Skip to main content

Applying GPR-FGRA hybrid algorithm for prediction and optimization of eco-friendly magnetorheological finishing Ti–6Al–4V alloy


To produce the mirror finish of the Ti–6Al–4V alloy workpieces, a newly developed polishing tool based on magnetic field assistance. This work has developed an environmentally friendly model of magnetic finishing with a carrier fluid natural origin combined with carbonyl and abrasive iron particles; and a new GPR-FGRA hybrid algorithm to predict, optimize and identify critical factors affecting material removal rate and surface quality. The best surface quality with the optimization method increased by 37.5% (Ra = 0.025 μm) when choosing the optimized cutting parameter with the GPR-FGRA hybrid algorithm compared with the Taguchi experimental analysis (Ra = 0.040 μm). The analysis results by the GPR-FGRA algorithm show that the prediction surface quality accuracy was more significant than 99.63%, and the working distances (K) had the most remarkable influence on the polishing effect, while the result of workpiece speed was the least important. This study provides excellent reference values for predicting, optimizing and identifying the main factors affecting surface quality and material removal rate in a polishing model for complex, expensive materials from low-cost and environmentally friendly materials.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14


  1. Yin, S., Nguyen, D., Chen, F., Tang, Q., Duc, L.A.: Application of compressed air in the online monitoring of surface roughness and grinding wheel wear when grinding Ti–6Al–4V titanium alloy. Int. J. Adv. Manuf. Technol. 101, 1315–1331 (2018)

    Article  Google Scholar 

  2. Nguyen, D., Yin, S., Tang, Q., Son, P.X., Duc, L.A.: Online monitoring of surface roughness and grinding wheel wear when grinding Ti–6Al–4V titanium alloy using ANFIS-GPR hybrid algorithm and Taguchi analysis. Precis. Eng. 55, 275–292 (2019)

    Article  Google Scholar 

  3. Ju, J., Li, J., Yang, C., Wang, K., Kang, M., Wang, J.: Evolution of the microstructure and optimization of the tensile properties of the Ti–6Al–4V alloy by selective laser melting and heat treatment. Mater. Sci. Eng. A 802, 140673 (2021)

    Article  Google Scholar 

  4. Tümer, D., Güngörürler, M., Havıtçıoğlu, H., Arman, Y.: Investigation of effective coating of the Ti–6Al–4V alloy and 316L stainless steel with graphene or carbon nanotubes with finite element methods. J. Mater. Res. Technol. 9, 15880–15893 (2020)

    Article  Google Scholar 

  5. Siva Surya, M., Gugulothu, S., Prasanthi, G.: Optimization of cutting parameters while turning Ti–6Al–4V using response surface methodology andmachine learning technique. Int. J. Interact. Des. Manuf. (IJIDeM) 15, 453–462 (2021)

    Article  Google Scholar 

  6. Qian, N., Fu, Y., Chen, J., Khan, A.M., Xu, J.: Axial rotating heat-pipe grinding wheel for eco–benign machining: a novel method for dry profile-grinding of Ti–6Al–4V alloy. J. Manuf. Process. 56, 216–227 (2020)

    Article  Google Scholar 

  7. Zhao, B., Jiang, G., Ding, W., Xiao, G., Huan, H., Wang, Y., et al.: Characterisation of the wear properties of a single-aggregated cubic boron nitride grain during Ti–6Al–4V alloy grinding. Wear 452–453, 203296 (2020)

    Article  Google Scholar 

  8. Siva Surya, M.: Optimization of turning parameters while turning Ti–6Al–4V titanium alloy for surface roughness and material removal rate using response surface methodology. Mater. Today Proc. 62, 3479–3484 (2022)

    Article  Google Scholar 

  9. Luo, H., Yin, S., Zhang, G., Liu, C., Tang, Q., Guo, M.: Optimized pre-thinning procedures of ion-beam thinning for TEM sample preparation by magnetorheological polishing. Ultramicroscopy 181, 165–172 (2017)

    Article  Google Scholar 

  10. Duy Trinh, N., Nhat Tan, N., Quang, N.M., Thi Thieu Thoa, P., Duc, L.A.: Application of magnetic liquid slurries and fuzzy grey analysis in polishing nickel-phosphorus coated SKD11 steel. Particul. Sci. Technol. 40, 401–414 (2021)

    Article  Google Scholar 

  11. Kumar, S., Jain, V.K., Sidpara, A.: Nanofinishing of freeform surfaces (knee joint implant) by rotational-magnetorheological abrasive flow finishing (R-MRAFF) process. Precis. Eng. 42, 165–178 (2015)

    Article  Google Scholar 

  12. Das, M., Barman, A.: Force analysis during spot finishing of titanium alloy using novel tool in magnetic field assisted finishing process. Int. J. Precis. Technol. 8, 190 (2019)

    Article  Google Scholar 

  13. Barman, A., Das, M.: Toolpath generation and finishing of bio-titanium alloy using novel polishing tool in MFAF process. Int. J. Adv. Manuf. Technol. 100, 1123–1135 (2019)

