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1 Bulletin of the JSME Mechanical Engineering Journal Vol.4, No.5, 7 Ultrasonic evaluation of the pitch of perioically rough surfaces from back sie Chanh Nghia NGUYEN*, Masaki SUGINO*, Yu KUROKAWA* an Hirotsugu INOUE* *Department of Mechanical an Control Engineering, Tokyo Institute of Technology -- O-okayama, Meguro, Tokyo 5-855, Japan nguyen.n.ab@m.titech.ac.jp Receive: 3 May 7; Revise: 3 July 7; Accepte: 5 September 7 Abstract The geometrical features of internal surfaces are important parameters in the fiel of non-estructive testing such as corrosion inspection or artistic qualities of material surfaces. Although stylus profiling an optical scattering are commonly use for measuring both ranom an perioically rough surface topography, they are only applicable to accessible surfaces. However, there are many cases in which the surface to be evaluate is inaccessible. For example, integrity monitoring of inner surfaces of pipes is require to ensure proper functions an safeguar quality. Unfortunately, little attention has been pai to the measurement of inaccessible perioic surfaces. Since inaccessible surfaces o not permit contact or optical measurement, application of ultrasonic technique from back sie is an appropriate caniate among others. In this paper, an ultrasonic pulse-echo technique is investigate to evaluate the pitch of perioically rough surfaces which is inaccessible or hien on the back sie. The pitch of back surface profile is evaluate base on the iffraction grating theory for oblique incience of P-wave, SV-wave, an SH-wave. The applicability of the propose technique was verifie by both numerical simulation an experiment. It is foun that the angle of incience shoul be larger than 45º to enhance the accuracy. SH-wave shows better results compare with SV-wave ue to the effect of moe conversion. Moreover, using SH-wave is an effective way for evaluation of the pitch because SH-wave is more sensitive than P-wave with shorter wavelength. On the other han, P-wave is the best solution to obtain the highest resolution of measurement with higher signal to noise ratio. Keywors : Perioicity, Pulse-echo technique, Inaccessible surface, Ultrasonic NDE, Back sie. Introuction The characterization of perioic surfaces is crucial for a variety of engineering applications, such as telecommunication, frequency filters, small-scale photonic or phononic crystals, tailore sliing friction, non-estructive testing an evaluation (NDT&E), etc. The eployment of perioic surface structures has receive much interest in ahesive bon quality (Leuc, 6), collimation of soun (Christensen, 7), heat exchangers consisting the tube bunles (Heckl, 995), NDE of non-planar surfaces (Kunu, 6), an inspection for machine part surfaces (Huynh, 99). In aition, perioic profile claings often applie on thick plates an pipes in orer to prevent corrosion in the nuclear power inustry (Krasnova, 6). Generally, integrity of perioic surfaces is inispensable for etermining prouct quality, since it irectly affects functional attributes of components, for example fatigue life, friction, wear, contact stress istribution (Whitehouse, 997). Several methos are available for characterizing the integrity of perioically rough surfaces, which inclue stylus profiling, optical an ultrasonic techniques. The stuy of methos for surface metrology is well evelope an reviews of these methos can be foun in the literature (Bennet, 99). The stylus profiling can provie a irect measurement with epenable an rationally representative numerical values of surface profile but requires fairly long time measurement for scanning large area an the har stylus tip may create surface scratches as an unexpecte manner (Oh, 994). Optical techniques are generally the most popular noncontact measurement, which can be performe relatively quickly an not restricte to electrically conuctive materials (Sherrington, 988). But these are responsive to the Paper No.7-78 J-STAGE Avance Publication ate: 4 September, 7 [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers

