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压电浮能;ansys优化分析;SCI级别文献
Joumal of the Ceramic Society of Japan 118 [10]909-915 2010 JCS-Japan 8.9.=106.5mm Table 1. Pavement and steel material properties Elasti dulc Material 9=0.7MPu E(MP Asphalt concrete 0.35 Steel 200.000 Surface E,, ur, hy 0.3 Subbase E,,Bs;, hs s CYmbal Asphalt 9=0.7MP &KAAA Subgrade Eo, Ho &KA A concrete y ig. 3. The loads and structure of pavement. Model a 1000mm mission coefficient d, However it is difficult tu calculate the Model b ective k and Amax in a complicated Cymbal-Pavement coupling 4 FEA ITl system. Instead of them, the storage clectric energy at open circuit, which is related to the energy convert efficiency and potential power, is used to evaluate the energy harvesting ability of Cymbal in this paper chosen as the pzt material because of its high(d g) value. TI At the same time, the embedded Cymbal should not reduce the material properties are listed in Table 1 and Eqs. ( 9)-(11). 4) performance of the pavement, and increase the fuel consumption 07410 of the vehicle. It can be controlled by the displacement on th 0 surface of asphalt pavement. If the surface displacement of the 0074100pC小N(9) pavement with Cymbal is almost same or even less than the 74593 displacement without Cymbal, it indicates that the cymbal has 12679.584.1000 good coupling with pavement 79.512684.1000 Summarizing from above, the storage electric energy at oper 84.184.1117000 ircuit and surface displacement on the pavement are used as the GP (10) evaluating factors in this paper 0002300 00230 5. FEA models and parameters 000023.3 ABAQUS is used in this paper to perform the mechanical and 17000 piezoelectric analysis, in which piezoelectric equations(1) and (2) 017000 (11) 01470 5.1 Pavement structure and load The responses of pavement are various with vehicle loads and constant at constant strain pavement structures and materials. In general, the vehicle can be 5.3FE cars(trucks and buses). The typical tire pressure is between 0.2 Considering the contacting of asphalt pavement and Cymbal 0. 25 MPa for small cars, and between 0.5-1.0 MPa for large cars. two types of cylinder models are submitted to FEA(see Fig. 4) The large cars are analyzed in this paper. For most analysis in The diameler of asphalt is 1 m. Its thickness is 40 mm above pavement engineering, the contact pressure between tire and cymbal and 110 mm under the cymbal. The diameter of the load pavement is assumed to cqual the tire pressure, and the shape of area is 213 mm. The load. size and material for model a and b contact area is assumed to round. Typical asphalt pavement are the same. The only different between them is contact between structure and dual tire loads are shown as Fig. 3. Only one tire Cymbal and asphalt concrete. Cymbal is surrounded by aspl load is considered in this paper because the size of Cymbal is concrete directly in model A, and is placed in a metal box small comparing to the contact area. Contact stress q MP model B. The axial symmetry modeling technique is used in (25 kN for one tire)is accepted in FEA The surface of asphalt pavement always includes 2 3 layers, in which the thickness of the top layer is about 40 mm. The Cymbal 5. 