Sensos and Actuatos A 100 (2002) 18 23 Flexible PVDF comb tansduces fo excitation of axisymmetic guided waves in pipe Thomas R. Hay *, Joseph L. Rose ESM Depatment, Pennsylvania State Univesity, 212 EES Building, Univesity Pak, PA 16802, USA Received 26 July 2001; eceived in evised fom 21 Decembe 2001; accepted 10 Januay 2002 Abstact Flexible PVDF pipe comb tansduces ae easy to install by wapping aound any size pipe. It is possible to mechanically couple these tansduces to the pipe theeby eliminating the need to bond electodes to the film and adhesively couple the tansduce to the pipe. The simple fabication pocess, installation, and affodability of these tansduces makes them ealistic candidates fo condition-based monitoing of some citical pipeline applications. These tansduces ae capable of exciting lowe ode axisymmetic modes with minimal adial displacement and maximum axial displacement as well as modes with both suface displacement components. This vesatility is extemely impotant since unde cetain loading conditions, modes with significant adial displacement ae almost completely attenuated. # 2002 Elsevie Science B.V. All ights eseved. Keywods: Axisymmetic guided waves; Comb tansduce; PVDF; Pipe 1. Intoduction Comb tansduces ae efficient geneatos of axisymmetic guided waves in pipe and have many advantages compaed to conventional angle beam techniques. Some of these advantages include [1 3] unifom cicumfeential loading, mode and fequency tuning capability to establish natual defect wave esonances, and highe fequency excitation fo impoved sensitivity and esolution. Excellent esults have been obtained using piezocomposite comb tansduces fo a vaiety of diffeent types of defects typically found in piping [4,5]. The flexibility of these tansduces is limited by the igidity of the piezocomposite. Hence, tansduce design equies element dicing and othe exta manufactuing steps to fit the tansduce to the pipe suface. The flexibility poblem can be ovecome using PVDF film since this film can be wapped aound and mechanically coupled to the pipe. Ealie esults have shown that intedigital tansduces using this film as the piezoelectic substate ae efficient geneatos of the lowe ode Lamb wave modes in steel and aluminum [6 8] plates. The typical tansduce design includes the consideation of a backing laye, electode patten and mateial, electode bonding to * Coesponding autho. E-mail addess: th157@psu.edu (T.R. Hay). the PVDF, and bonding the PVDF film to the waveguide. This pape shows that mechanical coupling is an excellent altenative to the bonding steps, theeby simplifying tansduce constuction and installation. Pipeline inspection with guided waves is an attactive altenative to conventional bulk wave ultasonic techniques because it is possible to inspect ove long distances and undeneath coatings and insulation. Inceased sensitivity is also an added advantage but the optimal mode and fequency must be selected such that the wave stuctue in the pipe coss-section is sensitive to the defect sought in the inspection. In addition, inspection can be complicated by the type of pocess fluid tanspoted in the pipe and coatings, insulation, and wate on the oute suface. As an example, an uncoated and non-insulated natual gas pipeline will typically be less difficult to inspect han a coated pipeline tanspoting a liquid poduct. This pape demonstates that PVDF comb tansduces ae extemely vesatile in exciting modes fo both of the above conditions. 2. Theoetical backgound The deivation of the fequency equation fo wave popagation in a hollow isotopic elastic cylinde is given in detail by Gazis [9] and is biefly summaized hee. The following foms of the scala and vecto potentials ae 0924-4247/02/$ see font matte # 2002 Elsevie Science B.V. All ights eseved. PII: S 0924-4247(02)00044-4
