Multi-objective optimization of machining conditions by geometric programming

Authors

  • Mohamed Djennane
  • Rachid Benbouta
  • Allaoua Kherraf

DOI:

https://doi.org/10.54021/seesv5n1-022

Keywords:

cutting parameters, geometric programming, multi-criteria optimization, turning processes

Abstract

In metal cutting processes, cutting conditions have an influence on reducing the production cost and time and deciding the quality of a final product. This paper outlines the development of an optimization strategy to determine the optimum cutting parameters for turning processes. Two objective functions are simultaneously optimized under a set of practical of machining constraints, the first objective function is production cost and the second one is the production time. The optimal values of the cutting conditions are found based on the objective function developed for the typified criterion by using a non-linear programming technique called “geometric programming”. In the optimization procedure, the objective functions are subject to constraints of maximum and minimum feed rates and speeds available, cutting power, tool life, deflection of work piece, axial pre-load and surface roughness. An example is presented to illustrate the procedure of this technique.

References

BELLOUFI, A.; ASSAS, M.; REZGUI I. Optimization of Turning Operations by Using a Hybrid Genetic Algorithm with Sequential Quadratic Programming. Journal of Applied Research and Technology, v. 11, pp. 88-94, 2013. DOI: 10.1016/S1665-6423(13)71517-7

EDGEWORTH, F. Y. Mathematical psychics. London: Kegan Paul, 1881.

PARETO, V. Manuale di Economia Politica Societa Editrice Libraria, Milano, 1906. English Translation: Pareto, V.: Manual of Political Economy, translated by Schwier, A. S.. Augustus 1170 M.Kelley Publishers, New York, 1971.

EICHFELDER, G.; JAHN, J. () Vector and set optimization. In: GRECO, S. (Ed.), Multiple Criteria Decision Analysis. State of the Art Surveys, Springer, Heidelberg, 2016. p. 695-737.

WANG, Y. C. (2007). A note on optimization of multipass turning operations using ant colony system. International Journal of Machine Tools and Manufacture, v. 47, n. 12-13, p. 2057-2059. DOI: 10.1016/j.ijmachtools.2007.

001

SHUTONG, X.; YINBIAO, G. Intelligent selection of machining parameters in multi-pass turnings using a GA-based approach. Journal of Computer Information Systems, v. 5, p. 1714-1721, 2011. DOI: 10.1155/2014/592627

CROOKALL, J. R.; VENKATARAMANI, N. Computer optimization of multipass turning. International Journal of Production Research, v. 9, n. 2, p. 247–259, 1971. DOI: 10.1080/00207547108929876

KALS, H. J. J. (1977). Computer aid in the optimization of turning conditions in multi-cut operations. Proceedings of CIRP Conference, p. 465–471.

LAMBERT, P. K.; WALVEKAR, A. G. Optimization of multipass machining operations. International Journal of Production Research, v. 16, n. 4, p. 259–265, 1978. DOI: 10.1080/00207547808930018

ÖZ, E.; GÜZEL, N.; ALP, S. An alternative approach to the solution of multi-objective geometric programming problems. Open Journal of Optimization, v. 6, p. 11-25, 1961. DOI: 10.4236/ojop.2017.61002

ÖZ, Ersoy; GÜZEL, Nuran; ALP, Selçuk. An Alternative Approach to the Solution of Multi-Objective Geometric Programming Problems. Open Journal of Optimization, v. 6, n. 1, p. 11-25, 2017. DOI: 10.4236/ojop.2017.61002

TOKSARI, M. D. () Taylor Series Approach to Fuzzy Multiobjective Linear Fractional Programming. Information Sciences, v. 178, p. 1189-1204, 2008. DOI: 10.1016/j.ins.2007.06.010

GÜZEL, N.; SIVRI, M. () Taylor Series Solution of Multi Objective Linear Fractional Programming Problem. Trakya University Journal of Science, v. 6, p. 91-98, 2005.

