外文原文-扭转波试验和一种新的磁致伸缩传感器配置

Torsional wave experiments with a new magnetostrictive transducer confi guration Yoon Young Kim, Chan Il Park, Seung Hyun Cho, and Soon Woo Han School of Mechanical and Aerospace Engineering and National Creative Research Initiatives Center for Multiscale Design, Seoul National University, Shinlim-Dong, San 56-1, Kwanak-Gu Seoul 151-742, Korea Received 20 April 2004; revised 13 March 2005; accepted 15 March 2005! For the effi cient long-range nondestructive structural health inspection of pipes, guided waves have become widely used. Among the various guided wave modes, the torsional wave is most preferred since its fi rst branch is nondispersive. Our objective in this work is to develop a new magnetostrictive transducer confi guration to transmit and receive torsional waves in cylindrical waveguides. The conventional magnetostrictive transducer for the generation and measurement of torsional waves consists of solenoid coils and a nickel strip bonded circumferentially to test pipes. The strip must be premagnetized by a permanent magnet before actual measurements. Because of the premagnetization, the transducer is not suitable for the long-term on-line monitoring of pipes buried underground. To avoid the cumbersome premagnetization and to improve the transduction effi ciency, we propose a new transducer confi guration using several pieces of nickel strips installed at 45 with respect to the pipe axis. If a static bias magnetic fi eld is also applied, the transducer output can be substantially increased. Several experiments were conducted to study the performance of the proposed transducer confi guration. The proposed transducer confi guration was also applied for damage detection in an aluminum pipe. 2005 Acoustical Society of America. DOI: 10.1121/1.1904304# PACS numbers:43.20.Mv, 43.20.Gp, 43.35.Cg AJZ#Pages: 34593468 I. INTRODUCTION The guided-wave technology has received much atten- tion recently as a powerful tool for the nondestructive in- spection of cylindrical waveguides such as pipes and tubes.16Since guided waves can travel over several meters along the waveguide axis, the guided-wave technology is very effi cient in inspecting a large portion of a waveguide. Several wave modes such as longitudinal, torsional, and fl ex- ural modes can be utilized for nondestructive inspection, but the torsional wave mode is preferred because its fi rst branch is nondispersive and favorable for signal processing. There- fore, an effi cient generation of the torsional wave is perhaps an important issue in the torsional wave-based nondestruc- tive evaluation technology. As far as the generation and measurement of the tor- sional wave are concerned, two approaches are available: one approach based on piezoelectric transducers7and the other based on magnetostrictive transducers.8Each approach has its own advantages and disadvantages, but we are con- cerned with the development of a new magnetostrictive transducer because magnetostrictive transducers are cost ef- fective and easy to install. The magnetostrictive transducers use the coupling effect between the elastic deformation and the magnetic fi eld of ferromagnetic materials. Although mag- netostrictive transducers including sensors! have been ap- plied and studied in many cases,914their applications for torsional wave generation were made only recently by Kwun.8 The confi guration of Kwuns transducer for generating torsional waves in a cylindrical waveguides is shown in Fig. 1a!. The transducer consists of a nickel strip and a solenoid coil surrounding the strip. The strip is bonded circumferen- tially to a test specimen such as a pipe and a permanent magnet is rubbed on the nickel strip for premagnetization. Any material exhibiting strong magnetization can be used as the strip material, but nickel is easily available and cost ef- fective.! The premagnetization will induce static magnetic fi eld strength in the circumferential direction, which is indi- cated by HSin Fig. 1b!. When alternating current is sent through the solenoid coil, the alternating magnetic fi eld strength (HD) is also developed on the nickel strip in the z axis direction. If the magnitudes of HDand HSare almost the same, the resulting magnetic strength vector will point in the direction that is about 45 from the z axis, as illustrated in Fig. 1b!. By developing a new magnetostrictive transducer to generate torsional waves, Kwun8made