2 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) property of the transmitting meium, the contamination of the surface, an generally effective only for rough surfaces on the orer of μm or less of RMS roughness (Shin, 995). On the other han, ultrasonic techniques has several avance capabilities over stylus an optical methos an is generally accepte as a useful metho of surface characterization incluing quality control of machine parts an process control (Coker, 996; Dwyer-Joyce, ). Let us consier ultrasonic techniques an review some of works especially for evaluating the perioically rough surface parameters using ultrasonic techniques. Since a perioic surface functions as an acoustic iffraction grating, its geometrical features can be immeiately ientifie by analyzing the associate iffracte moes (Blessing, 993). Woo anomalies (Woo, 9) have been use to etermine geometric parameters of a perioic surface. These appeare as sharp iscontinuities or valleys in the frequency spectra as iffracte phenomena foun in optics as well (Claeys, 983). The Rayleigh-Fourier metho has successfully been use to theoretically preict iffraction effects incluing Woo anomalies an Scholte-Stoneley wave generation on perioically corrugate surfaces (Jungman, 98; Mampaert, 988). Meanwhile, Scholte-Stoneley waves can potentially be use for the etection of surface efects, making both of these iffraction effects relevant to ultrasonic NDE (De Billy, 98; Claeys, 98; Loewen, 997). In aition, the experimental an theoretical investigations have been conucte to the use of oblique incience, since normal incience analysis often limits the range of obtainable information (De Billy, 976; Mampaert, 989). Moreover, by taking the effect of moe conversion into account, theoretical investigation of elastic waves iffracte by a stress-free, two solis an soli-flui interfaces of perioically rough surfaces was consiere rigorously. Then, a metho to etect surface parameters base on the moe conversion of an incient bulk wave on perioic grooves was evelope (Fokkema, 98; Roberts, 985; Jungman, 988). Recently, Liu prove experimentally an ultrasonic imaging technique applicable to accurately characterize the lateral an vertical imensions of D corrugate surfaces. This technique is base on the amplitue an the time-of-flight (TOF) from echoes reflecte by corrugation surfaces with small focuse immersion transucer in pulse-echo moe (Liu, 3). The techniques mentione so far are only suitable for accessible surfaces, while inspections of inaccessible surfaces locate at the insie of many inustrial components are require to prevent serious catastrophe an vital isasters. In reality, the internal surface morphology an profile of mechanical components are important properties to ensure the proucts quality. For example, monitoring of inner surfaces for oil an gas pipelines an piping systems to prevent leakage ue to corrosion is an important safety issue. In other manner, the integrity measurement of inner surface in hole rilling or eep an narrow grooving operations shoul be carrie out in orer to ensure the esire quality of proucts. However, the access for inspection is not an easy task. These lea to a strong eman for evelopment of a new technique suitable to measure the back surface roughness. In this manner, ultrasonic evaluation of rough surface carrie out from the back sie turn into an appropriate alternative. Unfortunately, relatively little attention has been pai so far to the problem of back surface roughness evaluation by ultrasonic wave. Within this purpose, several stuies have investigate both theoretically an experimentally the ultrasonic nonestructive testing to measure the profile parameters of internal perioically corrugate surfaces. Subsequent backscattering spectroscopy analysis of reflecte signals spectra by using a broa ban pulse an yiels the possibility to evaluate the perioicity of internal corrugate surfaces (De Billy, 98). Kersemans evelope an ultrasonic backscatter polar scan metho to characterize D surface corrugation, which is hien on the backsie of a polycarbonate sample (Kersemans, 4). The perioicities an surface symmetries as the orientation of the vertical insonification plane were successfully etermine within the experimental measurement protocol. However, these techniques are only performe in immersion of water so that they are not suitable for inspection internal or hien perioic surfaces in practice, such as checking corrosion, roughness or sticking of inner surfaces of oil pipelines. Recently, an ultrasonic methoology to reconstruct the height correlation function of inaccessible ranom rough surfaces was evelope by the using Kirchhoff theory of iffusely elastic waves (Shi, 6). However, the presence of perioic surfaces may rener this technique inaccurate, since the height correlation function of perioic surfaces remain constant. In aition, the evaluations of perioic surface parameters were not investigate. Therefore, ifferent ultrasonic techniques than those use for the characterization of ranom rough surfaces must be evelope for perioically rough surfaces. It follows that most of the existing ultrasonic NDE methos for perioic surfaces characterization are limite to estimating geometric parameters of accessible surface using water immersion configuration without consiering moe conversion. In this paper, an ultrasonic characterization metho is evelope which iffers from previous stuies in the way that it enables the irect evaluation of the pitch of inaccessible perioically rough surfaces from back sie without immersing [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers

3 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) in the water. This technique is investigate base on the iffraction grating theory for oblique incience taking into account the effect of moe conversion, which is applie to the elastic scattering fiel. As a very first step, the present analysis is mainly concerne to the perioically rough surfaces with triangular profile.. Reflection from Perioic Surface: Diffraction Grating Theory Incient wave fronts Grating Normal + Diffracte wave fronts α+ β- sin sin h Grating Plane Fig. Geometry of the two-imensional iffraction grating problem When a coherent monochromatic ultrasonic beam is incient on a perioically triangular surface, it is reflecte into an angular istribution of iscrete components: the specular component an other ominant components with ifferent iffraction orers. Diffraction by grating can be visualize schematically as shown in Fig.. An ultrasonic ray of wavelength λ i incient at an angle α is iffracte as ultrasonic wave of wavelength λ along an angle β, where the perioically triangular profile with the pitch an the height h is assume. These angles are measure from the grating normal an the sign convention for these angles epens on whether iffracte wave is on the same sie or opposite sie with respect to the incient wave. The geometrical path ifference between ultrasouns from ajacent grooves is inicate to be sinα an sinβ. The principle of interference ictates that the ultrasonic wave from ajacent grooves will be in phase (leaing to constructive interference) when this ifference equals the wavelength of ultrasoun, or some integral multiples thereof. At all other angles β, there will be some measure of estructive interference between the wavelets originating from the groove facets. Accoringly, at ifferent angles of incience, the various frequencies will iffract to ifferent angular positions. The iffraction maxima combine with moe conversion are given by the classical grating equation as n n, () sin sin sin sin f n i ci c where n =,, 3 is integer representing the iffraction orer, f n is the frequency of n-th iffracte orer, c i an c are the wave velocities of the incient an the iffracte waves, respectively. For a pulse-echo arrangement, the transucer is use as the transmitter an the receiver. Consiering the grating at an angular position ifferent with zero, Eq. () can be simplifie as nc f sin, () n [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers 3

