Relevant bibliographies by topics / Ultrasonic testing

Academic literature on the topic 'Ultrasonic testing'

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Published: 4 June 2021
Last updated: 29 July 2024

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Journal articles on the topic "Ultrasonic testing"

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WATANABE, Tomotaro. "Ultrasonic Testing." Journal of the Japan Society for Technology of Plasticity 53, no. 618 (2012): 631–35. http://dx.doi.org/10.9773/sosei.53.631.

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Ravichandran, S. "Robotic Ultrasonic Testing." Indian Journal of Science and Technology 10, no. 13 (April 1, 2017): 1–3. http://dx.doi.org/10.17485/ijst/2017/v10i13/103338.

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American NDT Inc. "Ultrasonic testing instrumentation." NDT & E International 24, no. 1 (February 1991): 61. http://dx.doi.org/10.1016/0963-8695(91)90814-j.

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Mulet, A., J. Benedito, J. Bon, and N. Sanjuan. "Review: Low intensity ultrasonics in food technology / Revisión: Ultrasonidos de baja intensidad en tecnología de alimentos." Food Science and Technology International 5, no. 4 (August 1999): 285–97. http://dx.doi.org/10.1177/108201329900500401.

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Ultrasonic applications can be classified into low intensity or high intensity applications. The latter are used to modify a process or product with ultrasonics, while in low intensity applications the process or product modifies the ultrasonic signal, thus providing information about the product. Low inten sity ultrasonics in food technology can be used to monitor a process (liquid level, flowmeters) or to determine the quality of food products. Since ultrasonic techniques are rapid, non-destructive, easy to automate and relatively inexpensive, the number of applications is rapidly growing in this field. Ultrasonics can also be considered for use in laboratory testing devices to determine physical and chemical properties of foods. Ultrasonics has been used to determine texture, composition and physical state in liquid and solid foods. The commonly measured ultrasonic parameters are velocity, attenua tion and frequency spectrum composition. Velocity is the parameter used most since it is the simplest and most reliable measurement. This paper reviews the basic principles of ultrasonics, the most suit able techniques for each type of application, the testing devices needed to make measurements and the most interesting applications.
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G. A, Ibe,. "Ultrasonic Wedges for Testing Of Turbine Blade Roots." International Journal of Engineering Research 4, no. 1 (January 1, 2015): 1–3. http://dx.doi.org/10.17950/ijer/v4s1/101.

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NGUYEN, Chanh Nghia, Masaki Sugino, Yu Kurokawa, and Hirotsugu Inoue. "OS6-18 Evaluation of Back Surface Roughness Using Ultrasonic Scattering(Measurement Techniques using Ultrasonics (2),OS6 Ultrasonic non-destructive testing and evaluation,MEASUREMENT METHODS)." Abstracts of ATEM : International Conference on Advanced Technology in Experimental Mechanics : Asian Conference on Experimental Mechanics 2015.14 (2015): 89. http://dx.doi.org/10.1299/jsmeatem.2015.14.89.

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Zhong, Fei, Wei Zhang, Biao Qiang Jiao, and Yue Xian Zhong. "Survey of Materials Testing Using Ultrasonic." Advanced Materials Research 146-147 (October 2010): 412–16. http://dx.doi.org/10.4028/www.scientific.net/amr.146-147.412.

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In this paper, ultrasonic materials testing researches are reviewed. The latest progress of ultrasonic testing technology is introduced, including water-squirting ultrasonic C-scan testing, laser ultrasound, ultrasonic feature scan imaging, signal processing and pattern recognition technology in the application of ultrasonic testing.
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Kurokawa, Yu, Masaki Sugino, and Hirotsugu Inoue. "OS6-20 2-Dimensional Back-Surface Roughness Evaluation by Ultrasonic Method(Measurement Techniques using Ultrasonics (2),OS6 Ultrasonic non-destructive testing and evaluation,MEASUREMENT METHODS)." Abstracts of ATEM : International Conference on Advanced Technology in Experimental Mechanics : Asian Conference on Experimental Mechanics 2015.14 (2015): 91. http://dx.doi.org/10.1299/jsmeatem.2015.14.91.