a breakthrough in the fi eld. Nevertheless, the confi guration of his transducer has some drawbacks. First, the nickel strip always needs be pre- magnetized before the transducer is used. When the trans- ducer is to be used for long-term on-line monitoring of un- derground pipes, the strip needs periodic magnetization, which is diffi cult to achieve. Second, if the magnitudes of HDand HSare not of the same order, undesirable wave modes are also generated in addition to the torsional wave mode. To overcome the above-mentioned drawbacks, a new transducer confi guration shown in Fig. 2 is proposed. Several pieces of nickel strips are attached to the test specimen with the alignment angleaequal to 45. Since the relative per- meability of the nickel strips is higher than that of the test specimen, most of the magnetic fl ux by the solenoid coil fl ows along nickel strips. Therefore, the elastic deformation of the nickel strips developed by the magnetostriction effect 3459J. Acoust. Soc. Am. 117 (6), June 20050001-4966/2005/117(6)/3459/10/$22.50 2005 Acoustical Society of America Downloaded 05 Mar 2013 to 34. Redistribution subject to ASA license or copyright; see /terms results in the main elastic deformation of the test specimen in the direction parallel to the strip alignment direction. Obvi- ously, the generated strain will develop torsional waves along the specimen axis. The main difference between Kwuns transducer and the proposed transducer is simply the alignment angle of the nickel strip. However, the alignment change has a signifi cant impact on the transducer characteristics; premagnetization is not needed and the generated wave mode is insensitive to the magnitude of the current input to the solenoid coil. The pro- posed transducer can perform even without the bias solenoid, although the applied bias fi eld will defi nitely improve the transducer performance. The effect of the bias magnetic fi eld will be investigated in the subsequent section. Earlier, Ohzeki and Mashine15used skew-oriented ferro- magnetic patches attached to the test specimen with respect to the test specimen axis. Their motivation was to estimate the torque transmitted in the shaft of a milling machine. The proposed transducer in this work, however, can not only measure but also generate torsional waves. Damage location estimations in aluminum pipes will be also considered as a typical application problem. To verify the performance of the proposed transducer, several experiments were performed. II. THEORETICAL BACKGROUND In this section, the theory on the guided torsional waves and the magnetostrictive effects will be discussed. A. Guided torsional waves Thin-walled pipes are used as waveguides throughout this investigation, so the mechanics of elastic waves as well as their dispersion characteristics will be given mainly in cylindrical shells shown in Fig. 1a!. Figure 3 shows the dispersion curve as thenp2vrelation (np: the phase veloc- ity,v: angular frequency!. As can be seen from Fig. 3, the fi rst branch, the lowest-energy branch, is nondispersive. Therefore, the phase velocity of the wave belonging to the fi rst branch is independent of frequency. If the excitation frequency is not much higher than the fi rst cutoff frequency 1.6 MHz in this case!, the fi rst branch becomes the main carrier of wave energy. Therefore, the excitation pulse shape will be nearly preserved. Since no other wave mode or branch has the nondispersive characteristics, it is best to use the pulse that can be decomposed within the fi rst branch of the torsional wave mode for long-range damage detection. For general discussions on the dispersion characteristics, see Achenbach,16Miklowitz,17Graff,18or Rose.19 B. Magnetostrictive effects The proposed transducer uses the magnetostrictive ef- fects in actuating and measuring torsional waves, so the physics of the magnetostrictive effects such as the Joule ef- fect and the Villari effect should be explained. The Joule effect20refers to the phenomenon of the dimension change of a piece of ferromagnetic material when it is placed under a magnetic fi eld. The Villari effect21represents the inverse phenomenon of the Joule effect. The Joule effect and the Villari effect may be expressed by the following two equations for one-dimensional situa- tions: FIG. 1. Kwuns magnetostrictive transducer for generating and measuring torsional waves. a! The schematic confi guration; b! the