CST004. Modeling of Double-Ellipsoidal Heat Source for Submerged Arc Welding Process. Nareudom Khajohnvuttitragoon and Chainarong Srikunwong*

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1 Modeling of Double-Ellipsoidal Heat Source for Submerged Arc Welding Process Nareudom Khajohnvuttitragoon and Chainarong Srikunwong* Department of Mechanical and Aerospace Engineering Faculty of Engineering King Mongkut s University of Technology North Bangkok Bangkok 10800, Thailand Corresponding author: csw@kmutnb.ac.th Abstract Submerged arc welding (SAW) process is widely used as a promising technique for structural member fabrication since it offers several key benefits such as low heat input, minimum welding distortion and potential for automated welding process. In this paper, welding experiments were conducted with direct-current electrode positive (DCEP) and alternating current (AC) power supply mode for joining structural steel plates. Welding schedule in accordance with the American Welding Society recommendation (AWS-D1.1/D1.1M:010) was employed for preparing a set of weld specimens. The Goldak double ellipsoidal heat source modeling approach along with intensive experimental data was taken into account in order to establish a 3-D physical heat source model for SAW process. It is disclosed that computational result of this model is reliable particularly for welding simulation in the lower domain of weldability. Keywords: Submerged arc welding, Double-ellipsoidal heat source, Weld geometry 1. Introduction In welding process simulation, several welding parameters are required as preprocessing input data including thermophysical properties of material, descriptive phase transformation of involved materials, workpiece geometry and joint design, clamping conditions, etc. However among these parameters, heat source model can be considered as a dominant input parameter having a direct role on both thermal distribution and final weld size. Selected heat source geometry, heat input or energy distribution, and arc density must be physically suitable for interested actual welding process. In the past, major progress in heat source modeling and welding simulation were the point heat source developed analytically by Rosenthal [1] and further numerical study for the one- and two-dimensional heat flow simulation conducted by Rykalin []. However, their models had a limitation on extreme calculated temperature values above the fusion point of material at the weld center, which is not the case in reality. Recent development in heat source modeling is suggested by Goldak [3]. Goldak proposes the Gaussian distribution-base doubleellipsoidal model defining a volumetric heat source that provides more accurate results in

2 terms of weld size and temperature distribution in joined workpieces than the above mentioned numerical studies. A key benefit of such numerical model is due to the versatility and flexibility in modification of both volume and shape of imposed heat source model. Li et al. [4] developed a methodology for estimating model parameters for hybrid heat source model which was a combination of surface heat source and double-ellipsoidal heat source model for submerged arc welding. However, it is quite complicated to employ this integrated model basing on the artificial neural network and the support vector machine regression algorithms in order to determine relevant model parameters from welding practice. Xiaolei et al. [5] employed the Goldak heat source model with a regression method to estimate heat source parameters in gas metal arc welding simulation. The result showed that proposed regression algorithm was feasible for the determination of heat source parameters. In this study, a 3-D moving heat source as the Goldak model is implemented to study thermal distribution and to quantify final weld size on structural steel plates. Heat source model parameters are predefined statistically by multiple linear regression algorithm for a set of welding tests covering actual welding parameters in the upper and the lower limits of the weldability domain. This technique offers reliable model parameters for a wide range of applied welding schedules and can ensure that numerical model is consistent in predicting final weld size within a specific domain.. Experimental Method and Regression Model.1 Experimental procedure and welding facility used Welding schedule was conform to AWS specification [6]. Lincoln gantry automatic submerged welding machine was used for joining all weld specimens. Dimension of structural steel JIS Grade SS400 specimen was mm. Diameter of selected filler electrode was 4.8 mm. The variable parameters were; travel speed ( T ) varied between 60 and 80 cm/min., voltage (V ) in the range of 3 and 38 volts, and welding currents ( I ) being between 600 and 800 amperes. These welding parameters were selected for both DCEP and AC power supply modes.. Multiple linear regression model Multiple linear regression technique is chosen for estimating the parameters of heat source model from actual weld size. General form of multiple linear regression equation is X X,...,, Y b b X b X... b X 1 1 k k Where Y X k 0 (1) is the criterion variable, 1 are the explanatory variables, 0 is the interception and b 1, b,..., bk are the estimated slope in linear regression. Purpose of multiple regression is to estimate the unknown Y value corresponding to a set of X values and also identify relationship between them. In this study, the criterion variable is the molten pool geometry predicted by welding parameters as explanatory variables. There are three explanatory variables used including total heat input ( V I ), reciprocal of travel speed ( T ) and voltage (V ). b

