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Hybrid prediction model for residual stress profile induced by multi-axis milling Ti-6Al-4 V titanium alloy combined finite element with experiment

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Abstract

Complex curved thin-walled structures, typically produced by multi-axis milling, are highly susceptible to deformation induced by residual stress. It is, therefore, that there is a considerable amount of research on developing predictive models for machining-induced residual stress. However, these developed models for residual stress prediction mainly focus on turning and three-axis milling. In the current study, a hybrid model combining experimental results and a finite element (FE) model is established to predict the residual stress profile of Ti-6Al-4 V titanium alloy for multi-axis milling. The residual stress profile is fitted by using the hyperbolic tangent function with the firefly algorithm (FA) based on the simulation and experiment. The R2 values change from 85.3 to 99.1% in the σx direction and change from 80.7 to 98.1% in the σy direction, which indicates a high fitting accuracy. The radial basis function (RBF) neural network is employed to establish the association between the process parameters and the model coefficients. Thus, the residual stress profile can be expressed by the cutting speed, feed rate, and inclination angle. And the prediction accuracy is verified to achieve 92.7% and 91.4% in the σx and σy directions, respectively. The effects of the cutting speed, feed rate, and inclination angle on surface residual stress and response depth are investigated. The findings demonstrate a strong nonlinear connection between process parameters and surface residual stress. The proposed hybrid prediction model of residual stress can be used for further machining optimization of complex curved thin-walled structures.

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All data and materials used or analyzed during the current study are included in this manuscript.

References

  1. Akhtar W, Lazoglu I, Liang SY (2022) Prediction and control of residual stress-based distortions in the machining of aerospace parts: a review. J Manuf Process 76:106–122. https://doi.org/10.1016/j.jmapro.2022.02.005

    Article  Google Scholar 

  2. Xu L, Huang C, Li C, Wang J, Liu H, Wang X (2021) An improved case based reasoning method and its application in estimation of surface quality toward intelligent machining. J Intell Manuf 32:313–327. https://doi.org/10.1007/s10845-020-01573-2

    Article  Google Scholar 

  3. Zhao X, Zheng L, Wang Y, Zhang Y (2022) Services-oriented intelligent milling for thin-walled parts based on time-varying information model of machining system. Int J Mech Sci 219:107125. https://doi.org/10.1016/j.ijmecsci.2022.107125

    Article  Google Scholar 

  4. Imad M, Hopkins C, Hosseini A, Yussefian, N Z, Kishawy, H A (2021) Intelligent machining: a review of trends, achievements and current progress. Int J Comput Integr Manuf 1–29. https://doi.org/10.1080/0951192x.2021.1891573

  5. Zhou J, Ren J, Tian W (2017) Grey-RBF-FA method to optimize surface integrity for inclined end milling Inconel 718. Int J Adv Manuf Technol 91:2975–2993. https://doi.org/10.1007/s00170-016-9897-1

    Article  Google Scholar 

  6. Madariaga A, Kortabarria A, Hormaetxe E, Garay A, Arrazola PJ (2016) Influence of tool wear on residual stresses when turning Inconel 718. Procedia CIRP 45:267–270. https://doi.org/10.1016/j.procir.2016.02.359

    Article  Google Scholar 

  7. Zlatin N, Field M (1973) Procedures and precautions in machining titanium alloys. Titan Sci Technol 489–504. https://doi.org/10.1007/978-1-4757-1346-6_37

  8. Sun J, Guo YB (2009) A comprehensive experimental study on surface integrity by end milling Ti–6Al–4V. J Mater Process Technol 209:4036–4042. https://doi.org/10.1016/j.jmatprotec.2008.09.022

    Article  Google Scholar 

  9. Ullah I, Zhang S, Waqar S (2022) Numerical and experimental investigation on thermo-mechanically induced residual stress in high-speed milling of Ti-6Al-4V alloy. J Manuf Process 76:575–587. https://doi.org/10.1016/j.jmapro.2022.02.039

    Article  Google Scholar 

  10. Ratchev SM, Afazov SM, Becker AA, Liu S (2011) Mathematical modelling and integration of micro-scale residual stresses into axisymmetric FE models of Ti6Al4V alloy in turning. CIRP J Manuf Sci Technol 4:80–89. https://doi.org/10.1016/j.cirpj.2011.03.002

    Article  Google Scholar 

  11. Holmberg J, Prieto JMR, Berglund J, Sveboda A, Jonsén P (2018) Experimental and PFEM-simulations of residual stresses from turning tests of a cylindrical Ti-6Al-4V shaft. Procedia CIRP 71:144–149. https://doi.org/10.1016/j.procir.2018.05.087

