-list></back></article>