Multi-objective Optimization of Weld Bead Geometry

J. Manuf. Sci. Prod. 2014; aop

Kondapalli Siva Prasad*, Chalamalasetti Srinivasa Rao and Damera Nageswara Rao

Multi-objective Optimization of Weld Bead Geometry Parameters of Pulsed Current Micro Plasma Arc Welded AISI 304L Stainless Steel Sheets Using Enhanced Non-dominated Sorting Genetic Algorithm Abstract: Pulsed Current Plasma Arc Welding (PCPAW) is one of the most widely used welding processes in sheet metal manufacturing industry. In any fusion arc welding process, the weld bead geometry plays an important role in determining the mechanical properties of the weld and hence quality of the weld. Moreover, the geometry of weld bead involves several simultaneously multiple quality characteristics such as front width, back width, front height and back height, which must be closely monitored, controlled and optimized. The present study is focused on the multi-objective optimization of performance parameters of weld bead geometry of PCMPAW welded AISI 304L sheets. The enhanced elitist non-dominated sorting genetic algorithm (NSGA-II) is used to solve this multi- objective problem. A mathematical predictive model for each of the weld bead parameters was developed using Response Surface Method (RSM) based Central Composite Design (CCD) design matrix. Further, an enhanced NSGA-II algorithm is used to optimize the models developed by RSM. Experiments were carried out to validate the results obtained from RSM and enhanced NSGA-II. Keywords: Pulsed Current, Micro Plasma Arc Welding, AISI 304L stainless steel, weld pool geometry, ANOVA, genetic algorithms PACS® (2010). 81.06 DOI 10.1515/jmsp-2014-0002 Received January 15, 2014; accepted June 15, 2014.

*Corresponding author: Kondapalli Siva Prasad: Department of Mechanical Engineering, Anil Neerukonda Institute of Technology & Sciences, Visakhapatnam, India. E-mail: [email protected] Chalamalasetti Srinivasa Rao: Department of Mechanical Engineering, Andhra University, Visakhapatnam, India Damera Nageswara Rao: Centurion University of Technology & Management, Odisha, India

1 Introduction AISI 304L is a austenitic stainless steel with excellent strength and good ductility at high temperature. Typical applications include aero-engine hot section components, miscellaneous hardware, tooling and liquid rocket components involving cryogenic temperature. AISI 304L can be joined using variety of welding methods, including Gas Tungsten Arc Welding (GTAW), Plasma Arc Welding (PAW), Laser Beam Welding (LBW) and Electron Beam Welding (EBW). Of these methods, low current PAW (Micro PAW) has attracted particular attention and has been used extensively for the fabrication of metal bellows, diaphragms which require high strength and toughness. PAW is conveniently carried out using one of two different current modes, namely a Continuous Current (CC) mode or a Pulsed Current (PC) mode. Pulsed current MPAW involves cycling the welding current at selected regular frequency. The maximum current is selected to give adequate penetration and bead contour, while the minimum is set at a level sufficient to maintain a stable arc [1, 2]. This permits arc energy to be used effectively to fuse a spot of controlled dimensions in a short time producing the weld as a series of overlapping nuggets. By contrast, in constant current welding, the heat required to melt the base material is supplied only during the peak current pulses allowing the heat to dissipate into the base material leading to narrower Heat Affected Zone (HAZ). Advantages include improved bead contours, greater tolerance to heat sink variations, lower heat input requirements, reduced residual stresses and distortion, refinement of fusion zone microstructure and reduced with of HAZ. Based on the worked published [3–8], four independent parameters that influence the process are peak current, back current, pulse rate and pulse width. In this investigation, experiments conducted using the design of experiments concept were used for developing

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K.S. Prasad et al., Multi-objective Optimization of Weld Bead Geometry Parameters

mathematical models to predict such variables. Many works were reported in the past for predicting bead geometry, heat-affected zone, bead volume, etc., using mathematical models for various welding processes [9–11]. Usually, the desired welding process parameters are de termined based on the experience of skilled workers or from the data available in the handbook. This does not ensure the formation of optimal or near optimal weld pool geometry [12]. It has been proven by several researchers that efficient use of statistical design of experiment techniques and other optimization tools can impart scientific approach in welding procedure [13, 14]. These techniques can be used to achieve optimal or near optimal bead geometry from the selected process parameters. Kim et al. reviewed that optimization using regression modeling, neural network, and Taguchi methods could be effective only when the welding process was set near the optimal conditions or at a stable operating range [15], but, near-optimal conditions cannot be easily determined through full-factorial experiments when the number of experiments and levels of variables are increased. Also, the method of steepest ascent based upon derivatives can lead to an incorrect direction of search due to the non- linear characteristics of the welding process. Genetic algorithm, being a global algorithm, can overcome the above problems associated with full-factorial experiments and the objective function to be optimized using GA need not be differentiable [16]. The present paper discusses the application of RSM and enhanced NSGA-II for the multi-objective optimization of PCMPAW weld AISI 304L sheets. The task is to maximize front width and back width and minimize front height and back height of the weld bead geometry.

