{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T05:23:55Z","timestamp":1780723435302,"version":"3.54.1"},"reference-count":30,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2020,10,8]],"date-time":"2020-10-08T00:00:00Z","timestamp":1602115200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Major Research Plan of the National Natural Science Foundation of China","award":["91960109"],"award-info":[{"award-number":["91960109"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61575056"],"award-info":[{"award-number":["61575056"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51805117"],"award-info":[{"award-number":["51805117"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The accurate measurement of stress at different depths in the end face of a high-pressure compressor rotor is particularly important, as it is directly related to the assembly quality and overall performance of aero-engines. The ultrasonic longitudinal critically refracted (LCR) wave is sensitive to stress and can measure stress at different depths, which has a prominent advantage in stress non-destructive measurements. In order to accurately characterize the propagation depth of LCR waves and improve the spatial resolution of stress measurement, a finite element model suitable for the study of LCR wave propagation depths was established based on a wave equation and Snell law, and the generation and propagation process of LCR waves are analyzed. By analyzing the blocking effect of grooves with different depths on the wave, the propagation depth of the LCR wave at seven specific frequencies was determined in turn. On this basis, the LCR wave propagation depth model is established, and the effects of wedge materials, piezoelectric element diameters, and excitation voltages on the propagation depth of LCR waves are discussed. This study is of great significance to improve the spatial resolution of stress measurements at different depths in the end face of the aero-engine rotor.<\/jats:p>","DOI":"10.3390\/s20195724","type":"journal-article","created":{"date-parts":[[2020,10,9]],"date-time":"2020-10-09T10:19:23Z","timestamp":1602238763000},"page":"5724","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Study on Propagation Depth of Ultrasonic Longitudinal Critically Refracted (LCR) Wave"],"prefix":"10.3390","volume":"20","author":[{"given":"Yongmeng","family":"Liu","sequence":"first","affiliation":[{"name":"Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, China"},{"name":"Key Lab of Ultra-Precision Intelligent Instrumentation Engineering (Harbin Institute of Technology), Ministry of Industry and Information Technology, Harbin 150080, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Enxiao","family":"Liu","sequence":"additional","affiliation":[{"name":"Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, China"},{"name":"Key Lab of Ultra-Precision Intelligent Instrumentation Engineering (Harbin Institute of Technology), Ministry of Industry and Information Technology, Harbin 150080, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanlin","family":"Chen","sequence":"additional","affiliation":[{"name":"Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, China"},{"name":"Key Lab of Ultra-Precision Intelligent Instrumentation Engineering (Harbin Institute of Technology), Ministry of Industry and Information Technology, Harbin 150080, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoming","family":"Wang","sequence":"additional","affiliation":[{"name":"Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, China"},{"name":"Key Lab of Ultra-Precision Intelligent Instrumentation Engineering (Harbin Institute of Technology), Ministry of Industry and Information Technology, Harbin 150080, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chuanzhi","family":"Sun","sequence":"additional","affiliation":[{"name":"Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, China"},{"name":"Key Lab of Ultra-Precision Intelligent Instrumentation Engineering (Harbin Institute of Technology), Ministry of Industry and Information Technology, Harbin 150080, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiubin","family":"Tan","sequence":"additional","affiliation":[{"name":"Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, China"},{"name":"Key Lab of Ultra-Precision Intelligent Instrumentation Engineering (Harbin Institute of Technology), Ministry of Industry and Information Technology, Harbin 150080, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1016\/j.ast.2017.10.003","article-title":"Experimental testing for the influences of rotation and tip clearance on the labyrinth seal in a compressor stator well","volume":"71","author":"Kong","year":"2017","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.paerosci.2017.05.003","article-title":"Review of design optimization methods for turbomachinery aerodynamics","volume":"93","author":"Li","year":"2017","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"26997","DOI":"10.3390\/s151026997","article-title":"Fault Diagnosis of Demountable Disk-Drum Aero-Engine Rotor Using Customized Multiwavelet Method","volume":"15","author":"Chen","year":"2015","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1016\/j.ijpvp.2010.07.001","article-title":"Control of vibration and resonance in aero engines and rotating machinery\u2014An overview","volume":"87","author":"Ewins","year":"2010","journal-title":"Int. J. Press. Vessels Pip."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.ymssp.2011.12.001","article-title":"Studies on dynamic characteristics of the joint in the aero-engine rotor system","volume":"29","author":"Liu","year":"2012","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/BF00045080","article-title":"Impact phenomena of rotor-casing dynamical-systems","volume":"5","author":"Li","year":"1994","journal-title":"Nonlinear Dyn."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"106164","DOI":"10.1016\/j.ultras.2020.106164","article-title":"Residual stress relief of welded aluminum alloy plate using ultrasonic vibration","volume":"107","author":"Zhang","year":"2020","journal-title":"Ultrasonics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1016\/j.matdes.2012.11.023","article-title":"Influence of ultrasonic stress relief on stainless steel 316 specimens: A comparison with thermal stress relief","volume":"46","author":"Shalvandi","year":"2013","journal-title":"Mater. Des."