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Metal cutting processes are important due to increased consumer demands for quality metal cutting related products (more precise tolerances and better product surface roughness) that has driven the metal cutting industry to continuously improve quality control of metal cutting processes. This paper presents optimum surface roughness by using milling mould aluminium alloys (AA6061-T6) with Response Ant Colony Optimization (RACO). The approach is based on Response Surface Method (RSM) and Ant Colony Optimization (ACO). The main objectives to find the optimized parameters and the most dominant variables (cutting speed, feedrate, axial depth and radial depth). The first order model indicates that the feedrate is the most significant factor affecting surface roughness.

Roughness plays an important role in determining how a real object will interact with its environment. Rough surfaces usually wear more quickly and have higher friction coefficients than smooth surfaces. Roughness is performance of a mechanical component, since irregularities in the surface may form nucleation soften a good prediction for cracks or corrosion. Although roughness is usually undesirable, it is difficult and expensive to control in manufacturing. Decreasing the roughness of a surface will usually exponentially increase its manufacturing costs. This often results in a trade-off between the manufacturing cost of a component and its performance in an application.

Planning of experiments through design of experiments has been used quite successfully in process optimization by Chen and Chen [

Aslan _{2}O_{3} + TiCN mixed ceramic tool used an orthogonal array and the analysis of variance (ANOVA) to optimization of cutting parameters. The flank wear (VB) and surface roughness (Ra) had investigated. Nalbant

A recent investigation performed by Alauddin

This is a method for obtaining an approximate function using results of several numerical calculations to increase calculation efficiency and thereby implement design optimization. In the response surface method, design parameters are changed to formulate an approximate equation by the design of experiments method. An approximate sensitivity calculation of a multicrestedness problem can be performed using a convex continuous function and applied to optimization. The Box-Behnken Design is normally used when performing non-sequential experiments. That is, performing the experiment only once. These designs allow efficient estimation of the first and second–order coefficients. Because Box-Behnken designs have fewer design points, they are less expensive to run than central composite designs with the same number of factors. Box-Behnken designs do not have axial points, thus we can be sure that all design points fall within the safe operating zone. Box-Behnken designs also ensure that all factors are never set at their high levels simultaneously [_{0}_{1}_{2}_{3}_{0}_{1}_{2}_{3}

Ant colony optimization algorithms are part of swarm intelligence, that is, the research field that studies algorithms inspired by the observation of the behaviour of swarms. Swarm intelligence algorithms are made up of simple individuals that cooperate through self-organization, that is, without any form of central control over the swarm members. A detailed overview of the self organization principles exploited by these algorithms, as well as examples from biology, can be found in [

One of the first researchers to investigate the social behaviour of insects was the French entomologist Pierre-Paul Grassé. In the 1940s and 1950s, he was observing the behaviour of termites in particular, the

Goss _{1} ants had used the first bridge and m_{2} the second one, the probability p_{1} for the (m + 1)^{th} ant to choose the first bridge can be given by ^{th} ant chooses the second bridge is _{2(m+1)} = 1 − _{1}_{(m+1)}. Monte Carlo simulations, run to test whether the model corresponds to the real data [

Ant colony optimization has been formalized into a combinatorial optimization metaheuristic by Dorigo

A model

a search space S defined over a finite set of discrete decision variables and a set

an objective function f:

Ant System was the first ACO algorithm to be proposed in the literature [_{ij}, that is, for edge joining cities i and j, is performed as follows [_{k}

The 27 experiments were carried out on a 6-axes Haans machining centre as shown in

After conducting the first pass (one pass is equal to 90 mm length) of the 27 cutting experiments, the surface roughness readings are used to find the parameters appearing in the postulated first order model (_{speed}_{depth}_{depth}

Generally, reduction of cutting speed, axial depth of cut caused a larger surface roughness. On the other hand, the increase in feed rate and radial depth caused a slight reduction of surface roughness. The feed rate is the most dominant factor on the surface roughness, followed by the axial depth, cutting speed and radial depth, respectively. Hence, a better surface roughness is obtained with the combination of low cutting speed and axial depth, high feed rate and radial depth. Similar to the first-order model, by examining the coefficients of the second-order terms, the feedrate (_{speed}