2 Materials and methodology AISI 304L stainless steel sheets of 100 × 150 × 0.25 mm are welded autogenously with square butt joint without edge preparation. The chemical composition of AISI 304L stainless steel sheet procured from Salem Steel Plant, India is given in Table 1. High purity argon gas (99.99%) is used as a shielding gas and a trailing gas right after welding to prevent absorption of oxygen and nitrogen from the atmosphere. From the literature four important factors of pulsed current MPAW as presented in Table 2 are chosen. The welding has been carried out under the welding conditions presented in Table 3. A large number of trail experiments are carried out using 0.25 mm thick AISI 304L stainless steel sheets to find out the feasible working limits of pulsed current MPAW process parameters. Exper-

Table 1: Chemical composition of AISI 304L stainless steel sheets (weight %) C

Si

Mn

P

S

Cr

Ni

Mo Ti

0.021 0.35 1.27 0.030 0.001 18.10 8.02 –

N

–

0.053

Table 2: Important factors and their levels Levels Input factor

Unit

−2

−1

0

+1

+2

Peak current Back current Pulse rate Pulse width

Amperes Amperes Pulses/second %

6 3 20 30

6.5 3.5 30 40

7 4 40 50

7.5 4.5 50 60

8 5 60 70

Table 3: Welding conditions Power source Model number Polarity Mode of operation Electrode Electrode diameter Plasma gas Plasma gas flow rate Shielding gas Shielding gas flow rate Purging gas Purging gas flow rate Copper nozzle diameter Nozzle to plate distance Welding speed Torch position Operation type

Secheron micro plasma arc machine PLASMAFIX 50E DCEN Pulse mode 2% thoriated tungsten electrode 1 mm Argon & hydrogen 6 Lpm Argon 0.4 Lpm Argon 0.4 Lpm 1 mm 1 mm 260 mm/min Vertical Automatic

iments are conduced Response Surface Method (RSM) based four factors, five levels, rotatable Central Composite Design (CCD) matrix. Table 4 indicates the 31 set of coded conditions used to form the design matrix. The method of designing such matrix is dealt elsewhere [17, 18].

3 Measurement of weld bead geometry Three metallurgical samples were cut from each joint, with the first sample being located at 25 mm behind the trailing edge of the crater at the end of the weld and mounted using Bakelite. Sample preparation and mounting was done as per ASTM E 3-1 standard. The transverse



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Table 4: Design matrix and experimental results Serial no.

Peak current (amperes)

Back current (amperes)

Pulse rate (pulses/second)

Pulse width (%)

Front width (mm)

Back width (mm)

Front height (mm)

Back height (mm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

6.5 7.5 6.5 7.5 6.5 7.5 6.5 7.5 6.5 7.5 6.5 7.5 6.5 7.5 6.5 7.5 6 8 7 7 7 7 7 7 7 7 7 7 7 7 7

3.5 3.5 4.5 4.5 3.5 3.5 4.5 4.5 3.5 3.5 4.5 4.5 3.5 3.5 4.5 4.5 4 4 3 5 4 4 4 4 4 4 4 4 4 4 4

30 30 30 30 50 50 50 50 30 30 30 30 50 50 50 50 40 40 40 40 20 60 40 40 40 40 40 40 40 40 40

40 40 40 40 40 40 40 40 60 60 60 60 60 60 60 60 50 50 50 50 50 50 30 70 50 50 50 50 50 50 50

1.448 1.592 1.383 1.504 1.454 1.487 1.469 1.462 1.529 1.591 1.520 1.562 1.442 1.384 1.506 1.420 1.521 1.580 1.452 1.427 1.596 1.466 1.400 1.461 1.531 1.581 1.523 1.519 1.504 1.501 1.401

1.374 1.522 1.324 1.442 1.401 1.418 1.378 1.402 1.451 1.508 1.447 1.506 1.372 1.306 1.430 1.356 1.451 1.514 1.380 1.358 1.527 1.397 1.337 1.384 1.462 1.512 1.452 1.450 1.432 1.433 1.332

0.0609 0.0588 0.0630 0.0569 0.0581 0.0595 0.0599 0.0578 0.0599 0.0571 0.0572 0.0552 0.0605 0.0590 0.0600 0.0584 0.0598 0.0569 0.0575 0.0564 0.0582 0.0564 0.0636 0.0602 0.0606 0.0597 0.0607 0.0606 0.0607 0.0576 0.0597

