MTL22_sent.pdf - Non-Destructive Material Testing Lab 2.2 PDF

Chair offürMetrology Lehrstuhl and Quality Fertigungsmesstechnik Management und Qualitätsmanagement Non-destructive material testing using ultrasound Lab 2.2 Chair of Metrology...

Chair offürMetrology Lehrstuhl and Quality Fertigungsmesstechnik Management und Qualitätsmanagement Non-destructive material testing using ultrasound Lab 2.2 Chair of Metrology and Quality Management Prof. Dr.-Ing. Robert Schmitt Lab 2.2: Non-destructive testing using ultrasound 2 Contents Objective of the lab............................................................................................................... 3 Ultrasonic testing.................................................................................................................. 3 Physical basics................................................................................................................. 3 Material testing using ultrasound.................................................................................... 10 2.2.1 Determination of wall-thicknesses, defect depth and equivalent flaw sizes.............. 16 2.2.2 Acoustic microscopy................................................................................................ 18 2.2.3 Phased Array ultrasonic technology......................................................................... 20 Experiments....................................................................................................................... 21 Determination of wall-thicknesses and defect positions.................................................. 21 Calibration of sound velocity........................................................................................... 22 Filling level measurement............................................................................................... 23 Automated robot-based testing....................................................................................... 24 Literature............................................................................................................................ 25 Contact............................................................................................................................... 25 Lab 2.2: Non-destructive testing using ultrasound 3 Objective of the lab Lab 2.2 deals with various techniques for non-destructive material testing using ultrasound. Both macroscopic defects in the material (pores, cracks, inclusions and inhomogeneity) and geometric dimensions of internal structures (wall thickness, coating thickness) of components can be visualized by ultrasound measurement. Within the experiments, hand-held ultrasonic sensors as well as automated testing devices are used. Ultrasonic testing Physical basics In ultrasonics high frequency sound waves are used to characterize internal structures of parts without destroying them. Sound is a mechanical wave, resulting from excited vibrations of individual particles. Unlike electromagnetic waves, a medium in solid, liquid or gaseous form is always required for their propagation. The term "Ultra" refers to the frequency range of sound that is above the hearing level of humans (20 kHz). In the process of wave propagation, the particles vibrate in one place periodically around their resting position and thereby transmit their movement to adjacent particles. This movement is spreading with the characteristic speed of the respective propagation medium, called the speed of sound c. Depending on whether the elementary particles oscillate in parallel or perpendicular to the propagation direction, multiple wave types can be distinguished. The two main types of waves are shown in Figure 1. Lab 2.2: Non-destructive testing using ultrasound 4 Longitudinal wave Longitudinalwelle  Direction Schwingungsrichtung Ausbreitungsrichtung of vibration Transverse wave Transversalwelle  Direction Schwingungsrichtung Ausbreitungsrichtung of vibration Figure 1: Wave types If the vibration direction is parallel to the propagation direction, the wave is called a longitudinal wave. As in this wave mainly compressive and tensile forces are active, it is also called a pressure or compression wave. This wave type can be excited in gases, liquids and solids. An important parameter for longitudinal waves is the sound pressure. At the locations of increased particle density, the pressure is higher than the atmospheric pressure, whereas it is smaller in the dilution zones. A small, inertia-free manometer would show sinusoidal changes in the sound wave with over- and under-pressure. This alternating pressure is called sound pressure. If the direction of vibration and propagation are perpendicular to each other, the wave is called a transverse wave. Due to the thereby present voltage states such waves are called shear waves. Shear waves can propagate only in solids, because gases and liquids have no resistance towards shear stress. Their propagation velocity is always less than that of the longitudinal wave. Figure 1 represents a snapshot of both mentioned modes, where a periodic arrangement of the vibrational states can be recognized. The distance of these periods is defined as wavelength ʎ. The duration of a defined vibration defines the frequency f of the sound pulse. Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 5 The following formula shows the relation between wavelength, frequency and speed of sound c: c  (Eq. 2-1) f The sound velocity or propagation velocity c is a material property and constant for a given material in general for all frequencies and wavelengths. However, it depends on the wave type, the respective state of aggregation, the crystalline structure of the temperature and the static pressure of the transmission medium. It can be calculated as follows: E 1  Longitudinal wave c  (Eq. 2-2) L  (1   )(1  2 ) G 1 E Transverse wave cT   (Eq. 2-3)   21    E = Elastic Modulus ρ = Density µ = Possion Constant In Table 1 some sound velocities for different materials are indicated. Material cL in m/s cT in m/s Aluminium 6200-6360 3100-3130 Steel 5920 3250 Cast iron 3800-5800 220-3200 Epoxy resin 2400-2900 1100 Tungsten carbide 6655 3988 Table 1: Sound velocities of different materials When a sound wave propagates through the interface between two media with different material properties, reflection, transmission and refraction appears, depending on the acoustic impedance of Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 6 the media involved. For us the acoustic impedance Z is relevant. Z is equal to the product of acoustic wave velocity c and the density ρ: Z = c * ρ. It is a specific measure of how much a material opposes the displacement of its voxels (volume elements) caused by the sound wave. Figure 2 shows R and T for different material combinations. R  100% Feststoff Solid  Luft  Air Air  Luft  Solid Feststoff T  0% R  89% Stahl Oil Steel  Öl  Steel ÖlOil  Stahl T  11% R  71% Quarz   Quartz Oil Öl  Quartz ÖlOil  Quarz T  29% Figure 2: Reflection loss at sound coupling The reflectance is proportional to the difference between the impedances of the two media. The reflected and transmitted portion of a wave at an interface is given by the magnitude of the reflection coefficient R and the sum of the transmission coefficient T. The following applies: (Eq. 2-4) Because of the fact that during the sound propagation between solids and ambient air almost total reflection occurs, a sound-conductive connection / couplant (e.g. a fluid) between the ultrasonic sensor and test specimens is necessary in order to obtain usable results of the component depth. Therefor couplants such as water, oil, gel or grease are used. They form a film and close the existing gap. The ultrasonic waves are introduced in this way with only small reflection losses from the sensor surface via the coupling agent into the component. Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 7 Generation of ultrasound waves The principle most commonly used for generating ultrasound signals is based on the piezoelectric effect. Certain crystals (e.g. quartz, lithium sulfate, Rochelle salt, tourmaline, sphalerite) are subjected to mechanical tensile or compressive stresses. These stresses and deformations cause charge displacements in the crystal structure, which can be perceived as an electrical voltage on the surface. The size of the measurable voltage directly depends on the size of the mechanical deformation of the crystal lattice. Figure 3 illustrates this principle. Direkter Direct Piezoeffekt piezoelectric effect Reziproker Inverse Piezoeffekt piezoelectric effect p + + + + + + + + d Piezoelement piezo element d d - d Piezoelement piezo element ~ - - - - - - - - - - p Figure 3: Piezoelectric effect Conversely, when a voltage to a piezoelectric body is applied it is stretched or compressed. This phenomenon is called the inverse piezoelectric effect. If an AC voltage source is applied, the body changes in its thickness with the same frequency and begins to oscillate. In this way, high-frequency mechanical vibrations can be generated and used as an ultrasonic signal. For signal detection the direct piezoelectric effect is used. Depending on the material (sound velocity c) and the thickness of the piezoelectric disc there exist preferred excitation frequencies. The resonance frequency f r is obtained from the condition that the thickness d must correspond to half a wavelength: c fr  (Eq.2-5) 2d Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 8 Attenuation of ultrasonic waves When ultrasound waves travel through a medium, their intensity naturally diminishes with distance. This effect is mainly caused by scattering and absorption due to the grain structure of a material. Attenuation