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MURAI, Junichi. "Ultrasonic Phased Array Testing." JOURNAL OF THE JAPAN WELDING SOCIETY 81, no. 4 (2012): 235–38. http://dx.doi.org/10.2207/jjws.81.235.

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Friesel, Mark A. "Ultrasonic testing of materials." Materials Science and Engineering: A 160, no. 2 (February 1993): 281–82. http://dx.doi.org/10.1016/0921-5093(93)90457-p.

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Dissertations / Theses on the topic "Ultrasonic testing"

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Whitcomb, Richard W. "Quantitative ultrasonic evaluation of concrete." Thesis, Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/19004.

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McLaren, S. "High-resolution ultrasonic non-destructive testing." Thesis, City University London, 1987. http://openaccess.city.ac.uk/8335/.

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The use of ultra-short pulse wideband ultrasonic transducers in Non-Destructive-Testing (NDT) has been investigated both theoretically and experimentally. It is demonstrated that the resolution of pulse-echo NDT is affected by diffraction effects which also complicate the interpretation of echo signals. These diffraction effects are interpreted in terms of the plane- and edge-wave model of *transducer fields. Improverents can be obtained by the use of non-uniformly excited transducers of two basic types: the first, the plane-wave-only (PWO) source; is more strongly excited at its centre than towards the rim, where the excitation is gradually reduced to zero in order to remove the edge wave. The second type, an edge-wave-only (EWO) source, is more strongly excited at its rim than in the centre, thereby effectively removing the plane wave. Computer modelling of pressure waveforms in the field of PWO and EWO sources has been carried out using an extension to the impulse response method. Experimental point-pressure waveform measurements in the field of a prototype EWO transducer, made using a miniature ultrasonic probei are in reasonable agreement with the calculated results. Detailed calculations are made of the transmit-receive mode (pulse-echo) responses arising from solid targets of various size in a flu- id medium interrogated by uniformly and non-uniformly excited sources. The theoretically predicted results are in good agreement with experimentally measured results obtained using a conventional transducer and an equivalent prototype EWO transducer. The effects of target size, field position and material on both the amplitude and shape of the echo responses are investigated. The structure of the responses is explained in terms of the plane and edge waves radiated by the source. Implications for the use of techniques to both size (Distance, Gain, Size curves) and characterise (ultrasonic spectroscopy) defects are examined. The applications of new, nonuniformly excited transducers in high-resolution NDT and ultrasonic imaging are evaluated.
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Wright, William Matthew David. "Air-coupled ultrasonic testing of materials." Thesis, University of Warwick, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319811.

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Engström, Torsten. "Ultrasonic Testing of INCONEL Alloy 600." Thesis, KTH, Fysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-193126.

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Mamilla, Amala Kishore. "Ultrasonic Couplants at Elevated Temperatures." Fogler Library, University of Maine, 2004. http://www.library.umaine.edu/theses/pdf/MamillaAK2004.pdf.

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Tsang, Wai-ming Peter. "Computer aided ultrasonic flaw detection and characterization /." [Hong Kong : University of Hong Kong], 1987. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12344928.

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Isleyici, Umut. "Effect Of Surface Roughness On Ultrasonic Testing." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606937/index.pdf.

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This study investigates the effect of front surface roughness on ultrasonic echo amplitude. Experiments were carried out on specimens whose front surfaces are machined by milling machine. Machining parameters were changed in milling process in order to obtain desired roughness values and milling head was tilted to a very small angle to obtain periodic rough surfaces. Experiments were performed with these specimens having roughness value of 0.5, 4.5, 11, 26.5 µ
m. Ra. The back surface roughness of all specimens was kept constant at 1.5 µ
m Ra by grinding operation. 1.5, 2, 3, 4 mm. holes were drilled at constant depth and to same side of each specimen to represent reference discontinuities. Ultrasonic tests, using pulse echo technique were carried out to monitor echo amplitudes corresponding to different roughness values. The tests were also repeated by using different ultrasonic probes having different frequencies. For additional comparison, different couplants were used through the tests. The results showed that there was a significant increase in the reduction of the sound pressure level with the increase in the surface roughness. Although there was no uncertainty observed about not being able to detect discontinuity because of roughness but correct couplant and frequency selection has a positive effect on correctly sizing the discontinuity and at attenuation measurements. The results obtained with this work can be used as a guide for testing rough surfaces, predicting the effect on ultrasonic examination before testing and discontinuity detecting capability under rough surface conditions.
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Roberts, D. R. "Ultrasonic spot weld testing with automatic classification." Thesis, Swansea University, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.638690.