0.0498 0.0458 0.0490 0.0439 0.0453 0.0466 0.0468 0.0448 0.0470 0.0441 0.0441 0.0423 0.0474 0.0456 0.0470 0.0464 0.0468 0.0439 0.0445 0.0434 0.0453 0.0434 0.0516 0.0472 0.0476 0.0467 0.0477 0.0476 0.0477 0.0446 0.0456

Fig. 2: Macrographs of weld bead [19]

Fig. 1: Typical weld bead geometry

face of the samples were surface grounded using 120 grit size belt with the help of belt grinder, polished using grade 1/0 (245 mesh size), grade 2/0 ( 425 mesh size) and grade 3/0 (515 mesh size) sand paper. The specimens were further polished by using aluminum oxide initially and the by utilizing diamond paste and velvet cloth in a

olishing machine. The polished specimens were macrop etched by using 10% oxalic acid solution to reveal the geometry of the weld pool (Fig. 1) [19]. Several critical parameters, such as front width, back width, front height and back height of the weld pool geometry (Fig. 2) [19] are measured. The weld bead geometry was measured using Metallurgical Microscope (Make: Dewinter Technologie, Model No. DMI-CROWN-II) at 100× magnification.


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4 Developing mathematical models for weld bead geometry In RSM design, mathematical models are developed using polynomial equations. The type of polynomial equation depends on the type of the problem. In most RSM problems [20–22], the form of the relationship between the response (Y) and the independent variables is unknown. Thus the first step in RSM is to find a suitable approximation for the true functional relationship between the response and the set of independent variables. Usually, a low order polynomial is some region of the independent variables is employed. If the response is well modeled by a linear function of the independent variables then the approximating function in the first order model. Y = bo + ∑bixi + ∈

(1)

If interaction terms are added to main effects or first order model, then we have a model capable of representing some curvature in the response function. Y = bo + ∑bixi + ∑∑bijxixj + ∈

(2)

The curvature, of course, results from the twisting of the plane induced by the interaction term bijxixj. There are going to be situations where the curvature in the response function is not adequately modeled by Equation 6.3. In such cases, a logical model to consider is Y = bo + ∑bixi + ∑biixi2 + ∑∑bijxixj + ∈

(3)

where bii represent pure second order or quadratic effects. Equation 3 is a second order response surface model. Using MINITAB 14 statistical software package, the significant coefficients are determined and final models are developed using only these coefficients to estimate Front width, Back width, Front height and Back height of the weld bead geometry. Front width (FW) FW = 1.50857 + 0.01538X1 − 0.00629X2 − 0.03187X3 + 0.01154X4 − 0.02007X42 − 0.03044X1X3 − 0.02469X3X4

(4)

Back width (BW) BW = 1.43900 + 0.01704X1 − 0.00462X2 − 0.03212X3 + 0.00871X4 − 0.02024X42 − 0.03006X1X3

(5)

Front height (FH) FH = 0.059943 − 0.000942X1 − 0.000317X2 + 0.000025X3 − 0.000600X4 − 0.000704X22 − 0.000617X32 + 0.000800X3X4

(6)

Back height (BH) BH = 0.046786 − 0.00946X1 − 0.000396X2 − 0.000004X3 − 0.000704X4 − 0.000670X22 + 0.000692X42 + 0.000869X3X4

(7)

where X1, X2, X3 and X4 are the coded values of Peak Current, Back Current, Pulse rate and Pulse width respectively. The adequacy of the developed models is tested using the analysis of variance technique (ANOVA). As per this technique, if the calculated value of the Fratio of the developed model is less than the standard Fratio (from Fisherstable) value at a desired level of confidence (say 99%), then the model is said to be adequate within the confidence limit. Coefficient of determination R2 is used to find how close the predicted and experimental values lie. The value of R2 for the above developed models is found to be about 0.84, which indicates good correlation exists be tween the experimental values and the predicted values.

5 Non-dominated sorting genetic algorithm-II (NSGA-II) In the following section the working of the NSGA-II algorithm is described as given in [21–22]. The original ver sion has been enhanced by improving the non-dominated sorting method as given in [23]. This enhanced version is discussed further. In NSGA-II, first the offspring population Qt (of size N) is created using the parent population Pt (of size N). The usual genetic operators such as single-point crossover and bit-wise mutation operators are used in this process. Next, the two populations are combined to form an intermediate population Rt of size 2N. Thereafter, the fitness of each offspring in the 2N population is evaluated using the multiple objective functions. At this stage, the nondominated sorting procedure is carried out over the 2N population to rank and divide the individuals into dif ferent non-dominated fronts. Thereafter, the new parent population Pt + 1 is created by choosing individuals of the non-dominated fronts, one at a time. The individuals of best ranked fronts are chosen first, followed by the nextbest and so on, till N individuals are obtained.



