{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:41:42Z","timestamp":1760229702371,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T00:00:00Z","timestamp":1655856000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51374264","cstc2018jszx-cyztzxX0032"],"award-info":[{"award-number":["51374264","cstc2018jszx-cyztzxX0032"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Major Project of Chongqing","award":["51374264","cstc2018jszx-cyztzxX0032"],"award-info":[{"award-number":["51374264","cstc2018jszx-cyztzxX0032"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The accurate estimation of axial stresses is a major problem for high-strength bolted connections that needs to be overcome to improve the assembly quality and safety of aviation structures. However, the conventional acoustoelastic effect based on velocity-stress dependence is very weak for short bolts, which leads to large estimation errors. In this article, the effect of axial stress on ultrasonic scattering attenuation is investigated by calculating the change in the energy attenuation coefficient of ultrasonic echoes after applying axial preload. Based on this effect, a stress-dependent attenuation estimation model is developed to measure the bolt axial stress. In addition, the spectrum of the first and second round-trip echoes is divided into several frequency bands to calculate the energy attenuation coefficients, which are used to select the frequency band sensitive to the axial stress changes. Finally, the estimation model between axial stress and energy attenuation coefficients in the sensitive frequency band is established under 20 steps of axial preloads. The experimental results show that the energy attenuation coefficient in the sensitive band corresponds well with axial stress. The average relative error of the predicted axial stress is 6.28%, which is better than that of the conventional acoustoelastic effect method. Therefore, the proposed approach can be used as an effective method to measure the axial stress of short bolts in the assembly of high-strength connections.<\/jats:p>","DOI":"10.3390\/s22134692","type":"journal-article","created":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T04:12:01Z","timestamp":1655871121000},"page":"4692","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A New Axial Stress Measurement Method for High-Strength Short Bolts Based on Stress-Dependent Scattering Effect and Energy Attenuation Coefficient"],"prefix":"10.3390","volume":"22","author":[{"given":"Tong","family":"Fu","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering, Chongqing University, Chongqing 400044, China"}]},{"given":"Ping","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Chongqing University, Chongqing 400044, China"}]},{"given":"Aijun","family":"Yin","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Chongqing University, Chongqing 400044, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1177\/0020294020932354","article-title":"Torque control of bolt tightening process through adaptive-gain second-order sliding mode","volume":"53","author":"Wu","year":"2020","journal-title":"Meas. Control"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"359","DOI":"10.4236\/eng.2012.47047","article-title":"Experimental Strain Investigation of Bolt Torque Effect in Mechanically Fastened Joints","volume":"4","author":"Younis","year":"2012","journal-title":"Engineering"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1115\/1.2400262","article-title":"Study of Bolt Load Loss in Bolted Aluminum Joints","volume":"129","author":"Jaglinski","year":"2007","journal-title":"J. Eng. Mater. Technol."},{"key":"ref_4","first-page":"11","article-title":"Angular Torque Methodology for Cylinder Head Bolted Joint and Validation by FE and Experimental Work","volume":"6","author":"Marathe","year":"2016","journal-title":"Int. J. Manuf. Mater. Mech. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1186\/s10033-020-0431-x","article-title":"Research Review of Principles and Methods for Ultrasonic Measurement of Axial Stress in Bolts","volume":"33","author":"Pan","year":"2020","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Shao, J., Wang, T., Yin, H., Yang, D., and Li, Y. (2016). Bolt Looseness Detection Based on Piezoelectric Impedance Frequency Shift. Appl. Sci., 6.","DOI":"10.3390\/app6100298"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"104010","DOI":"10.1088\/1361-665X\/aa6e93","article-title":"A fractal contact theory based model for bolted connection looseness monitoring using piezoceramic transducers","volume":"26","author":"Huo","year":"2017","journal-title":"Smart Mater. Struct."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1177\/1045389X19891534","article-title":"A nonlinear ultrasonic method for real-time bolt looseness monitoring using PZT transducer\u2013enabled vibro-acoustic modulation","volume":"31","author":"Zhao","year":"2019","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"914","DOI":"10.1016\/j.ultras.2013.11.003","article-title":"Bolt axial stress measurement based on a mode-converted ultrasound method using an electromagnetic acoustic transducer","volume":"54","author":"Ding","year":"2014","journal-title":"Ultrasonics"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Ogi, H., and Hirao, M. (1997, January 15\u201320). Electromagnetic Acoustic Spectroscopy in the Bolt Head for Evaluating the Axial Stress. Proceedings of the Eighth International Symposium on Nondestructive Characterization of Materials, Boulder, CO, USA.","DOI":"10.1007\/978-1-4615-4847-8_105"},{"key":"ref_11","unstructured":"Ogi, H., and Hirao, M. (2003). EMATs for Science and Industry: Noncontacting Ultrasonic Measurements, Kluwer Academic Publishers."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.ndteint.2008.09.005","article-title":"Measurement of axial stress using mode-converted ultrasound","volume":"42","author":"Kim","year":"2009","journal-title":"NDT E Int."