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 Β© 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, 10β14] 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 [5β18]. 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 (π
π, ππ ), feed rates in rough
and finish machining (ππ, ππ ), and depth of cut for each pass
of rough and finish machining (ππ, ππ ).
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 = πΆπ
+ πΆπΌ+ πΆπ + πΆπ,
πΆπ
= π0[
ππ·πΏ
1000ππππ
(ππ‘β ππ
ππ
) +ππ·πΏ
1000ππ ππ
] ,
πΆπΌ= π0[π‘π+ (β1πΏ + β2) (
ππ‘β ππ
ππ
+ 1)] ,
πΆπ = π0
π‘π
ππ
[ππ·πΏ
1000ππππ
(ππ‘β ππ
ππ
) +ππ·πΏ
1000ππ ππ
] ,
πΆπ=
ππ‘
ππ
[ππ·πΏ
1000ππππ
(ππ‘β ππ
ππ
) +ππ·πΏ
1000ππ ππ
] .
(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 : πππΏ
β€ ππβ€ πππ,
feed rate : πππΏ
β€ ππβ€ πππ,
depth of cut : πππΏ
β€ ππβ€ πππ.
(2)
Tool-Life Constraint. The constraint on the tool life is taken as
ππΏβ€ ππβ€ ππ. (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:
πΉπ= π1(ππ)π
(ππ)π
β€ πΉπ’. (4)
Power Constraint. The nominal power of the machine ππ
limits the cutting process:
ππ=
πΉπππ
6120πβ€ ππ, (5)
efficiency π = 0.85.
Stable Cutting Region Constraint. This constraint is given as
(ππ)π
ππ(ππ)]β₯ SC. (6)
Chip-Tool Interface Temperature Constraint.This constraint isgiven as
ππ= π2(ππ)π
(ππ)π
(ππ)πΏ
β€ ππ’. (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
π, given by technological criteria, so that the
following equation is satisfied:
ππ
2
8π β€ SRπ. (8)
Constraints for roughing and finishing parameter rela-tions are
ππ β₯ π3ππ,
ππβ₯ π4ππ ,
ππβ₯ π5ππ .
(9)
The Number of Rough Cuts. The possible number of roughcuts is restricted by
π =ππ‘β ππ
ππ
, (10)
where ππΏβ€ π β€ π
π,
ππΏ=
(ππ‘β ππ π)
πππ
,
ππ=
(ππ‘β ππ πΏ)
πππΏ
.
(11)
The optimization problem in multipass turnings can bedivided into π = (π
πβ ππΏ+ 1) subproblems, in each of
which the number of rough cuts π is fixed. So the solutionof the whole optimization problem is divided into searchingthe optimal results of π subproblems and the minimum ofthem is the objective of whole optimization problem [3].
Modelling and Simulation in Engineering 3
Input:π (π§) , π§ = [π§
1, π§2, . . . , π§
π]π (Cost function)
π = [ππ, ππ] , βπ = 1, . . . , π (Constraints)
π, π½0, πΎ,min π’
π,max π’
π(Algorithmβs parameters)
Output:π₯πmin
beginrepeat
πmin
β arg minππ (π₯π) , π₯πmin β arg min
π₯ππ (π₯π)
For π = 1 toπ doFor π = 1 toπ doIf π (π₯
π) < π (π₯
π) then
ππβ Calculate distance (π₯
π, π₯π)
π½ β π½0πβπΎππ
π’πβ Generate Random Vector (min π’
π,max π’
π)
For π = 1 to π do π₯π,π
β (1 β π½) π₯π,π
+ π½π₯π,π
+ π’π,π
π’πmin β Generate Random Vector (min π’
π,max π’
π)
For π = 1 to π do π₯πmin,πβ π₯πmin,π+ π’πmin,π
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 functionπ(π₯) forπ₯ β π β Rπ; that is, find π₯β such that:
π (π₯β
) = minπ₯βπ
π (π₯) . (12)
Assume that there exists a swarm of π agents (fireflies)solving optimization problem iteratively and π₯
πrepresents a
solution for a firefly π in algorithmβs iteration π, whereas π(π₯π)
denotes its cost.Each firefly has its distinctive attractiveness π½ which
implies how strong it attracts other members of the swarm.As a firefly attractiveness one should select anymonotonically
decreasing function of the distance ππ
= π(π₯π, π₯π) to the
chosen firefly π, for example, as Yang suggests, the exponentialfunction:
π½ = π½0πβπΎππ , (13)
where π½0and πΎ are predetermined algorithm parameters:
maximum attractiveness value and absorption coefficient,respectively.
Every member of the swarm is characterized by its lightintensity πΌ
πwhich can be directly expressed as an inverse of a
cost function π(π₯π).
Initially all fireflies are dislocated in π (randomly oremploying some deterministic strategy).