4 Comparing of model a and B ld be embedded in the pavement as close as possible to the a Cymbal with dc=32 mIm, do= 22 mm, d;= 10 mm, surface to get more energy. However, it is very hard to embed h=2mm,tc=0.3 mm, and tp=2 mm is modeled to compar- Cymbals in one asphalt pavement layer. Thus, the bottom of the ing the efficiency of model A and B( thickness of steel top layer of the pavement is the best location to set the Cymbals shell is 0.3 mm). The electric potential in the Cymbal of which is about 40 mm depth In order to put more attention on model a is shown as Fig 5. the electric potential is set to zero y the surface layers of asphalt pavement are It the bottom metal cap. The maximum electric potential is considered in fea 97.33Vin el a and 7653v in model b. there is about 0.07% increasing of the pavement surface displacement at the 5.2 Material properties center point in model A, which is almost same as the norm Elastic material properties are used for asphalt pavement, end pavement. Thus, the model A is chosen to discuss for the ap and P/T Steel is used to model the end cap and P/ is following feA 911 JCs-Japan Zhao et al. Finite element analysis of Cymbal piezoelectric transducers for harvesting energy from asphalt pavement 0.00 0.2 36,50 48.67 60.83 0.2 0.4 t p=0. 2mm tp=0.51 97.33 tp=1.0mm Fig. 5. Electric potential in cymbal of modela -0.8 tp=2.0mm Table 2. Shape paramctcrs of Cymbals Fig. 7. Displacement difference of model A Value(mm) de 10 30 d d 16 dc=30mm. di=12mm 力 10 10 目 0.06 dc=40mm. di=12mm 0.4 0.4 0.4 0.4 0.02 0.080 0.00 tp-0lInn 681012141618202224 0.060 tp=1.0mm do(mm) tp=2. 01 Fig 8. Ue vary in do 0.020 0.000 0.08 20d(mm)30 0.07 tp0 2mm tp0.5mm Fig. 6. Potential electric energy with various d, 0.06 tp=1.0mm 0.05 tp-2 Or 0.04 6. Selecting the diameter of PZT 0.03 The size of Cymbal will significantly influence the output 0.02 electric energy. Variant sizes of pzt disk are available in the 0.0 market. The Cymbals with dc=10 mm, 20 mm, 30 mm and 0.00 40 mm are analyzed. The other shape parameters are listed in 12141618202224 Table 2 Fig. 9. U e vary Ill 6.1 Potential electrical energy The potential electric energy (Ue)stored in transducer can be calculated by Eq. ( 8), in which the electric potential is obtained Considering the cost of P/t disk, potential electrical energy by FEA. Figure 6 shows the potential electric energy of the and coupling with the pavement, the diameter of Cymbal had Cymbals with various de. It can be concluded that the potential better near 30 mm. In order to give the Cymbal a uniform contact, electric energy increases with de. From that puinL, larger Cymbal the size of Cymbal had better be 2-3 limes of the large size of the is recommended to get more energy. aggregate in asphalt pavement, which is 13-16 mm. Thus,a diameter at 32 mm is decided as the optimum size of Cymbal 6.2 Coupling with pavement Embedded Cymbal should not increase the surface displace 7. Defining other size parameters ment when they work in the pavement. The center displacement In addition to the diameter of Cymbal, other size parameters at the top of the model is used to examine the coupling effect of also influence the potential electric energy, such as do, di, h, te Cymbal and pavement. The displacement difterence percent with and tp and without cymbal can be calculated by Eg(12). As shown in Fig. 7, the surface displacement of pavement changes with do 7.1 Effects of do There is a maximum Pa near dc= 20 mm. The pd becomes The efTects of do with various d. are examined by FEA negative between d= 20-30 mm for thinner tm, which indicates (h=I mm and te=0.4 mm). As shown in Fig 8, the le the dw is larger than dwo. The pavement surface displacement are near linearly with do for all de. More details are all reduced by all size cymbals because of their high stiffness explored for the Cymbal with d 32 mm, h= 2.0 mm, 2.0mm t-0.3 mm, and di=8mm. The results are shown in Fig 9 Those curves in Fig 9 show that the Ue increases wit dn100% (12) However, the