3 .3 Experimental results and discussion Weld coupon is sectioned and the measurement of weld bead dimension is done by using macro-photographic technique. Weld bead dimensions such as ellipse height ( E h ), ellipse width ( E w ), bead width ( B w ), height ( B h ) and length ( B ) are shown in Fig. 1. Depth Regarding regression model established for weld bead geometric fitting, it is found that the discrepancy in weld bead geometry is less than Ellipse width 7.5 percent. Fig. 1 Geometric representation of Proposed regression model as written in cross-sectional weld bead matrix form represents a rigorous relationship Result of welding tests in terms of weld between welding parameters and relevant weld bead geometry and corresponding welding bead geometry. Each column of design matrix parameters for 16 cases are summarized in shows the influence of individual welding Table.1. A comparison made between case 4 and parameter affecting on entire weld bead geometry. 8 for DCEP welding or case 10 and 14 for AC Similarly, each row of design matrix takes into welding reveals that welding schedule with higher account welding parameters affecting a single amount of energy supply, in terms of high weld geometry. electrical potential, high current, and low travel The first matrix column ensures distinctly speed results in larger weld bead and deeper that increasing heat input yields larger value for penetration. every pool dimensions. The second column Multiple linear regression for the effect of Table. 1 Welding parameters according to the AWS specification and welding results for 16 cases Experiment case Type DCEP AC V I T Width Height Long Width Welding Parameter Bead dim. [mm.] Ellipse dim. [mm.] Ellipse height l Width Height welding parameters on the weld bead geometry developed from experimental data can be evaluated by Eq. and Eq.3 for DC and AC power supply modes, respectively Height Bw V I Bh T B l V Ew E h Bw V I Bh T B l V Ew E h () V (3) 1

4 provides an increasee of travel speed resulting in a reduction of all weld dimensions. However, this is not the case for the development of bead length in AC welding. Considering the last column in the matrix, it is found that almost smaller weld geometry is produced by using high electrical voltage or with equivalent amount of total heat input. It can be concluded that using high electric current can promote obviously larger weld size than that of high voltage at the same amount of power density. 3. Finite Element Method 3.1 Material properties Workpiece is the low-carbon structural steel plate. Density of steel is 7860 kg/m 3. Thermal conductivity and specific heat described as a function of temperature are plotted in Fig.. At the fusion state of material, a constant thermal conductivity of 10 mj/mm.sec. C [3] is assumed to take into account the heat transfer processs due to convective stirring effect in the molten pool. The latent heat of fusion is J/kg. 3. Geometry and mesh construction The welded plate with filler metal is constructed as a half-symmetrical model shown in Fig. 3. Weld bead dimension can be determinedd in accordance with actual welding parameters given in Eq. or Eq.3. The hexahedral elements are selected and refined mesh construction is concentrated around the bead region wheree thermal gradient is significant. Coarsened mesh topology is applied for regions where thermal gradient is less important, i.e. heat affected zone (HAZ) and base material. Range of total number of elements applied in all simulation cases is between 18, 780 and 0,80 basing on priorr mesh-sensibil lity examination. Thermal conductivity [J/m sec C] Temperature [ C] Thermal conductivity Specific heat Specific heat [J/kg C] Fig. Thermal conductivity and specific heat as a function of temperature Fig. 3 Mesh topology and model dimension 3.3 Boundary conditions and applied heat source Initial temperature is set to 5 C. Convection and radiation losses are negligible. The Goldak double-ellipsoidal heat flux distribution [3] has been represented as a body heat flux for welding heat distribution. The power