can be defined as the decay rate of the ultrasonic wave as it travels through material. The Beer-Lambert law shows the relation between intensity I, starting intensity I0, distance travelled through material x and attenuation coefficient α. I  I 0  e   x (Eq.2-6) Thus, the attenuation coefficient can be calculated from the first amplitude A1 and the distance travelled to this point x1 and the second amplitude A2 and the (further) distance travelled to this point x2: 1 A   ln( 2 ) (Eq.2-7) ( x1  x2 ) A1 In engineering, attenuation is usually measured in units of decibles per unit length of medium. dB dB [ ] [ ] 1  [ ]  cm  cm (Eq.2-8) cm 20 lg( e) 8,686 Damping is a material property and indicates in how far the intensity of the ultrasonic waves is reduced with regard to the propagation distance in a medium. Usually the damping/attenuation increases with increasing frequency. This means that low-frequency ultrasonic waves penetrate a material further than high frequency waves. However, ultrasonic waves of high frequencies achieve better resolutions, thus enabling more accurate defect detection in the component. Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 9 Sound field The sound field describes the propagation of sound from a sound source in a medium-filled space. Using ultrasonic probes the display is usually 2-dimensional, and this represents a section through the axis of symmetry of the field. The sound field is mainly dependent on the size of the transmitter and the radiated frequency. Parameters are the divergence angle ϑ of the sound cone and the near- field-length N. The principal sound field geometry of a perpendicular-sensor is displayed in Figure 4. Material Probe -20 db Piezoscheibe -6 db 20db 0 db DS -6 db 6 db -20 db N Figure 4: Geometry of the sound field The near field goes back to Huygens’ Principle, according to which from any point of a sound- emitting surface a spherical wave runs out. The sound field is the superposition of all of these elementary waves by amplitude and phase. Near the radiating surface of the probe, the distances to the individual points are very different. The large phase differences produce cancellations and reinforcements of sound pressure in the near field. At the end of the near field there is the greatest test sensitivity because of the strongest contraction of the sound beam. The following formula represents the mathematical connection between the near field length N, the wavelength λ and the vibration diameter D. D² N 4 (Eq.2-9) Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 10 Small oscillators have low divergence angles in the near field and large divergence angles in the far field. They are therefore particularly suitable for the detection of defects in a short distance. In contrast, large oscillators have a large near field and a strong focusing of the sound field. These features and the greater sound power make it possible to detect defects also at a great distance. Material testing using ultrasound The frequency spectrum of technically usable ultrasound extends currently in a range from 20 kHz to 2 GHz. Depending on the application there is a variety of process variants for material testing. However, all ultrasound systems have to implement the following basic functions: Signal generation, Sending and receiving sound pulses Signal indication The signals are generated with a pulse generator, which triggers in the sensor a sequence of brief electrical pulses. These lead to the contraction and relaxation of the silicon wafer in the transmitter and thus generate the sound pulses. The test head is held onto the test object for acoustic coupling. This type of acoustic coupling is called a contact technique and is usually done manually. The air gap between the probe and the object-surface (irregularities and roughness) is filled with a coupling medium (e.g. gel). Alternatively, there are special ultrasonic probes, which may be positioned a few centimeters away from the surface. The gap can be bridged by using an immersion technique (suspended into water) or a fluid jet. Due to the absence of wear and positioning tolerance of such systems, they are particularly well suited for automated testing. Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 11 Figure 5 shows an overview of these different types of probes. contact technique immersion technique squirter technique Figure 5: Probe overview Depending on whether the injected signal is reflected and received by the same ultrasonic probe or different probes for sending and receiving a signal are used, two ultrasonic transmission technologies can be distinguished. These are displayed in in Figure 6. Sender / Transmitter/ Empfänger Receiver Impuls-Echo: Pulse-Echo: Werkstück Workpiece Sender Transmitter Receiver Empfänger Durchschallung: Through-Transmission: Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 12 Figure 6: Ultrasonic testing methods The pulse-echo method uses only one probe for sending and receiving the acoustic pulses. The received signal is reflected from the back wall of the test object, opposite to the transmitter. If the sound is detected by a second probe it is called through-transmission method. In most applications, the pulse-echo method is preferred for error detection, because it has the following advantages: By calculation transit times the distance between a material defect and the probe surface can be determined The detection sensitivity for small defects is much higher with the through- transmission method Only one probe needs to be coupled and placed on the surface. The quality of the connection is not critical if a comparison echo exists During the through-transmission method the signal has to travel only a single sound path, which makes it advantageous for testing materials with greater sound damping. Regardless of whether a through-transmission- or a pulse-echo-method is used, the received sound pulses have to be visualized and analyzed. The amplitude level of the reflected or transmitted signal is plotted versus the running time. This type of display is called the A-image of the ultrasonic echo. Figure 7 shows the typical plot of an A-scan using the pulse-echo method. Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 13 Figure 7: A-Scan of ultrasonic echos In addition to the dominant surface echo (interface: probe ↔ component) a series of backwall echoes (interface: component ↔ environment) is visible. The duplications of the backwall echo result from additional sound reflections at the device rear panel and component surface (see also Figure 9). Due to the longer propagation in the material and the associated sound attenuation the amplitude levels are reduced. In the through-transmission method, an error in the test-object is detected via a signal attenuation. The receiver continuously detects the periodically introduced sound pulses. The transmitter and the receiver can be moved over the test-object. If an error in the material exists, the entire signal strength can no longer be transmitted to the receiver. The error detection with the ultrasonic transmission is illustrated with some examples in Figure 8. Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 14 Durchschallung Through-Transmission: Bildschirmanzeige A-scan A - Bild Transmitter Receiver Werkstück Workpiece Sendeimpuls Pulse Pulse Sender Transmitter Empfänger Receiver Fehler Defect Defect Fehler Figure 8: Defect detection by using the through-transmission method Precisely aligned and synchronously moving oscillators are essential, to prevent misinterpretation of the data - as can be seen in Figure 8 comparing the third and the fifth A-scan. The pulse-echo method, however, recognizes the reflections of the coupled ultrasonic pulses. If an error exists, it reflects the sound signal. The corresponding echo is visible in the A-image and one can draw conclusions about the size and location of the fault. Such intermediate- or fault-echo is also accompanied by a weakening of the back echo, as a part of the sound is reflected already in the error. The relationship between fault and received echo is shown in Figure 9. Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 15 Pulse-Echo: A-Scan: Workpiece Sended pulse (FE) Backwall Echo (BE) Probes Backwall Echo (BE) Defect FE BE Defects FE Defects FE BE c Figure 9: Defect detection with the Pulse-Echo-Method With digital ultrasound technology, it is possible to display a number of A-scans in one image with special algorithms. The signals in the A-scan are rectified and the signal strength is coded in colors. The thus generated B-scan shows a material cut in direction of the signal input. Each column of a B-scan contains the information of the waveform of an ultrasonic signal. A B-scan together with an example test-object is illustrated in Figure 10. Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 16 B-scan C-scan A-scan Figure 10: B- and C-scan Another possibility of representation is the generation of C-scans. These images are also generated from multiple A-scans with known test positions. C-scans show a color-coded material section parallel to the input surface at a desired depth. A pixel of a C-scan represents the signal value of an A-frame at a specified depth and time. The generation of a C-scan is complicated and is accompanied by a significant loss of test data. 2.2.1 Determination of wall-thicknesses, defect depth and equivalent flaw sizes If the sound velocity of the test material is known (cmaterial), both the wall thickness of the component and the depth of a possible defect can be easily determined from the recorded A-scan (Figure 11) The calculation of the wall thickness d and the flaw depth x occurs as a function of the determined runtimes td and