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The use of Taguchi and approximation methods to optimize the laser hybrid welding of a 5052-H32 aluminium alloy plate C Y Song1, Y W Park1, H R Kim2, K Y Lee1*, and J Lee1 1 School of Mechanical Engineering, Yonsei University, Seoul, Republic of Korea 2 Hyundai Heavy Industries, Ulsan, Republic of Korea The manuscript was received on 11 July 2007 and was accepted after revision for publication on 21 December 2007. DOI: 10.1243/09544054JEM946

Abstract: This study aims to identify the optimal welding conditions for laser hybrid welding on a 5052-H32 aluminium alloy. Non-linear transient thermal analysis is adopted to simulate the thermo-physical phenomena in the welding process. Taguchi’s parameter design method is applied to establish the optimal welding parameters that minimize residual stress and strain. The results obtained via design of experiments (DOE) and Taguchi’s parameter design using the welding simulations are compared with the experimental results. Using DOE data, approximation models such as the polynomial-based response surface method and the radial basis function neural network are constructed. Using such approximation models, the relationship between welding conditions and thermo-mechanical responses can easily be estimated according to the parameter variations. Keywords: laser hybrid welding, 5052-H32 aluminium alloy, welding parameters, Taguchi method, approximation models

1 INTRODUCTION For many years, weld joints have been extensively applied in many industries, for example the chemical, nuclear power, ship building, and petrochemical industries, etc. Welding processes have been developed according to the various applications and their joint technologies and materials. Over the past years, various welding methods have been developed according to the types of materials. In particular, the welding applications of aluminium alloy have been increased due to its superior properties such as low density and high heat conductivity, and its excellent forming characteristics. Laser welding has generally been adopted as a welding method for aluminium alloy. However, it is difficult to make the welding process stable due to the dependency on the focalization of a laser beam. The laser hybrid welding (LHW) technique has demonstrated several advantages such as deep penetration, improved gap tolerance, *Corresponding author: School of Mechanical Engineering, Yonsei University, Seoul 120-749, Republic of Korea. email: [email protected] JEM946
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better process stability, etc. LHW usually combines the laser beam with an electric arc; there are several combinations of different heat sources according to the types of laser beam and electric arc. There are a number of papers in the literature relating to the characteristics and effects of LHW [1–5]. However, the robustness of LHW is not easily evaluated due to the complexity of the physical phenomenon involved. The costly experiments investigating the LHW process are mainly used to determine the welding parameter conditions. The alternative, avoid the costly experiments, is to utilize a finite element method (FEM)-based numerical analysis. Generally, non-linear transient thermal analysis is able to realize the non-linear thermal distribution and thermo-mechanical characteristics in the welding process. It is very useful to use the numerical analysis (i.e. FEM) to study the thermal distribution and the thermo-mechanical characteristics such as residual stress and strain in the welding process [6–9]. A number of numerical models of welding processes have been used to evaluate the temperature and stress distributions during the welding process and predict the residual stress and strain of a welding structure. These include two-dimensional finite element models Proc. IMechE Vol. 222 Part B: J. Engineering Manufacture

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[10, 11] and three-dimensional finite element models of laser [12, 13] and arc welding [14]. In the LHW process, there are many parameters concerning the thermal phenomena such as laser welding output, arc welding output, initial temperature, ambient temperature, welding speed, welding wire feeding speed, temperature-dependent material properties, etc. For a complete understanding of the complicated physical characteristics of the LHW process, it is useful to apply the Taguchi method in order to evaluate the effects of the parameters on the responses and find out the optimal combination of parameters minimizing the residual stress and strain. Taguchi and Wu [15] proposed an effective experimental design method for characterizing the optimal parameters and reducing performance variation for a manufacturing process. The experimental design methodology of the Taguchi technique is distinguished by its orthogonal arrays and the analysis of signal-to-noise (S/N) ratio. The orthogonal array design provides an economic method for studying the interaction of process parameters on the mean and variance of a particular process response. Many experimental designs that are similar to the Taguchi method have also been adopted in various engineering fields to investigate the best setting for a number of decision variables in design problems [16]. In this study, the optimal parameter conditions of LHW are simulated via the FEM. The finite element model of a 5052-H32 aluminium alloy plate is considered to simulate the LHW process. The numerical simulation is performed for the design data generated from design of experiments (DOE) in the context of the Taguchi method. The main purpose of the Taguchi method used in the present study is to evaluate the effect of control parameters such as welding output and welding speed in LHW. The selection of control parameters depends on the realization of the comparison between numerical analysis and experiment. The ambient temperature is considered to be a noise parameter in the Taguchi method. The residual stress and plastic strain are considered as the main responses. S/N ratios are calculated for all the design data so that the optimal combination of welding parameters is determined to minimize residual stress and strain. The LHW experiment is conducted with similar variations in control parameters to those used in the Taguchi method, and the mechanical defects are investigated in terms of welding area. The results of the Taguchi method based on numerical analysis are compared with those of the experiment. Finally, the relations between control parameters and responses for the LHW of a 5052H32 aluminium alloy plate are represented using approximation methods such as the response surface model and a radial basis function-based neural network. Proc. IMechE Vol. 222 Part B: J. Engineering Manufacture