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"106178","DOI":"10.1016\/j.ultras.2020.106178","article-title":"Measurement of fastening force using dry-coupled ultrasonic waves","volume":"108","author":"Liu","year":"2020","journal-title":"Ultrasonics"},{"key":"ref_14","first-page":"1009212","article-title":"Ultrasonic Measurement Method of Bolt Axial Stress Based on Time Difference Compensation of Coupling Layer Thickness Change","volume":"70","author":"Liu","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1115\/1.2748821","article-title":"Combination of Longitudinal and Transverse Ultrasonic Waves for In Situ Control of the Tightening of Bolts","volume":"129","author":"Chaki","year":"2007","journal-title":"Vessel Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1299\/jsmea.42.111","article-title":"Ultrasonic Measurement of Axial Stress in Short Bolts with Consideration of Nonlinear Deformation","volume":"42","author":"Yasui","year":"1999","journal-title":"JSME Int. J. Ser. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"102210","DOI":"10.1016\/j.ndteint.2019.102210","article-title":"A shape factor based ultrasonic measurement method for determination of bolt preload","volume":"111","author":"Pan","year":"2020","journal-title":"NDT E Int."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"055005","DOI":"10.1088\/1361-665X\/ab06dc","article-title":"Bolt preload measurement based on the acoustoelastic effect using smart piezoelectric bolt","volume":"28","author":"Sun","year":"2019","journal-title":"Smart Mater. Struct. Smart Mater. Struct."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"025033","DOI":"10.1088\/1361-665X\/26\/2\/025033","article-title":"Smart washer\u2014A piezoceramic-based transducer to monitor looseness of bolted connection","volume":"26","author":"Huo","year":"2017","journal-title":"Smart Mater. Struct."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1109\/TUFFC.2011.1903","article-title":"EMAT noise suppression using information fusion in stationary wavelet packets","volume":"58","author":"Kubinyi","year":"2011","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4347","DOI":"10.1121\/1.4984290","article-title":"Ultrasonic attenuation of polycrystalline materials with a distribution of grain sizes","volume":"141","author":"Arguelles","year":"2017","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.ultras.2017.02.018","article-title":"Evaluating grain size in polycrystals with rough surfaces by corrected ultrasonic attenuation","volume":"78","author":"Li","year":"2017","journal-title":"Ultrasonics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"174301","DOI":"10.1103\/PhysRevLett.114.174301","article-title":"Attenuation of the dynamic yield point of shocked aluminum usings elastodynamic simulations of dislocation dynamics","volume":"114","author":"Balint","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"031907","DOI":"10.1063\/1.3464291","article-title":"Polycrystals under applied loads: Second-order grain statistics","volume":"97","author":"Turner","year":"2010","journal-title":"Appl. Phys. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"EL476","DOI":"10.1121\/1.4921676","article-title":"Acoustic attenuation coefficients for polycrystalline materials containing crystallites of any symmetry class","volume":"137","author":"Kube","year":"2015","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2613","DOI":"10.1121\/1.4932026","article-title":"Stress-dependent second-order grain statistics of polycrystals","volume":"138","author":"Kube","year":"2015","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1121\/1.4941253","article-title":"Stress-dependent ultrasonic scattering in polycrystalline materials","volume":"139","author":"Kube","year":"2016","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4183","DOI":"10.1121\/1.5135004","article-title":"Pressure influence on elastic wave attenuation in polycrystalline materials","volume":"146","author":"Kube","year":"2019","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Kube, C.M., Fateh, M., Ghoshal, G., and Turner, J.A. (2012, January 5\u201310). Measurement of thermally induced stresses in continuously welded rail through diffuse ultrasonic backscatter. Proceedings of the AIP Conference, Melville, NY, USA.","DOI":"10.1063\/1.4716414"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"109270","DOI":"10.1016\/j.measurement.2021.109270","article-title":"Investigation of frequency-dependent attenuation coefficients for multiple solids using a reliable pulse-echo ultrasonic measurement technique","volume":"177","author":"Zhang","year":"2021","journal-title":"Measurement"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.ndteint.2015.02.002","article-title":"Evaluation of mean grain size using the multi-scale ultrasonic attenuation coefficient","volume":"72","author":"Li","year":"2015","journal-title":"NDT E Int."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ultras.2016.03.004","article-title":"Material grain size characterization method based on energy attenuation coefficient spectrum and support vector regression","volume":"69","author":"Li","year":"2016","journal-title":"Ultrasonics"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1007\/s11770-019-0782-1","article-title":"Ultrasonic attenuation estimation based on time-frequency analysis","volume":"16","author":"Gao","year":"2019","journal-title":"Appl. Geophys."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/13\/4692\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:37:05Z","timestamp":1760139425000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/13\/4692"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,22]]},"references-count":33,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["s22134692"],"URL":"https:\/\/doi.org\/10.3390\/s22134692","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,6,22]]}}}