AGAPIOU, J. S. The optimization of machining operations based on a combined criterion, Part 2: Multipass operations. Journal of Engineering for Industry, v. 114, p. 508-513, 1992a. DOI: 10.1115/1.2900705

AGAPIOU, J. S. The optimization of machining operations based on a combined criterion, Part 1: The use of combined objectives in single-pass operations. Journal of Engineering for Industry, v. 114, n. 4, p. 500-507, 1992b. DOI: 10.1115/1.2900704

WANG, J.; KURIYAGAWA, T.; WEI, X. P.; GOU, G. M. Optimization of cutting conditions using a deterministic approach. International Journal of Machine Tools & Manufacture, v. 42, 1023-1033, 2002. DOI: 10.1016/S0890-6955(02)00037-8

DJENANE, M.; DJARI, D.; BENBOUTA, R.; ASSAS, M. Multi pass optimization of cutting conditions by using the genetic algorithms. Research Journal of Applied Sciences, Engineering and Technology, v. 13, n. 3, p. 223-231, 2016. DOI: 10.19026/rjaset.13.2934

SOFUOĞLU, M. A.; ARAPOĞLU, R. A.; ORAK S. Multi objective optimization of turning operation using hybrid decision making analysis. Anadolu University Journal of Science and Technology A- Applied Sciences and Engineering, v. 18, n. 3, p. 595-610, 2017. DOI:10.18038/aubtda.287801

DJARI, D.; ASSAS, M.; DJENANE, M. Optimization of the Conditions of Machining Based on a Criterion Combined by Genetic Algorithms. IRENA, v. 3, n. 4, p. 100-104, 2015.

AREZOO, B.; RIDGWAY, K.; AL-AHMARI, A. M. Selection of cutting tools and conditions of machining operations using an expert system. Computers in Industry, v. 42, p. 43-58, 2000. DOI: 10.1016/S0166-3615(99)00051-2

CHOUDHURY, S. K.; APPA RAO, I. V. K. Optimization of cutting parameters for maximizing tool life. International Journal of Machine Tools & Manufacture, v. 39, p. 343-353, 1999. DOI: 10.1016/ S0890-6955(98)00028-5

ZUPERL, U.; CUS, F. Optimization of cutting conditions during cutting by using neural networks. Robotics and Computer Integrated Manufacturing, v. 19, p. 189-199, 2003. DOI:10.1016/S0736-5845(02)00079-0

DU, M.; CHENG, Z.; ZHANG, Y.; WANG, S. Multiobjective optimization of tool geometric parameters using genetic algorithm. Complexity, p. 1-24, 2018. DOI: 10.1155/2018/9692764

MIODRAGOVIC, G. R.; DORDEVIC, V.; BULATOVIC, R.; PETROVIC, A. Optimization of multi-pass turning and multi-pass face milling using subpopulation firefly algorithm. Journal of Mechanical Engineering Science, v. 233, p. 1520–1540, 2019. DOI: 10.1177/0954406218774378

AMIOLEMHEN, P.; ESEIGBE, J. Genetic algorithms solution to the single -objective machining process optimization time model. Journal of Mechanical and Energy Engineering, v. 3, n. 41, p. 13-24, 2019. DOI: 10.30464/jmee.2019.31.13

SAI, N. K.; CHARYULU, T. N.; SIVA NAYAK, M. Multi objective optimization of machining parameters by using weighted sum genetic algorithm approaches. International journal of engineering research and technology, v. 1, n. 7, p. 1-7, 2012.

ARMAREGO, E. J. A.; BROWN, R. H. The machining of metals. Prentice-Hall, 1969.

LIBAO, A. Optimization of machining parameters in multi-pass turning and milling operations. Master (Dissertation) – Concordia University, 2003.

OJHA, A. K.; BISWAL, K. K. Multi-objective Geometric Programming Problem with Weighted Mean Method. International Journal of Computer Science and Information Security, v. 7, n. 2, p. 82-86, 2010. DOI:10.48550/arXiv.1003.1477

LIU, S. T. Posynomial Geometric Programming with parametric uncertainty. Europian Journal of Operation Research, v. 168, p. 345-353, 2006. DOI: 10.1016/j.ejor.2004.04.046

JHA, N. K. Optimizing the number of tools and cutting parameters in multi-tool turning for multiple objectives through geometric programming. Applied Mathematical Modeling, v. 10, p. 162-169, 1986. DOI: 10.1016/0307-904x(86)90041-7

DUFFIN, R. J.; PETERSON, E.L.; ZENER, C. Geometric programming: theory and application. New York: John Wiley and Sons, 1967.

DUFFIN, R. J. Linearizing geometric program. SIAM Review, v. 12, n. 2, 1970211-227, DOI: 10.1137/1012043

Downloads

Published

2024-03-06

How to Cite

Djennane, M., Benbouta, R., & Kherraf, A. (2024). Multi-objective optimization of machining conditions by geometric programming. STUDIES IN ENGINEERING AND EXACT SCIENCES, 5(1), 371–390. https://doi.org/10.54021/seesv5n1-022