T.R. Hay, J.L. Rose / Sensos and Actuatos A 100 (2002) 18 23 19 assumed: F ¼ f ðþ cosðmyþ cosðot þ kzþ; H ¼ g ðþ sinðmyþ sinðot þ kzþ; H y ¼ g y ðþ cosðmyþ sinðot þ kzþ; H z ¼ g z ðþ sinðmyþ cosðot þ kzþ (1) whee F is the scala potential and H the vecto potential. Substituting these equations into the scala and vecto potential wave equations, we get v 2 1 2 F ¼ @2 F @t 2 ; whee v2 2 2 H ¼ @2 H @t 2 (2) v 2 1 ¼ l þ 2m ; v 2 2 ¼ m (3) Hee l, m, ae the Lame s constants and density, espectively, we can obtain a geneal solution fo unknown functions f(), g (), g y (), and g z () in tems of Bessel and modified Bessel functions. This solution can be used to solve fo the displacements fields u ¼ f 0 þ M g 3 þ kg 1 cosðmyþ cosðot þ kzþ; u y ¼ M f þ kg 1 þ g 0 3 sinðmyþ cosðot þ kzþ; u z ¼ kf g 0 1 ðm þ 1Þg 1 cosðmyþ sinðot þ kzþ (4) whee M is the cicumfeential ode of the popagating mode and the pime denotes diffeentiation with espect to. The equations fo stesses ae obtained using the displacement stain and stess stain elationships. Using the following bounday conditions s ¼ s z ¼ s y ¼ 0, at ¼ a and ¼ b, the fequency equation of the following fom is obtained: D ¼jc ij j (5) whee c ij is a 6 6 matix. Fo a non-tivial solution, the deteminant D is equal to zeo. Fo axisymmetic longitudinal modes, M ¼ 0, and the dispesion cuves that esult fom the fequency equation ae shown in Fig. 2, whee fd is the fequency thickness poduct. The thickness efes to the thickness of the cylinde wall. Fo these modes, the displacement in the cicumfeential diection u y ¼ 0, and u and u z ae the nomalized displacement fields fo a 35 mm ID and 39 mm OD stainless steel pipe. Examples of displacement fields ae shown in Figs. 3 and 8. 3. Dispesion cuve analysis Tansduce design stats with the analysis of the phase velocity dispesion cuves and wave stuctue. Figs. 1 and 2 show the pipe geomety used and the coesponding phase Fig. 1. Pipe coodinates used to model the dispesion cuves. and goup velocity dispesion cuves, espectively. The design in this pape focused on exciting the L(0, 3) and L(0, 4) modes at maximum goup velocity to simplify expeimental veification and also because both modes have significant paticle displacement at both the inne and oute sufaces, demonstating potential fo suface defect detection. In addition, these ae points of minimum dispesion which is advantageous fo applications that equie popagation ove long distances. At the bulk wave longitudinal velocity the nomal component of the paticle velocity of the non-zeo-ode symmetic Lamb wave modes goes to zeo at the fee sufaces of a plate [10,11]. Simila esults can also be obtained by analyzing the wave stuctues of the longitudinal axisymmetic modes at the bulk wave longitudinal velocity as shown in Fig. 3. The wave stuctue shown is nomalized to the maximum in-plane displacement component. The out-of-plane and in-plane displacements ae epesented by the adial and axial components, espectively. At the pipe inne and oute sufaces the axial displacement is maximum while the adial component is close to zeo. Consequently, L(0, 4) is an excellent candidate fo inspection of a fluid loaded pipe since coupling of the mode into the fluid will be minimal. The comb tansduce electodes ae activated in phase and ae geneally sepaated by a cente to cente distance of a wavelength. In contast, intedigital devices typically activate adjacent electodes with evesed polaity. Both techniques wok well but since comb tansduces do not equie any phase diffeence between electodes, the assembly and activation of the tansduce ae slightly simple. The wavelength of L(0, 4) at 5.85 mm/ms is appoximately 2.5 mm and was used as the electode spacing. The wavelength of L(0, 3) close to the maximum goup velocity at a phase velocity of 6.1 mm/ms and an fd of 1.9 MHz mm was appoximately 3.4 mm and was used as the electode spacing. The activation lines (dotted lines) fo the coesponding comb sensos ae shown in Fig. 2. This constant wavelength line shows the phase velocities at which the comb tansduce will excite each mode while sweeping though fequency. Note that the slope of these lines is given by l/d, whee d is the pipe thickness.
