6340(Print), ISSN (Online) Volume 3, Issue 3, Sep- Dec (2012) IAEME AND TECHNOLOGY (IJMET)

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1 INTERNATIONAL International Journal of Mechanical JOURNAL Engineering OF MECHANICAL and Technology (IJMET), ENGINEERING ISSN 0976 AND TECHNOLOGY (IJMET) ISSN (Print) ISSN (Online) Volume 3, Issue 3, September - December (2012), pp IAEME: Journal Impact Factor (2012): (Calculated by GISI) IJMET I A E M E A GENETIC ALGORITHM APPROACH TO THE OPTIMIZATION OF PROCESS PARAMETERS IN LASER BEAM WELDING ABSTRACT Dr. G HARINATH GOWD 1* Professor, Department of Mechanical Engineering Madanapalle Institute of Technology & Science, Madanaaplle Andhra Pradesh., INDIA. gowdmits@gmail.com E VENUGOPAL GOUD Associate Professor, Department of Mechanical Engineering G. Pullareddy Engineering college, Kurnool 1* Corresponding author gowdmits@gmail.com Laser beam welding (LBW) is a field of growing importance in industry with respect to traditional welding methodologies due to lower dimension and shape distortion of components and greater processing velocity. Because of its high weld strength to weld size ratio, reliability and minimal heat affected zone, laser welding has become important for varied industrial applications. LBW process is so complex in nature that the selection of appropriate input parameters (Pulse duration, Pulse frequency, Welding speed and Pulse energy) is not possible by the trial-and-error method. So there is a need to develop a methodology to find the optimal process parameters in ND-YAG Laser beam welding process thereby producing sound welded joints at a low cost. In view of this, research is carried on INCONEL to find the optimal process parameters. Accurate prediction mathematical models to estimate Bead width, Depth of Penetration & Bead Volume were developed from experimental data using Response Surface Methodology (RSM). These predicted mathematical models are used for optimization of the process. Total volume of the weld bead, an important bead parameter, is optimized (minimized), keeping the dimensions of the other important bead parameters as constraints, to obtain sound and superior quality welds. As the amount of data generated in the iterative process for optimization is enormous and each design cycle requires substantial calculations, the popular evolutionary algorithm Genetic Algorithm is used for the optimization. In summary, the proposed methodology enables the manufacturing engineers to compute the optimal control factor settings depending upon the production requirements. Consequently, the process could be automated based on the optimal settings. 459

2 Keywords: ND-YAG Laser Beam welding, Modeling, Genetic algorithm, Optimization. 1. INTRODUCTION Laser Beam Welding (LBW) processes is a welding technique used to join multiple pieces of metal through the heating effect of a concentrated beam of coherent monochromatic light. Light amplification by stimulated emission of radiation (LASER) is a mechanism which emits electromagnetic radiation, through the process of simulated emission. Lasers generate light energy that can be absorbed into materials and converted into heat energy.lbw is a high-energy-density welding process and well known for its deep penetration, high speed, small heat-affected zone, fine welding seam quality, low heat input per unit volume, and fiber optic beam delivery [1]. The energy input in laser welding is controlled by the combination of focused spot size, focused position, shielding gas, laser beam power and welding speed. Because of the above advantages, LBW is widely used. For the laser beam welding of butt joint, the parameters of joint fit-up and the laser beam to joint alignment [2] becomes important. An inert gas, such as helium or argon, is used to protect the weld bead from contamination, and to reduce the formation of absorbing plasma. Depending upon the type of weld required a continuous or pulsed laser beam may be used. There are three basic types of lasers viz., the solid state laser, the gas laser and the semi conductor laser. Among all these variants Nd:YAG lasers are being used most extensively for industrial applications because they are capable of durable multikilowatt operation. The principle of operation is that the laser beam is pointed on to a joint and the beam is moved along the joint. The process will melt the metals in to a liquid, fuse them together and then make them solid again thereby joining the two pieces. The beam provides a concentrated heat source, allowing for narrow, deep welds and high welding rates. The process is frequently used in high volume applications, such as in the automotive industry. In any welding process, bead geometrical parameters play an important role in determining the mechanical properties of the weld and hence quality of the weld [3]. In Laser Beam welding, bead geometrical variables are greatly influenced by the process parameters such as Pulse frequency, Welding speed, Input energy, Shielding gas [4] and [5]. Therefore to accomplish good quality it is imperative to setup the right welding process parameters. Quality can be assured with embracing automated techniques for welding process. Welding automation not only results in high quality but also results in reduced wastage, high production rates with reduce cost to make the product. Some of the significant works in literature regard to the modeling and optimization studies of welding are as follows: Yang performed regression analysis to model submerged arc welding process [6]. Gunaraj and Murugan minimized weld volume for the submerged arc welding process using an optimization tool in Matlab [7]. Bead height, bead width and bead penetration were taken as the constraints. The Taguchi method was utilized by Tarng and Yang to analyze the affect of welding process parameter on the weld-bead geometry [8]. Casalino has studied the effect of welding parameters on the weld bead geometry in laser welding using statistical and taguchi approaches [9]. Nagesh and Datta developed a back-propagation neural network, to establish the relationships between the process parameters and weld bead geometric parameters, in a shielded metal arc welding process [10]. Young whan park has applied Genetic algorithms and Neural network for process modeling and parameter optimization of aluminium laser welding automation [11]. Mishra and Debroy showed that multiple sets of welding variables capable of producing the target weld geometry could be determined in a realistic time frame by coupling a real-coded GA with and neural network model for Gas Metal Arc Fillet 460

