research article intelligent selection of machining...
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Research ArticleIntelligent Selection of Machining Parameters in MultipassTurnings Using Firefly Algorithm
Abderrahim Belloufi,1,2 Mekki Assas,1 and Imane Rezgui2
1 Laboratoire de Recherche en Productique (LRP), Departement de Genie Mecanique, Universite Hadj Lakhder, 05000 Batna, Algeria2 Departement de Genie Mecanique, Universite Kasdi Merbah Ouargla, 30000 Ouargla, Algeria
Correspondence should be addressed to Abderrahim Belloufi; [email protected]
Received 26 July 2013; Accepted 1 October 2013; Published 9 February 2014
Academic Editor: Mingcong Deng
Copyright ยฉ 2014 Abderrahim Belloufi et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.
Determination of optimal cutting parameters is one of the most important elements in any process planning of metal parts. Inthis paper, a new optimization technique, firefly algorithm, is used for determining the machining parameters in a multipassturning operation model. The objective considered is minimization of production cost under a set of machining constraints. Theoptimization is carried out using firefly algorithm. An application example is presented and solved to illustrate the effectiveness ofthe presented algorithm.
1. Introduction
The selection of optimal cutting parameters, like the numberof passes, depth of cut for each pass, feed, and speed, is a veryimportant issue for every machining processes [1].
Several cutting constraints must be considered inmachining operations. In turning operations, a cuttingprocess can possibly be completed with a single pass orby multiple passes. Multipass turning is preferable oversingle-pass turning in the industry for economic reasons [2].
The optimization problem of machining parameters inmultipass turnings becomes very complicated when plenty ofpractical constraints have to be considered [3].
Traditionally, mathematical programming techniqueslike graphical methods [4], linear programming [5], dynamicprogramming [6, 7], and geometric programming [8, 9]had been used to solve optimization problems of machiningparameters in multipass turnings. However, these traditionalmethods of optimization do not fare well over a broadspectrum of problem domains. Moreover, traditional tech-niquesmaynot be robust.Numerous constraints andmultiplepasses make machining optimization problems complicatedand hence these techniques are not ideal for solving suchproblems as they tend to obtain a local optimal solution.
Thus, metaheuristic algorithms have been developed to solvemachining economics problems because of their power inglobal searching. There have been some works regardingoptimization of cutting parameters [2, 3, 10โ14] for differentsituations; authors have been trying to bring out the utilityand advantages of genetic algorithm, evolutionary approach,and simulated annealing. It is proposed to use the newoptimization technique, firefly algorithm, for the machiningoptimization problems.
The firefly algorithm (FA) is a metaheuristic, nature-inspired, and optimization algorithm which is based on thesocial (flashing) behavior of fireflies, or lighting bugs, in thesummer sky in the tropical temperature regions [5โ18]. Itwas developed by Dr. Yang at Cambridge University in 2007,and it is based on the swarm behavior such as fish, insects,or bird schooling in nature. In particular, although thefirefly algorithm has many similarities with other algorithmswhich are based on the so-called swarm intelligence, suchas the famous Particle Swarm Optimization (PSO), ArtificialBee Colony optimization (ABC), and Bacterial Foragingalgorithms (BFA), it is indeed much simpler both in conceptand implementation [15, 16, 18, 19]. Furthermore, accordingto recent bibliography, the algorithm is very efficient and canoutperform other conventional algorithms, such as genetic
Hindawi Publishing CorporationModelling and Simulation in EngineeringVolume 2014, Article ID 592627, 6 pageshttp://dx.doi.org/10.1155/2014/592627
2 Modelling and Simulation in Engineering
algorithms, for solving many optimization problems, a factthat has been justified in a recent research, where the statisti-cal performance of the firefly algorithmwasmeasured againstother well-known optimization algorithms using variousstandard stochastic test functions [20].
The current paper focuses on the application of a newoptimization technique, firefly algorithm, to determine theoptimal machining parameters that minimize the unit pro-duction cost in multipass turnings.
