The use of thin-walled structures and assemblies in high-tech industries such as aerospace, energy, defense, etc. solves many technical problems related to weight and size reduction, but also creates new ones. The machining of such structures is a challenge for industry, as they do not have sufficient rigidity to ensure dimensional accuracy and macro-relief requirements. The main factor affecting the quality of the machined surface is the vibrations that occur during machining, and a significant amount of research is devoted to mitigating their impact. This work is devoted to the formation of the macro-relief of the machined surface during end milling of thin-walled structures. The work shows that the cutting speed significantly affects the nature of vibrations, the patterns, and the mechanism of regular macro-relief formation. This is explained by belonging to one of the speed vibrational zones. The paper also considers the influence of the type of milling—down-cut and up-cut—on the formation of macro-relief and provides practical recommendations on the conditions for their application. The novelty of the study is in combining two approaches to zoning machining conditions and, accordingly, analysing vibration phenomena during the machining of thin-walled structures based on the Defining Ratio and using Stability Lobe Diagrams. Such a combination is possible for conditions in which Attendant Free Vibrations does not apply. As a criterion for selecting the conditions and type of machining, it is proposed to use the phase coefficient, which characterises the transition from the damped natural vibrations of the part to the cutting period of the next milling cutter tooth, which should significantly simplify the selection process. The article also formulates the direction of further research, which will contribute to solving the current production problem.
- Open Access
- Article
Speed Vibrational Zones and Macro-Relief Formation of Machined Surfaces of Thin-Walled Structures under End Milling
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Received: 03 Feb 2026 | Revised: 27 Feb 2026 | Accepted: 04 Mar 2026 | Published: 28 Apr 2026
Abstract
Graphical Abstract
Keywords
down-cut milling | up-cut milling | surface topography | attendant free vibration | waviness | phase coefficient | defining ratio
References
- 1.
Kurpiel, S.; Zagórski, K.; Cieślik, J.; et al. Evaluation of the Vibration Signal during Milling Vertical Thin-Walled Structures from Aerospace Materials. Sensors 2023, 23, 6398. https://doi.org/10.3390/s23146398.
- 2.
Kurpiel, S.; Zagórski, K.; Cieślik, J.; et al. Investigation of Selected Surface Topography Parameters and Deformation during Milling of Vertical Thin-Walled Structures from Titanium Alloy Ti6Al4V. Materials 2023, 16, 3182. https://doi.org/10.3390/ma16083182.
- 3.
Hou, J.; Wang, B.; Lv, D.; et al. Investigation of the Influence of Electrolytic Milling Machining Parameters on the Machining Accuracy of Thin-Walled Parts. Sci. Rep. 2024, 14, 28288. https://doi.org/10.1038/s41598-024-80052-7.
- 4.
Zablotskyi, V.; Tkachuk, A.; Prozorovskyi, S.; et al. Influence of Turning Operations on Waviness Characteristics of Working Surfaces of Rolling Bearings. In Advances in Design, Simulation and Manufacturing V, Proceedings of the 5th International Conference on Design, Simulation, Manufacturing: The Innovation Exchange, DSMIE-2022, Poznan, Poland, 7–10 June 2022; Ivanov, V., Trojanowska, J., Pavlenko, I., Eds.; Lecture Notes in Mechanical Engineering; Springer: Cham, Switzerland, 2022; pp. 345–354. https://doi.org/10.1007/978-3-031-06025-0_34.
- 5.
Maes, V.K.; Macquart, T.; Weaver, P.M.; et al. Sensitivity of Cross-Sectional Compliance to Manufacturing Tolerances for Wind Turbine Blades. Wind Energy Sci. 2025, 9, 165–180. https://doi.org/10.5194/wes-9-165-2025.
- 6.
Kolmakova, D.; Baturin, O.; Popov, G. Effect of Manufacturing Tolerances on the Turbine Blades. In Proceedings of the ASME 2014 Gas Turbine India Conference; New Delhi, India, 15–17 December 2014. https://doi.org/10.1115/gtindia2014-8253.
- 7.
Moneta, G.; Jachimowicz, J. Impact of Manufacturing Tolerances on Stress in a Turbine Blade Fir-Tree Root. Fatigue Aircr. Struct. 2020, 12, 92–101. https://doi.org/10.2478/fas-2020-0009.