2 THE TAGUCHI METHOD FOR PARAMETER ESTIMATION AND DESIGN OF EXPERIMENT IN LHW 2.1 General description The weld flux is one of the important parameters in the welding simulation. In particular, the volumetric weld flux theory is applied to consider the deep penetration welding process [17]. The volumetric weld flux as the heat source is a double ellipsoidal shape [18] and is determined by the following equation pffiffiffi   6 3ff;r Q
3x2 pffiffiffiffi exp qf;r ðx; y; zÞ ¼ a2 abcf;r p p     ð1Þ 2
3y
3z2 · exp exp b2 c2 Q ¼ nVI

ð2Þ

where n is welding efficiency, V is voltage, and I is current; q is the weld flux rate per unit volume; a and b are the weld pool and weld width respectively; cf and cr are the welding magnitude of forward and backward welding direction respectively. ff and fr are represented by ff ¼

2 ð1 þ cr =cf Þ

ð3Þ

fr ¼

2 ð1 þ cf =cr Þ

ð4Þ

The weld flux rate can be further scaled by a factor. For two-dimensional problems such as planar and axisymmetric models, the scale factor is considered by equating the integral of the flux rate over the entire x–y plane and the out-of-plane thickness to the applied power ZZZ ZZ Q¼ qðx; y; zÞdx dy dz ¼ s qðx; yÞt dx dy ð5Þ

s¼

rffiffiffiffi p ðcr þ cf Þ 3 2t

ð6Þ

s¼

rffiffiffiffi pr 3t

ð7Þ

In the welding simulation, the transient thermal analysis and the non-linear thermo-mechanical analysis are carried out in sequence. In the transient thermal analysis, the transient temperature field is a function of time and the spatial coordinate, and is determined by the heat transfer equation as follows :

kTii þ Qint ¼ cr T

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where T is the transient time field, k the conductivity, Qint the internal heat source rate, c the specific heat, and r the density of material. 2.2 Numerical analysis of LHW For LHW, two plate halves, 150 · 300 · 2 mm, made of 5052-H32 aluminium alloy, were butt-jointed together as shown in Fig. 1, wherein the moving weld source was applied on the longitudinal top edge of the plate. It is assumed that the moving weld sources are a combined form consisting of the laser beam and the MIG arc. The mechanical boundary condition of the plate is the fixed condition at two ends parallel with welding direction. The symmetry along the weld seam was utilized by applying a symmetry boundary condition along the plane spanned by the seam and through-thickness

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axis. The cross-section of one of the plate halves was considered assuming the generalized twodimensional plane strain condition for the efficiency of computational time, as shown in Fig. 1. The finite element model used for computation simulation is shown in Fig. 2. The FEM consists of the base model part considered to be aluminium alloy plate and the weld filler model part used for the welding heat source. The material composition of 5052-H32 aluminium alloy plate is shown in Table 1. The material data used in the LHW simulation are referenced in literature reported by Zhu and Chao [7]. In order to review the non-linear thermal and thermo-mechanical phenomena in the welding process of aluminium alloy material, the temperature-dependent material properties of the 5052-H32 aluminium alloy plate were considered.

