{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:53:22Z","timestamp":1787028802310,"version":"build-2736575974"},"reference-count":44,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T00:00:00Z","timestamp":1579824000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Serra H\u00fanter program","award":["UPC-LE-304 (year 2018)"],"award-info":[{"award-number":["UPC-LE-304 (year 2018)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The objective of this work is to analyze the influence of the vibration-assisted turning process on the machinability of S235 carbon steel. During the experiments using this vibrational machining process, the vibrational amplitude and frequency of the cutting tool were adjusted to drive the tool tip in an elliptical or linear motion in the feed direction. Furthermore, a finite element analysis was deployed to investigate the mechanical response for different vibration-assisted cutting conditions. The results show how the specific cutting energy and the material\u2019s machinability behave when using different operational cutting parameters, such as vibration frequency and tool tip motion in the x-axis, y-axis, and elliptical (x-y plane) motion. Then, the specific cutting energy and material\u2019s machinability are compared with a conventional turning process, which helps to validate the finite element method (FEM) for the vibration-assisted process. As a result of the operating parameters used, the vibration-assisted machining process leads to a machinability improvement of up to 18% in S235 carbon steel. In particular, higher vibration frequencies were shown to increase the material\u2019s machinability due to the specific cutting energy decrease. Therefore, the finite element method can be used to predict the vibration-assisted cutting and the specific cutting energy, based on predefined cutting parameters.<\/jats:p>","DOI":"10.3390\/ma13030567","type":"journal-article","created":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T11:01:00Z","timestamp":1579863660000},"page":"567","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Estimation of Specific Cutting Energy in an S235 Alloy for Multi-Directional Ultrasonic Vibration-Assisted Machining Using the Finite Element Method"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5887-8006","authenticated-orcid":false,"given":"Luis C.","family":"Fl\u00f3rez Garc\u00eda","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Universidad Tecnol\u00f3gica de Pereira, Risaralda 660003, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8911-0115","authenticated-orcid":false,"given":"Hern\u00e1n A.","family":"Gonz\u00e1lez Rojas","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering (EPSEVG), Universitat Polit\u00e9cnica de Catalunya, 08800 Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8085-6869","authenticated-orcid":false,"given":"Antonio J.","family":"S\u00e1nchez Egea","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering (EEBE), Universitat Polit\u00e8cnica de Catalunya, 08019 Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.ijinfomgt.2019.03.002","article-title":"Connecting circular economy and industry 4.0","volume":"49","author":"Rajput","year":"2019","journal-title":"Int. J. Inf. Manag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.ijpe.2018.08.019","article-title":"The expected contribution of Industry 4.0 technologies for industrial performance","volume":"204","author":"Dalenogare","year":"2018","journal-title":"Int. J. Prod. Econ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3747","DOI":"10.1007\/s00170-018-1759-6","article-title":"A comprehensive review of finite element modeling of orthogonal machining process: Chip formation and surface integrity predictions","volume":"96","author":"Sadeghifar","year":"2018","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1081\/MST-200051211","article-title":"Effects of flow stress and friction models in finite element simulation of orthogonal cutting\u2014A sensitivity analysis","volume":"9","author":"Sartkulvanich","year":"2005","journal-title":"Mach. Sci. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.ijpe.2019.01.004","article-title":"Industry 4.0 technologies: Implementation patterns in manufacturing companies","volume":"210","author":"Frank","year":"2019","journal-title":"Int. J. Prod. Econ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1010","DOI":"10.1007\/s11665-016-1950-6","article-title":"A Hybrid Approach Based on Machining and Dynamic Tests Data for the Identification of Material Constitutive Equations","volume":"25","author":"Jomaa","year":"2016","journal-title":"J. Mater. Eng. Perform."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.1007\/s00170-012-4122-3","article-title":"Orthogonal Cutting of Hardened AISI D2 Steel with TiAlN-Coated Inserts\u2014Simulations and Experiments","volume":"64","author":"Jiang","year":"2013","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1016\/j.acme.2014.01.003","article-title":"Research and modeling workpiece edge formation process during orthogonal cutting","volume":"14","author":"Pres","year":"2014","journal-title":"Arch. Civ. Mech. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"103466","DOI":"10.1016\/j.ijmachtools.2019.103466","article-title":"Prediction of cutting forces during micro end milling considering chip thickness accumulation","volume":"147","author":"Wojciechowski","year":"2019","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.measurement.2018.10.033","article-title":"Numerical and experimental analysis of specific cutting energy in hot turning of Inconel 718","volume":"133","author":"Parida","year":"2019","journal-title":"Measurement"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s00170-014-6458-3","article-title":"Thermal Analysis of Chip Formation Using FEM and a Hybrid Explicit-Implicit Approach","volume":"77","author":"Coelho","year":"2015","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/j.procir.2018.05.027","article-title":"Elastic and plastic chip deformation mechanism in 1D vibration-assisted metal cutting","volume":"71","author":"Zhang","year":"2018","journal-title":"Procedia CIRP"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.ijmachtools.2016.04.008","article-title":"Review of micro\/nano machining by utilizing elliptical vibration cutting","volume":"106","author":"Zhang","year":"2016","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.precisioneng.2007.08.003","article-title":"Review of vibration-assisted machining","volume":"32","author":"Brehl","year":"2008","journal-title":"Precis. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s40799-016-0021-0","article-title":"Development of a Non-Resonant 3D Elliptical Vibration Cutting Apparatus for Diamond Turning","volume":"40","author":"Lin","year":"2016","journal-title":"Exp. Tech."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.ijmachtools.2015.11.012","article-title":"Surface generation of freeform surfaces in diamond turning by applying double-frequency elliptical vibration cutting","volume":"104","author":"Zhou","year":"2016","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.ijmecsci.2016.08.004","article-title":"Study on predictive model of cutting force and geometry parameters for oblique elliptical vibration cutting","volume":"117","author":"Jieqiong","year":"2016","journal-title":"Int. J. Mech. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/B978-0-08-096532-1.01111-0","article-title":"Ultrasonic Vibration Diamond Cutting and Ultrasonic Elliptical Vibration Cutting","volume":"Volume 11","author":"Shamoto","year":"2014","journal-title":"Comprehensive Materials Processing"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.precisioneng.2016.11.015","article-title":"Nanowire cutting by an ultrasonically vibrating micro tool","volume":"48","author":"Wang","year":"2017","journal-title":"Precis. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1016\/j.procir.2017.03.335","article-title":"Comparison between Dynamic and Non-Dynamic Cutting Tool Option in FEM Simulation for Producing Dimple Structure","volume":"58","author":"Dali","year":"2017","journal-title":"Procedia CIRP"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"121011","DOI":"10.1115\/1.4033605","article-title":"Theoretical and Experimental Investigation on Inclined Ultrasonic Elliptical Vibration Cutting of Alumina Ceramics","volume":"138","author":"Zhu","year":"2016","journal-title":"J. Manuf. Sci. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"061014","DOI":"10.1115\/1.4025740","article-title":"Finite Element Modeling of Cutting Force and Chip Formation During Thermally Assisted Machining of Ti6Al4V Alloy","volume":"135","author":"Xi","year":"2013","journal-title":"J. Manuf. Sci. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"118181","DOI":"10.1016\/j.jclepro.2019.118181","article-title":"An analytical model for predicting specific cutting energy in whirling milling process","volume":"240","author":"He","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Dahmus, J.B., and Gutowski, T.G. (2004, January 13\u201319). An Environmental Analysis of Machining. Proceedings of the ASME 2004 International Mechanical Engineering Congress and Exposition, Anaheim, CA, USA.","DOI":"10.1115\/IMECE2004-62600"},{"key":"ref_25","unstructured":"Astakhov, V.P. (2012). Geometry of Single-Point Turning Tools and Drills: Fundamentals and Practical Applications, Springer Series in Advanced Manufacturing."},{"key":"ref_26","first-page":"85","article-title":"The Impact of Machining Parameters on Peak Power and Energy Consumption in CNC Endmilling","volume":"3","author":"Simoneau","year":"2013","journal-title":"Energy Power"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1016\/j.ijmachtools.2009.06.007","article-title":"An analytical model to predict specific shear energy in high-speed turning of Inconel 718","volume":"49","author":"Pawade","year":"2009","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2019","DOI":"10.1177\/0954405416683431","article-title":"Minimisation of Specific Cutting Energy and Back Force in Turning of AISI 1060 Steel","volume":"232","author":"Paul","year":"2018","journal-title":"Proc. Inst. Mech. Eng. Part B J. Eng. Manuf."