- 8.
Zhao, B.; Ding, W.; Shan, Z.; et al. Collaborative Manufacturing Technologies of Structure Shape and Surface Integrity for Complex Thin-Walled Components of Aero-Engine: Status, Challenge, and Tendency. Chin. J. Aeronaut. 2023, 36, 1–24. https://doi.org/10.1016/j.cja.2023.02.008.
- 9.
Li, Y.; Ding, F.; Tian, W.; et al. Prediction of Modal Parameters for Thin-Walled Blade Milling Process Considering Material Removal Effect. PLoS ONE 2025, 20, e0323871. https://doi.org/10.1371/journal.pone.0323871.
- 10.
Dyadya, S.; Frolov, M.; Tanchenko, S.; et al. Attendant Free Vibrations and Assessment of Their Influence on the Machined Surface Macrogeometry While End Milling. In Advances in Design, Simulation and Manufacturing VIII, Proceedings of the 8th International Conference on Design, Simulation, Manufacturing: The Innovation Exchange, DSMIE-2025, Porto, Portugal, 17–20 June 2025; Ivanov, V., Silva, F., Trojanowska, J., Eds.; Lecture Notes in Mechanical Engineering; Springer: Cham, Switzerland, 2025; pp. 327–337. https://doi.org/10.1007/978-3-031-95211-1_27.
- 11.
Dyadya, S.; Frolov, M.; Tanchenko, S.; et al. Feed Rate Influence Research on the Machined Surface Waviness Parameters in End Up Milling of Thin-Walled Parts. In Smart Innovations in Energy and Mechanical Systems; Pavlenko, D., Tryshyn, P., Honchar, N., Eds.; Lecture Notes in Networks and Systems; Springer: Cham, Switzerland, 2025; pp. 79–89. https://doi.org/10.1007/978-3-031-95191-6_8.
- 12.
Kouahla, I.; Yallese, M.A.; Belhadi, S.; et al. Tool Vibration, Surface Roughness, Cutting Power, and Productivity Assessment Using RSM and GRA Approach during Machining of Inconel 718 with PVD-Coated Carbide Tool. Int. J. Adv. Manuf. Technol. 2022, 122, 1835–1856. https://doi.org/10.1007/s00170-022-09988-2.
- 13.
Wang, X.; Li, S.; Guo, Z.; et al. Research on TA2 Dry/Wet Milling Force–Vibration Characteristics and Vibration Prediction Model. Noise Vib. Worldw. 2026, 57, 59–67. https://doi.org/10.1177/09574565251382128.
- 14.
Zhao, W.; Liu, X.; Li, R. A Geometric-Matrix Method for Cutting Force Modeling. Mech. Syst. Signal Process. 2026, 242, 113663. https://doi.org/10.1016/j.ymssp.2025.113663.
- 15.
Dongre, P.; Zoting, J.; Gokhe, D. Exploring Surface Roughness and Tool Vibration through Experimental Investigation and Modeling with EDM-Textured Cutting Tools. In Recent Advances in Condition Monitoring; Andhare, A., Ganesh Kumar, P., Eds.; Springer: Singapore, 2024; pp. 221–231. https://doi.org/10.1007/978-981-96-5791-9_23.
- 16.
Ozoegwu, C.G.; Ofochebe, S.M.; Omenyi, S.N. A Method of Improving Chatter-Free Conditions with Combined-Mode Milling. J. Manuf. Process. 2016, 21, 1–13. https://doi.org/10.1016/j.jmapro.2015.10.008.
- 17.
Yi, J.; Wang, X.; Zhu, Y.; et al. Deformation Control in Mesoscale Micro-Milling of Curved Thin-Walled Structures. Materials 2024, 17, 5071. https://doi.org/10.3390/ma17205071.
- 18.
Kononenko, S.; Dobrotvorskiy, S.; Basova, Y.; et al. Impact of Overlapping Method on Cutting Forces and Surface Formation in End Milling of Thin-Walled Parts. In Smart Innovations in Energy and Mechanical Systems; Pavlenko, D., Tryshyn, P., Honchar, N., Eds.; Lecture Notes in Networks and Systems; Springer: Cham, Switzerland, 2025; pp. 67–78. https://doi.org/10.1007/978-3-031-95191-6_7.