surface displacement of pavement also increases with do as shown in Fig. 10. The surface displacement with Where pa is the displacement difference percent; dwo is the Cymbal begins larger than the value without Cymbal (pa <0 displacement without Cymbal; dw is the displacement with near d,= 22 mm for t =2.0mm. It indicates that do had better Cymbal no larger than 22 mm for tp=2.0mm 912 Joumal of the Ceramic Society of Japan 118 [10]909-915 2010 JCS-Japan 10000 64 0.20 0.0 0.2 tp=0.2mm 0.4 P0.5mm 0.00 0802 tp-20mm tp-30mm 12141618202224 121416 202224 Fig. 12. do vs. radial stress in bonding layer ig. 10. Rela -do=12mm do=16mm 0.10 do=20mm do=22mm 0.08 do=24mm 0.06 02 4o0 011416 0.02 lo=16mm 0.00 do=20mm 468101214161820 do=24mm d(mm) Distance from the center of cymbal(mm) Fig. 13. Ue vary in d (a) Top of Pzt 1.2 3.0 do=12mn 16mm do=16mm 0.9 do=20mt do=20mm 2.0 do=24mm 0.6 do=24mm ∑1.5 0.3 oi 8 0.0 0.5 0.368101214161820 d mm) Fig. 14. Displacement difference with d 1.0 Distance from the center of cymbal(mm) b)Center of PZT Fig. 11. Radial stress in PZT. Fig. 13 and Fig. 14. There is a maximum Ce for various d; as shown in Fig. 13. The optimum d; at do=22 mm is about 10mm. At the same time, the surface displacement of pavement has been reduced when d =10 mm and d.< 22 mm. Thus At the same time, enough area is needed to bond the pzt di= 10 mm is suggested as the top diameter of cymbal nd end cap by the binder such as epoxy. The radial stress in PZT caused by the pressure applying on the top of the p 7.3 Effects of tc is shown as fig, 11. The radial stress under the cayi the The thickness of end cap will also influence the perfor- PZT is almost uniform about 2 MPa. At the inner contact point mance of Cymbal. A Cymbals with dc= 32 mm, do=22 mm of P7T and steel cap, there is a concentrate of stress. Out of that t,=2 mm, d;=10 mm and various te and h are analyzed through point the radial stress is very small. Assuming the radial stress FEA. The FEA results are shown as Fig. 15 and Fig. 16. From in PZT under the cavity is driven by the bonder uniformly, and Fig. 15, it can be concluded that there is a maximum Ue at to then the radial stress in the bonding layer should not larger than about 0.3 mm for various h. The pd increases with the increasing peel strength of the bonder. The of te. For tc=0.3 mm, the P are larger than zero when h is no strength and d, is shown in Fig. 12. The peel strength of epoxy less than 2 mm. Thus, the f=0.3 mm is suggested to build the bonder is between 0.3-1.2 MPa. 16)The curve in Fig. 12 shows Cymbal that the radial stresses in bonding layer are all less than the peel strength (0. 3 MPa) for d, <24 mm. Considering the Ue 7. 4 Effects of h coupling effects with pavement and bonding, do= 22 mm is a Cymbals with de= 32 mm, do=22 mm, t,= 2 mm, determined te=0.3 mm and various di and h are analyzed for h effects The Ue reach its maximum about h= 2-3 mm for all d; except 7.2 Effects of d d;= 16 mm(see Fig. 17). The surface displacement of pavement The FEA results of Ue and Pd vary in di for d=32 mm, decreases with the increasing of h as shown in Fig. 18. Then h=2mm, p=2 mm, te=0.3 mm and various do are shown as h=2 mm is determined for di=10 mm Cymbal 913 JCs-Japan Zhao et al. Finite element analysis of Cymbal piezoelectric transducers for harvesting energy from asphalt pavement 0.06 0.120 -dc=10mm -dc=20mm 0.05 0.100 dc=30mm dc=32mm 0.04 0.080 dc=40mm 0.03 0.060 0.02 h=0.5mm -h=1mm 0.040 0.01 In b=3mm h=4mm 0.020 0.00 0.000 0.20.30.40.50.60.70.80.91 tc(mm 0.511.522.53 ,(mm) Fig. 15. Ue Fig. 19. e vary in tp 14 -h=0.5mm h=ln 14 h=2mm dc=10mm -+dc=20mm 