tx. (Eq.2-10) Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 17 td Prüfkopf Probe tx Couplant Koppelfluid x Fehlstelle Defect d Part Bauteil OE Defect Backwall Surface FE RE Echo Echo Echo Figure 11: Determination of wall thickness and defect depth by an A-scan For the classification of a defect an AVG diagram is used (Figure 12). This diagram is probe-specific and provides as a result the diameter of a circular disc replacement error, which is perpendicular to the direction of signal input in the component and would have the same acoustic behavior as the “real” defect. V [dB] S DKSR A G N Deff A: Sound auf path referring die Nahfeldlänge to near fieldSchallweg bezogener S: Sound path Schallweg N: Near field length Nahfeldlänge V: Gain Verstärkung G: Flaw size referring Fehlstellengröße aufto probe diameter den Schwingerdurch- messer bezogen Diameter of equivalent DKSR: Durchmesser des flaw size / circular disc Kreisscheibenreflektors replacement error (Ersatzfehler) Allgemeines Effective probe diameter Deff: Effektiver Schwinger- AVG-Diagramm durchmesser G [-] A [-] Figure 12: AVG diagram Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 18 Based on the decrease in amplitude of the received backwall echo relating to the defect, the additional amplification V is determined, which is required to raise the weakened back wall echo signal back to the value without defects. To determine the reference value for the back-wall-signal five individual measurements must be made and averaged for a fixed gain. The difference between the previous and the new gain value is V. The size A is the distance between the fault and the test head with respect to the near field, and can be determined from the signal propagation time. If the values of A and V are known, the amount of error G is determined from the diagram. G depends on the oscillater-diameter of the probe and the diameter of the substitute error. 2.2.2 Acoustic microscopy Ultrasonic microscopy uses the pulse-echo method with specific probes that provide acoustic pulses of high frequency (up to 2 GHz) and a high repetition rate which are received and analyzed. A bulge in the surface of the probe bundles the sound field and focuses it onto a defined point in front of the sensor. The location of the focal point is dependent on the radius of curvature and represents the point of highest sensitivity and highest sound energy. By adjusting the Z-axis the focus point can be set on the component surface or a specific depth. To produce an image (for example, C-image) the probe is clamped in a moving system and guided in meandering fashion over the component surface. The coupling of the ultrasonic signal takes place in immersion technique with distilled water. Figure 13 illustrates the principle of ultrasonic microscopy using a device of the company SAM TEC. Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 19 Umschalter Switch Transmit Senden Receive Empfangen y x z Water Wasser 1mm 20µm Beschichtung m m 10 Substrat 10mm Courtesy of: SAM TEC Figure 13: Principle of ultrasonic microscopy Ultrasound microscopes are characterized by a very high resolution and very precise axe kinematics. They are preferably used for the investigation of microsystem components and can even visualize smallest structures or inhomogeneity in the material. (Figure 14). 50 mm 15 mm Mikro-Chip Microchip C-scan C-Bild Figure 14: C-scan of a microchip Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 20 2.2.3 Phased Array ultrasonic technology Phased array probes consist of numerous identical elements each subserving as source of ultrasonic waves generating their own wavefront. On interfering with one another an overall wavefront is generated. This overall wavefront can easily be adjusted to special needs of an industrial non- destructive testing process. For example, the different sources can be time-delayed or synchronized in order to modify angle or focal distance. Figure 15 shows how a defined angle is generated through time-delayed activation of the piezo elements. Figure 15: Time-delayed activation The phased array technology provides a number of advantages in industrial non-destructive testing. Using time-delayed activation otherwise hardly detectable defects can be visualized such as cracks perpendicular to the surface of the probe. Moreover the testing speed can often be increased significantly. Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 21 Experiments Determination of wall-thicknesses and defect positions In this experiment manual ultrasonic testing is applied, followed by the interpretation of the results obtained from a sample component. To simulate various defects, stepped bores were introduced into the component. The preparation and presentation of the ultrasonic signal is also performed via the measuring software InSonic. Figure 16: Manual identification of defects Task: To perform the experiment, a hand-held ultrasonic probe is used in contact technique (Figure 5). Specifically, the following steps must be performed. 