- 19.
Abebe, R.; Gopal, M. Exploring the Effects of Vibration on Surface Roughness during CNC Face Milling on Aluminum 6061-T6 Using Sound Chatter. Mater. Today Proc. 2023, 90, 43–49. https://doi.org/10.1016/j.matpr.2023.04.332.
- 20.
Sedehi, S.M.R.; Norouzi Palangani, F.; Maleki, Z.; et al. Effect of Conventional and Climb Milling on the Mechanical Properties and Biocompatibility of Pure Titanium; Application of the Williamson-Hall Method. J. Mod. Process. Manuf. Prod. 2025, 17, 51–61. https://doi.org/10.58209/ijwph.17.1.51.
- 21.
Ciecielag, K.; Skoczylas, A.; Matuszak, J. Measurement of Cutting Forces in Conventional and Climb Milling by Recurrence Analysis. In Proceedings of the 2024 11th International Workshop on Metrology for AeroSpace (MetroAeroSpace), Lublin, Poland, 3–5 June 2024; pp. 531–536. https://doi.org/10.1109/MetroAeroSpace61015.2024.10591550.
- 22.
Lassila, A.A.; Svensson, D.; Wang, W.; et al. Numerical Evaluation of Cutting Strategies for Thin-Walled Parts. Sci. Rep. 2024, 14, 1459. https://doi.org/10.1038/s41598-024-51883-1.
- 23.
Wang, R.; Sun, Y. Chatter Prediction for Parallel Mirror Milling of Thin-Walled Parts by Dual-Robot Collaborative Machining System. Robot. Comput. Integr. Manuf. 2024, 88, 102715. https://doi.org/10.1016/j.rcim.2024.102715.
- 24.
Yue, C.; Gao, H.; Liu, X.; et al. A Review of Chatter Vibration Research in Milling. Chin. J. Aeronaut. 2019, 32, 215–242. https://doi.org/10.1016/j.cja.2018.11.007.
- 25.
McClements, D. Climb Milling vs. Conventional Milling: Their Key Differences. Available online: https://www.xometry.com/resources/machining/climb-milling-vs-conventional-milling/ (accessed on 15 January 2026).
- 26.
Li, X.; Ni, J.; Liu, X.; et al. Chatter-Free Milling of Aerospace Thin-Walled Parts. J. Mater. Process. Technol. 2025, 341, 118903. https://doi.org/10.1016/j.jmatprotec.2025.118903.
- 27.
Li, Y.W.; Sun, Y.S.; Zhou, X.G. Theoretical Analysis and Experimental Verification that Influence Factors of Climb and Conventional Milling on Surface Roughness. Appl. Mech. Mater. 2013, 459, 407–412. https://doi.org/10.4028/www.scientific.net/AMM.459.407.
- 28.
Munoa, J.; Beudaert, X.; Dombovari, Z.; et al. Chatter Suppression Techniques in Metal Cutting. CIRP Ann. 2016, 65, 785–808. https://doi.org/10.1016/j.cirp.2016.06.004.
- 29.
Vnukov, Y.N.; Dyadya, S.I.; Kozlova, E.B.; et al. Auto Oscillations at Milling of Thin-Walled Elements of the Details; ZNTU: Zaporizhzhia, Ukraine, 2017.
- 30.
Germashev, А.I.; Byelikov, S.B.; Logominov, V.A. Automation of the Process of Selecting the Milling Modes of Thin-Wall Elements of Parts. Herald Aeroenginebuild. 2018, 1, 83–89. https://doi.org/10.15588/1727-0219-2018-1-12.
- 31.
Frolov, M.; Dyadya, S.; Tanchenko, S.; et al. Attendant Free Vibrations and Their Role in the Formation of Macrorelief at the End Milling of Thin-Walled Structures When Changing the Radial Depth of Cut. J. Mech. Eng. Manuf. 2026, 2, 2. https://doi.org/10.53941/jmem.2026.100002.
- 32.
Ramachandran, K.M.; Tsokos, C.P. Mathematical Statistics with Applications; Elsevier Academic Press: Amsterdam, The Netherlands, 2009.
- 33.
Stone, B. Chatter and Machine Tools; Springer: Cham, Switzerland, 2014. https://doi.org/10.1007/978-3-319-05236-6.
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