3 Welding [12]. Saurav data has applied RSM to modeling and optimization of the features of bead geometry including percentage dilution in submerged arc welding using mixture of fresh flux and fused slag [13]. The literature shows that the most dominant modeling tools used till date are Taguchi based regression analysis and artificial neural networks. However, the accuracy and possibility of determining the global optimum solution depends on the type of modeling technique used to express the objective function and constraints as functions of the decision variables. Therefore effective, efficient and economic utilization of laser welding necessitates an accurate modeling and optimization procedure. In the present work, RSM is used for developing the relationships between the weld bead geometry and the input variables. The models derived by RSM are utilized for optimizing the process by using the Genetic Algorithm. 2. EXPERIMENTAL WORK The experiments are conducted on High peak power pulsed Nd:YAG Laser welding system with six degrees of freedom robot delivered through 300 um Luminator fiber as shown in Figure 1. Fig.1. Nd:YAG Robotic Laser Beam welding equipment In this research Butt welding of Inconel 600 is carried out at by varying the input parameters. The size of each plate welded is 30mm long x 30mm width with thickness of 2.5mm. The laser beam is focused at the interface of the joints. An inert gas such as argon is used to protect the weld bead from contamination, and to reduce the formation of absorbing plasma. Based on the literature survey and the trial experiments, it was found that the process parameters such as pulse duration (x 1 ), pulse frequency (x 2 ), speed (x 3 ), and energy (x 4 ) have significant effect on weld bead geometrical features such as penetration (P), bead width (W), and bead volume (V).In the present work, they are considered as the decision variables and trial samples of butt joints are performed by varying one of the process variables to determine the working range of each process variable. Absent of visible welding defects and at least half depth penetrations were the criteria of choosing the working ranges. 461

4 After conducting the experiments as per the design matrix, for measuring the output responses i.e bead geometry features such as Bead penetration & Bead width, welded joint is sectioned perpendicular to the weld direction. The specimens are then prepared by the usual metallurgical polishing methods and then etched. Then the bead dimensions were measured using Toolmaker s microscope. For each response the readings were measured at three different sections of the weld joint and the average value is taken. The study is focused to investigate the effects of process variables on the structures of the welds. An average of three measurements taken at three different places and the output responses are recorded for each set. The output responses recorded are shown in the Table 1. Experiment No. x 1 ( µs) x 2 (Hz) Table 1. Experimental Observations x 3 (mm/min) x 4 (J) Penetration (mm) Bead width (mm) Bead Volume (mm 3 )

5 3. DEVELOPMENT OF EMPIRICAL MODELS The need in developing the mathematical relationships from the experimental data is to relate the measure output responses Penetration, Bead width and Bead volume to the input process parameters such as pulse duration (x 1 ), pulse frequency(x 2 ), speed (x 3 ), and energy (x 4 ) thereby facilitating the optimization of the welding process. RSM is used to predict the accurate models. P e n e t r a t i o n = x x x x x x x x x x x x x x x x x x x x Eq. (1) B e a d w i d t h = x x x x x x x x x x x x x x x x Eq. (2) B e a d v o l u m e = x x x x x x x x x x x x x x x x x x x x Eq. (3) The developed mathematical models are checked for their adequacy using ANNOVA and normal probability plot of residuals. Then these models are used for Optimization of process parameters using Genetic Algorithms. 4. FORMULATION OF OPTIMIZATION PROBLEM In the present work, the bead geometrical parameters were chosen to be the constraints and the minimization of volume of the weld bead was considered to be the objective function. Minimizing the volume of the weld bead reduces the welding cost through reduced heat input and energy consumption and increased welding production through a high welding speed [14]. The present problem is formulated an optimization model as shown below: Minimize B e a d v o l u m e = x x x x x x x x x x x x x x x 3 x x x x x 4 Subject to: P e n e t r a t i o n = x x x x x x x x x x x x x x x x x x x x & B e a d w i d t h = x x x x x x x x x x x x x x x x

