Proceedings of te 5 t Internationa Conference of Contro, Dynamic Systems, and Robotics (CDSR'18) Niagara Fas, Canada June 7 9, 218 Paper No. 12 DOI: 1.11159/cdsr18.12 Optimization Design of a Piezoeectric Actuator it Ortogona Teory Xijin Zang, Jia Zai, Qian Yang, Jun Yan, Tao Yang, Saojie Hou Sannxi Engineering Laboratory for Transmission and Contro, Nortestern Poytecnica University Xi an Cina zangxijin@npu.edu.cn;1833471671@163.com Abstract - In tis paper, an optimization design metod it ortogona teory for piezoeectric actuator is presented, and it focuses on getting te maximum output dispacement of piezoeectric actuator by optimizing four factors: te engt, idt, tickness of PZT-5 and te tickness of eastic ayer. Based on Finite eement anaysis as e as Range anaysis and Variance anaysis of ortogona test resuts, te degree of infuence of tese factors to te maximum output dispacement are anaysed, and optimization design is done. In addition, a RBF netork mode of piezoeectric actuator aso be researced. Keyords: Optimization Design, Piezoeectric Actuator, Ortogona Teory, Range, Variance. 1. Introduction Wit te deveopment and cross-appication of bionics, micro eectronic mecanica system and oter discipine tecnoogies, te researc of fapping micro air veice it sma size, igt, steat and great operabiity becomes more and more popuar after te end of te 2t century [1-6]. Te driving mecanism of fapping micro air veice must meets te driving poer and ig ift requirements ie te size is as sma as possibe. Wit te advantages of great unit mass output poer, sma size, good fexibiity etc., piezoeectric actuator can be used in te fapping micro air veice. Tis paper optimizes te size of piezoeectric actuator it ortogona teory and Finite eement anaysis, and te metod can acieve te optima size of piezoeectric actuator it feer experiments and cacuations. In addition, a RBF netork mode of piezoeectric actuator aso be researced, tus Finite eement anaysis can be eiminated to simpy to te design process of a piezoeectric actuator. 2. Piezoeectric Actuator s Structure and Operationa Principe In tis paper, Piezoeectric materia is PZT-5 and eastic ayer s materia is stainess stee. PZT-5 are pasted it an epoxy resin on bot sides of eastic ayer. Wit te DC votage circuit, piezoeectric actuator s eectrica structure as son in Fig 1. Fig. 1: Piezoeectric actuator s eectrica structure. 12-1
From te Fig 1, it is cear tat te poarization direction of PZT-5 on bot sides of eastic ayer is te same. It can be knon from te inverse piezoeectric effect, ie te direction of te votage and te poarization is te same, PZT-5 i be stretced; on te contrary, PZT-5 i be compressed. Wen te circuit is cosed and votage is proper, top PZT-5 i stretc ie te bottom compress in orizonta direction, tus te piezoeectric actuator i bend don. If te DC votage is repaced by Aternating votage, piezoeectric actuator i bend up and don in turn, tus te micro air veice can fap up and don accordingy. 3. Finite Eement Anaysis Metod of Piezoeectric Actuator A piezoeectric actuator is consist of to kinds of materias, its cacuation and anaysis is difficut, ere te finite eement metod is used. Tickness of piezoeectric ceramics is tin, and it is certain tat some sigt fas i appear in poarization process. Hoever, te poarization process is sti reativey uniform, and uniform distribution of poarization is a ypoteses for finite eement anaysis. By using te metod of direct modeing, nodes are created, and te nodes are used to generate te eement, tus te finite eement mode is obtained. Tis metod can generate a arge amount of data, but it can get more accurate resut and can contro te density of te finite eement mes. APDL anguage is used to define to kinds of materias (piezoeectric ceramic and stainess stee) and teir materia properties. Te grid density of piezoeectric ayer and eastic ayer are determined respectivey, and te coordinates of eac node are got from te parameters. After te first node is estabised, it is copied to produce oter nodes, tus a sub-microscopic structure of an actuator can be got. In turn, te