4 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) where is incient an iffracte angle of transucer oriente to perioically rough surface relative to the surface normal, c is the wave velocity of the incient an reflecte waves which coul be longituinal (P) or shear (S) waves. 3. Two-imensional Finite Difference Simulation 3. Numerical Moel Infinite bounary 75 mm Infinite bounary Transucer Type 34 of stainless steel R = 74 mm Infinite bounary Perioic rough surface 5 mm Fig. Schematic iagram of numerical simulation moel A finite ifference two-imensional ultrasonic wave propagation simulation software (Wave, CyberLogic) has been chosen for this stuy. As illustrate in Fig., a perioic surface is introuce at the bottom surface of a rectangular moel (5 75 mm) by using triangular profile with the pitch in the range of to.6 mm an the height h, which is set to have the ratio of h/ =.5. The top, left, an right sies are taken as infinite bounary to prevent reflection. The moel is assume a homogenous isotropic elastic meium an type 34 stainless steel is chosen as its material. Material properties are taken from the material library embee in the software an incorporate in the simulation moel, as shown in Table. In the moel, ultrasonic transucer is represente by a straight line ( mm) an oriente to the rough surface at every 5 (5 ~ 75 ) on the arc of raius R = 74 mm. The wave reflecte from the rough surface is receive by the same probe in pulse-echo moe. The gri size of μm is use an then the time step of.9 ns is automatically etermine by the software an the total simulation time is 4 µs. Table Material properties. Mechanical Properties Type 34 stainless steel Density 79 kg/m 3 First Lamé constant 5. GPa Secon Lamé constant 79.9 GPa Longituinal Wave Velocity 579 m/s Shear Wave Velocity 38 m/s In this simulation, a longituinal wave with sine Gaussian pulse b t p() t exp sin ft a (3) [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers 4

5 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) is emitte from the ultrasonic probe, where the center frequency f = 4.5 MHz, the uration b = 5 μs, an time constant a =. μs. The transmitte wave an its frequency spectrum are shown in Fig. 3. Amplitue.5 Amplitue Fig. 3 Transmitte wave an its frequency spectrum 3. Numerical Simulation Results Figure 4 shows the visualization results at 3.4 μs when incient P-wave impinges the smooth, slightly rough ( =.6 mm), an highly rough ( =. mm) surfaces with angle of 45, respectively. The strength of white color in these images represents intensity of ultrasouns propagating in the moel. It can be seen that the reflection is concentrate in the specular irection, which is escribe by the Fresnel reflection law coupling with moe conversion. When the surface becomes rougher, the incient wave is partly reflecte in the specular irection, an also partly scattere in all irections. Rougher surface enhances scattering fiel, meanwhile the magnitue of the coherent fiel ecreases as surface becomes rough. Fig. 4 Incient P-wave at angle of 45 at 3.4 μs of simulation time for (a) smooth surface, (b) slightly rough surface ( =.6 mm, h =.3 mm), an (c) highly rough surface ( =. mm, h =.6 mm). Amplitue.5 (a) Smooth surface Amplitue.5 (b) =.6 mm Fig. 5 Receive waveforms for incient P-wave at angle of 45 in time-omain from: (a) smooth surface; (b) rough surface with =.6 mm. Figure 5 shows time-omain signals receive by P-wave ultrasonic probe for smooth surface an rough surface with =.6 mm. The initial portion of the signals in both situations (aroun.5 μs) resembles the incient ultrasonic pulse. It is clear in Fig. 5(b) that the moel with rough surface has an associate surface roughness signal from to 35 µs, [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers 5

6 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) meanwhile no such signal exists for the simulation moel with smooth surface as shown in Fig. 5(a). Figure 6 summarizes the receive waveforms for incient P-wave at angle of 45 obtaine from various rough surfaces. As the surface is perfectly smooth or just slightly rough ( =.,.4 mm) the amplitue of surface roughness signal is inee small because the coherent fiel mainly reflecte in specular irection. In contrast, when the surface becomes rougher, the scattering fiel significantly istribute in all irections. Therefore, the intensity of such appeare signals enhances an becomes more complex as superimposing of multiple signals with respect to iffracte frequencies. Amplitue.. -. Smooth surface =. mm =.4 mm =.6 mm =.8 mm =. mm =. mm =.4 mm =.6 mm Fig. 6 Receive waveforms for incient P-wave at angle of 45 in time-omain obtaine from various rough surfaces. Figure 7 shows the visualization results at 3.4 μs for the moels of rough surface with the pitch =. mm for angles of incience from 5 to 75. It can be obviously seen that the angle of incience plays an important role in the behavior of scattering wave from perioically rough surface. Due to pulse-echo configuration, the transucer at large angle of incience mainly receives scattering component, meanwhile coherent component is consiere as noise. The signal to noise ratio is significantly larger at large angle of incience, which is cause by ecrease of the specular reflection. Fig. 7 Incient P-wave at 3.4 μs for rough surface with =. mm at various incient angles: (a) 5º, (b) 3º, (c) 6º, an () 75º. [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers 6