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Spot welds are used to join sheet steel in automobile bodies. To ensure vehicle integrity, these welds, must be tested. Ideally, non-destructive testing would be employed. However, spot weld quality in the automotive industry is currently assessed using destructive methods. Spot welds can be tested non-destructively with ultrasound. Operators place a single crystal ultrasonic probe on a weld and interpret the returning signal to estimate the quality of the weld. However, this ultrasonic method has not been widely accepted in the past, possibly due to difficulties in manually quantifying the information contained in the signals. In an attempt to make ultrasonic testing viable for automotive use, a system has been created which automatically interprets the ultrasonic signals and classifies welds as good or bad. There are two main aspects to the systems. Firstly, echoes occurring within the signal are identified by an algorithm. This was developed after discovering the sequence in which the critical intermediate echoes occur. The second aspect of the system is classification of the spot weld based upon certain features of the identified echoes. The strength of the intermediate echoes was found to be primary source of information on weld size. Extensive experimental studies were designed and conducted to identify other potential information sources. Notably, the attenuation rate of the back-wall echoes in the signal was investigated. Most published papers in the field report that signal attenuation may be used to estimate weld size. It has been generally believed that the grain structure of the welded steel significantly increases ultrasound scattering, leading to higher attenuation is not caused by weld grain structure. The evidence gathered strongly favours weld surface irregularities as the primary cause of ultrasound attenuation in spot welds.
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Lin, Lin. "On the Generation and Detection of Ultrasonic Plate Waves in Microporous Polymeric Material." Fogler Library, University of Maine, 2003. http://www.library.umaine.edu/theses/pdf/LinL2003.pdf.

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曾偉明 and Wai-ming Peter Tsang. "Computer aided ultrasonic flaw detection and characterization." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1987. http://hub.hku.hk/bib/B31231007.

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Books on the topic "Ultrasonic testing"

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American Society for Nondestructive Testing, ed. Ultrasonic testing. Columbus, OH: The American Society for Nondestructive Testing, Inc., 2013.

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L, Workman Gary, and Kishoni Doron, eds. Ultrasonic testing. 3rd ed. Columbus, OH: American Society for Nondestructive Testing, 2007.

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Krautkrämer, Josef. Ultrasonic testing of materials. 4th ed. Berlin: Springer-Verlag, 1990.

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Krautkrämer, Josef, and Herbert Krautkrämer. Ultrasonic Testing of Materials. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-662-10680-8.

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Krautkramer, Josef. Ultrasonic testing of materials. 4th ed. Berlin: Springer-Verlag, 1989.

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Krautkrämer, Josef. Ultrasonic Testing of Materials. 4th ed. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990.

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United States. National Aeronautics and Space Administration., ed. The acousto-ultrasonic approach. [Washington, D.C.]: National Aeronautics and Space Administration, 1987.

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United States. National Aeronautics and Space Administration., ed. The acousto-ultrasonic approach. [Washington, D.C.]: National Aeronautics and Space Administration, 1987.

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Marks, Paul T. Ultrasonic testing classroom training book. Columbus, OH: American Society for Nondestructive Testing, 2005.

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Bindal, V. N. Transducers for ultrasonic flaw detection. New Delhi: Narosa, 1999.