sub-microscopic structure is copied to obtain te finite eement mode of te actuator. Soid5 eements are used in te process of modeing. Because tere is no gap beteen any neigbouring eements, teir boundary nodes are sared in te finite eement mode. Positive votage is appied to one eectrode, and votage is appied to te corresponding anoter eectrode. Finay, te finite eement cacuation is carried out. 4. Ortogona Optimization Design Basing on four factors(te engt,idt and tickness of PZT-5 and te tickness of eastic ayer), te paper optimizes te output dispacement of piezoeectric actuator using ortogona teory. In te paper, A, B, C, and D correspond to te engt,idt and tickness of PZT-5 and te tickness of eastic ayer, respectivey. Te factors and eves of tese experiments are son in Tabe 1. Tabe 1: Factor and eve tabe. Factor Leve A B C D An ortogona tabe 1 1 2 2 3 3 4 4 L (4 5 ) 16 (mm) (mm) (um) (um) 1 2 3 4 1 2 3 4 1 2 3 4 (five factors tat eac factor ave four eves) is cosed to design tabe eader, and te bank coumn ic is te fift coumn can be regarded as te random error. Te range anaysis resut of te bank coumn can refect eter tere exists interaction beteen tese factors. According to above, e can make ortogona design sceme easiy. 12-2
5. Ortogona Optimization Anaysis According to te design requirements, te origina range of te four factors ave been confirmed. Ten eac of tem as been cosen four eves just as foos, =14 1618 2, =1.8 2.4 3. 3.6, =8 1 12 14, = 4 6 8 1, te proper votage E=+1V. Combining it te caracteristics of PZT-5, te modes are modeed and te corresponding optimization anaysis are competed. Te resuts of te first group s mode is as foos in Fig 2. Te resuts of a groups are as son in Tabe 2. Factor and coumn Sceme Fig. 2: te output dispacement of te first group s mode. Tabe 2: Output dispacement of a groups mode. A B C D Random 1 2 3 4 5 Dispacement 1 1 1 1 1 1.453 2 1 2 2 2 2.279 3 1 3 3 3 3.198 4 1 4 4 4 4.138 5 2 1 2 3 4.326 6 2 2 1 4 3.411 7 2 3 4 1 2.216 8 2 4 3 2 1.27 9 3 1 3 4 2.281 1 3 2 4 3 1.236 11 3 3 1 2 4.671 12 3 4 2 1 3.16 13 4 1 4 2 3.39 14 4 2 3 1 4.442 15 4 3 2 4 1.466 16 4 4 1 3 2.735 K 1.267.3423.5675.3563.3833 K 2.357.342.2943.3778.3299 K 3.3235.3878.2978.256.3163 K 4.488.3123.2248.2443.3548 R.221.755.3428.1335.67 12-3
6. Range Anaysis Te etter R in Tabe 2 means te D-vaue beteen te maximum and minimum vaue of te same factor s K j. It is caed te range. It is te basis to divide te degree of infuence and significance of factors to te aim. Te bigger te R vaue is, te iger te degree of infuence and significance of tis factor is. Tus, te key factor can be ensured. K j is te mean vaue of one factor at te j eve. Tabe 2 sos tat te sequence of te vaue beteen te random coumn s D-vaue and eac factor s D-vaue in order of magnitude is te tickness of PZT-5(factor C), te engt of PZT-5(factor A), te tickness of eastic ayer(factor D), te idt of PZT-5(factor B). Tus, te degree of infuence and significance of tese factors to te output dispacement of piezoeectric actuator in order of magnitude is C, A, D, B. Te vaue beteen te random coumn s D-vaue and te factor B s D-vaue is so sma tat te infuence of it to te output dispacement of piezoeectric actuator can be ignored. Te infuence trend of eac factor to te aim is as son in Fig 3. (a)d-vaue of eac factor (b) Infuence trend of eac factor Fig. 3: Infuence trend of eac factor to te aim. Te resut of te 16t group is te biggest of a resuts, so te preiminary seection factor eve combination is A4, B4, C1, D3. According to Figure 4-(b), decreasing te magnitude of factor D can increase te output dispacement of piezo- eectric actuator. 7. Variance Anaysis Range anaysis can t provide a certain standard to measure te significance of one factor, and it aso can t distinguis te error s infuence from te cange of te experiment environmenta conditions to te aim. But Variance anaysis can reduce tese defects. Tus it is necessary to do variance anaysis. In tis paper, te F-vaue of one factor is compared it te corresponding vaue of te F-Distribution Tabe, according to its to degree te significance. According to Tabe 2, te variance square sum (SS), variance ( MS), degree of freedom (DF) and F-vaue [6] are as son in Tabe 3. 12-4