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/j.ultras.2011.11.004","article-title":"Ultrasonic-assisted manufacturing processes: Variational model and numerical simulations","volume":"52","author":"Siddiq","year":"2012","journal-title":"Ultrasonics"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"138093","DOI":"10.1016\/j.msea.2019.138093","article-title":"Measurement of residual stress in laser additive manufacturing TC4 titanium alloy with the laser ultrasonic technique","volume":"762","author":"Zhan","year":"2019","journal-title":"Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhao, W.S., Zhong, K., and Chen, W.Z. (2020). A Fiber Bragg Grating Borehole Deformation Sensor for Stress Measurement in Coal Mine Rock. Sensors, 20.","DOI":"10.3390\/s20113267"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.ultras.2018.08.013","article-title":"On-line measurement of clamping force for injection molding machine using ultrasonic technology","volume":"91","author":"Zhao","year":"2019","journal-title":"Ultrasonics"},{"key":"ref_13","first-page":"87","article-title":"An experimental method for measuring the clamping force in double lap simple bolted and hybrid (bolted-bonded) joints","volume":"39","author":"Goldarag","year":"2015","journal-title":"Trans. FAMENA"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Chen, Z.Y., Guo, M.F., Zhang, R., Zhou, B., and Wei, Q. (2018). Measurement and Isolation of Thermal Stress in Silicon-On-Glass MEMS Structures. Sensors, 18.","DOI":"10.3390\/s18082603"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.ndteint.2008.09.005","article-title":"Measurement of axial stress using mode converted ultrasonic","volume":"42","author":"Kim","year":"2009","journal-title":"NDT E Int."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4191","DOI":"10.1016\/j.actamat.2010.04.010","article-title":"Novel approaches to determining residual stresses by ultra micro indentation techniques: Application to sandblasted austenitic stainless steel","volume":"58","author":"Frutos","year":"2010","journal-title":"Acta Mater."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.ijpvp.2007.10.007","article-title":"Recent advances in residual stress measurement","volume":"85","author":"Withers","year":"2008","journal-title":"Int. J. Press. Vessels Pip."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2595","DOI":"10.1177\/0954406215619648","article-title":"Ultrasonic tightening control of a screw joint: A comparison of the clamp force accuracy from different tightening methods","volume":"230","author":"Persson","year":"2016","journal-title":"Proc. Inst. Mech. Eng. Part C J. Eng. Mech. Eng. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Li, Z.H., He, J.B., Liu, D.K., Liu, N.X., Long, Z.L., and Teng, J. (2019). Influence of Uniaxial Stress on the Shear-Wave Spectrum Propagating in Steel Members. Sensors, 19.","DOI":"10.3390\/s19030492"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.ndteint.2019.04.003","article-title":"Determination of acoustoelastic\/acoustoplastic constants to measure stress in elastic\/plastic limits by using LCR wave","volume":"104","author":"Mohammadi","year":"2019","journal-title":"NDT E Int."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1016\/j.measurement.2018.03.022","article-title":"Absolute stress field measurement in structural steel members using the Lcr wave method","volume":"122","author":"He","year":"2018","journal-title":"Measurement"},{"key":"ref_22","first-page":"160","article-title":"Numerical simulation of residual stress measurement with acoustic wave","volume":"2","author":"Pei","year":"2011","journal-title":"E-J. Adv. Maint."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.ultras.2012.03.014","article-title":"Numerical and experimental analysis of the critically refracted longitudinal beam","volume":"53","author":"Chaki","year":"2013","journal-title":"Ultrasonics"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/s11340-009-9283-0","article-title":"Microstructure effect on the Lcr elastic wave for welding residual stress measurement","volume":"50","author":"Qozam","year":"2010","journal-title":"Exp. Mech."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1016\/j.matdes.2013.02.050","article-title":"Ultrasonic inspection of a welded stainless steel pipe to evaluate residual stresses through thickness","volume":"59","author":"Javadi","year":"2013","journal-title":"Mater. Des."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1016\/j.matdes.2013.06.032","article-title":"Using ultrasonic waves and finite element method to evaluate through-thickness residual stresses distribution in the friction stir welding of aluminum plates","volume":"52","author":"Sadeghi","year":"2013","journal-title":"Mater. Des."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.ultras.2006.03.004","article-title":"Relationship between Rayleigh wave polarization and state of stress","volume":"44","author":"Junge","year":"2006","journal-title":"Ultrasonics"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/S0963-8695(98)00046-2","article-title":"Ultrsonic evaluation of stresses in orthotropic materials using Rayleigh waves","volume":"32","author":"Dequennoy","year":"1999","journal-title":"NDT E Int."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.3233\/JAE-2010-1223","article-title":"Development of simulation method for EMAT signals and application to TBC inspection","volume":"33","author":"Pei","year":"2010","journal-title":"Int. J. Appl. Electromagn. Mech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"041502","DOI":"10.1115\/1.4023432","article-title":"Ultrasonic Evaluation of Welding Residual Stresses in Stainless Steel Pressure Vessel","volume":"135","author":"Javadi","year":"2013","journal-title":"J. Press. Vessel Technol. Trans. ASME"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/19\/5724\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:17:37Z","timestamp":1760177857000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/19\/5724"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,8]]},"references-count":30,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2020,10]]}},"alternative-id":["s20195724"],"URL":"https:\/\/doi.org\/10.3390\/s20195724","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,8]]}}}