    Article  Google Scholar 

  12. Ulutan D, Özel T (2013) Multiobjective optimization of experimental and simulated residual stresses in turning of nickel-alloy IN100. Mater Manuf Process 28:835–841. https://doi.org/10.1080/10426914.2012.718474

    Article  Google Scholar 

  13. Arısoy YM, Özel T (2015) Prediction of machining induced microstructure in Ti–6Al–4V alloy using 3-D FE-based simulations: effects of tool micro-geometry, coating and cutting conditions. J Mater Process Technol 220:1–26. https://doi.org/10.1016/j.jmatprotec.2014.11.002

    Article  Google Scholar 

  14. Shan C, Zhang M, Zhang S, Dang J (2020) Prediction of machining-induced residual stress in orthogonal cutting of Ti6Al4V. Int J Adv Manuf Technol 107(5):2375–2385. https://doi.org/10.1007/s00170-020-05181-5

    Article  Google Scholar 

  15. Ulutan D, Özel T (2013) Determination of tool friction in presence of flank wear and stress distribution based validation using finite element simulations in machining of titanium and nickel based alloys. J Mater Process Technol 213:2217–2237. https://doi.org/10.1016/j.jmatprotec.2013.05.019

    Article  Google Scholar 

  16. Sahu NK, Andhare AB (2019) Prediction of residual stress using RSM during turning of Ti–6Al–4V with the 3D FEM assist and experiments. SN Appl Sci 1:1–14. https://doi.org/10.1007/s42452-019-0809-5

    Article  Google Scholar 

  17. Arrazola PJ, Özel T, Umbrello D, Davies M, Jawahir IS (2013) Recent advances in modelling of metal machining processes. CIRP Ann - Manuf Technol 62:695–718. https://doi.org/10.1016/j.cirp.2013.05.006

    Article  Google Scholar 

  18. Capello E (2005) Residual stresses in turning: part I: influence of process parameters. J Mater Process Technol 160:221–228. https://doi.org/10.1016/j.jmatprotec.2004.06.012

    Article  Google Scholar 

  19. El-Axir MH (2002) A method of modeling residual stress distribution in turning for different materials. Int J Mach Tools Manuf 42:1055–1063. https://doi.org/10.1016/S0890-6955(02)00031-7

    Article  Google Scholar 

  20. Yang D, Liu Z, Ren X, Zhuang P (2016) Hybrid modeling with finite element and statistical methods for residual stress prediction in peripheral milling of titanium alloy Ti-6Al-4V. Int J Mech Sci 108:29–38. https://doi.org/10.1016/j.ijmecsci.2016.01.027

    Article  Google Scholar 

  21. Wang J, Zhang D, Wu B, Luo M (2017) Numerical and empirical modelling of machining-induced residual stresses in ball end milling of Inconel 718. Procedia CIRP 58:7–12. https://doi.org/10.1016/j.procir.2017.03.177

    Article  Google Scholar 

  22. Ulutan D, Arisoy YM, Özel T, Mears L (2014) Empirical modeling of residual stress profile in machining nickel-based superalloys using the sinusoidal decay function. Procedia CIRP 13:365–370. https://doi.org/10.1016/j.procir.2014.04.062

    Article  Google Scholar 

  23. Zhou J (2018) Modeling of cutting residual stress and distortion prediction for machining thin-walled structure. Dissertation, Northwestern Polytechnical University (in Chinese). https://doi.org/10.27406/d.cnki.gxbgu.2018.000039

  24. Arısoy YM, Guo C, Kaftanoğlu B, Özel T (2016) Investigations on microstructural changes in machining of Inconel 100 alloy using face turning experiments and 3D finite element simulations. Int J Mech Sci 107:80–92. https://doi.org/10.1016/j.ijmecsci.2016.01.009

    Article  Google Scholar 

  25. Ee KC, Dillon OW Jr, Jawahir IS (2005) Finite element modeling of residual stresses in machining induced by cutting using a tool with finite edge radius. Int J Mech Sci 47:1611–1628. https://doi.org/10.1016/j.ijmecsci.2005.06.001

    Article  MATH  Google Scholar 

  26. Ren J, Cai J, Zhou J, Shi K, Li X (2018) Inverse determination of improved constitutive equation for cutting titanium alloy Ti-6Al-4V based on finite element analysis. Int J Adv Manuf Technol 97:3671–3682. https://doi.org/10.1007/s00170-018-2178-4

    Article  Google Scholar 

  27. Wang Q, Liu Z, Yang D, Mohsan AUH (2017) Metallurgical-based prediction of stress-temperature induced rapid heating and cooling phase transformations for high speed machining Ti-6Al-4V alloy. Mater Des 119:208–218. https://doi.org/10.1016/j.matdes.2017.01.076