7 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) Amplitue.. -. =. mm = 5 = Amplitue.. -. =. mm = 6. = Fig. 8 Time omain P-wave receive waveforms from rough surface with =. mm at various incient angles: (a) 5º, (b) 3º, (c) 6º, an () 75º. The ultrasonic wave scattere from a rough surface is heavily affecte by the angle of incience as inicate in Fig. 8. For small angle of incience of 5, the receive waveform is combine from coherent an scattering parts of signal with one large initial part an followe by small ecaying of complex combine sinusoial waves. For large angle of incience, the receive waveform inclues mainly scattere fiel, which is generate by the interference. This signal becomes more complex by combining of multiple sinusoial waves generate from a number of overlap frequencies accoring to iffraction grating phenomena. However, as angle of incience increases, the intensity of receive signal becomes smaller since shaowing an multiple scattering are important. 3.3 Frequency Analysis A rectangular winow function is use to select the portion of the surface roughness signal to be processe in orer to eliminate the unwante information. Two vertical ashe bars plotte in Fig. 5(b) inicate this region ( 35 µs). This gate position is use throughout this numerical simulation. The selecte signal is then converte from time-omain into frequency-omain by using the Fast Fourier Transform (FFT) algorithm. The amplitue frequency spectrum is then ivie by that of incient waveform shown in Fig. 3 to obtain frequency response function. Normalize Amplitue Smooth surface =.6 mm =. mm =. mm =.8 mm =.4 mm =.4 mm =. mm =.6 mm Fig. 9 Frequency response functions at incient angle of 45 for various rough surfaces. [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers 7

8 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) Figure 9 shows the frequency response function for P-wave incience at angle of 45 an various rough surfaces. These spectrum exhibits several sharp peaks, which are visible in the frequency range from to MHz corresponing to the iffracte orer n. This typical pattern has been iscusse previously as the principle of iffraction grating theory (Fokkema, 977; De Billy, 976, 98). It is important to point out that the position of peaks is unchange regarless of the with of rectangular winow function (Jungman, 983). As the angle of incience increases, the number of peaks increases, frequencies of these peaks becomes smaller as well as peaks are sharper ue to iffraction grating phenomena, as illustrate in Fig.. Figure summarizes the peak frequencies f n for various rough surfaces with respect to the pitch at various angles of incience in logarithmic scale. Curve fitting functions of each iffracte orer are constructe. It is clear that peak frequencies are inversely proportional to the pitch as expecte from Eq. (). Normalize Amplitue =. mm.5 = 5.5 = 3.5 Amplitue =. mm.5 = 6.5 = Fig. Frequency spectrum responses at various angles of incience for rough surface with =. mm. = 3 = 6 f f [mm] f f f f4..4 [mm] = 75 f f f [mm] f f f 3 f [mm] Fig. Plot of frequencies fn of iffraction peaks versus the pitch for various angle of incience, n = orer of iffraction. [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers 8