1.0 h =4mm 1.0 dc=3 0mm dc=32mm 0.8 0.8 06 de-40nm 0.6 0.4 00 02 0.2 0.0 0.2 0.6 -0.4 00.5115、22.53 020.30.40.50.60.70.80.91 tc(mm) Fig. 20. Displacement difference with tp Fig. 16. Displacement difTerence with t I, is thicker than I mm. The differences of displacement at the 0.07 center point of pavement surface with and without Cymbal are shown in Fig 20. The curve of d= 32 mm in Fig. 20 shows that 0.06 the displacements with Cymbal are less than without Cymbal 0.05 when the t is larger than about 2 mm. For those aspects, thicker 目004 PZT is better to build Cymbals. However, the cost increases with 0.03 Hdi=4mm -+di=omr the pzt thickness. Combining those factors, tp=2 mm is 0.02 -di=8mm -di=10r mm suggested for Cymbal d i=12mm di=14mm 8. Cymbal transducer design 0.00 di=16mm 0.5 1.5 2.533.54 8. 1 Size h(m Through the above FEA Tor Ue ng effects with Fig. 17. Uc vary in h pavement, the optimum Cymbal size is determined. The Cymbal ith de= 32 mm, d,=22 mm, d;=10mm, te=0.3 mm, h=2 mm,and tp= 2 mm is designed for harvesting energy from 0.6 asphalt pavement 0.4 0.2 8.2 Performance 0.0 Under the vehicle load, the designed Cymbal can generate a -0.2 97.33 V electric potential between the PZT surfaces based on the -0.4 Hdi=4mm Hdi=6mm FEA model A. The potential maximum output electric energy -0.6 di=8mm -di=10n estimated about 0.06 m. by Eq(8). Assuming the frequency of -0.8 d i=12mm di=14mm the vehicle load is at 20 Hz. then maximum 0 06x 20=1.2 mw 1.0 electric energy will be harvested by each designed Cymbal from 0.511.522.533.54 the asphalt pavement. The output power will be more if higher performance PZT material is used to build the Cymbal Fig. 18. Displacement difference with h. 9. Conclusions 7.5 Effects of to This paper discussed the performance of Cymbals for harvest- ng energy from the asphalt pavement. The potential electr The thickness of pzt is a key parameter influencing the energy (Ue) generated by Cymbals are evaluated through FEA, performance of Cymbal. The Cymbals with p=0.2,0.5, 1.0, which indicates the capability of a Cymbal transducer. At the 2.0, 3.0 mm, te=0.3 mm, h=2 mm are evaluated via FEa same time, the surface displacements of pavement are analyzed (other sizes are listed in Table 2). The relation between Up and t, to examine the coupling effects between Cymbals and the is shown in Fig. 19. Ue increases with the thickness of PZT in the pavement. Bas on the research presented in this paper, the pavement environment. The increase rate becomes smaller when following conclusions are made. 914 Joumal of the Ceramic Society of Japan 118 [10]909-915 2010 JCS-Japan (1) The displacement difference Pa 20 is used to guarantee Vibration under Moving Vehicle and the Coupling Effects with that the surface displacement of pavement with Cymbal is less Piczoclcctric Transduccr(No 50908177) than the displacement without Cymbal. Maximum clectric energy Ue and low cost are also used to choosing the size parameters (2)Two ABAQUS FEA models are compared under the References contact load at 0.7 MPi. The model A, which the Cymbal is 1) Ministry of Transportation of the Peoples republic of China embedded directly in the asphalt pavement, is suggested to FEA http://www.moc.gov.cn/zhuzhan/tongjixinxi/fenxigongbao because of its higher electric potential tongjigongbao/ 201004/t20100430-68 1272 html 2)A. Dogan, J. F. Fernandez, K. Uchino and R. E. New nham (3)Ue increases with the diameter of Cymbal (de). However, Proceedings of the lOth Ieee International Symposium on the cost also increases with de. There is a largest pu near Applications of Ferroelectrics, Aug. 18-21, East Brunswick, For cases with thin PZT, Pa become negative US.A,(1996)pp.213-216. between de=20-30 mm except the thickness of PZt 'p=2 mm 3A. Dogan, K. Uchino and r. E. Newnham, IEEE Trans Combing the energy harvesting capability, coupling effects with Ultrason. Ferroelectr. Freq. ControL, 44, 597-605(1997) pavement and cost, d= 32 mm is suggested )A. Dogan,J.