    Article  Google Scholar 

  28. Pan Z, Liang SY, Garmestani H, Shih D, Hoar E (2019) Residual stress prediction based on MTS model during machining of Ti-6Al-4V. Proc Inst Mech Eng Part C J Mech Eng Sci 233:3743–3750. https://doi.org/10.1177/0954406218805122

    Article  Google Scholar 

  29. Grove T, Köhler J, Denkena B (2014) Residual stresses in milled β-annealed Ti6Al4V. Procedia CIRP 13:320–326. https://doi.org/10.1016/j.procir.2014.04.054

    Article  Google Scholar 

  30. Jiang W, Chen W, Woo W, Tu S, Zhang X, EM V, (2018) Effects of low-temperature transformation and transformation-induced plasticity on weld residual stresses: numerical study and neutron diffraction measurement. Mater Des 147:65–79. https://doi.org/10.1016/j.matdes.2018.03.032

    Article  Google Scholar 

  31. Cui X, Wu X, Wan M, Ma B, Zhang Y (2019) A novel constitutive model for stress relaxation of Ti-6Al-4V alloy sheet. Int J Mech Sci 161:105034. https://doi.org/10.1016/j.ijmecsci.2019.105034

    Article  Google Scholar 

  32. Denkena B, Nespor D, Böß V, Köhler J (2014) Residual stresses formation after re-contouring of welded Ti-6Al-4V parts by means of 5-axis ball nose end milling. CIRP J Manuf Sci Technol 7:347–360. https://doi.org/10.1016/j.cirpj.2014.07.001

    Article  Google Scholar 

  33. Wan M, Ye XY, Yang Y, Zhang W-H (2017) Theoretical prediction of machining-induced residual stresses in three-dimensional oblique milling processes. Int J Mech Sci 133:426–437. https://doi.org/10.1016/j.ijmecsci.2017.09.005

    Article  Google Scholar 

  34. Nespor D, Denkena B, Grove T, Böß V (2015) Differences and similarities between the induced residual stresses after ball end milling and orthogonal cutting of Ti–6Al–4V. J Mater Process Technol 226:15–24. https://doi.org/10.1016/j.jmatprotec.2015.06.033

    Article  Google Scholar 

  35. Yang X-S, He X (2013) Firefly algorithm: recent advances and applications. arXiv Prepr arXiv13083898 1:36–50. https://doi.org/10.1504/IJSI.2013.055801

  36. Jain AK, Mao J, Mohiuddin KM (1996) Artificial neural networks: a tutorial. Computer (Long Beach Calif) 29:31–44. https://doi.org/10.4018/978-1-4666-5888-2.ch626

    Article  Google Scholar 

  37. Liang X, Liu Z, Wang B, Hou X (2018) Modeling of plastic deformation induced by thermo-mechanical stresses considering tool flank wear in high-speed machining Ti-6Al-4V. Int J Mech Sci 140:1–12. https://doi.org/10.1016/j.ijmecsci.2018.02.031

    Article  Google Scholar 

Download references

Funding

This work is supported by the National Natural Science Foundation of China (Grant No. 52075451), the National Science and Technology Major Project (Grant No. J2019-VII-0001–0141), the Aeronautical Science Foundation of China (Grant No. 2019ZE053008), Science Center for Gas Turbine Project (P2022-B-IV-012–001), and the China Postdoctoral Science Foundation (Grant No. 2020M683551).

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Authors and Affiliations

  1. Key Laboratory of High Performance Manufacturing for Aero Engine, Ministry of Industry and Information Technology, School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China

    Zongyuan Wang, Jinhua Zhou, Junxue Ren & Ailing Shu

  2. Engineering Research Center of Advanced Manufacturing Technology for Aero Engine, Ministry of Education, School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China

    Zongyuan Wang, Jinhua Zhou, Junxue Ren & Ailing Shu

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  1. Zongyuan Wang
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Contributions

Zongyuan Wang: methodology, investigation, formal analysis, and writing draft. Jinghua Zhou: project administration, formal analysis, review, and editing. Junxue Ren: supervision and review. Ailing Shu: review.

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Correspondence to Jinhua Zhou.

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Wang, Z., Zhou, J., Ren, J. et al. Hybrid prediction model for residual stress profile induced by multi-axis milling Ti-6Al-4 V titanium alloy combined finite element with experiment. Int J Adv Manuf Technol 126, 4495–4511 (2023). https://doi.org/10.1007/s00170-023-11406-0

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