9 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) 3.4 Evaluation of the Pitch When a broaban pulse is emitte from ultrasonic probe, the frequency spectrum function of the backscattere ultrasonic wave at an angle of incience observes several iffracte sharp peaks at the frequencies f n. The pitch is evaluate by substituting f n along with its iffracte orer n into Eq. (). The results from propose metho are summarize in Table. For rough surface having =.4 mm at angle of incience of 3 an 45, as well as for the case of =. mm at all angles of incience, coul not be evaluate ue to no visible peak obtaine from numerical spectrum. In these situations, higher center frequency transucer can be use to achieve that surface parameter measurement. Meanwhile, for all rough surfaces at incient angle of 5, coul not be measure because the transucer at small angle of incience mainly receives coherent component consiering as noise. Therefore, no visible peak coul be obtaine from numerical spectrum. In other cases, the propose metho provies a high accuracy evaluation of the pitch, the errors are smaller than.5% for all iffracte orers. Table The pitch evaluate from propose metho base on iffraction grating theory. Design Evaluate values with respect to iffracte orer of peaks [mm] value = 5 = 3 = 6 = 75 [mm] st st n st n 3 r st n 3 r 4 th st n 3 r 4 th. N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A.4 N/A N/A N/A N/A N/A N/A.4 N/A N/A N/A.399 N/A N/A N/A.6 N/A.6 N/A.599 N/A N/A.599 N/A N/A N/A.599 N/A N/A N/A.8 N/A.799 N/A.799 N/A N/A N/A N/A N/A N/A. N/A.998 N/A.999. N/A.998. N/A N/A N/A. N/A N/A N/A N/A.4 N/A N/A It can be observe that the pitch of. mm coul not be measure. In this numerical simulation, the P-wave velocity is 579 m/s an the center frequency is 4.5 MHz, hence the wavelength is.9 mm. The wavelength of.9 mm is too long to measure the pitch of. mm. Meanwhile, the pitch of.4 mm coul be evaluate only with large incient angles, such as 6 an 75. However, this wavelength coul evaluate the pitch, which is approximately a half of wavelength.9 mm in the large range of incient angles from 3 to 75, such as the pitch of.6 mm. The relation is that the pitch within a half of wavelength coul be measure might be a guiance about the selection of the appropriate center frequency or wavelength of transucer to observe the optimum measurement in practice. Accoring to Eq. (), for the first iffracte orer, wavelength can be expresse as sin, (4) where λ = c/f is first orer iffracte wavelength. Therefore, only wavelengths that satisfy the conition of λ can be appropriate to measure the pitch. The conition obtaine from iffraction grating theory matches well with the numerical relation between the pitch an the wavelength. It can be seen that the wavelength plays an important role in the evaluation of the pitch, therefore optimal selection of wavelength shoul be carefully consiere for slightly rough surfaces with small pitch. 3.5 Investigation on Other Perioic Surfaces Eight ifferent perioic profiles are investigate numerically to examine the applicability of the propose technique for not only triangular profile but also other perioic profiles, as shown in Fig.. These perioic surfaces as stuie here can be primarily characterize by two geometric parameters: pitch (), an height (h) with the ratio h/ of.5, the corrugate profiles have the plateau with equal to the valley with (/3). Accoring to the propose metho in Section 3.4, the pitch is evaluate by substituting f n in frequency response function along with its iffracte orer n into Eq. (). [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers 9

10 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) (a) Triangular profile (e) Up-wash Elliptical profile h (b) Saw-tooth profile front angle (f) Down-wash Elliptical profile (c) Saw-tooth profile back angle /3 (g) Corrugate profile plateau () Sinusoial profile (h) Corrugate profile valley Fig. Perioic profiles use in numerical simulation. Table 3 The pitch evaluate from propose metho for several ifferent perioic profiles. (θ = 6 ) Evaluate values with respect to iffracte orer of peaks [mm] [mm] Profile st st st n st n st n 3 r st n 3 r 4 th st n 3 r 4 th (a) (b) (c) () (e) (f) (g) (h) The numerical results for 6 of incient angle are summarize in Table 3. It can be observe that the evaluate pitches along with each iffracte orer are almost the same for ifferent perioic profiles. There are slight ifferences between esigne an evaluate values, but the maximum error is.4%. Therefore, the change of profile shape has very little effect on the evaluation of the pitch. [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers

11 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) 4. Experimental Valiation 4. Experiment Set-up In orer to ensure that the technique propose in the previous section is applicable to the practice, experiments were conucte. The ultrasonic spectroscopy system, schematically isplaye in Fig. 3(a), was assemble aroun the pulser/receiver (57PR, Olympus) functione as a signal source in a pulse-echo configuration with iffracte signal receive by the same probe. The specimen was a carbon steel semi-cylinrical block (JIS G 45 S45C, raius: 75 mm, thickness: 37 mm) with triangular rough surface manufacture on the bottom by the milling machine using a rilling cutter. The triangular profile was corrugate to maintain a constant height only in the irection of the thickness with a set of =.,.,. mm an the ratio of h/ =.5 as shown in Fig. 3(b), meanwhile other faces of the specimen were smooth enough. The ultrasonic transucer was place on the top roun surface of the specimen to transmit P- or S-waves incient on the perioically rough surface at a esire angle by using a projector. The receive signal was transferre to a 4-bit igitizer (PXI-5, National Instruments), an finally store in PC through the ExpressCar Interface. Fig. 3 (a) Schematic iagram of experiment. (b) Specimen triangular profiles. P-wave S-wave - - Normalize Amplitue Amplitue [V] P-wave.5 S-wave Fig. 4 Incient waveforms an their frequency spectrums. [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers

12 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) P- an S-wave transucers (V9-RM an V55-RM, Panametrics, respectively) with 5 MHz of center frequency an.7 mm iameter were eploye for scanning. Appropriate ultrasonic couplants (Sonicoat BS-4, Taiyo Nippon Sanso Gas & Weling an GSONIC Couplant SH-H, GNES) for P- an S-wave, respectively were use to facilitate the ultrasonic waves into the specimen. For observing the incient waveforms an specifications of each transucers, pitchcatch measurement was conucte by putting two same type transucers face to face. Figure 4 shows incient waveforms an their frequency spectrums for P- an S-wave transucers. In orer to etermine the P- an S-wave velocities in the specimen, a pulse-echo arrangement was epicte for the reflection of normal incient wave from the smooth surface. For a given thickness of the test piece, the velocity of ultrasonic wave was etermine from the average interval time between the multiple echoes of receive signals. The specifications of incient waves an wave velocities are inicate in Table 4. Table 4 Specifications of incient waves an wave velocities in S45C carbon steel. Type of Probe Center Frequency Peak Frequency Wave Velocity [MHz] [MHz] [m/s] P-wave S-wave The Pitch Evaluation 4.. P-wave of Incience The scan results are shown in Fig. 5 for the P-wave transucer at various angles. When the specimen surface is slightly rough ( =. mm), the amplitue of receive signals are small at all incient angles. As the surface become rougher ( =. an. mm), the intensity of signals increase an become more complex. The signal in the region (5-35 µs) was converte from time-omain into frequency-omain by using FFT algorithm, then normalize by the amplitue frequency spectrum of incient P-waveform shown in Fig. 4 to obtain frequency response function. Figure 6 shows the frequency response function for P-wave incience at various angles. It is unable to confirm peak frequencies for slightly rough surface with =. mm. For rougher surface, more ominant peaks can be foun an they becomes sharper as larger incient angle =. mm = =. mm = =. mm = 3 Amplitue [V] = = = 6. = 75. = 75. = Fig. 5 Receive signals obtaine by P-wave transucer at various angles of incience. [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers

13 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7).5.5 =. mm =. mm =. mm.5.5 = 3 = 3 = Normalize Amplitue.5.5 = = = 6 = 75 = 75 = Fig. 6 Frequency spectrum responses of receive signals obtaine by using P-wave transucer at various angles of incience. The evaluation results of by P-wave transucer are summarize in Table 5. The pitch evaluate by the propose technique is sufficiently accurate for various iffracte orers. Especially, excellent accuracy is observe in case of angles of incience larger than 45. However, for specimen with slightly rough surface ( =. mm), cannot be evaluate ue to the range limitation of significant frequencies of transucer. In this experiment, the P-wave velocity is 595 m/s an the center frequency is 3.74 MHz, hence the wavelength is.58 mm. Since the conition of λ coul not be satisfie, the wavelength of.58 mm is too long to measure the pitch of. mm. This result agrees well with the numerical results in Subsection 3.4. Nevertheless, it has been confirme that the technique propose in this stuy works well for P-wave. Table 5 Measurement results of the pitch using P-wave transucer. Design value [mm] Angle of incience [º] Experimental value [mm] st Peak n Peak 3 r Peak 3.73 N/A N/A Error [%] 7.3 N/A N/A N/A. Error [%].. N/A N/A Error [%] N/A N/A Error [%].6.67 N/A N/A Error [%].34.7 N/A Error [%] Error [%] Error [%] [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers 3

14 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) 4.. S-wave of Incience Two ifferent cases, SV- an SH-wave inciences were consiere. SV-wave has a complex interaction with P-wave when scattere at the rough surface, while SH-wave only scatters into SH-wave. Figure 7 etails the receive waveforms an their frequency response functions obtaine by using incient SH- an SV-waves for specimen having =. mm at incient angles of 45º an 6º. The signals in the region (35-55 µs) inicate by two vertical ashe bars plotte in Fig. 7 were selecte for this analysis. As seen in this figure, the intensity of signals receive by SH-wave are higher than the one receive by SV-wave, an hence sharper peaks with higher intensity are obtaine in the frequency spectrum responses of SH-wave. The peak frequencies in the two cases are almost same ue to the same velocity of SV- an SH-waves but the amplitue ratio of SV- an SH-peaks with respect to particular iffracte orer in the frequency spectrum responses for each incient angle are ifferent. As a result, some peaks appeare in the frequency spectrum responses of SH-wave incience but not be ientifie by SV-wave incience. Firstly, because moe conversion occurs in the case of SV-wave incience, the energy of SV-wave after reflecte from rough surface is converte into not only SV-wave but also P-wave one. Therefore, the intensity of signals receive by SV-wave is lower comparing to the case of SH-wave incience. Seconly, ultrasonic pulse emitte from S-wave transucer has lower energy than P-wave transucer so that the gain setting on the pulser/receiver is really high. Consequently, the receive signal is istorte as inappropriate manner. As a result, SH-wave of incience showe stronger intensity of receive signal an clearly exhibite ominant peaks in frequency spectrum response. This leas to higher accuracy of measurement of the pitch by the propose technique. The evaluate results of an the errors of measurement by using SH-wave incience are summarize in Table 6. As in the P-wave case, goo accuracy is observe for incient angles larger than 45º. It has been confirme that the technique propose in this stuy provies goo results also for SH-wave. Amplitue [V] SV-wave = Normalize Amplitue SV-wave = Amplitue [V] SH-wave = SH-wave 4 6 Fig. 7 Receive waveforms an their normalize amplitue spectrum obtaine by using SV- an SH-waves at incient angles of 45º an 6º for specimen =. mm In the viewpoint of wavelength, SH-wave is more sensitive than P-wave because SH-wave has shorter wavelength. Therefore, by using SH-wave, the perioic surface with smaller pitch can be measure by the evelope technique. In the viewpoint of the signal to noise ratio (S/N ratio), it coul be observe when comparing Fig. 6 an Fig. 7, S/N ratio for the results using P-wave looks much larger than that for results using SH-wave. Because the transmission efficiency Normalize Amplitue = 6 8 [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers 4

