Determination of Optimal Process Parameters of Friction Stir Welding to Join Dissimilar Aluminum Alloys Using Artificial Bee Colony Algorithm

Abstract

This paper presents the efforts of joining dissimilar aluminum alloys (AA6351-T6 and AA6061-T6) by friction stir welding (FSW) process. FSW experiments are conducted according to the three factors five level central composite rotatable design method, and the response surface methodology was used to establish the empirical relationship between FSW process parameters such as tool rotational speed (N), tool traverse speed (S) and axial force (F), and the response variables such as ultimate tensile strength, yield strength, and percentage of elongation. The developed empirical models’ adequacies are estimated using the analysis of variance technique. This paper also presents the application of the artificial bee colony algorithm to estimate the optimal process parameters to achieve good mechanical properties of FS weld joints. Results suggest that the estimations of the algorithm are in good agreement with the experimental findings.

Appendix

The pseudo code of ABC algorithm [26] is presented below:

• 1. Initialize the Colony Size (CS), Number of Food Sources/Solutions (SN), Number of dimensions to each solution (D), Modification Rate (MR), SPP (Scout Production Period-limit).

• 2. Initialize the population of solutions x _i,j where i = 1… SN and j = 1…D.

• 3. Evaluate the population.

• 4. cycle = 1.

• 5. REPEAT

• 6. Produce a new solution v _i for each employee bee by using (6) and evaluate it as

  $$v_{ij} = x_{ij} + \emptyset_{ij} \left( {x_{ij} {-} x_{kj} } \right) {\text{if}}\,R_{j} < {\text{MR}},{\text{ otherwise}}\,\,x_{ij} \ldots$$

  (9)

  [$\emptyset_{ij}$—is a random number in the range [−1, 1]. k ∈ {1, 2…SN} (SN: Number of solutions in a colony) is randomly chosen index. Although k is determined randomly, it has to be different from i. R _j is a randomly chosen real number in the range [0, 1] and j ∈ {1, 2,…D} (D: Number of dimensions in a problem). MR, modification rate, is a control parameter.]

• 7. Apply greedy selection process for the employee bees between the v _i and x _i.

• 8. Calculate the probability values P _i using (7) for the solutions x _i

  $$P_{i} = \frac{{Fitness_{i} }}{{\mathop \sum \nolimits_{N = 1}^{SN} \left( {Fitness_{N} } \right)}} \ldots.$$

  (10)

• 9. For each onlooker bee, produce a new solution v _i by using (6) in the neighborhood of the solution selected depending on P _i and evaluate it.

• 10. Apply greedy selection process for the onlooker bees between the v _i and x _i.

• 11. If Scout Production Period (SPP) is completed, determine the abandoned solutions by using “limit” parameter for the scout, if it exists, replace it with a new randomly produced solution using (8).

• 12.
  $$x_{j}^{i } = x_{min}^{ji} + rand\left( {0,1} \right)\left( {x_{jmax}^{j } - x_{jmin}^{j } } \right) \ldots$$

  (11)

• 13. Memorize the best solution achieved so far.

• 14. cycle = cycle +1.

• 15. UNTIL (Max Cycle Number or Max CPU time).