20 T.R. Hay, J.L. Rose / Sensos and Actuatos A 100 (2002) 18 23 Fig. 2. Phase (top) and goup (bottom) velocity dispesion cuves fo a 35 mm ID and 38 mm OD stainless steel pipe. Fig. 3. Nomalized L(0, 4) adial (u ) and axial (u z ) displacements at the bulk wave phase velocity 5.8 mm/ms and fd of 3.873 MHz. 4. Tansduce fabication and installation The objective of the tansduce design and fabication pocesses was to develop a comb tansduce that is easy to wap aound a pipe, simple to manufactue, and simple to install. As discussed in [6] it can be difficult to deposit metal electodes onto PVDF. Theefoe, bonding an electode patten etched on flexible polyamide pinted cicuit boad (PCB) to the PVDF was suggested as an altenative. The fabication pocess fo the pipe comb tansduce used the pattened PCB appoach but simplified the pocess by mechanically coupling the electodes to the PVDF (Fig. 4). By eliminating the bonding pocess, the labo associated with the adhesive application and the cost of adhesive mateial ae eliminated. The electodes wee etched onto a polyamide backing using 4 oz. coppe. An electode width of 0.5 mm was used fo both designs. The length of the electodes is 200 mm, which coesponds to the oute cicumfeence of the pipe. Fig. 5 shows the coppe finge patten on the polyamide backing. The commecially available 100 mm thick PVDF film manufactued by Measuement Specialties (MSI) was used as the active element fo the tansduce. The film was supplied with no electodes so that the custom electode pattens could be used on the film. An ammoniacal etching pocess was used to obtain the desied electode patten on
T.R. Hay, J.L. Rose / Sensos and Actuatos A 100 (2002) 18 23 21 The comb was installed by fist wapping the PVDF aound the pipe followed by wapping the electodes ove the PVDF. Pipe clamps wee then installed at maximum pessue. No couplant o adhesive was used. The pipe was used as the gound by soldeing the tansduce s gound electode to the pipe. 5. Expeimental setup and esults Fig. 4. PVDF comb tansduce clamped to a stainless steel pipe. Expeiments wee pefomed using a TISEC stuctual wave analysis tool (SWAT) system. The system outputs a gated sinusoid in the 50 khz to 15 MHz fequency ange at a maximum voltage of 300 V. The eceive has an output level of 4 V and a dynamic ange of 70 db. Fo both modes the fequency was swept in the vicinity of the design fequency to maximize the amplitude of the eceived mode. A pulse width of appoximately 11.0 ms was used fo both modes and the eceive gain was set to 32 db fo L(0, 3) and L(0, 4). Goup velocity measuements wee in the though tansmission mode at a tansduce sepaation distance of 1800 mm. The attenuation due to wate loading was also measued fo each mode. Table 2 summaizes the expeimental esults to demonstate the impotance of mode selection. Table 2 Mode goup velocity and attenuation Mode Opeating fd (MHz mm) Expeimental goup velocity (mm/ms) Wate loaded loss (db) L(0, 3) 2.8 3.65 31 L(0, 4) 3.7 4.82 5.24 Fig. 5. Electode finge patten on flexible polyamide shown wapped aound a pipe. the 50 mm thick flexible PCB supplied by Amistead Technologies. Since the PVDF wave impedance was small compaed to that of the aluminum, the effect of senso on the suface of the pipe is equivalent to applying stess on the suface [10]. Futhemoe, it is assumed that no shea component can be coupled into the specimen and as a esult, stess is only applied nomal to the oute suface of the pipe. Theefoe, both the sending and eceiving tansduces opeate in the thickness mode. Table 1 compaes the piezoelectic constants of PVDF and the piezoceamic used in peviously developed comb tansduces [12]. Table 1 Piezoelectic stess and stain Mateial d 31 d 33 g 31 g 33 PVDF 23 33 216 330 PZT-5A 171 374 11.4 24.9 Fig. 6. L(0, 3) at 2.8 MHz mm in a 35 mm ID and 38 mm OD stainless steel pipe (top) and wate loaded pipe (bottom).
22 T.R. Hay, J.L. Rose / Sensos and Actuatos A 100 (2002) 18 23 between the attenuation of the modes due to wate loading. The attenuation of the L(0, 3) mode is almost 25 db geate than the L(0, 4) mode. The second wavefom in Fig. 7 is a esult of mode convesion due to the wate loading of the pipe ID. 6. Conclusions Fig. 7. L(0, 4) at 3.7 MHz mm in a 35 mm ID and 38 mm OD stainless steel pipe (top) and wate loaded pipe (bottom). Fo both modes the optimal fd was found to be slightly lowe than that used in the dispesion cuve analysis but the goup velocities compaed excellently. Sample RF wavefoms fo both modes ae povided in Figs. 6 and 7. The out-of-plane suface displacement at the inne adius was also calculated to show the effect of optimizing wave stuctue fo diffeent loading conditions. The comb tansduces excite both modes extemely well. The calculated nomalized out-of-plane displacement component fo the L(0, 3) mode is shown in Fig. 8. Fig. 3 shows the L(0, 3) displacement field. The axial/adial displacement atio fo the L(0, 3) mode is consideably smalle compaed to that of the L(0, 4) mode. As a