    Article  Google Scholar 

  14. Nagdeve, L., Jain, V.K., Ramkumar, J.: Preliminary investigations into nano-finishing of freeform surface (femoral) using inverse replica fixture. Int. J. Adv. Manuf. Technol. 100, 1081–1092 (2019)

    Article  Google Scholar 

  15. Barman, A., Das, M.: Magnetic field assisted finishing process for super-finished Ti alloy implant and its 3D surface characterization. J. Micromanuf. 1, 251659841878550 (2018)

    Article  Google Scholar 

  16. Singh, H., Prakash, C., Singh, S.: Plasma spray deposition of HA-TiO2 on β-phase Ti–35Nb–7Ta–5Zr alloy for hip stem: characterization of bio-mechanical properties, wettability, and wear resistance. J. Bionic Eng. 17, 1029–1044 (2020)

    Article  Google Scholar 

  17. Rao, P.S., Jain, P.K., Dwivedi, D.K.: Optimization of key process parameters on electro chemical honing (ECH) of external cylindrical surfaces of titanium alloy Ti 6Al 4V. Mater. Today Proc. 4, 2279–2289 (2017)

    Article  Google Scholar 

  18. Kong, D., Chen, Y., Li, N.: Gaussian process regression for tool wear prediction. Mech. Syst. Signal Process. 104, 556–574 (2018)

    Article  Google Scholar 

  19. Zhang, J., Wang, T., Xu, L., Wang, P., Zhang, M., Xu, M.: Development and validation of a prognostic model based on the albumin-to-fibrinogen ratio (AFR) and gamma-glutamyl transpeptidase-to-platelet ratio (GPR) in hepatocellular carcinoma patients. Clin. Chim. Acta 511, 107–116 (2020)

    Article  Google Scholar 

  20. Olabanji, O.M., Mpofu, K.: Appraisal of conceptual designs: coalescing fuzzy analytic hierarchy process (F-AHP) and fuzzy grey relational analysis (F-GRA). Results Eng. 9, 100194 (2021)

    Article  Google Scholar 

  21. Zeng, J.E.Y., Jin, Y., Zhang, B., Huang, Z., Wei, K., et al.: Heat dissipation investigation of the power lithium-ion battery module based on orthogonal experiment design and fuzzy grey relation analysis. Energy 211, 118596 (2020)

    Article  Google Scholar 

  22. Roozbahani, A., Ghased, H., Hashemy Shahedany, M.: Inter-basin water transfer planning with grey COPRAS and fuzzy COPRAS techniques: a case study in Iranian Central Plateau. Sci. Total Environ. 726, 138499 (2020)

    Article  Google Scholar 

  23. Siva Surya, M., Vepa, K.S., Karanam, M.: Optimization of machining parameters using ANOVA and grey relational analysis while turning aluminium 7075,". Int. J. Recent Technol. Eng. 8, 5682–5686 (2019)

    Google Scholar 

  24. Hema Latha, K., Usha Sri, P., Seetharamaiah, N.: Design and manufacturing aspects of magneto-rheological fluid (MRF) clutch. Mater. Today Proc. 4, 1525–1534 (2017)

    Article  Google Scholar 

  25. Shahinian, H., Cherukuri, H., Mullany, B.: Evaluation of fiber-based tools for glass polishing using experimental and computational approaches. Appl. Opt. 55, 4307–4316 (2016)

    Article  Google Scholar 

  26. Fengdong, Z., Xuejun, Z., Jingchi, Y.: Mathematics model of magnetorheological finishing. In: Proceedings of the SPIE (2000)

  27. Pal, A., Chatha, S.S., Sidhu, H.S.: Experimental investigation on the performance of MQL drilling of AISI 321 stainless steel using nano-graphene enhanced vegetable-oil-based cutting fluid. Tribol. Int. 151, 106508 (2020)

    Article  Google Scholar 

  28. Nguyen, D., Wu, J., Quang, N.M., Duc, L.A., Son, P.X.: Applying fuzzy grey relationship analysis and Taguchi method in polishing surfaces of magnetic materials by using magnetorheological fluid. Int. J. Adv. Manuf. Technol. 112, 1675–1689 (2021)

    Article  Google Scholar 

  29. Duc, L.A., Li, K., Nguyen, T.T., Yen, V.M., Truong, T.K.: A new effective operator for the hybrid algorithm for solving global optimisation problems. Int. J. Syst. Sci. 49, 1088–1102 (2018)

    MathSciNet  Article  Google Scholar 

  30. Parameswari, G., Jain, V.K., Ramkumar, J., Nagdeve, L.: Experimental investigations into nanofinishing of Ti6Al4V flat disc using magnetorheological finishing process. Int. J. Adv. Manuf. Technol. 100, 1055–1065 (2019)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Trinh Nguyen Duy.

Ethics declarations

Conflict of interest

The authors have nothing to disclose and no conflict of interests regarding the publication of this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tien, D.H., Duy, T.N. & Thoa, P.T.T. Applying GPR-FGRA hybrid algorithm for prediction and optimization of eco-friendly magnetorheological finishing Ti–6Al–4V alloy. Int J Interact Des Manuf (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI:


  • Magnetorheological finishing
  • Ti–6Al–4V alloy
  • Polishing
  • Surface roughness
  • Eco-friendly