J U L Y 2 0 2 1 • M A T E R I A L S E V A L U A T I O N 721 high-frequency excitation current flows generates a dynamic magnetic field and induces an eddy current in the specimens at skin depth. The magnetic field distribution is an important parameter for optimizing the transducer efficiency of an EMAT. Figure 5 shows the spiral coil and cylindrical magnet (12.7 mm diameter and 28.5 mm height) used in this study. The excitation frequency required to excite Lamb waves using a spiral coil was determined using the dispersion curva- ture. For a specific spiral coil, the approximate relationship between the optimal wavelength (!) generated by the spiral coil and spacing of the coil is given by: (1) where OD and ID are the outer and inner diameters of the coil, respectively. For the coil used in this study, the corresponding OD and ID were 12.7 and 0 (zero) mm, respectively. Typically, in an EMAT, a matching condition should be satisfied between the wavelength of the Lamb wave and coil configuration of the spiral coil. The phase velocity and group-velocity dispersion curves corresponding to Lamb waves in a 3.048 mm thick stainless steel structure are shown in Figure 6. When an EMAT is used to generate Lamb waves, the activated modes are selected based on the combination of the periodicity of the transducer and the excitation frequency sent to the trans- ducers. According to the fundamental relation, ! = c/f, the wavelength or period generated by the spiral coil is related to the frequency and phase velocity. The sloped line in Figure 6 represents the activation line at 12.7 mm and the intersecting points of the line with dispersion curves indicate preferential excitation points. There are several ways to select the excita- tion modes for Lamb wave testing. In general, it is preferable to use only the fundamental modes (A0 and S0) and the simplest way is to limit the frequency to a value below the cut- off frequencies in higher modes (such as an excitation frequency in the range of 1 to 600 kHz). As can be observed from the dispersion curvatures, the A0 mode for this spiral coil is highly dispersive. Therefore, S0 was selected for inspection purposes. The red dot in Figure 6 indicates the activation zone when a toneburst excitation with a frequency of #401 kHz was applied to the transducer. Meanwhile, the group velocity of S0 at this frequency was 4924 m/s. Regarding gripper design, the key question is whether or not coils should be formed on the curved surface. Experi- mental tests were conducted, as described in the following section, to answer this question. Experimental Setup To integrate the robotic gripper and EMATs, the first step is to evaluate the effect of tube curvature on the properties of the generated Lamb waves, as sample curvature can signifi- cantly affect the physical properties of the guided waves. In a circular sample, the curvature is defined as the reciprocal of radius as follows: (2) where is the curvature, and r is the radius of the sample. ' = [ OD ID r 1 ¤ = 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10 000 0.5 1 1.5 2 Frequency (Hz) × 106 2.5 3 3.5 4 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0.5 1 1.5 2 Frequency (Hz) × 106 2.5 3 3.5 4 Symmetric S 0, 1, 2, ... Antisymmetric A 0, 1, 2, ... Symmetric S 0, 1, 2, ... Antisymmetric A 0, 1, 2, ... S 0 S 0 A 0 A 0 λ = 12.7 mm Figure 6. Dispersion curves for Lamb wave modes of the 3.048 mm stainless steel plate: (a) phase velocity (b) group velocity. (a) (b) Phase velocity (m/s) Phase velocity (m/s)

722 M A T E R I A L S E V A L U A T I O N • J U L Y 2 0 2 1 Preliminary tests were conducted to describe the effect of curvature on Lamb wave excitation. Tubes with different diameters (73.025, 88.9, and 114.3 mm) and a plate with an infinite diameter were considered (Figure 7). All samples were made of 316L stainless steel with the same thickness (3.048 mm) to minimize errors in measurement. A data acquisition system was used to generate and receive Lamb waves using the designed EMAT. In all measurements, the EMAT was driven by a five-cycle toneburst with a center frequency of 401 kHz. The waves were excited using the computed burst frequency with an arranged receiver gain of 60 dB. Note that there is also a matching requirement for the receiver and input preamplifier. Depending on the burst frequency, bandpass filtering with a cut-off frequency of 325 to 475 kHz was applied. Results and Discussion In the following sections, two sets of experiments are carried out. First, the EMAT is used to investigate how tube curva- tures influence Lamb waves propagation. Then, the tests are performed in a semiautomatic manner in which the designed gripper was attached to a robotic arm. Effect of Tube Curvature on Lamb Wave Excitation Using EMATs There are two potential configurations for integrating EMATs into the fingers of an LTI robot. In the first configuration, the coils conform with the tube’s surface. This configuration requires a softer design for embedding coils in the pads. In the second configuration, the coils can be placed on the flat surfaces of fingers this does not require embedding the coils into the pads. To investigate the effect of tube curvature on Lamb wave propagation, the samples in Figure 7 were used with two different configurations. First, the coils were fully attached to the magnets. In this case, the coils do not conform with the surface (there is no full contact between the coil and curved surface). This case was called “nonconformed.” Mean- while, in the second condition, the coil was in full contact with the surface (“conformed” case). A schematic of these two cases is shown in Figure 8a with an arbitrary pipe cross section. ME TECHNICAL PAPER w modular robotic gripper for tubular components 3.048 × 304.8 × 609.6 mm 316L stainless steel sheet 316L welded stainless steel pipes OD = 114.3 mm OD = 88.9 mm OD = 73.025 mm (κ = 0.017 mm ) 1 (κ = 0.022 mm ) 1 (κ = 0.027 mm ) 1 Figure 7. Hollow cylinders (pipes) and the plate used in this study. Figure 8. Schematic view of the coil configuration in EMATs testing: (a) nonconformed case (left) and conformed case (right) (b) Lamb wave excitation in pipes with spiral coils and cylindrical magnet (using the conformed configuration). (a) (b) N N Cylindrical magnet Coils Surface