2. Cutting Process Model
2.1. Decision Variables. In the constructed optimizationproblem, six decision variables are considered: cutting speedsin rough and finish machining (๐
๐, ๐๐ ), feed rates in rough
and finish machining (๐๐, ๐๐ ), and depth of cut for each pass
of rough and finish machining (๐๐, ๐๐ ).
2.2. Objective Function. Based on theminimumunit produc-tion cost, UC, criterion, the objective function for amultipassturning operation can be given by the equation [10]:
UC = ๐ถ๐
+ ๐ถ๐ผ+ ๐ถ๐ + ๐ถ๐,
๐ถ๐
= ๐0[
๐๐ท๐ฟ
1000๐๐๐๐
(๐๐กโ ๐๐
๐๐
) +๐๐ท๐ฟ
1000๐๐ ๐๐
] ,
๐ถ๐ผ= ๐0[๐ก๐+ (โ1๐ฟ + โ2) (
๐๐กโ ๐๐
๐๐
+ 1)] ,
๐ถ๐ = ๐0
๐ก๐
๐๐
[๐๐ท๐ฟ
1000๐๐๐๐
(๐๐กโ ๐๐
๐๐
) +๐๐ท๐ฟ
1000๐๐ ๐๐
] ,
๐ถ๐=
๐๐ก
๐๐
[๐๐ท๐ฟ
1000๐๐๐๐
(๐๐กโ ๐๐
๐๐
) +๐๐ท๐ฟ
1000๐๐ ๐๐
] .
(1)
2.3. Constraints. There are some constraints which affect theselection of the optimal cutting conditions and will be takeninto account.
The constraints in rough and finish machining are asoutlined below [10].
2.3.1. Rough Machining
Parameter Bounds. Due to the limitations on themachine andcutting tool and due to the safety of machining the cuttingparameters are limited with the bottom and top permissiblelimit:
cutting speed : ๐๐๐ฟ
โค ๐๐โค ๐๐๐,
feed rate : ๐๐๐ฟ
โค ๐๐โค ๐๐๐,
depth of cut : ๐๐๐ฟ
โค ๐๐โค ๐๐๐.
(2)
Tool-Life Constraint. The constraint on the tool life is taken as
๐๐ฟโค ๐๐โค ๐๐. (3)
Cutting Force Constraint. The maximum amount of cuttingforces Fu should not exceed a certain value as higher forcesproduce shakes and vibration.This constraint is given below:
๐น๐= ๐1(๐๐)๐
(๐๐)๐
โค ๐น๐ข. (4)
Power Constraint. The nominal power of the machine ๐๐
limits the cutting process:
๐๐=
๐น๐๐๐
6120๐โค ๐๐, (5)
efficiency ๐ = 0.85.
Stable Cutting Region Constraint. This constraint is given as
(๐๐)๐
๐๐(๐๐)]โฅ SC. (6)
Chip-Tool Interface Temperature Constraint.This constraint isgiven as
๐๐= ๐2(๐๐)๐
(๐๐)๐
(๐๐)๐ฟ
โค ๐๐ข. (7)
2.3.2. Finish Machining. All the constraints other than thesurface finish constraint are similar for rough and finishmachining [21].
Surface Finish Constraint. In the finishing operations, theobtained surface roughness must be smaller than the spec-ified value, SR
๐, given by technological criteria, so that the
following equation is satisfied:
๐๐
2
8๐ โค SR๐. (8)
Constraints for roughing and finishing parameter rela-tions are
๐๐ โฅ ๐3๐๐,
๐๐โฅ ๐4๐๐ ,
๐๐โฅ ๐5๐๐ .
(9)
The Number of Rough Cuts. The possible number of roughcuts is restricted by
๐ =๐๐กโ ๐๐
๐๐
, (10)
where ๐๐ฟโค ๐ โค ๐
๐,
๐๐ฟ=
(๐๐กโ ๐๐ ๐)
๐๐๐
,
๐๐=
(๐๐กโ ๐๐ ๐ฟ)
๐๐๐ฟ
.