上.上 crnandcz,k. Uchino and r.上. Newnham, 4)Ue increase with the diameter of the cavity base (d) IEEEJ. Oceanic Eng, 32, 408-415(2007) However, Pu decreases with the increasing of do For lp =2 mm 5)J. F. Tressler, A. Dogan,J F Fernandez, J. T. Fielding, Jr,K. Pd becomes negative near d,= 22 mm. The bonding area is Uchino and R. E. Newnham, Proceedings of the 1995 IEEE enough to bond the steel end cap and pzt when do= 22 mm Ultrasonics Symposium, Nov. 7-10, Seattle, U.SA.(1995) pp.897-900 (5) There is a maximum Ue when changing the top diameter of 6) J F. Tressler, W. Cao, K. Uchino and R. E. Newnham, IEEE the end cap(di) For dc= 32 mm, do= 22 mm and t,= 2 mm, the Trans. Ultrason. Ferroelectr. Freg. ControL, 45, 1363-1369 (6) Ue reaches its largest value when the thickness of cap steel (1998) 7)RE.Newnham, A. Dogan, D. C. Markley, J. F. Tressler, J. is near 0.3 mm. There is also a maximum Ue near h= 2 mm Zhang, E. Uzgur, R J. Meyer, Jr, A C. Hlacky-Hennion and (7)Ue and cost increases with the thickness of PZT(p) w.J. Hughes. Proceedings of the MTS/IEEE Oceans 2002 However, the increasing rate uf Ue decreases after Ip l mm Conference and Exhibition, Oct 29-31, Biloxi, U.SA(2002) hus tp=2 mm is chosen to build the Cymbal 2315-2321 ( 8) Through a bunch of FEA, dc= 32 mm, do= 22 mm, 8)G. Wang, L. Wang, G. Li, G. Luan and F. 7ang, Electron d=10 0.3 mm. h=2 mm, and tn= 2 mm is designed Compon. Mater, 23, 33-35(2004)in Chinese] 9)C. Sun, S. Guo, w. Li, Z. Xing, G. Liu and x. Zhao, Sens for Cymbal to harvest energy from asphalt pavement. Its Ue is Actuators,A,121,213-220(2005) about 0.06 mJ. 1.2 m w maximum output power can be generated 10)F Tian, J. Cai, L Lv and J Qian, Torpedo technol., 15, 51-54 if the vehicle load is at 20 Hz (2007)[in Chinese] (9)Only single Cymbal is discussed in this paper based on I1)H. w. Kim, A Batra, S. Priya, K. Uchino, D Markley, R.E. FEA. The laboratory evaluating test needs to be done in the Newnham and H F Hofmann, Jpn..Appl. Phys., 43, 6178. future. Cymbal arrays will be used in the field according the 6183(2004) traffic and vchicle type. The performance of Cymbal array, such 12)II. w. Kim, S. Priya, K. Uchino and r. E Newnham, J as efficiency, cost and coupling with pavement needs to be Electroceram. 15, 27-34(2005) explored in the future as well. Following those works, how to 13)II.W.Kim, s Priyal and K Uchino, / Appl Plys, 45, 5836 5840(2006) storage electric energy and use them to light the traffic signal and 14)D. Song and M. Xiao, " Piczoclcctric cffccts and application. light will be studied in the future 15) A pular science press, Beijing, China(1987) A.Ⅴ Piezoelectric transducers and applications Acknowledgements This work is completed at Pavement second edition, " Springer, New York, U.SA(2008) Research Center of UC Berkeley and UC Davis. The authors 16)A Dogan, "Flextensional 'Moonie and cymbal'actuators "A appreciated Professor John Harvey for providing the research thesis in materials program submitted in partial fulfillment of requirement. This paper is supported by the Chinese National the requirements for the degree of Doctor of Philosophy(1994 Natural Science Foundation Project: Research on Asphalt Pavement pp.63-66 915

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