esult, thee is a significant diffeence The flexible PVDF comb tansduces developed in this wok successfully excited and eceived L(0, 3) and L(0, 4) close to thei maximum goup velocities. The design appoach focused on affodability and ease of installation. It was shown that no bonding of the PVDF film to the electodes o test stuctue was necessay as was done in ealie wok. The electode positioning on the film and tansduce installation on the pipe ae both pefomed when the mateials ae clamped to the pipe. This technique is potentially useful fo some long tem monitoing applications since issues associated with deteioation of the bond quality o coupling to the pipe ae eliminated. It is also feasible to not ecove these types of tansduces fom such applications since the loss of investment is minimal. The wave stuctue of the excited modes was also consideed, showing that the PVDF comb is capable of exciting modes with both stong in-plane and out-of-plane suface displacements. This vesatility is extemely impotant since cetain loading conditions on the pipe can significantly attenuate the popagating mode. A compaison of mode popagation in a wate loaded pipe was given to demonstate the impotance of mode selection and tansduce vesatility. It was shown that L(0, 3) is attenuated appoximately 25 db moe than L(0, 4) at thei maximum goup velocities ove a popagation distance of 1800 mm. The diffeence in attenuation was due to the elatively weak out-of-plane suface displacement component of L(0, 4) compaed to L(0, 3). Acknowledgements The authos would like to thank the Office of Naval Reseach and D. Vinod Agawala fo thei suppot. Refeences Fig. 8. Wave stuctue of L(0, 3) at an fd of 2.8 MHz mm fo a 35 mm ID and 38 mm OD stainless steel pipe. [1] J. Li, J.L. Rose, Implementing guided wave mode contol by use of a phased tansduce aay, IEEE Tans. Ultasonics Feoelecton. Fequency Cont. 48 (2001) 761 768. [2] M.J. Quay, J.L. Rose, Multimode guided wave inspection of piping using comb tansduces, Mate. Eval. 45 (1997) 504 508. [3] J.L. Rose, Feasibility of ultasonic guided waves fo non-destuctive evaluation of gas pipelines, GRI-99/0076, 1999. [4] M. Quay, A time delay comb tansduce fo guided wave mode tuning in piping, Ph.D. Thesis, Pennsylvania State Univesity, Univesity Pak, PA, 2000.
T.R. Hay, J.L. Rose / Sensos and Actuatos A 100 (2002) 18 23 23 [5] J.L. Rose, M.J. Quay, A. Bay, C. Coley, Guided waves fo coosion detection potential in piping unde insulation, in: Poceedings of the ASNT Fall Confeence, 1997, pp. 27 29. [6] R.S.C. Monkhouse, P.D. Wilcox, P. Cawley, Flexible intedigital PVDF Lamb wave tansduces fo the development of smat stuctues, QNDE 15 (1996) 884 887. [7] A. Gachagan, P. Reynolds, G. Haywad, R. Monkhouse, P. Cawley, Piezoelectic mateials fo application in low pofile intedigital tansduce designs, in: Poceedings of the IEEE Ultasonics Symposium, 1997, pp. 1025 1028. [8] P.D. Wilcox, M. Castaings, R. Monkhouse, P. Cawley, M.J.S. Lowe, An example of the use of intedigital PVDF tansduces to geneate and eceive a high ode Lamb wave mode in a pipe, QNDE 16 (1997) 919 926. [9] D.C. Gazis, Thee-dimensional investigation of the popagation of waves in hollow cicula cylindes, J. Acoust. Soc. Am. 31 (5) (1959) 568 573. [10] I.A. Viktoov, Rayleigh and Lamb Waves: Physical Theoy and Applications, Plenum Pess, New Yok, 1967, pp. 121 122. [11] A. Pilaski, J.J. Diti, J.L. Rose, Remaks on symmetic Lamb waves with dominant longitudinal displacements, J. Acoust. Soc. Am. Pat I 4 (1993) 2228 2230. [12] G.S. Kino, Acoustic Wave Devices, Pentice-Hall, Englewood Cliffs, NJ, 1987. Biogaphies Thomas R. Hay eceived his BEng fom Concodia Univesity in mechanical engineeing in 1998 and is cuently a PhD candidate in engineeing mechanics at Pennsylvania State Univesity. His cuent eseach is funded by the Office of Naval Reseach. Since joining Pennsylvania State s Ultasonic Non-destuctive Evaluation Cente he has eceived the Ameican Society fo Non-destuctive Testing Fellowship (2000), the National Science and Engineeing Reseach Council of Canada Fellowship (2001 2003), and the Godon M. MacNabb Scholaship fo intelligent systems (2001). His inteests include integating ultasonic guided wave technology with condition-based maintenance applications. Joseph L. Rose (M 74) is the Paul Moow Pofesso in Design and Manufactuing, Depatment of Engineeing Science and Mechanics at Pennsylvania State. He is the autho of ove 10 patents, fou textbooks, and ove 350 aticles on ultasonic NDE, wave mechanics, medical ultasound, adhesive bonding, concete inspection, pipe and tubing inspection, and composite mateial inspection. Textbooks include Basic Physics in Diagnostic Ultasound (Wiley, New Yok, 1979) and Ultasonic Waves in Solid Media (Cambidge Univesity Pess, Cambidge, 1999). Cuent eseach activity is diected towads wave mechanics, aging aicaft inspection, tubing and piping inspection fo the powe geneation and chemical pocessing industy, and hidden coosion detection.