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Book chapters on the topic "Ultrasonic testing"

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Hull, Barry, and Vernon John. "Ultrasonic Testing." In Non-Destructive Testing, 57–89. London: Macmillan Education UK, 1988. http://dx.doi.org/10.1007/978-1-349-85982-5_5.

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Hull, Barry, and Vernon John. "Ultrasonic Testing." In Non-Destructive Testing, 57–89. New York, NY: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4684-6297-5_5.

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Zhao, Chunsheng. "Testing Techniques for Ultrasonic Motors." In Ultrasonic Motors, 419–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-15305-1_14.

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Xu, Chunguang, and Weibin Li. "Array Ultrasonic Testing Technology." In Fundamentals of Ultrasonic Testing, 260–93. Boca Raton: CRC Press, 2024. http://dx.doi.org/10.1201/9781032625096-8.

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Kočiš, Štefan, and Zdenko Figura. "Non-destructive testing (NDT)." In Ultrasonic Measurements and Technologies, 124–46. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-1199-7_5.

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Krautkrämer, Josef, and Herbert Krautkrämer. "Introduction." In Ultrasonic Testing of Materials, 1–3. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-662-10680-8_1.

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Krautkrämer, Josef, and Herbert Krautkrämer. "Historical Survey of Developments." In Ultrasonic Testing of Materials, 160–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-662-10680-8_10.

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Krautkrämer, Josef, and Herbert Krautkrämer. "The Pulse-Echo Method; Design and Performance of a Pulse-Echo Flaw Detector." In Ultrasonic Testing of Materials, 167–221. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-662-10680-8_11.

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Krautkrämer, Josef, and Herbert Krautkrämer. "Transit-Time Methods." In Ultrasonic Testing of Materials, 222–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-662-10680-8_12.

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Krautkrämer, Josef, and Herbert Krautkrämer. "The Shadow Method." In Ultrasonic Testing of Materials, 239–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-662-10680-8_13.

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Conference papers on the topic "Ultrasonic testing"

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Sandhu, Jaswinder S., Honghui Wang, Milind M. Sonpatki, and Witold J. Popek. "Acoustography-based ultrasonic testing." In NDE For Health Monitoring and Diagnostics, edited by Andrew L. Gyekenyesi, Steven M. Shepard, Dryver R. Huston, A. Emin Aktan, and Peter J. Shull. SPIE, 2002. http://dx.doi.org/10.1117/12.470712.

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Blum, William E., and Thomas Gryba¨ck. "Ultrasonic Testing in 25 Minutes." In International Joint Power Generation Conference collocated with TurboExpo 2003. ASMEDC, 2003. http://dx.doi.org/10.1115/ijpgc2003-40095.

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Nondestructive Testing (AKA NDT, NDI, NDE) is an integral part of any power generation program. Ultrasonic Testing (UT) is one NDT method used to determine the integrity of materials and components. Managers, engineers, quality control personnel and others often require a fundamental understanding of the nondestructive testing methods used in their operations. This paper introduces basic theory, advantages and disadvantages, typical equipment and applications of ultrasonic testing. It is designed to give the reader a basic understanding of ultrasonic testing.
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Daw, J., B. Tittmann, B. Reinhardt, G. Kohse, P. Ramuhalli, R. Montgomery, H.-T. Chien, J.-F. Villard, J. Palmer, and J. Rempe. "Irradiation testing of ultrasonic transducers." In 2013 3rd International Conference on Advancements in Nuclear Instrumentation, Measurement Methods and their Applications (ANIMMA). IEEE, 2013. http://dx.doi.org/10.1109/animma.2013.6728097.

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Haszler, Alfred. "Ultrasonic Testing Beyond Flaw Detection." In ASNT Research Symposium 2019. ASNT, 2019. http://dx.doi.org/10.32548/rs.2019.006.

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Gokce, Zeki. "Guided wave testing and the differences in Long Range Ultrasonic Testing (LRUT) and Medium Range Ultrasonic Testing (MRUT)." In Rio Pipeline Conference and Exhibition. IBP, 2023. http://dx.doi.org/10.48072/2447-2069.rpc.2023.032.