Fig. 1 Configuration of LHW plate (units: mm)

Fig. 2 Configuration of the finite element model used for welding simulation Table 1

Material composition of 5052-H32 aluminium alloy plate (%)

Alloy

Si

Fe

Cu

Mn

Mg

Cr

Zn

Al

5052-H32

0.25

0.40

0.10

0.10

2.2–2.8

0.15–0.35

0.10

Remainder

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2.3 DOE for welding simulation In order to find out the optimal combination of welding parameters, the Taguchi method was considered. The focus in the Taguchi method is to reduce the variation of system performance responses caused by uncertainty of noise parameter values, or to reduce system sensitivity. Solutions, which are system designs represented through settings of the control parameters, are sought to minimize response variation, in addition to the achievement of performance targets. The Taguchi method is built on the foundation of statistical DOE. In Taguchi’s parameter design method, the mean performance and performance variation are evaluated through a product array experimental design constructed by control parameters and noise parameters. In this study, the welding output and the welding speed were selected as the parameters with four levels. The welding output consisted of laser output and arc output estimated from torch voltage and current. The ambient Table 3 Welding output (level) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Table 2

Level Level Level Level

1 2 3 4

Control parameters and noise parameters, and their levels used in DOE Control parameters Welding output Welding speed (kW) (mm/s)

Noise parameters Ambient temperature ( C)

2.85 3.42 4.18 4.75

20 25 30 —

68 77 94 100

L16 design data for responses of residual stress (Pa)

Welding speed (level)

Noise (row 1)

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

1.45 · 10 1.56 · 108 1.66 · 108 1.87 · 108 1.35 · 108 1.41 · 108 1.58 · 108 1.67 · 108 1.25 · 108 1.34 · 108 1.46 · 108 1.51 · 108 9.92 · 107 1.05 · 108 1.11 · 108 1.19 · 108

Noise (row 2) 8

Table 4

temperature was also considered to be the noise parameter, which is also referred to as an uncontrollable parameter. The arrangement of parameters and their levels are shown in Table 2. The residual stress and plastic strain were selected as the response that has smaller-the-better characteristics. The combination of factor levels to be used for the L16 Taguchi orthogonal array is given in Tables 3 and 4. A total of 48 simulations were conducted in the numerical analysis of the LHW process. The S/N ratio

Noise (row 3)

1.41 · 10 1.46 · 108 1.56 · 108 1.67 · 108 1.31 · 108 1.36 · 108 1.50 · 108 1.57 · 108 1.15 · 108 1.18 · 108 1.33 · 108 1.42 · 108 9.80 · 107 1.02 · 108 1.06 · 108 1.12 · 108 8

Mean

1.40 · 10 1.42 · 108 1.43 · 108 1.50 · 108 1.28 · 108 1.30 · 108 1.43 · 108 1.47 · 108 1.05 · 108 1.12 · 108 1.18 · 108 1.22 · 108 9.51 · 107 9.54 · 107 9.62 · 107 9.67 · 107 8

1.42 · 10 1.48 · 108 1.55 · 108 1.68 · 108 1.32 · 108 1.36 · 108 1.51 · 108 1.57 · 108 1.15 · 108 1.22 · 108 1.33 · 108 1.39 · 108 9.74 · 107 1.01 · 108 1.05 · 108 1.09 · 108 8

Variance

S/N ratio

4.67 · 10 3.47 · 1013 8.87 · 1013 2.29 · 1014 8.22 · 1012 2.02 · 1013 3.76 · 1013 6.67 · 1013 6.67 · 1013 8.62 · 1013 1.31 · 1014 1.47 · 1014 2.94 · 1012 1.76 · 1013 3.89 · 1013 8.42 · 1013


163.065
163.436
163.834
164.526
162.383
162.680
163.560
163.913
161.251
161.733
162.492
162.877
159.774
160.100
160.401
160.782

12

L16 design data for responses of plastic strain (mm)

Welding output (level)

Welding speed (level)

Noise (row 1)

Noise (row 2)

Noise (row 3)

Mean

Variance

S/N ratio

1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

9.69 · 10
2 9.30 · 10
2 9.51 · 10
2 9.88 · 10
2 8.98 · 10
2 7.95 · 10
2 8.39 · 10
2 9.28 · 10
2 8.19 · 10
2 7.62 · 10
2 8.04 · 10
2 8.38 · 10
2 7.41 · 10
2 6.95 · 10
2 7.21 · 10
2 7.68 · 10
2

8.59 · 10
2 8.35 · 10
2 8.60 · 10
2 9.47 · 10
2 7.82 · 10
2 7.12 · 10
2 7.81 · 10
2 8.68 · 10
2 7.89 · 10
2 7.32 · 10
2 7.73 · 10
2 8.10 · 10
2 6.98 · 10
2 6.30 · 10
2 6.69 · 10
2 7.10 · 10
2

