Volume 1 • Issue 1 • 1000101 J Applied Mechanic Engg ISSN:2168-9873 JAME, an open access journal Open Access Research Article Belloufi et al., J Applied Mechanic Engg 2012, 1:1 Keywords: Multi-pass turning; Genetic algorithm; Sequential quadratic programming; Cutting conditions Abbreviations: C 1 ($/piece): Machine idle cost due to loading and unloading operations and tool idle motion time; C M ($/piece): Cutting cost by actual time in cut; C R ($/piece): Tool replacement cost; C T ($/ piece): Tool cost; d r, d s (mm): Depth of cut for each pass of rough and fnish machining; d rL, d rU (mm): Lower and upper bound of depth of cut in rough machining; d sL d sU (mm): Lower and upper bound of depth of cut in fnish machining; d t (mm): Depth of material to be removed; D, L(mm): Diameter and length of work piece; f r, f s (mm/rev): Feed rates in rough and fnish machining; f rL, f rU (mm/rev): Lower and upper bound of feed rate in rough machining; f sL, f sU (mm/rev): Lower and upper bound of feed rate in fnish machining; F r, F s (kgf): Cutting forces during rough and fnish machining; F u (kgf): Maximum allowable cutting force; h 1, h 2 (mm): Constants relating to cutting tool travel and approach/departure time; k o ($/mm): Direct labor cost plus overhead; k t ($/edge): Cutting edge cost; k 1 ,μ,υ: Constants of cutting force equation; k 2 ,τ,ϕ,δ: Constants related to chip-tool interface temperature equation; k 3 ,k 4 ,k 5 : Constants for roughing and fnishing parameter relations; λ,ν: Constants related to expression of stable cutting region; n: Number of rough cuts (an integer); N U ,N L : Upper and lower bounds of n; p,q,r, C 0 : Constants of tool-life equation; P r ,P s (kW): Cutting power during rough and fnish machining; P U (kW): Maximum allowable cutting power; Q r, Qs(°C): Chip–tool interface rough and fnish machining temperatures; Q U (°C): Maximum allowable chip-tool interface temperature; q: A weight for T p [0,1]; R(mm): Nose radius of cutting tool; SC: Limit of stable cutting region constraint; SR U (mm): Maximum allowable surface roughness; T,T r ,T s (mm): Tool life, expected tool life for rough machining and expected tool life for fnish machining; T P (mm): tool life of weighted combination of T R and T S ; T U ,T L (mm): Upper and lower bounds for tool life; UC $: Unit production cost except material cost; V r ,V s (M/mm): Cutting speeds in rough and fnish machining; V rL ,V rU (M/mm): Lower and upper bound of cutting speed in rough machining; V sL ,V sU (M/mm): Lower and upper bound of cutting speed in fnish machining Introduction Te selection of optimal cutting parameters, like the number of passes, depth of cut for each pass, feed and speed, is a very important issue for every machining process [1]. Several cutting constraints must be considered in machining operations. In turning operations, a cutting process can possibly be completed with a single pass or by multiple passes. Multi-pass turning is preferable over single-pass *Corresponding author: Abderrahim Bellouf, Mechanical Engineering Depart- ment, University Hadj Lakhdar, Batna, Algeria, Tel: +213 661 57 04 24, E-mail: abellouf@yahoo.fr Received January 03, 2012; Accepted February 21, 2012; Published February 23, 2012 Citation: Bellouf A, Assas M, Rezgui I (2012) Optimization of Cutting Conditions in Multi-Pass Turning Using Hybrid Genetic Algorithm-Sequential Quadratic Programming. J Applied Mechanic Engg 1:101. doi:10.4172/2168-9873.1000101 Copyright: © 2012 Bellouf A, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Optimization of Cutting Conditions in Multi-Pass Turning Using Hybrid Genetic Algorithm-Sequential Quadratic Programming Abderrahim Bellouf 1 *, Mekki Assas 2 and Imane Rezgui 3 1 Mechanical Engineering Department, University Mohamed Kheider, Biskra, Algeria 2 Engineering Production Laboratory, University HadjLakhdar, Batna, Algeria 3 Mechanical Engineering Department, University HadjLakhdar, Batna, Algeria Abstract In this paper, a new, hybrid genetic algorithm-sequential quadratic programming is used for the resolution of cutting conditions. It used for the resolution of a multi-pass turning optimization case by minimizing the production cost under a set of machining constraints. The result indicates that the proposed hybrid genetic algorithm-sequential quadratic programming is effective when compared to other techniques carried out by different researchers. turning in the industry for economic reasons [2]. Te optimization problem of machining parameters in multi-pass turnings becomes very complicated when plenty of practical constraints have to be considered [3]. Traditionally, mathematical programming techniques like graphical methods [4], linear programming [5], dynamic programming [6,7] and geometric programming [8,9] had been used to solve optimization problems of machining parameters in multi-pass turnings. However, these traditional methods of optimization do not fare well over a broad spectrum of problem domains. Moreover, traditional techniques may not be robust. Numerous constraints and multiple passes make machining optimization problems complicated and hence these techniques are not ideal for solving such problems as they tend to obtain a local optimal solution. Tus, meta-heuristic algorithms have been developed to solve machining economics problems because of their power in global searching. Tere have been some works regarding optimization of cutting parameters [2,3,10-14] for diferent situations, authors have been trying to bring out the utility and advantages of genetic algorithm, evolutionary approach and simulated annealing. It is proposed to use the hybrid genetic algorithm-sequential quadratic programming for the machining optimization problems. Te current paper focuses on the application of a new optimization technique, hybrid genetic algorithm-sequential quadratic programming, to determine the optimal machining parameters that minimize the unit production cost in multi-pass turnings. Cutting process model Decision variables: In the constructed optimization problem, six decision variables are considered: cutting speeds in rough and fnish machining (V r , V s ), feed rates in rough and fnish machining (f r , f s ) and depth of cut for each pass of rough and fnish machining ( ) , r s d d . Objective function: Based on the minimum unit production DOI: 10.4172/2168-9873.1000101 Journal of Applied Mechanical Engineering J o u r n a l o f A p p l i e d M e c h a n i c a l E n g i n e e r i n g ISSN: 2168-9873