1.) Apply couplant onto the component’s surface; 2.) Setting the optimal filtering and amplification parameters; 3.) Move along a scan line at a constant speed; 4.) Simultaneous observation of the resulting A-scan on the computer screen; 5.) Recording of a characteristic A-scan with surface, error and back wall echo; 6.) Calculation of wall thickness and defect depth Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 22 Calibration of sound velocity For the determination of wall thicknesses and defect depths, the accurate knowledge of the sound velocity within the material is important. Although in the literature there is information on the sound velocity for almost every common material, the data can vary, depending on the added alloy elements and of certain manufacturing processes (e.g. hardening, burnishing or coating). Therefore in this part of the experiment the exact sound velocity of a material is determined with the help of one gauge block with known geometric dimensions and the ultrasonic measuring software InSonic, developed at the WZL. Task: In this experiment firstly, the sound velocity cMaterial of a gauge block of known thickness is determined manually. Secondly, the determined sound velocity is used to measure the thickness of the gauge again. Figure 17: Manual determination of sound velocity To perform the calibration of the sound velocity, in the measurement program the tab "Thickness Measurement" must be selected. The further use of the software for determining the sound velocity (by means of known material thickness) is explained during the experiment by the supervising instructor. 1.) Apply couplant onto the component’s surface 2.) Setting the optimal filtering and amplification parameters 3.) Determine cMaterial 4.) Setting: Thickness [mm]: 2,5mm 5.) Determine thickness using cMaterial 6.) Setting: sound velocity [m/s]: previously determined cMaterial Laboratory for Machine Tools and Production Engineering (WZL) Chair of Metrology and Quality Management Lab 2.2: Non-destructive testing using ultrasound 23 Filling level measurement The third experiment provides an overview of filling level measurement. Filling level measurement is important in various industrial processes. Filling level measurement using ultrasonic waves are especially suitable for monitoring liquids. Since the measurement is conducted outside the container this method can also be used to control the filling level of aggressive liquids. Figure 18: Filling level monitoring Task: In this experiment the filling level of an opaque container is determined. To conduct the measurement, a probe is placed on the bottom of the tank. The filling level can be derived from the determined runtimes. 1.) Positioning of the probe at the bottom; 2.) Determination of the runtime; 3.) Calculation of the filling level using the runtime In industrial processes, limit value observation is also an important task. To perform this kind of monitoring probes are placed on the sides of the container. Lab 2.2: Non-destructive testing using ultrasound 24 Automated robot-based testing A higher automation leads to various advantages such as higher accuracy and reproducibility as well as reduction of personnel costs. In order to guarantee reproducibility an exact and standardized positioning of the probes is important but hard to achieve using contact technology. Therefor a liquid- jet-probe as shown in Figure 5 is used. The probe is mounted on the 6th axis of a jointed-arm robot and is guided automatically along the surface of the component. The water supply is realized through a water pump. Figure 19: Robot and probe for automated ultrasonic testing Task: 1.) Turn on pump; 2.) Setting the optimal filtering and amplification parameters; 3.) Executing the robot-testing path; 4.) Simultaneous observation of A-Scan and C-Scan; 5.) Generation of an A-Scan featuring relevant characteristics of the gauge 6.) Generation of a B-Scan featuring relevant characteristics of the gauge Lab 2.2: Non-destructive testing using ultrasound 25 Literature  Barbian, O. A.: Handbuch Automatische Ultraschallprüfsysteme. 1. Auflage Berlin: DVS-Verlag, 2003  Beitz, W.; Grote, K.-H.: Dubbel. Taschenbuch für den Maschinenbau. 19. Auflage Berlin: Springer-Verlag, 1997  Deutsch, V., Platte, P., Vogt M.: Ultraschallprüfung – Grundlagen und industrielle Anwendungen. Berlin: Springer-Verlag, 1997  GAMPT mbH: Versuchsanleitungen Ultraschall. Ausgabe 10/2007  Matthies, K.: Dickenmessung mit Ultraschall. 2. Auflage. Berlin: DVS-Verlag, 1998  Pfeifer, T. Fertigungsmesstechnik. München: Oldenburg-Verlag, 1998  Splitt, G.; Kauth, G.: Phased Arrays – eine zeitgemäße Lösung von Prüfaufgaben in der ZfP. Berlin, DGZfP-Jahrestagung 2001 Contact Philipp Nienheysen E-Mail: [email protected]