15 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) of S-wave through the interface between the transucer an the specimen is much lower than that of P-wave, even if highly viscos couplant is use. These two points of view have opposite influences, so using P-wave or SH-wave in the evelope technique shoul be carefully consiere epening on purposes of measurements. Using SH-wave is a better choice if one esires to measure a smaller range of the pitch, an errors ue to S/N ratio is acceptable. Meanwhile, P-wave is the best solution to obtain the highest resolution of measurement with higher S/N ratio. Table 6 Measurement results of the pitch using SH-wave transucer. Design value [mm] Angle of incience [º] Experimental value [mm] st Peak n Peak 3 r Peak N/A Error [%] N/A Error [%] Error [%] Error [%] Conclusions In this paper, an ultrasonic pulse-echo technique for evaluating the pitch of inaccessible surface having perioic profile from back-sie has been evelope. Numerical simulation results show that peak frequencies in frequency spectrum response function are inversely proportional to the pitch that has precisely consistent with the iffraction grating theory. It has been confirme that the pitch of perioically rough surface can be evaluate by the propose technique both in the numerical simulation an in the experiment. This technique can be applie by using not only P-wave but also S-wave, incluing SV-wave an SH-wave. When the incient angle is larger than 45º, this technique provies a goo accuracy because the noise from the coherent component in specular irection is negligible. SH-wave shows better results compare with SV-wave ue to the effect of moe conversion. It shoul be note that SH-wave is more sensitive than P- wave since SH-wave has shorter wavelength than P-wave. Therefore, SH-wave is a better choice to measure the perioic surface with smaller pitch. However, P-wave is the best solution to obtain the highest resolution of measurement with higher signal to noise ratio. There may be another possibility of a combination of P-wave transmitter an SV-wave receiver, or vice versa with consiering the moe conversion. In this paper, a constant height-to-pitch ratio has been assume to focus on evaluation of the pitch. However, evaluation of the height is also necessary in orer to evaluate the roughness. In this respect, further research shoul be conucte. In aition, a limitation of the present technique is the D assumption, namely, the perioically rough surface is assume to maintain a constant height only in one irection. Consieration of 3D problem woul be interesting for practical inspection. References Bennet, J.M., Recent evelopments in surface roughness characterization, Measurement Science an Technology, Vol.3, No. (99), pp.9 7. Blessing, G.V., Slotwinski, J.A., Eitzen, D.G. an Ryan, H.M., Ultrasonic measurements of surface roughness, Applie Optics, Vol.3, No.9 (993), pp Christensen, J., Fernanez-Dominguez, A.I., De Leon-Perez, F., Martin-Monreno, L. an Garcia-Vial, F.J., Collimation of soun assiste by acoustic surface waves, Nature Physics, Vol.3 (7), pp Claeys, J.M. an Leroy, O., Diffraction of plane waves by perioic surface, Revue u Cetheec, Vol.7 (98), pp [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers 5