To effectively explore considered search space π it isassumed that each firefly π is changing its position iterativelytaking into account two factors: attractiveness of other swarmmembers with higher light intensity, that is, πΌ
π> πΌπ, for all
π = 1, . . . , π, π = π, which is varying across distance and a fixedrandom step vector π’
π.
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 Valuesπ· (mm) 50 πΏ (mm) 300 π
π‘(mm) 6
πππ
(m/min) 500 πππΏ(m/min) 50 π
ππ(mm/rev) 0.9
πππΏ(mm/rev) 0.1 π
ππ(mm) 3.0 π
ππΏ(mm) 1.0
ππ π
(m/min) 500 ππ πΏ(m/min) 50 π
π π(mm/rev) 0.9
ππ πΏ(mm/rev) 0.1 π
π π(mm) 3.0 π
π πΏ(mm) 1.0
π 5 π 1.75 π 0.75π1
108 π 0.75 π 0.95π 0.85 π 2 ] β1π2
132 π 0.4 π 0.2πΏ 0.105 π (mm) 1.2 π
0($/min) 0.5
πΆ0
6 Γ 1011 β1
7 Γ 10β4 β2
0.3ππΏ(min) 25 π‘
π(min/piece) 0.75 π‘
π(min/edge) 1.5
ππ(kW) 5 π
π(min) 45 πΉ
π’(N) 1961.3
SC 140 SRπ(πm) 10 π
π’(βC) 1000
π3
1.0 π4
2.5 π5
1.0ππ‘($/edge) 2.5
Table 2: The optimized turning parameters.
πCutting parameters (rough machining) Cutting parameters (finish machining) UC ($)
ππ(m/min) π
π(mm/rev) π
π(mm) π
π (m/min) π
π (mm/rev) π
π (mm)
1 98.4102 0.8200 3.0000 162.2882 0.2582 3.0000 1.93582 145.7281 0.6067 2.3964 207.0844 0.1519 1.2072 2.72133 144.1821 0.7907 1.5958 191.9014 0.1590 1.2125 3.10754 145.8086 0.7886 1.2429 180.1447 0.1821 1.0285 3.54285 166.5327 0.8998 1.0000 191.3605 0.2582 1.0000 3.4586
Table 3: Results of optimization using different algorithms.
Algorithms Unit cost ($)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),
πΌ = 0.25 (randomness),
π½0= 0.20 (minimum value of beta),
πΎ = 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 π = 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
πΆπΌ: Machine idle cost due to loading and
unloading operations and tool idle motiontime ($/piece)
πΆπ: Cutting cost by actual time in cut ($/piece)
Modelling and Simulation in Engineering 5
πΆπ : Tool replacement cost ($/piece)
πΆπ: Tool cost ($/piece)
ππ, ππ : Depth of cut for each pass of rough and
finish machining (mm)πππΏ, πππ: Lower and upper bound of depth of cut in
rough machining (mm)ππ πΏ, ππ π: Lower and upper bound of depth of cut in
finish machining (mm)ππ‘: Depth of material to be removed (mm)
π·, πΏ: Diameter and length of workpiece (mm)ππ, ππ : Feed rates in rough and finish machining
(mm/rev)πππΏ, πππ: Lower and upper bound of feed rate in rough
machining (mm/rev)ππ πΏ, ππ π: Lower and upper bound of feed rate in finish
machining (mm/rev)πΉπ, πΉπ : Cutting forces during rough and finish
machining (N)πΉπ’: Maximum allowable cutting force (N)
β1, β2: Constants related to cutting tool travel and
approach/departure time (min)π0: Direct labor cost plus overhead ($/min)
ππ‘: Cutting edge cost ($/edge)
π1, π, π: Constants of cutting force equationπ2, π, π, πΏ: Constants related to chip-tool interface tem-
perature equationπ3, π4, π5: Constants for roughing and finishingparameter relations
π, ]: Constants related to expression of stablecutting region
π: Number of rough cuts (an integer)ππ, ππΏ: Upper and lower bounds of π
π, π, π, πΆ0: Constants of tool-life equation
ππ, ππ : Cutting power during rough and finish
machining (kW)ππ: Maximum allowable cutting power (kW)
ππ, ππ : Chip-tool interface rough and finish
machining temperatures (βC)ππ: Maximum allowable chip-tool interface
temperature (βC)π: A weight for π
π[0, 1]
π : Nose radius of cutting tool (mm)SC: Limit of stable cutting region constraintSRπ: Maximum allowable surface roughness
(mm)π, ππ, ππ : Tool life, expected tool life for rough
machining, and expected tool life for finishmachining (min)
ππ: Tool life of weighted combination of π
πand
ππ (min)
ππ, ππΏ: Upper and lower bounds for tool life (min)
UC: Unit production cost exceptmaterial cost ($)ππ, ππ : Cutting speeds in rough and finish machin-
ing (m/min)πππΏ, πππ: Lower and upper bound of cutting speed in
rough machining (m/min)ππ πΏ, ππ π: 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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