resulting direction of the magnetic fi eld strength as the sum of HSand HD. FIG. 2. The proposed magnetostrictive transducer for generating and mea- suring torsional waves. FIG. 3. The phase-velocity dispersion curve for the axisymmetric torsional wave in an cylindrical aluminum shell with the inner and outer radii a511.5 mm and b512.5 mm. 3460J. Acoust. Soc. Am., Vol. 117, No. 6, June 2005Kimet al.: Torsional wave experiments with magnetostrictive transducers Downloaded 05 Mar 2013 to 34. Redistribution subject to ASA license or copyright; see /terms 5 s EH 1q*H,1! B5msH1qs,2! where ,s, B, and H represent the strain, stress, magnetic fl ux density, and magnetic strength, respectively. The mate- rial constants EH, q*,ms, and q denote the Youngs modu- lus under a constant magnetic strength, the coupling coeffi - cient of the Joule effect, the permeability under a constant stress and the coupling coeffi cient of the Villari effect, re- spectively. A general theory on the magnetostrictive effect including explanations on hysteresis and irreversibility can be found in Jiles.22The elastic wave or deformation in a ferromagnetic material can be easily converted to the voltage change of the solenoid surrounding the material.12 III. PROPOSED MAGNETOSTRICTIVE TRANSDUCER FOR TORSIONAL WAVES A. Transducer confi guration and fi rst-order stress analysis To explain the mechanism to generate torsional waves by the Joule effect in a pipe, consider a generic point P on the pipe surface illustrated in Fig. 4a!. When the pipe shown in Fig. 4a! is at the state of pure torsion, the stress state at P in the z-uplane should look like the state shown in Fig. 4b!. The pure shear state in the z-ucoordinate system can be represented by two normal stresses (s,2s) in the principle axes 1 and 2 that are oriented 645 from the z axis. There- fore, if the normal stresses having the opposite signs are applied along the two principle axes, pure torsional waves can be generated along the pipe axis. Based on the simple stress analysis in Fig. 4b!, we pro- pose to align the ferromagnetic strip made of nickel! at 45 from the pipe axis. Figure 5a! shows four nickel strips bonded on the outer surface of an aluminum pipe, and Fig. 5b! shows the magnetostrictive transducer consisting of the nickel strips and the solenoid coil. The solenoid coil serves both as the actuating coil and the sensing coil. The aluminum pipe will be excited by the elastic defor- mation of the nickel strip through the magnetostrictive effect. Therefore, it is important to investigate the direction of the fl ux line in the strip when elastic current fl ows through the solenoid coil. Figure 6 shows the pattern of the fl ux line in the z-uplane. For the analysis, a two-dimensional linear static model was used. The actual numerical calculation was performed byANSYS.23 In Fig. 6, the magnetic fl ux in the strip fl ows mainly along axis 1, since the permeability of nickel is much larger than those of aluminum and air. There- fore, the Joule effect causes the strip to deform mainly along the axis 1 direction when electric current fl ows through the solenoid coil. To investigate the wave generated by the nickel strip, let us consider the elastic deformation of the nickel strip at the moment of the electric current input to the solenoid coil and carry out a fi rst-order stress analysis. The uniform stretch or contraction! along axis 1 and the accompanied uniform con- traction or stretch! along axis 2 developed in the nickel strip before being bonded may be expressed approximately by the following strain components: 115qH,2252nN1152nNqH,1250,3! wherenNis Poissons ratio of nickel. When the nickel strip is bonded to the aluminum pipe, the elastic deformation of the nickel strip develops stress in FIG. 4. The stress state corresponding to pure torsion in a pipe. a! The generic point P on the pipe surface; b! the two-dimensional view of the stress state. FIG. 5. Nickel strips bonded on the surface of pipe a! with and b! without the actuating and sensing solenoid coil installed. FIG. 6. The magnetic fl ux lines. 