7.39 · 10
2 7.35 · 10
2 7.90 · 10
2 8.28 · 10
2 7.12 · 10
2 6.52 · 10
2 7.11 · 10
2 7.13 · 10
2 7.31 · 10
2 7.01 · 10
2 7.17 · 10
2 7.48 · 10
2 6.49 · 10
2 6.12 · 10
2 6.25 · 10
2 6.58 · 10
2

8.56 · 10
2 8.33 · 10
2 8.67 · 10
2 9.21 · 10
2 7.97 · 10
2 7.20 · 10
2 7.77 · 10
2 8.36 · 10
2 7.80 · 10
2 7.32 · 10
2 7.65 · 10
2 7.99 · 10
2 6.96 · 10
2 6.46 · 10
2 6.72 · 10
2 7.12 · 10
2

8.82 · 10
5 6.34 · 10
5 4.34 · 10
5 4.60 · 10
5 5.88 · 10
5 3.44 · 10
5 2.74 · 10
5 8.21 · 10
5 1.33 · 10
5 6.20 · 10
6 1.30 · 10
5 1.41 · 10
5 1.41 · 10
5 1.27 · 10
5 1.54 · 10
5 2.02 · 10
5

21.726 21.911 21.517 20.914 22.330 23.158 22.418 21.846 22.304 22.833 22.476 22.091 23.332 24.022 23.668 23.176

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for smaller-the-better characteristics is calculated in the following equation ! n 1X 2 y SNi ¼
10log ð9Þ n j¼1 ij where n is the number of simulations and yij is the ijth response of stress or strain. From the results of Tables 3 and 4, it is noted that each response of the design output has a different optimal set of design variables. The combination of level 4 welding output and level 1 welding speed was the best set to minimize the residual stress. In the case of plastic strain, a combination of level 4 welding output and level 2 welding speed was the best set. The main effects of

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the factors are shown in Figs 3 and 4 for each response. From the results of the main effects, it is noted that the welding speed has more influence than the welding output. For the combination of level 4 welding output and level 1 welding speed, the results of the temperature distribution contour are shown in Fig. 5. When considering the combination of level 4 welding output and level 1 welding speed, Fig. 6 shows the results of residual stresses, which are the results under the condition of applying the mapped loading by means of the transient temperature distribution. The maximum residual stresses occur in the area near the welding heat source.

Fig. 3 Main effects of residual stress on S/N ratio

Fig. 4 Main effects of plastic strain on S/N ratio JEM946
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Fig. 5 Welding temperature distribution results (units:  C) Fig. 6 Residual stress contour results (units: Pa)

2.4 Experimental confirmation and discussion In order to evaluate the validation of the Taguchi method results, LHW experiments on 5052-H32 aluminium alloy plate were carried out. The specification of 5052-H32 aluminium alloy plate and the boundary conditions are the same as for the numerical analysis. An Nd:YAG laser beam machine, MIG arc welder, and A5356 welding wire were applied in the experiment. The MIG arc welder was able to supply the correct amount of molten welding wire, break oxide film on the metal surface, and provide a suitable bead shape, although the moving speed of the welding sources is faster than a general arc welding method. A detailed schematic diagram of the welding sources is shown in Fig. 7, wherein the laser beam is irradiated on the 5052-H32 aluminium alloy plate perpendicularly and the MIG torch is inclined with an angle a ¼ 30o. The distance d between the laser beam and the MIG torch was set to 2 mm. Helium shielding gas was also supplied from the MIG torch nozzle. Through a number of experiments, the optimal welding conditions were investigated, varying the welding parameters such as welding speed, laser beam output, MIG output, and feeding speed of welding wire. Proc. IMechE Vol. 222 Part B: J. Engineering Manufacture

Fig. 7 Detailed schematic diagram of welding sources in LHW

Mechanical defects were also investigated by tension and bending experiments, observing the American Welding Society (AWS) regulation. Both the tension and bending characteristics of the welding part were directly related to the residual stress and strain. Figure 8 shows the welding bead appearance and metallurgical organization of the cross-section as the laser output was varied under conditions where JEM946
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Table 5

Comparison of Taguchi method results with experiment Optimal condition by Taguchi method