16 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) Claeys, J.M., Leroy, O., Jungman, A. an Aler, A., Diffraction of ultrasonic waves from perioically rough liqui-soli surface, Journal of Applie Physics, Vol.54, No. (983), pp Coker, S.A. an Shin, Y.C, In-process control of surface roughness ue to tool wear using a new ultrasonic system, International Journal of Machine Tools an Manufacture, Vol.36, No.3 (996), pp.4 4. De Billy, M., Cohen-Tenouji, F., Jungman, A. an Quentin, G.J., The possibility of assigning a signature to rough surface using ultrasonic backscattering iagrams, IEEE Transactions on Sonics an Ultrasonics, Vol.SU-3, No.5 (976), pp De Billy, M., Cohen-Tenouji, F., Quentin, G., Lewis, K. an Aler, L., Ultrasonic evaluation of geometrical an surface parameters of rough efects in solis, Journal of Nonestructive Evaluation, Vol., No.4 (98), pp De Billy, M. an Quentin, G., Measurement of the perioicity of internal surfaces by ultrasonic testing, Journal of Physics D: Applie Physics, Vol.5, No. (98), pp Dwyer-Joyce, R., Drinkwater, B., an Quinn, A., The use of ultrasoun in the investigation of rough surface interfaces, Journal of Tribology, Vol. 3, No. (), pp Fokkema, J.T., Reflection an transmission of elastic waves by the spatially perioic interface between two solis (Numerical results for the sinusoial interface), Wave Motion, Vol.3, No. (98), pp Fokkema, J.T. an Van en Berg, P.M., 977. Elastoynamic iffraction by a perioic rough surface (Stress-free bounary), Journal of the Acoustical Society of America. Vol.6, No.5 (977), pp.95. Heckl, M.A. an Mulhollan, L.S., Some recent evelopment in the theory of acoustic transmission in tube bunles. Journal of Soun an Vibration, Vol.79, No. (995), pp Huynh, V.M. an Fan, Y., Surface-texture measurement an characterization with applications to machine-tool monitoring, International Journal of Avance Manufacturing Technology, Vol.7, No. (99), pp.. Jungman, A., Aler, L., Achenbach J.D. an Roberts, R., Reflection from a bounary with perioic roughness: Theory an experiment, Journal of the Acoustical Society of America, Vol.74, No.3 (983), pp.5 3. Jungman, A., Aler, L. an Quentin G., Ultrasonic anomalies in the spectrum of acoustic waves iffracte by perioic interfaces, Journal of Applie Physics, Vol.53, No.7 (98), pp Jungman, A., Leroy, O., Quentin, G. an Mampaert, K., Theoretical an experimental stuy of ultrasonic surface moes at a soli-flui perioic interface, Journal of Applie Physics, Vol.63, No. (988), pp Kersemans, M., Van Paepegem, W., Van Den Abeele, K., Pyl, L., Zastavnik, F., Sol, H. an Degrieck, J., Ultrasonic characterization of subsurface D corrugation, Journal of Nonestructive Evaluation, Vol.33, No.3 (4), pp Krasnova, T. an Jansson, P.A., Wave scattering from a slightly wavy interface between two anisotropic meia, Journal of Nonestructive Evaluation, Vol.5, No.4 (6), pp Kunu, T., Banerjee, S. an Jata, K.V., An experimental investigation of guie wave propagation in corrugate plates showing stop bans an pass bans, Journal of the Acoustical Society of America, Vol., No.3 (6), pp.7 6. Leuc, D., Morvan, B., Hlaky, A.C., Pareige, P. an Izbicki, J.L., Lamb wave propagation in a plate with a groove surface with several spatial perioicities, Ultrasonics, Vol.44 (6), pp.e359 e363. Liu, J. an Declercq, N.F., Ultrasonic geometry characterization of perioically corrugate surfaces, Ultrasonics, Vol.53, No.4 (3), pp Loewen, E.G. an Povov, E., Diffraction Gratings an Applications (997), New York, Marcel Dekker. Mampaert, K. an Leroy, O., Reflection an transmission of normally incient ultrasonic waves on perioic soli-liqui interfaces, Journal of the Acoustical Society of American, Vol.83, No.4 (988), pp Mampaert, K., Nagy, P.B., Leroy, O., Aler, L., Jungman, A. an Quentin, G., On the origin of the anomalies in the reflecte ultrasonic spectra from perioic surfaces, Journal of the Acoustical Society of America, Vol. 86, No. (989), pp Oh, S.J., Shin, Y.C. an Furgason, E.S., Surface roughness evaluation via ultrasonic scattering, IEEE Transactions on Ultrasonics, Ferroelectrics an Frequency Control, Vol.4, No.6 (994), pp Roberts, R., Achenbach, J.D., Ko, R., Aler, L., Jungman, A. an Quentin, G., Reflection of a beam of elastic-waves by a perioic surface profile, Wave Motion, Vol. 7, No. (985), pp Sherrington, I., Moern measurement techniques in surface metrology: part II; optical instruments, Wear, Vol. 5, No. 3 (988), pp [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers 6

17 Nguyen, Sugino, Kurokawa an Inoue, Mechanical Engineering Journal, Vol.4, No.5 (7) Shi, F., Lowe, M., Craster, R., Recovery of correlation function of internal ranom rough surfaces from iffusely scattere elastic waves, Journal of Mechanics an Physics of Solis, Vol.99 (6), pp Shin, Y.C., Oh, S.J. an Coker, S.A., Surface roughness measurement by ultrasonic sensing for in-process monitoring, Transactions of the ASME, Journal of Engineering for Inustry, Vol.7, No.3 (995), pp Whitehouse, D.J., Surface metrology, Measurement Science an Technology, Vol.8, No.9 (997), pp Woo, R.W., On a remarkable case of uneven istribution of light in a iffraction grating spectrum, Philosophical Magazine, Ser.6, Vol.4, No. (9), pp [DOI:.99/mej.7-78] 7 The Japan Society of Mechanical Engineers 7