3461J. Acoust. Soc. Am., Vol. 117, No. 6, June 2005Kimet al.: Torsional wave experiments with magnetostrictive transducers Downloaded 05 Mar 2013 to 34. Redistribution subject to ASA license or copyright; see /terms the aluminum pipe. The evaluation of the magnitude of the stress requires a somewhat complicated analysis, so some assumptions will be made for the fi rst-order analysis. If lNnwN(lN, wN: length and width of each strip, n: number of the nickel strip! in Fig. 2, the stress developed in the pipe where the nickel strip is attached may be assumed as s11s0,s222nNs0,s120,4! wheres0stands for the normal stress component in axis 1. To convert the stress components expressed along axes 1 and 2 into those along the z-ucoordinate system, the follow- ing transformation formula will be used see, e.g., Timosh- enko and Goodier24!: si8i851 2 sii1sjj!1 1 2 sii2sjj!cos2a1sijsin2a sj8j851 2 sii1sjj!2 1 2 sii2sjj!cos2a2sijsin2a 5! si8j852 1 2 sii2sjj!sin2a1sijcos2a, whereais the angle between the two orthogonal coordinate systems(i,j),(i8,j8)#. Substituting (i8,j8)5(z,u), (i,j) 5(1,2) anda545, the stress components in Eq. 4! are written as szz512nN 2 s0, suu512nN 2 s0,6! szu52 11nN 2 s0. Though the pure shear state (szz5suu50,szu?0) is desir- able, the normal stress is also developed, as can be seen in Eq. 6!. Therefore, not only the torsional wave due toszu), but also the longitudinal wave due toszz) will be generated. Figure 7 shows the stress state decomposed into three stress components. To study the stress wave propagation, it is very impor- tant to note that the longitudinal wave speed cL5AEA/rAis differentfromthetorsionalwavespeed cT5AEA/2rA(11nA) (EA,rA,nA: Youngs modulus, den- sity, Poissons ratio of aluminum!. Therefore,szzcomponent generating the longitudinal wave andszucomponent gener- ating the torsional wave separate as they propagate. Since cL.cT, the longitudinal wave travels ahead of the torsional wave. To continue the fi rst-order stress analysis, one may ne- glect the dynamic effect of the propagating waves, and the damping effect occurring during wave propagation. When the generated longitudinal stress wave is measured by the transducer, the stress state will be approximated as szz512nN 2 s0,suu50,szu50.7! Then the following stress component will be measured through the nickel strip: s11 L 512nN 4 s0,8! where the superscript L stands for the longitudinal wave. In obtaining the result in Eq. 8!, Eq. 5!, and Eq. 6! are used, with (i8,j8)5(1,2), (i,j)5(z,u),a5245. Likewise, the magnitude of thes11 T stress component due to the torsional wave can be calculated as s11 T 511nN 2 s0.9! From the above stress analysis, the following conclusions can be drawn. 1! By the proposed transducer confi guration, both the torsional wave and the longitudinal wave are simultaneously generated. However, the magnitude of the torsional stress s11 T is much larger than that of the longitudinal stresss11 L . The relative ratio, with dynamic and damping effects ne- glected, is approximated as U s11 T s11 LU FOA 5U 11nN 2 s0 12nN 4 s0U 5 211nN! 12nN 3.80fornN50.31!.10! In Eq. 10!, the subscript FOA is used to emphasize that the result is predicted by the fi rst-order analysis. 2! The torsional wave will be preceded by the longitu- dinal wave of a small magnitude due to the difference be- tween their wave speeds. So, the torsional wave can be dis- tinguished against the longitudinal wave. Though the stress analysis is based on some assump- tions, the present analysis shows the characteristics of the waves measured by the proposed transducer. The photo of the proposed transducer is shown in Fig. 8. The bias coil shown in Fig. 8b! is installed to supply the static bias magnetic fi eld. The bias fi eld is very useful to increase the transducer output, as shall be shown later. FIG. 7. The decomposition of the stress state in a pipe developed by the nickel strip deformation. 3462J. Acoust. Soc. Am., Vol. 117, No. 6, June 2005Kimet al.: Torsional wave experiments with magnetostrictive transducers Downloaded 05 Mar 2013 to 34. Redistribution subject to ASA license or copyright; see /terms 1. Comparison with Kwuns transducer When Kwuns transducer illustrated in Fig. 1 is used, the strain developed in the unbounded nickel strip may be ap- proximated as 115qAHS 21H D 2 ,2252nN11, 1250,and tana5 HS HD .11! In this case, the directions of principle axes 1 and 2 depend on the magnitude of HS/HD. Unless HDis adjusted to be the same as HS, i.e.,a545, torsion-dominant waves can- not be generated. If HDis much larger than HS, for instance, the generated wave by the Kwuns transducer will be domi- nated by the longitudinal wave mode. Since the HS fi eld is created by rubbing a permanent magnet on the nickel strip along the circumferential direction