(11)
The optimization problem in multipass turnings can bedivided into ๐ = (๐
๐โ ๐๐ฟ+ 1) subproblems, in each of
which the number of rough cuts ๐ is fixed. So the solutionof the whole optimization problem is divided into searchingthe optimal results of ๐ subproblems and the minimum ofthem is the objective of whole optimization problem [3].
Modelling and Simulation in Engineering 3
Input:๐ (๐ง) , ๐ง = [๐ง
1, ๐ง2, . . . , ๐ง
๐]๐ (Cost function)
๐ = [๐๐, ๐๐] , โ๐ = 1, . . . , ๐ (Constraints)
๐, ๐ฝ0, ๐พ,min ๐ข
๐,max ๐ข
๐(Algorithmโs parameters)
Output:๐ฅ๐min
beginrepeat
๐min
โ arg min๐๐ (๐ฅ๐) , ๐ฅ๐min โ arg min
๐ฅ๐๐ (๐ฅ๐)
For ๐ = 1 to๐ doFor ๐ = 1 to๐ doIf ๐ (๐ฅ
๐) < ๐ (๐ฅ
๐) then
๐๐โ Calculate distance (๐ฅ
๐, ๐ฅ๐)
๐ฝ โ ๐ฝ0๐โ๐พ๐๐
๐ข๐โ Generate Random Vector (min ๐ข
๐,max ๐ข
๐)
For ๐ = 1 to ๐ do ๐ฅ๐,๐
โ (1 โ ๐ฝ) ๐ฅ๐,๐
+ ๐ฝ๐ฅ๐,๐
+ ๐ข๐,๐
๐ข๐min โ Generate Random Vector (min ๐ข
๐,max ๐ข
๐)
For ๐ = 1 to ๐ do ๐ฅ๐min,๐โ ๐ฅ๐min,๐+ ๐ข๐min,๐
until stop condition trueend
Pseudocode 1
3. Firefly Algorithm (FA)
Firefly algorithm is inspired by biochemical and social aspectsof real fireflies. Real fireflies produce a short and rhythmicflash that helps them in attracting (communicating) theirmating partners and also serves as protective warningmecha-nism. FA formulates this flashing behavior with the objectivefunction of the problem to be optimized.The following threerules are idealized for basic formulation of FA.
(i) All fireflies are unisex so that fireflies will attract eachother regardless of their sex.
(ii) Attractiveness is proportional to their brightness,which decreases as distance increases between twoflies. Thus the less bright one will move towards thebrighter one. In case it is unable to detect brighter oneit will move randomly.
(iii) The brightness of a firefly is determined by thelandscape of the objective function.
3.1. Firefly Algorithm Concept [17]. The algorithm is consid-ered in the continuous constrained optimization problemsetting where the task is to minimize cost function๐(๐ฅ) for๐ฅ โ ๐ โ R๐; that is, find ๐ฅโ such that:
๐ (๐ฅโ
) = min๐ฅโ๐
๐ (๐ฅ) . (12)
Assume that there exists a swarm of ๐ agents (fireflies)solving optimization problem iteratively and ๐ฅ
๐represents a
solution for a firefly ๐ in algorithmโs iteration ๐, whereas ๐(๐ฅ๐)
denotes its cost.Each firefly has its distinctive attractiveness ๐ฝ which
implies how strong it attracts other members of the swarm.As a firefly attractiveness one should select anymonotonically
decreasing function of the distance ๐๐
= ๐(๐ฅ๐, ๐ฅ๐) to the
chosen firefly ๐, for example, as Yang suggests, the exponentialfunction:
๐ฝ = ๐ฝ0๐โ๐พ๐๐ , (13)
where ๐ฝ0and ๐พ are predetermined algorithm parameters:
maximum attractiveness value and absorption coefficient,respectively.
Every member of the swarm is characterized by its lightintensity ๐ผ
๐which can be directly expressed as an inverse of a
cost function ๐(๐ฅ๐).