The optimised surface roughness model is tested with experimental results. The predicted minimum surface roughness using optimised surface roughness model by RACO are compared with the measured surface roughness and these results are reported in

This research illustrates the machining of aluminium alloy (AA6061-T6) with end-milling methods and predicting their subsequent surface roughness. There is becoming a need for investigating the machining of various types of aluminium and their surface roughness, which in turn can be useful in developing more cost effective personalised products. The authors have shown the use of RACO to formulate an optimised minimum surface roughness prediction model for end machining of AA6061-T6. This prediction model is tested on the validation experimental and the error analysis of the prediction result with the measured results is estimated at 4.65% for minimum surface roughness which is small and shows the efficacy of the prediction model. Finally, the simulation results show that ACO combine with RSM can be very successively used for reduction of the effort and time required. This means that it can solve many problems that have mathematical and time constraints.

The researchers thank the Faculty of Electrical and Electronic Engineering under the project number RDU 080324 and Faculty of Mechanical Engineering under the project RDU090398, that funded the project with resources received for research from Malaysia Pahang University.

Haans CNC milling with 6-axes.

Comparison between the experimental and predicted results.

Feed rate

Comparison of minimum optimised surface roughness with experimental and RSM.

Physical properties for workpiece.

95.8–98.6 | 0.04–0.35 | 0.15–0.4 | Max 0.7 | 0.8–1.2 | Max 0.15 | 0.4–0.8 | Max 0.15 | Max 0.25 |

Design Parameters.

140 | 0.15 | 0.10 | 5.0 |

140 | 0.15 | 0.15 | 3.5 |

100 | 0.15 | 0.15 | 5.0 |

140 | 0.15 | 0.15 | 3.5 |

180 | 0.15 | 0.20 | 3.5 |

180 | 0.15 | 0.15 | 2.0 |

100 | 0.20 | 0.15 | 3.5 |

140 | 0.15 | 0.15 | 3.5 |

180 | 0.15 | 0.15 | 5.0 |

100 | 0.15 | 0.20 | 3.5 |

140 | 0.20 | 0.10 | 3.5 |

180 | 0.10 | 0.15 | 3.5 |

140 | 0.15 | 0.20 | 2.0 |

180 | 0.15 | 0.10 | 3.5 |

140 | 0.10 | 0.15 | 2.0 |

140 | 0.15 | 0.20 | 5.0 |

100 | 0.15 | 0.10 | 3.5 |

140 | 0.20 | 0.15 | 2.0 |

100 | 0.15 | 0.15 | 2.0 |

140 | 0.20 | 0.15 | 5.0 |

140 | 0.10 | 0.10 | 3.5 |

140 | 0.20 | 0.20 | 3.5 |

140 | 0.15 | 0.10 | 2.0 |

100 | 0.10 | 0.15 | 3.5 |

180 | 0.20 | 0.15 | 3.5 |

140 | 0.10 | 0.20 | 3.5 |

140 | 0.10 | 0.15 | 5.0 |

Mechanical properties of the workpiece.

Hardness, Brinell | 95 |

Hardness, Knoop | 120 |

Hardness, Rockwell A | 40 |

Hardness, Rockwell B | 60 |

Hardness, Vickers | 107 |

Ultimate Tensile Strength | 310 MPa |

Tensile Yield Strength | 276 MPa |

Elongation at Break | 12 % |

Elongation at Break | 17 % |

Modulus of Elasticity | 68.9 GPa |

Density | 2.7 g/cc |

Analysis of variance for first-order equation.

Regression | 4 | 0.9309 | 0.9309 | 0.2327 | 0.78 | 0.552 |

Linear | 4 | 0.9309 | 0.9309 | 0.2327 | 0.78 | 0.552 |

Residual Error | 22 | 6.5937 | 6.5937 | 0.2997 | ||

Lack-of-Fit | 20 | 6.3151 | 6.3151 | 0.3158 | 2.27 | 0.351 |

Pure Error | 2 | 0.2786 | 0.2786 | 0.1393 | ||

Total | 26 | 7.5246 |