Optimal condition by experiment

Welding output (sum of laser beam and MIG)

4.75 kW

4.5 kW

Welding speed

68–77 mm/s

60–80 mm/s

Welding parameters

Fig. 8 Bead appearance and metallurgical organization with variation in laser output

other welding parameters were fixed at a MIG torch current of 70–90 A, MIG torch voltage of 12.6 V, welding speed of 80 mm/s, and welding wire feeding speed of 5.3 m/min. Mechanical failures were detected in the case of both 2.5 and 3 kW laser output, but there was no defect as 3.5 kW was applied. Photographs similar to Fig. 8 were obtained as the welding speed was varied while other welding parameters were fixed at a MIG torch current of 70–90 A, MIG torch voltage of 12.6 V, laser output of 3.5 kW, and welding wire feeding speed of 5.3 m/min. There were no mechanical defects with the variation of welding speed. Images were also taken as the MIG torch voltage was varied while other welding parameters were fixed at a welding speed of 80 mm/s, laser output of 3.5 kW, and welding wire feeding speed of 5.3 m/min. Mechanical failures were detected in the case of 10 V MIG torch voltage, but there were no defects when both 12.6 V and 20 V MIG torch voltage were applied. Finally, images were also taken as the welding wire feeding speed was varied while other welding parameters were fixed at a welding speed of 80 mm/s, laser output of 3.5 kW, MIG torch current of 70–90 A, and MIG torch voltage of 12.6 V. Mechanical failures were detected in the case of both 4.5 and 6 m/min welding wire feeding speed, but there were no defects as the 5.3 m/min speed was applied. From the experimental results, the optimal combination of welding parameters can be set as a laser output of 3.5 kW, welding speed of 60–80 mm/s, MIG torch current of 70–90 A, MIG torch voltage of JEM946
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12.6 V, and welding wire feeding speed of 5.3 m/ min. Comparison of the results of the experiment with the Taguchi method is shown in Table 5. Only welding output and welding speed are considered as parameters because numerical analysis is not able to adopt the welding wire feeding speed as the input factor. As shown in Table 5, the results from the Taguchi method are in reasonable agreement with those of the experiment. In order to evaluate the validation of the reasoning process for optimal welding condition, the transient temperature history near the welding heat source was measured for both numerical analysis and experiment. In the experiment, an engineering optical camera was used for measuring welding temperature and the measuring point was set at 90 mm from the welding heat source. The camera had the capability to measure the 2.48 s duration and the gauging area of 80 mm2. The comparison of the transient temperature history near the welding heat source is shown in Fig. 9, wherein the results from the numerical method are in reasonable agreement with those of the experiment. It is also possible to estimate the temperature variant considering the application of welding heat source and the cooling effects of the material properties and ambient temperature for LHW of a 5052-H32 aluminium alloy plate. 3 APPROXIMATION MODELS Approximation models can be used to reduce the number of computer-intensive, detailed analyses or experiments through the use of mathematical approximations of the design optimization objective and constraint functions. In particular, application of an approximation model is very much required in the optimization problem of a non-linear numerical simulation such as crash, contact, and fluid or thermal– structural coupled analysis. In this paper, from the results of Taguchi methods based on the numerical analysis, the relationships of the parameters and responses are represented using approximation models built using the response surface method and a radial basis function neural network (RBFNN). From the approximation models, the relationship between welding parameters and thermo-mechanical response Proc. IMechE Vol. 222 Part B: J. Engineering Manufacture

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Fig. 9 Comparison of transient temperature results (units:  C)

is continuously estimated within the range of the experimental levels. 3.1 Response surface model (RSM) From the approximation models, the relationship between factors and responses can be estimated without an additional experiment or numerical analysis. In general, the accuracy of the approximation model is highly dependent on the amount of information used for its construction, the shape of the exact response function being approximated, and the volume of the design space in which the model is constructed [19]. In a sufficiently small volume of the design space, any smooth function can be approximated by a quadratic polynomial with good accuracy. For highly non-linear functions, polynomials with third or fourth order can be used. In the present study, the RSM is approximated by a fourthorder polynomial. The fourth-order approximation model is represented by a polynomial of the following form f~ðxÞ ¼ a0 þ

N X

bi xi þ

i¼1

+

N X i¼1

di xi3

þ

N X

i¼1 N X

cii xi2

X

cij xi xj

ijði