Initially all fireflies are dislocated in ๐ (randomly oremploying some deterministic strategy).
To effectively explore considered search space ๐ it isassumed that each firefly ๐ is changing its position iterativelytaking into account two factors: attractiveness of other swarmmembers with higher light intensity, that is, ๐ผ
๐> ๐ผ๐, for all
๐ = 1, . . . , ๐, ๐ = ๐, which is varying across distance and a fixedrandom step vector ๐ข
๐.
If no brighter firefly can be found only the randomizedstep is being used.
3.2. Pseudocode of the Firefly Algorithm. See Pseudocode 1.
4. Application Example
Now an application example is considered to demonstrateand validate the firefly algorithm (FA) for the optimizationof process parameters of themultipass turning operation.Theparameters used for the numerical application arementionedin Table 1.
4.1. Results and Discussion. The Firefly algorithm was runwith these parameters:
4 Modelling and Simulation in Engineering
Table 1: Machining data [10].
Parameter Values Parameter Values Parameter Values๐ท (mm) 50 ๐ฟ (mm) 300 ๐
๐ก(mm) 6
๐๐๐
(m/min) 500 ๐๐๐ฟ(m/min) 50 ๐
๐๐(mm/rev) 0.9
๐๐๐ฟ(mm/rev) 0.1 ๐
๐๐(mm) 3.0 ๐
๐๐ฟ(mm) 1.0
๐๐ ๐
(m/min) 500 ๐๐ ๐ฟ(m/min) 50 ๐
๐ ๐(mm/rev) 0.9
๐๐ ๐ฟ(mm/rev) 0.1 ๐
๐ ๐(mm) 3.0 ๐
๐ ๐ฟ(mm) 1.0
๐ 5 ๐ 1.75 ๐ 0.75๐1
108 ๐ 0.75 ๐ 0.95๐ 0.85 ๐ 2 ] โ1๐2
132 ๐ 0.4 ๐ 0.2๐ฟ 0.105 ๐ (mm) 1.2 ๐
0($/min) 0.5
๐ถ0
6 ร 1011 โ1
7 ร 10โ4 โ2
0.3๐๐ฟ(min) 25 ๐ก
๐(min/piece) 0.75 ๐ก
๐(min/edge) 1.5
๐๐(kW) 5 ๐
๐(min) 45 ๐น
๐ข(N) 1961.3
SC 140 SR๐(๐m) 10 ๐
๐ข(โC) 1000
๐3
1.0 ๐4
2.5 ๐5
1.0๐๐ก($/edge) 2.5
Table 2: The optimized turning parameters.
๐Cutting parameters (rough machining) Cutting parameters (finish machining) UC ($)
๐๐(m/min) ๐
๐(mm/rev) ๐
๐(mm) ๐
๐ (m/min) ๐
๐ (mm/rev) ๐
๐ (mm)
1 98.4102 0.8200 3.0000 162.2882 0.2582 3.0000 1.93582 145.7281 0.6067 2.3964 207.0844 0.1519 1.2072 2.72133 144.1821 0.7907 1.5958 191.9014 0.1590 1.2125 3.10754 145.8086 0.7886 1.2429 180.1447 0.1821 1.0285 3.54285 166.5327 0.8998 1.0000 191.3605 0.2582 1.0000 3.4586
Table 3: Results of optimization using different algorithms.
Algorithms Unit cost ($)FEGA [2] 2.3084SA/SP [3] 2.2795PSO [10] 2.2721GA [11] 2.2538SS [12] 2.0754GA-based approach [13] 2.0298ACO [14] 1.9680Firefly 1.9358
nf = 40 (number of fireflies),
๐ผ = 0.25 (randomness),
๐ฝ0= 0.20 (minimum value of beta),
๐พ = 1 (Absorption coefficient).
The results found by the Firefly algorithm are mentionedon Table 2.
We find that the lowest value is 1.9358$ under which theminimum number of rough cuts ๐ = 1 is taken.