6 With the parameter feasible ranges: 1 µs x 1 5 µs, 6 Hz x 2 22 Hz, 100 mm/min x mm/min, 9 J x 4 21 J The bead parameters and the feasible ranges of the input variables were established with a view to have defect-free welded joint. Once the optimization problem is formulated, then it is solved using Genetic algorithms (GA). The GA optimization module available in MATLAB is used to find out the optimal parameters. Tables 2, 3 and 4 exhibit the implementation of GA for minimizing the Bead volume as objective. Sample calculations are shown for one iteration of the algorithm. The bit lengths chosen for x 1, x 2, x 3 and x 4 are chosen 4, 4, 5 and 4 respectively. As a first step, an initial population of 40 chromosomes is generated randomly as shown in Table 2. Chromosome strings of individual input variables are decoded and substituted to determine the objective function value of Bead volume. From Table 2, the first string ( ) is decoded to values equal to x 1 =1, x 2 =20, x 3 =874 and x 4 =19 using linear mapping rule. Then the objective function value is computed which is obtained as The fitness final value at this point using the transformation rule F(x (1) ) = 1.0/( ) is obtained as This fitness function value is used in the reproduction operation of GA. Similarly, other strings in the population are evaluated and fitness values are calculated. Table 2 shows the objective function value and the fitness value for all the 40 strings in the initial population. In the next step, good strings in the population are to be selected to form the mating pool. In this work, roulette-wheel selection procedure is used to select the good strings. As a part of this procedure, average fitness [15] of the population is calculated by adding the fitness values of all strings and dividing the sum by the population size and the average fitness of the population ( F _ ) is obtained as The expected count is subsequently calculated by dividing each fitness value with the average fitness; F( x) _ F For the first string, the expected count is (0.6723/0.7772) = Similarly, the expected count values are calculated for all other strings in the population and shown in Table 3. Then, the probability of each string being copied in the mating pool can be computed dividing the expected count values with the population size. For instance, the probability of first string is (0.8649/40) = Similarly, the values of probability of selection for all the strings are calculated and cumulative probability is henceforward computed. The probabilities of selection are listed in Table 3. Next random numbers between zero and one are generated in order to form the mating pool. From Table 3, random number generated for the first string is 0.30 which means the twelfth string from the population gets a copy in the mating pool, because that string occupies the probability interval (0.27, 0.30) as shown in the column of cumulative probability in the Table 3. In a similar manner, other strings are selected according to the random numbers generated in Table 3 and the complete mating pool is formed. The mating pool is displayed in 464

7 Table By adopting the reproduction operator, the inferior points have been automatically eliminated from further consideration. As a next step in the generation, the strings in the mating pool are used for the crossover operation. Table 2. Initial population with fitness values in GA S.No Chromosomes x 1 x 2 x 3 x 4 Objective Fitness values

8 Table 3. Selection in GA S.No Expected Cumulative Random Selected string Probability Count Probability number number

9 In the crossover operation, two strings are selected at random and crossed at a random site. Since the mating pool contains strings at random, pairs of strings are picked up form top of the list as shown in Table 4. S.N Mating pool Chromosomes Table 4. Crossover and Mutation in GA Crossover? Crossover site Offspring Mutation site Mutated chromosome No , No Yes 6, Yes 6, No No No No No No No No Yes 9, Yes 9, No , No Yes 15, Yes 15, No No No No Yes 9, , Yes 9, No No No No No , No No No Yes 12, Yes 12, No No No No Yes 4, Yes 4, , Thus strings 12 and 27 participate in the first crossover operation. In this work, two point crossover [15] is adopted with the probability, P c = 0.85 to check whether a crossover is desired or not. To perform crossover, a random number is generated with crossover probability (P c ) of If the random number is less than P c then the crossover operation is performed, otherwise the strings are directly placed in an intermediate population for subsequent genetic operation. When crossover is required to be performed then crossover sites are to be decided at random by creating random numbers between (0, l-1), where l represents the total length of the string. For Example, when crossover is required to be performed for the strings 3, 4 two sites of crossover are to be selected randomly. Here, the random sites are happened to be 6, 12. Thus the portions between sites 6 and 12 of the strings 3 and 4 are swapped to create the new offspring as shown in Table 4. However with the random sites, the children strings produced may or may not have a combination of good 467