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Suzuki, Hirofumi. "Ultrasonic Vibration Assisted Polishing of Micro Aspherical Molds." In Optical Fabrication and Testing. Washington, D.C.: OSA, 2008. http://dx.doi.org/10.1364/oft.2008.otub2.

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Kalivoda, Raymond J., Jim H. Smith, and Nicole L. Gailey. "Dynamic Testing." In 2014 10th International Pipeline Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/ipc2014-33758.

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Dynamic factory testing is an important step in the manufacturing of ultrasonic meters for custody transfer and other high accuracy petroleum applications. By utilizing a multiple product, high accuracy test system and a proper test program, a meter’s performance can be simulated over a wide flow and viscosity operating range. The test results give the user a detailed graph of the meter’s performance over the actual site operating parameters. The test verifies the meter’s performance prior to shipment but more importantly provides k-factor sensitivity to optimize measurement accuracy throughout the operating range. This paper outlines the theoretical basis and fundamentals of dynamic testing. It illustrates the process with data from an ultrasonic meter factory test recently conducted for a North Sea operating company. The meter was a 12 inch multi-path ultrasonic meter operating over a flow range of 636 to 1,113 m3/h (4,000 to 7,000 BPH) and a viscosity range of 5 to 350 cSt. The details of dynamic testing and the relationship between the measurement accuracy of a meter and dynamic testing will be the focus of this paper. It will include: • The fundamental operating principle of ultrasonic • Fluid dynamic properties such as boundary layer and flow profiles • The characteristics of the flow profiles in the different flow regimes that affect crude oil measurement • The dynamic operating range of crude oil meters • How dynamic testing is used in factory testing to verify the performance of a meter • Results of the 12 inch multi-path ultrasonic meter factory testing This paper will provide the necessary information to fully understand the basis and proper methods for dynamic testing to determine the operating performance of an ultrasonic meter.
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Hashimoto, H., K. Imai, D. Dornfeld, and K. Blaedel. "Speculation on Ultrasonic-Assisted Grinding with an Engineered Wheel." In Optical Fabrication and Testing. Washington, D.C.: Optica Publishing Group, 1998. http://dx.doi.org/10.1364/oft.1998.omb.3.

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The ability to perform high-quality, shear-mode grinding of brittle materials such as glass critically depends on an adequate flow of coolant through the contact zone between the tool and the workpiece. A long contact zone limits the induction of coolant and thereby promotes high temperatures in the contact zone where heat is generated. For workpiece materials like glass, the high temperature and subsequent quenching causes surface and subsurface damage. High temperature of the wheel also tends to promote faster wheel wear. In contrast, short contact lengths tend to reduce the temperature of both the workpiece and the wheel. For some grinding geometries, where a long contact length is difficult to avoid, an alternative is to excite the wheel at ultrasonic frequency, which also admits coolant between wheel and workpiece. Results are shown of grinding force with and without ultrasonic excitation and the analyses of the resultant surfaces.
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Messer, Barry, Jose R. Fuentes, Bart Tarleton, and Peter den Boer. "Novel Ultrasonic Testing of Complex Welds." In ASME 2005 Pressure Vessels and Piping Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/pvp2005-71408.

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Fluor and RTD have recently applied an ultrasonic testing (UT) technique that incorporates a phased array to field and shop operations. The new technique allows verification of weld integrity for difficult to access welds such as branch connection fittings and full penetration groove welds with fillet reinforcements. Verification of these types of welds is a necessity for power, oil and gas facilities, in particular, those operating under high pressure, high temperature, and corrosive environments. Historically, visual inspections of welds and radiograph testing (RT) have been used, but these methods are costly, time-consuming, and cannot match the benefits of the new UT phased array (UT-PA) method. The UT-PA technique has an arrangement of multiple piezoelectric elements that are independently controlled for developing synchronized and manageable sonic waves. The technique requires less time than conventional UT, is not hazardous as compared to RT, and allows for 100% volumetric inspection. Other advantages of UT-PA include its ease of use, increased accuracy, and development of instantaneous digital inspection records for tracking defect propagations in the future. The present work describes the application of this nondestructive examination (NDE) technique to a branched connection of an ASTM B564 outlet fitting to both an ASTM A608 modified 20Cr-32Ni-Nb statically cast header and an HP45 modified tee. An outline of the advantages for the UT-PA method is also included which explains the rationale that, in the future, will cause the welding industry to rely more on modified UT advanced imaging.
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Ryngach, N. A., and A. V. Emirov. "Composite material ultrasonic phased array testing." In HIGH-ENERGY PROCESSES IN CONDENSED MATTER (HEPCM 2019): Proceedings of the XXVI Conference on High-Energy Processes in Condensed Matter, dedicated to the 150th anniversary of the birth of S.A. Chaplygin. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5117453.