The performance of the Firefly algorithm and others canbe seen in Table 3.
According to Table 3 one notices that the firefly algorithmyields much better results than the other algorithms. Thusthe firefly algorithm can tackle the optimization of multipassturning operations problem efficiently to achieve betterresults in reducing the unit production cost.
5. Conclusion
This paper presents a firefly algorithm optimization forsolving themultipass turning operations problem.The resultsobtained from comparing the Firefly algorithm with thosetaken from recent literature prove its effectiveness.
The results of the Firefly algorithm are compared withresults of genetic algorithms, simulated annealing, particleswarm intelligence, scatter search, and ant colony approaches.
The firefly algorithm obtains near optimal solution; itcan be used for machining parameter selection of complexmachined parts that require many machining constraints.Also, it can be extended to solve the other metal cuttingoptimization problems such as milling and drilling.
Abbreviations
๐ถ๐ผ: Machine idle cost due to loading and
unloading operations and tool idle motiontime ($/piece)
๐ถ๐: Cutting cost by actual time in cut ($/piece)
Modelling and Simulation in Engineering 5
๐ถ๐ : Tool replacement cost ($/piece)
๐ถ๐: Tool cost ($/piece)
๐๐, ๐๐ : Depth of cut for each pass of rough and
finish machining (mm)๐๐๐ฟ, ๐๐๐: Lower and upper bound of depth of cut in
rough machining (mm)๐๐ ๐ฟ, ๐๐ ๐: Lower and upper bound of depth of cut in
finish machining (mm)๐๐ก: Depth of material to be removed (mm)
๐ท, ๐ฟ: Diameter and length of workpiece (mm)๐๐, ๐๐ : Feed rates in rough and finish machining
(mm/rev)๐๐๐ฟ, ๐๐๐: Lower and upper bound of feed rate in rough
machining (mm/rev)๐๐ ๐ฟ, ๐๐ ๐: Lower and upper bound of feed rate in finish
machining (mm/rev)๐น๐, ๐น๐ : Cutting forces during rough and finish
machining (N)๐น๐ข: Maximum allowable cutting force (N)
โ1, โ2: Constants related to cutting tool travel and
approach/departure time (min)๐0: Direct labor cost plus overhead ($/min)
๐๐ก: Cutting edge cost ($/edge)
๐1, ๐, ๐: Constants of cutting force equation๐2, ๐, ๐, ๐ฟ: Constants related to chip-tool interface tem-
perature equation๐3, ๐4, ๐5: Constants for roughing and finishingparameter relations
๐, ]: Constants related to expression of stablecutting region
๐: Number of rough cuts (an integer)๐๐, ๐๐ฟ: Upper and lower bounds of ๐
๐, ๐, ๐, ๐ถ0: Constants of tool-life equation
๐๐, ๐๐ : Cutting power during rough and finish
machining (kW)๐๐: Maximum allowable cutting power (kW)
๐๐, ๐๐ : Chip-tool interface rough and finish
machining temperatures (โC)๐๐: Maximum allowable chip-tool interface
temperature (โC)๐: A weight for ๐
๐[0, 1]
๐ : Nose radius of cutting tool (mm)SC: Limit of stable cutting region constraintSR๐: Maximum allowable surface roughness
(mm)๐, ๐๐, ๐๐ : Tool life, expected tool life for rough
machining, and expected tool life for finishmachining (min)
๐๐: Tool life of weighted combination of ๐
๐and
๐๐ (min)
๐๐, ๐๐ฟ: Upper and lower bounds for tool life (min)
UC: Unit production cost exceptmaterial cost ($)๐๐, ๐๐ : Cutting speeds in rough and finish machin-
ing (m/min)๐๐๐ฟ, ๐๐๐: Lower and upper bound of cutting speed in
rough machining (m/min)๐๐ ๐ฟ, ๐๐ ๐: Lower and upper bound of cutting speed in
finish machining (m/min).
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper.
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