Abstract
In this work, an experimental study was carried out to investigate the influence of the cutting parameters namely cutting speed \(({V}_{c})\), feed per tooth \(({f}_{z})\), and depth of cut \(({a}_{p})\) on three machining performance aspects, including cutting temperature \(({Q}_{s})\), surface roughness \(({R}_{a})\), and microhardness \((H)\) when milling of AISI 1060 steel. Response surface methodology \(({\text{RSM}})\) was used for evaluating and predicting the impact of the considered cutting parameters on the selected machining characteristic indices. The results revealed that the error rates of the developed models compared to experimental ones were found to be as follows: 3.19% for \({Q}_{s}\), 5.32% for \({R}_{a}\), 1.63% for \(H\), These error rates underscore the robustness and reliability of the developed models in accurately predicting the respective machining characteristics. Moreover, this study stands out in its approach by leveraging the experimentally developed RSM models as constraints within the optimization framework, providing a more precise and tailored approach compared to relying on generalized empirical models commonly found in industry handbooks. This is why a multi-objective optimization using genetic algorithm (GA) was performed to minimize both the production time and the production cost per unit by defining the problem with three key cutting parameters and utilizing the experimentally derived response surface methodology (RSM) models as constraints. For instance, the \(({R}_{a})\) and \(H\) -based RSM model served as constraints ensuring surface roughness and microhardness values below a specified threshold while satisfying other machining constraints (tool life, cutting force, cutting power). As a result, a set of optimal solutions of combinations of cutting parameters is achieved for simultaneously minimum production time and cost per unit.
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Abbreviations
- \({a}_{p}\) :
-
Depth of cut (\({\text{mm}}\))
- \({a}_{P{\text{min}}}\) :
-
The minimum depth of cut\(\mathrm{ mm}\) (mm)
- \({a}_{P{\text{max}}}\) :
-
The maximum depth of cut (\({\text{mm}}\))
- \({a}_{e}\) :
-
Cutting width (\({\text{mm}}\))
- \(C\) :
-
Machining index
- \({C}_{c}\) :
-
The total cost per unit product (\({\text{Euro}}\))
- \({C}_{h}\) :
-
Cost of part handling time (\({\text{Euro}}\))
- \({C}_{m}\) :
-
Cost of machining time (\({\text{Euro}}\))
- \({C}_{th}\) :
-
Cost of tool change time (\({\text{Euro}}\))
- \({C}_{tc}\) :
-
Tooling cost (\({\text{Euro}}\))
- \({C}_{0}\) :
-
The cost rate (\({\text{Euro}}/{\text{min}}\))
- \({C}_{t}\) :
-
The cost per cutting edge (\({\text{Euro}}\))
- \(D\) :
-
The cutter diameter (\({\text{mm}}\))
- \({f}_{z}\) :
-
Feed per tooth (\({\text{mm}}/{\text{tooth}}\))
- \({f}_{{z}_{{\text{min}}}}\) :
-
The minimum feed per tooth (\({\text{mm}}/{\text{tooth}}\))
- \({f}_{{z}_{{\text{max}}}}\) :
-
The maximum feed per tooth (\({\text{mm}}/{\text{tooth}}\))
- \({F}_{u}\) :
-
The maximum cutting force (\(N\))
- \({F}_{c}\) :
-
Cutting force (\(N\))
- \(H\) :
-
Microhardness (\({H}_{v}\))
- \({H}_{s}\) :
-
Specified value of microhardness (\({H}_{v}\))
- \({K}_{c}\) :
-
Specific cutting force (\({N/{\text{mm}}}^{2}\))
- \(L\) :
-
Workpiece length (\({\text{mm}}\))
- \(n\) :
-
Tool life index
- \({n}_{e}\) :
-
Number of cutting edges per insert
- \({n}_{p}\) :
-
The number of pieces cut in one tool life (the number of pieces cut with one cutting edge until the tool is changed)
- \(MRR\) :
-
Material removal rate (\({{\text{mm}}}^{3}/{\text{min}}\))
- \({P}_{c}\) :
-
Cutting power (\(W\))
- \({P}_{m}\) :
-
Net Power (\(W\))
- \({P}_{t}\) :
-
Price of the insert (\({\text{Euro}}\))
- \({P}_{u}\) :
-
The nominal power of the machine (\(W\))
- \({Q}_{c}\) :
-
Cutting temperature (\(^\circ {\text{C}}\))
- \({R}_{a}\) :
-
Surface roughness (\(\upmu m\))
- \({R}_{as}\) :
-
Specified value of surface roughness (\(\upmu m\))
- \(S\) :
-
Spindle speed (\({\text{Rpm}}\))
- \(T\) :
-
Tool life (\({\text{min}}\))
- \({T}_{c}\) :
-
Production cycle time per piece (\({\text{min}}\))
- \({T}_{h}\) :
-
Part handling time (\({\text{min}}\))
- \({T}_{m}\) :
-
Machining time (\({\text{min}}\))
- \({T}_{t}\) :
-
Tool change time (\({\text{min}}\))
- \({T}_{min}\) :
-
The minimum tool life (\({\text{min}}\))
- \({T}_{{\text{max}}}\) :
-
The maximum tool life (\({\text{min}}\))
- \({V}_{c}\) :
-
Cutting speed (\({\text{m}}/{\text{min}}\))
- \({V}_{{c}_{{\text{min}}}}\) :
-
The minimum cutting speed (\({\text{m}}/{\text{min}}\))
- \({V}_{{c}_{{\text{max}}}}\) :
-
The maximum cutting speed (\({\text{m}}/{\text{min}}\))
- \({V}_{f}\) :
-
Feed (\({\text{mm}}/{\text{min}}\))
- \(Z\) :
-
The number of teeth
- \(\eta\) :
-
Machine efficiency
- \({C}_{F}\),\({\chi }_{F}\), \({y}_{F}\), \({t}_{F}\), \({w}_{F}\), \({q}_{F}\), \({p}_{F}\), \({k}_{F}\) :
-
Constants and exponents for the cutting force equation
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Acknowledgements
The authors sincerely thank the staff of the Department of Engineering and Management of Industrial Systems, Faculty of Engineering, “Vasile Alecsandri” University of Bacau, Romania, for their technical support during the preparation of this research project.
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Mohammed Toufik Amira: experimental investigation; data collection; writing—original draft; validation; formal analysis.
Imane Rezgui: conceptualization; methodology; writing—original draft; validation; formal analysis; analysis and interpretation of results.
Abderrahim Belloufi: conceived the original idea; methodology; supervision; project administration; analysis and interpretation of results.
Mourad Abdelkrim: experimental investigation; data collection; helped supervise the project.
Youssef Touggui: review and editing; proofreading.
Elhocine Chiba: writing—original draft; data collection.
Tampu Catalin: material preparation, experimental investigation.
Bogdan Chiriță: material preparation, project administration.
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Amira, M.T., Rezgui, I., Belloufi, A. et al. Modeling and multi-objective optimization of the milling process for AISI 1060 steel. Int J Adv Manuf Technol (2024). https://doi.org/10.1007/s00170-024-13693-7
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DOI: https://doi.org/10.1007/s00170-024-13693-7