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Since the intermediate population Rt has a size of 2N, those fronts which could not be accommodated are discarded. In case there is space only for a part of a front in the new population, the individuals as per existing order are selected, so as to complete the new parent population. The complete NSGA-II procedure is explained below: BEGIN While generation count is not reached Begin Loop Apply selection, crossover and mutation to new parent population Pt + 1 and obtain the new offspring population Qt + 1. Combine parent Pt and offspring population Qt to obtain population Rt of size 2N. Perform Non-dominated Sorting on Rt and assign ranks to each pareto front with fitness Fi. Starting from the Pareto front with fitness F1, add each Pareto-front Fi to the new parent population Pt + 1 until a complete front Fi cannot be included. From the current Pareto-front Fi, add individual members to new parent population Pt + 1 until it reaches the size N. Increment generation count. End Loop END.

6 Enhanced non-dominated sorting genetic algorithm In the current enhanced version of non-dominated sorting genetic algorithm-II [23], sorting of individuals based on each of the objectives are performed, one after the other, till all objectives are considered. During this sort, the index of each individual is tracked so that the position value of any given individual in each sorted array is known. This information is critical since it helps in ranking the fronts in the next step. Each individual is ranked by summing up the position value of that individual in all the objectives. Since similar position values were assigned to individuals having similar objective values, the sum of the position values becomes equivalent to the rank which the individual would have obtained through non-dominated comparison. Hence the non-dominated sort is completed in a

Fig. 3: Flow chart of enhanced NSGA-II

single iteration of the sorted individuals, thereby reducing the time required for processing each generation. The flow chart for optimization of the weld bead geometry parameters using enhanced non-dominated sorting genetic algorithm is shown in Fig. 3. In this figure, generate initial population means the possible solutions of the optimization problem, and each possible solution is called an individual. The possible solution is formed by binary strings of peak current, back current, pulse rate and pulse width. Later these binary strings are converted into decimals to obtain the output. Thus generated population is selected based on roulette wheel selection and they are arranged depending on the dominance of one solution over the other.


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The crossover and mutation genetic operators are applied on the selected population in a manner similar to that used during single objective GA. For real parameter implementations, binary crossover and mutation operators are used. Further an elitist recombination strategy is used by combining the current population and the offspring population. For an initial population size of N, the combined population contains 2N members. The new population is obtained by picking members from each front successively until the size exceeds N. A suitable number of members from the first front that cannot be completely added are then picked so that a total of N members are obtained. All the steps starting from nondominated sorting are repeated until the desired number of generations is completed.

7 Implementation of enhanced NSGA-II for RSM Optimization A multi objective algorithm was implemented using enhanced NSGA-II for performing the evolutionary optimization. C-programming language was used to code the algorithm. Each of the objective function was coded along with the parameters used for RSM Optimization. The constraints on each parameter were also specified in the program. As described in the NSGA-II algorithm in the previous section, a population of 100 individuals was generated with various initial values of parameters which were initialized randomly, keeping appropriate minimum and maximum ranges in view. Thereafter the program was allowed to iterate over 1000 generations and the final optimized parameter values of the non-dominated solu-

Table 5: Comparison of experimental results

Input parameters Peak current (Amperes) Back current (Amperes) Pulse rate (pulses/second) Pulse width (%) Output parameters Front width (mm) Back width (mm) Front height (mm) Back height (mm)

Experimental NSGA-II

Grey Relational Analysis

7 4 40 50

8 5 20 50

1.581 1.512 0.0597 0.0467

7.9052 5 60 36.8612 1.683138 1.619368 0.052813 0.024401

1.712 1.658 0.052 0.024

tions resulting from this run were noted. The values obtained in NSGA-II are compared with Experimental and results obtained from Grey Relational Analysis and are tabulated in Table 5. From Table 5 it is observed that the values obtained in Experiment No 26 of Table 4 and Grey Relational Analysis are close to results obtained in NSGA-II.

8 Conclusions In this study, the Response Surface Methodology was applied for analyzing weld bead geometry parameters of PCMPAW AISI 304L sheets. Further, enhanced Nondominated Sorting Genetic Algorithm-II (NSGA-II) an improved version of NSGA was used to optimize the RSM models developed by experimentation. It can be observed from the analysis that RSM can be used to develop second order equations for weld bead geometry parameters in terms of welding parameters. Genetic algorithm codes are developed in C-language for multi objective optimization of the responses. The results obtained in Grey relational analysis is compared with experimental and Grey Relational Analysis results. It is observed that that results obtained by genetic algorithm are in very close agreement with those obtained by Grey Relational Analysis. Acknowledgments: The authors would like to thank Shri. R. Gopla Krishnan, Director, M/s Metallic Bellows (I) Pvt Ltd, Chennai for his support to carry out experimentation work.

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