Multi-objective optimization of turning titanium-based alloy Ti-6Al-4V under dry, wet, and cryogenic conditions using gray relational analysis (GRA)

  • Muhammad Ali Khan
  • Syed Husain Imran JafferyEmail author
  • Mushtaq Khan
  • Muhammad Younas
  • Shahid Ikramullah Butt
  • Riaz Ahmad
  • Salman Sagheer Warsi


In modern manufacturing industries, the importance of multi-objective optimization cannot be overemphasized particularly when the desired responses are differing in nature towards each other. With the emergence of new technologies, the need to achieve overall efficiency in terms of energy, output, and tooling is on the rise. Resultantly, endeavor is to make the machining process sustainable, productive, and efficient simultaneously. In this research, the effects of machining parameters (feed, cutting speed, depth of cut, and cutting condition including dry, wet, and cryogenic) were analyzed. Since sustainable production demands a balance between production quality and energy consumption, therefore, response parameters including specific cutting energy, tool wear, surface roughness, and material removal rate were considered. Taguchi-gray integrated approach was adopted in this study. Multi-objective function was developed using gray relational methodology, and its regression analysis was conducted. Response surface optimization was carried out to optimize the formulated multi-objective function and derive the optimum machining parameters. Concurrent responses were optimized with best-suited values of input parameters to make the most out of the machining process. Analysis of variance results showed that feed is the most effective parameter followed by cutting condition in terms of overall contribution in multi-objective function. The proposed optimum parameters resulted in improvement of tool wear and surface roughness by 30% and 22%, respectively, whereas specific cutting energy was reduced by 4%.


Titanium Ti-6Al-4 V Cryogenic machining Sustainable machining Multi-objective optimization Gray relational grade Response surface methodology 



Analytic hierarchy process


Material removal rate (cm3/s)


Analysis of Variance


Wear rate


Workpiece diameter (mm)


Surface roughness (μm)


Depth of cut (mm)


Response surface methodology


Feed (mm/rev)


Specific cutting energy


Gray relational analysis


Cutting time


Gray relational coefficient


Technique for order of preference by similarity to ideal solution


Gray relational grade


Cutting speed (m/min)


Spiral length of cut (mm)


Flank wear (mm)


Multi-objective optimization



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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  • Muhammad Ali Khan
    • 1
  • Syed Husain Imran Jaffery
    • 1
    Email author
  • Mushtaq Khan
    • 1
  • Muhammad Younas
    • 1
  • Shahid Ikramullah Butt
    • 1
  • Riaz Ahmad
    • 1
  • Salman Sagheer Warsi
    • 2
  1. 1.School of Mechanical and Manufacturing EngineeringNational University of Sciences and Technology (NUST)IslamabadPakistan
  2. 2.Capital University of Science and Technology (CUST)IslamabadPakistan

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