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1007\/s00170-016-8562-z","article-title":"Electroplastic cutting influence on power consumption during drilling process","volume":"87","author":"Hameed","year":"2016","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"958","DOI":"10.1016\/j.ijmachtools.2009.06.008","article-title":"Measurement of specific cutting energy for evaluating the efficiency of bandsawing different workpiece materials","volume":"49","author":"Sarwar","year":"2009","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/0045-7825(84)90026-4","article-title":"Explicit algorithms for the nonlinear dynamics of shells","volume":"42","author":"Belytschko","year":"1984","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"31","DOI":"10.4028\/www.scientific.net\/AMR.214.31","article-title":"Multiphysics Fully-Coupled Modelling of the Electromagnetic Compression of Steel Tubes","volume":"214","author":"Goes","year":"2011","journal-title":"Adv. Mater. Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1016\/j.jmatprotec.2011.03.018","article-title":"Effect of strain rate on the forming behaviour of sheet metals","volume":"211","author":"Verleysen","year":"2011","journal-title":"J. Mater. Process. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"26495","DOI":"10.1016\/j.matpr.2018.08.105","article-title":"Experimental investigation of the shear angle variation during orthogonal cutting","volume":"5","author":"Berezvai","year":"2018","journal-title":"Mater. Today Proc."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1016\/S0890-6955(02)00046-9","article-title":"From the basic mechanics of orthogonal metal cutting toward the identification of the constitutive equation","volume":"42","author":"Tounsi","year":"2002","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1715","DOI":"10.1016\/S0020-7403(99)00070-3","article-title":"Thermal Modeling of the Metal Cutting Process Part I - Temperature Rise Distribution Due to Shear Plane Heat Source","volume":"42","author":"Komanduri","year":"2000","journal-title":"Int. J. Mech. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1007\/s00170-010-2940-8","article-title":"Analytical Prediction of Cutting Forces in Orthogonal Cutting Using Unequal Division Shear-Zone Model","volume":"54","author":"Binglin","year":"2011","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_38","first-page":"1","article-title":"Evaluation of Ductile Fracture Models in Finite Element Simulation of Metal Cutting Processes","volume":"136","author":"Jian","year":"2014","journal-title":"J. Manutacturing Sci. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.procir.2017.03.202","article-title":"An Evaluation of Different Damage Models when Simulating the Cutting Process Using FEM","volume":"58","author":"Nasr","year":"2017","journal-title":"Procedia CIRP"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Hameed, S., Rojas, H.A.G., Benavides, J.I.P., Alberro, A.N., and Egea, A.J.S. (2018). Influence of the Regime of Electropulsing-Assisted Machining on the Plastic Deformation of the Layer Being Cut. Materials, 11.","DOI":"10.3390\/ma11060886"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1177\/0954408918812271","article-title":"Theoretical and numerical modeling of tool\u2013chip friction in ultrasonic-assisted turning","volume":"233","author":"Lotfi","year":"2018","journal-title":"Proc. Inst. Mech. Eng. Part E J. Process. Mech. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.ijmecsci.2019.06.038","article-title":"Development of a friction model based on oblique cutting theory","volume":"160","author":"Lotfi","year":"2019","journal-title":"Int. J. Mech. Sci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s12541-019-00021-3","article-title":"FE Modeling and Experimental Analysis of Residual Stresses in Vibration Assisted Turning of Ti6Al4V","volume":"20","author":"Naresh","year":"2019","journal-title":"Int. J. Precis. Eng. Manuf."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s40436-015-0115-4","article-title":"Ultrasonic Vibration-Assisted Machining: Principle, Design and Application","volume":"3","year":"2015","journal-title":"Adv. Manuf."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/13\/3\/567\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:20:36Z","timestamp":1760361636000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/13\/3\/567"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,24]]},"references-count":44,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["ma13030567"],"URL":"https:\/\/doi.org\/10.3390\/ma13030567","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,24]]}}}