10 strings from parent strings, depending on whether or not the crossing sites fall in the appropriate locations. If good strings are not created by crossover, they will not survive too long because reproduction will select against those chromosomes in subsequent generation. In order to preserve some of the good chromosomes that are already present in the mating pool, all the chromosomes are not used in crossover operation. When a crossover probability P c is used, the expected number of strings that will be subjected to crossover is only 100P c and the remaining percent of the population remains as they are in the current population. The calculations of intermediate population are shown in the Table 4. The crossover is mainly responsible for the creation of new strings. The third operator, mutation, is then applied on the intermediate population. Mutation is basically intended for local search around the current solution. Bit-wise mutation is performed with a probability, P m = A random number is generated with P m ; if random number is less than Pm then the bit is altered form 1 to 0 or 0 to 1 depending on the bit value otherwise no action is taken. Mutation is implemented with the probability, P m =0.10 as shown in Table 4. The procedure is repeated for all the strings in the intermediate population. This completes one iteration of the GA. The above procedure is continued until the maximum number of generations is completed. For better convergence of the present problem, the Genetic algorithm is run for 120 generations. GA narrows down the search space as the search progresses and the algorithm is converged to the objective function value of The convergence graph is displayed in Fig.2 and the optimal values of the control factors are listed in Table 5. The following inference discusses the performance of proposed methodology: From the experimental observations presented in the Table 1, the 10 th experiment resulted for for Bead volume and Bead penetration as After optimization using GA, it is observed from Table 5, that Bead volume can be decreased to (by 55 %) for the same Bead penetration. Fig. 2. Convergence graph for minimization of Bead volume 468

11 Table 5. Optimal values Variable x 1 (Pulse Duration) (µs) x 2 (Pulse frequency) (Hz) x 3 (Welding Speed) (J) x 4 (Pulse Energy) (mm/min) Penetration Bead Width Bead Volume Value CONCLUSIONS In the present study, Design based experiments and analysis have been carried out in order to optimize the bead volume considering the effects of bead geometrical parameters like: Bead penetration and Bead width in butt welding of INCONEL 600 using ND:YAG Laser beam welding setup. First Experiments were carried out by as per Central Composite Rotatable factorial design to substantially reduce the number of experiments. Then RSM is used to develop second order polynomial models between the bead geometrical parameters: Bead volume, Bead width, Depth of penetration and the chosen control variables: Pulse duration, Pulse frequency, Welding speed and the Pulse energy. Later A constrained optimization problem is then formulated to minimize the bead volume subject to the bead width and bead penetration as constraints. A binary coded Genetic algorithm was used to solve the above said problem. The genetic algorithm was able to reach near the globally optimal solution, after satisfying the above constraints. The optimal values obtained by the proposed methodology could serve as a ready reckoner to conduct the welding operations with great ease to achieve the quality and the production rate demanded by the consumers. In summary, the proposed work enables the manufacturing engineers to select the optimal values depending on the production requirements and as a consequence, automation of the process could be done based on the optimal values. REFERENCES [1] Steen W.M., Laser material processing, Springer, London, [2] Dawes C., Laser Welding, Abington Publishing, Newyork, [3] Howard B.Cary., Modern Welding Technology, Prentice Hall, New Jersey, [4] Murugan N., Bhuvanasekharan G., Effects of process parameters on the bead geometry of laser beam butt welded stainless sheets, Int J Adv. Man Tech, 32: , [5] Benyounis K Y., Olabi A.G., Effect of laser welding parameters on the heat input and weld bead profile, Journal of materials processing technology, , [6] Yang L.J., Chandel R.S., An analysis of curvilinear regression equations for modeling the submerged-arc welding process, Journal of Materials Processing Technology, 37, , [7] Gunaraj V., Murugan N., Prediction and optimization of weld bead volume for the submerged arc process Part 2, Welding Journal, 78, 331s 338s, [8] Tarng Y.S., Yang W.H., Optimization of the weld-bead geometry in gas tungsten arc welding by the Taguchi method, Int. Journal of Advanced Manufacturing Technology 14 (8), ,

12 [9] Casalino G., Investigation on Ti6A14V laser welding using statistical and taguchi approaches, Int. Journal of Advanced Manufacturing technology, [10] Nagesh D S., Datta G L., Prediction of weld bead geometry and penetration in shielded metal arc welding using artificial neural networks, J. Material Process. Technol.123, , [11] Young whan park., Genetic algorithms and Neural network for process modeling and parameter optimization of aluminium laser welding Automa tion, Int. J Adv Manuf Technology [12] Mishra S., Debroy T., Tailoring gas tungsten arc weld geometry using a genetic algorithm and a neural network trained with convective heat flowcalculations, Materials Science and Engineering, , , [13] Saurav data., Modeling and optimization of the features of bead geometry including percentage dilution in submerged arc welding using mixture of fresh fluz and fused slag, International journal of advanced manufacturing technology. [14] Deb K., Multiobjective optimization using evolutionary algorithms, John Wiley & Sons (ASIA) Pvt. Ltd., Singapore, [15] Deb K., Optimization for engineering: algorithms and examples, Prentice Hall of India, New Delhi,