Tabe 3: te variance anaysis tabe. Variance SS MS DF F Significance A.1141.38 3 1.9388 Hig B.116.39 3 1.1165 Very o C.2751.917 3 26.3661 Very Hig D.462.154 3 4.4248 o Tabe 3 sos te infuence degree of tese factors for te output dispacement of piezoeectric actuator. In order of magnitude is te tickness of PZT-5 ( factor C), te engt of PZT-5(factor A), te tickness of eastic ayer (factor D), te idt of PZT-5(factor B). And te factor B s infuence is very sma. Range anaysis(quaitative anaysis) is consistent it te resut of Variance anaysis(quantitative anaysis). So te preiminary seection factor eve combination is A4, B4, C1, D3. To acieve bigger output dispacement, te fina factor eve combination is A4, B3, C1, D2 according to te resut of Range anaysis and te dispacement contour of te actuator is son in Fig 4. Fig. 4: te dispacement contour of te piezoeectric actuator. 8. Netork Mode of Piezoeectric Actuator Te tip dispacement of a piezoeectric actuator varies it suc factor as dieectric constant, piezoeectric strain constant, piezoeectric stress constant, eastic moduus, geometry parameters, etc. Wen te materias of piezoeectric ayers and eastic ayer are determined, te design of a piezoeectric actuator invoves it geometry parameters. To simpify te design process, it is necessary to kno te reation beteen te tip dispacement and geometry parameters. Herein e obtain te reationsip it artificia neura netork metod. Radia basis function (RBF) netorks can be used for universa approximation itout oca minimum, so e use RBF mode to describe te reationsip beteen te tip dispacement and geometry parameters. Basing on te above infuence anaysis of eac factor, e use 66 sets of data to train netork. Function nerb in Matab is cosen to train te netork. After training te RBF netork, e got paramters 1, b1, 2,b2. If te input vector is X, te output of te midde ayer and output ayer can be expressed as foos: Y1 = e ( 1 X b1)2 (1) Y2 = 2Y1 + b2 (2) We use 4 sets of data to vaidate te RBF mode, te resut is son in tabe 4. It is cear tat te maximum error is ess tan 1%, and te mode is effective. If te RBF mode soud be improved, more training data are needed. 12-5
Tabe 4: vaidation of te RBF mode. A B C D resut resut error from FEA from RBF 14 1.8.8.6.41.417 2.4% 18 3..12.1.286.275-3.8% 16 2.4.1.4.398.4197 5.5% 2 3.6.14.8.296.376 3.9% 9. Concusion Tis paper bases on four factors (te engt, idt and tickness of PZT-5 and te tickness of eastic ayer) to investigate te output dispacement of piezoeectric actuator, and te fooing ork as carried out: (1) Presents an optimization design metod it ortogona teory for piezoeectric actuator, and competes Range anaysis and Variance anaysis. (2) Netork mode of piezoeectric actuator is created it RBF netork. Acknoedgements Tis ork is supported under Nationa Natura Science Foundation of Cina (51175426) and Natura Science Basic Researc Pan in Saanxi Province of Cina (212JM71), and te autors gratefuy acknoedge tese financia supports. References [1] M. H. Dickinson, et a., Wing rotation and te aerodynamic basis of insect figt, J. Science, vo. 284, pp. 1954-196, 1999. [2] R. J. Wood, Te First Takeoff of a Bioogicay Inspired At-Scae Robotic Insect, IEEE Transactions on Robotics, vo. 24, no. 2, pp. 341-347, 28. [3] Q. V. Nguyen,H. C. Park,N. S. Goo,D. Byun Caracteristics of a Beete s Free Figt and a Fapping-Wing System tat Mimics Beete Figt, Journa of Bionic Engineering, vo. 7, pp. 77-86, 21. [4] M. Sitti, D. Campoo, J. Yan, R. S. Fearing, Deveopment of PZT and PZN-PT based unimorp actuators for micromecanica fapping mecanisms, IEEE Internationa Conference on Robotics and Automation, Korea, vo. 4, pp. 3839-3846, 21. [5] S. Mukerjee, R. Gangu, Non-inear Dynamic Anaysis of a Piezoeectricay Actuated Fapping Wing, Journa of Inteigent Materia Systems and Structures, vo. 21, pp. 1157-1167, 21. [6] K. Y. Ma, et a., Controed Figt of a Bioogicay Inspired, Insect-Scae Robot, Science, vo. 34, pp. 63-67, 213. 12-6