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Reports on the topic "Ultrasonic testing"

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Terrence A. Grimley. ULTRASONIC METER TESTING FOR STORAGE APPLICATIONS. Office of Scientific and Technical Information (OSTI), December 1998. http://dx.doi.org/10.2172/766361.

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DAVIS, S. J. Perform Ultrasonic Testing on Cs Capsule Overpacks. Office of Scientific and Technical Information (OSTI), April 2000. http://dx.doi.org/10.2172/802988.

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Duncan, M. G. Precision pulse-timing instrumentation for ultrasonic nondestructive testing. Office of Scientific and Technical Information (OSTI), August 1990. http://dx.doi.org/10.2172/6762029.

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Chinn, D. J., R. D. Huber, J. J. Haskins, J. A. Rodriguez, P. R. Souza, and T. V. Le. Ultrasonic Testing of NIF Amplifier FAU Top Plates. Office of Scientific and Technical Information (OSTI), May 2002. http://dx.doi.org/10.2172/15003397.

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Daw, Joshua, Lance Hone, Andrew Casella, Richard Jacob, Robert Montgomery, and Pradeep Ramuhalli. Integration Testing of Ultrasonic Deformation Sensor for TREAT Experiments. Office of Scientific and Technical Information (OSTI), October 2019. http://dx.doi.org/10.2172/1668671.

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JT Evans. Testing Results of Magnetostrictive Ultrasonic Sensor Cables for Signal Loss. Office of Scientific and Technical Information (OSTI), May 2005. http://dx.doi.org/10.2172/883695.

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WOLFF, J. J. Alternatives Generation and Analysis for Lower Knuckle Ultrasonic Testing Technology. Office of Scientific and Technical Information (OSTI), February 2001. http://dx.doi.org/10.2172/806022.

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Spanner, J., S. Doctor, T. Taylor, and J. Muscara. Qualification process for ultrasonic testing in nuclear inservice inspection applications. Office of Scientific and Technical Information (OSTI), March 1990. http://dx.doi.org/10.2172/7228750.

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Lykins, M. L. Results of ultrasonic testing evaluations on UF{sub 6} storage cylinders. Office of Scientific and Technical Information (OSTI), February 1997. http://dx.doi.org/10.2172/459897.

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Morgan. L52019 Evaluating the Size of Weld Defects Using Automated Ultrasonic Testing. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), October 2001. http://dx.doi.org/10.55274/r0011267.

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The use of X-rays to test the girth welds of pipelines during construction is gradually giving way to new automated ultrasonic technology.� This has many advantages, including the ability to measure the size of any defect present.� This allows small, benign defects to be left in the weld without any reduction in its strength. The critical size of any defect is its extent through the pipe wall thickness (its �height�), and, to a lesser extent, its length along the weld.� The accuracy of measuring these quantities is clearly important in ensuring that the small effects left are indeed small.� There has been little data available on the effectiveness of the sizing process.� This study used existing ultrasonic data to evaluate size accuracies against measurements taken when the weld was cut open.� A good range of types of defect was available. It is concluded that the size values estimated are generally safely over-sized.� This makes for a conservative estimate of the defects significance.� Except for one defect of difficult shape, other exceptions can be ascribed to the variability of operator interpretation.
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