5 density distribution at any point (x, y, z) can be expressed as q 6 3 f f, r 3x a 3y b 3 zv t x, y, z, t e e e abc Q c Where, Q is the total power, f f, r are the front and rear distribution fractions, v is the travel speed, t is the time and a, b, c are semi-axes of the ellipsoid in the direction of the x, y, z axes as shown in Fig. 4. (4) depositing on the plate. The weld bead length is 80 mm. Imposed 3-D heat source moving along the center line of specimen is depicted in Fig. 5. Ellipse width (W) and height (H) of the numerical result are measured from cross-sectional geometry of weld bead by fitting fusion zone boundary with elliptic equation as illustrated in Fig. 6. Fig. 5 Imposed 3-D heat source traveling along the center of welded specimen Fig. 4 Double-ellipsoidal heat source geometry Heat source model parameters including a, b and c have an influence not only on heat source shape but also on weld pool dimensions. s SF are needed to correct these values basing on experimental weld bead defined by the following equations: E a SF w (5) b c E SF h (6) B SF l (7) Value of size fraction is initially set to Numerical results and discussion In welding simulation process, welding heat source starts initially at 0 mm. away from the plate edge and moves along the bead Fig. 6 Measurement of simulated weld pool Range of computed peak temperature in the molten pool is approximately between 1,800 and,150 C. Thermal history including heating and cooling stage at four positions normal to and

6 away from the center line of weld bead is illustrated in Fig. 7. Comparison of weld pool dimension discrepancy is shown in Fig. 8 where ellipse width and height disparity is compared with the experimental result. Numerical result reveals that molten pool dimension disparity are governed principally by the type of electric power while voltage, current and travel speed cause minor effect on the disparity of molten pool dimension. Temperature [ C] Time [s] 0 mm mm mm mm. Fig. 7 Thermal history at 0, 4.36, 7.58, and 9.37 mm. normal to and away from the center line of weld bead Average of ellipse width and height discrepancy in slower and higher travel speed is presented in Figs. 9 and 10 for DCEP and AC welding mode, respectively. Influence of size fractions on weld pool are clearly displayed by these plots. For DCEP power mode, average minimum discrepancy of ellipse width and height can obtain for optimal size fractions of 1.58 and 1.0, respectively. Similarly for AC power mode, minimal inconsistency in ellipse width and height is obtained for optimal size fractions of 1.76 and 1.44, respectively Case 1-4 (DCEP mode with slower travel speed) Case01-W Case0-W Case03-W Case04-W Case01-H Case0-H Case03-H Case04-H Case05-W Case06-W Case07-W Case08-W Case05-H Case06-H Case07-H Case08-H Case 5-8 (DCEP mode with higher travel speed) Case 9-1 (AC mode with slower travel speed) Case (AC mode with higher travel speed) Case09-W Case10-W Case11-W Case1-W Case09-H Case10-H Case11-H Case1-H Case13-W Case14-W Case15-W Case16-W Case13-H Case14-H Case15-H Case16-H Fig. 8 Disparity of weld pool dimension as a function of size fraction a) b) c) d)

7 Fig. 9 Average of ellipse dimension inconsistency (DCEP mode) Fig. 10 Average of ellipse dimension inconsistency (AC mode) DC-Slow-W DC-Slow-H DC-Fast-W DC-Fast-H DC-Ave. AC-Slow-W AC-Slow-H AC-Fast-W AC-Fast-H AC-Ave. 4. Validation Comparison of fusion zone predicted by finite element analysis and experimental value is shown in Fig. 11. In the case of welding with low-energy input or welding practice at the lower domain of weldability such as the case 13, computed bead geometry is agreeably accurate comparing with that of experiment. Very little discrepancy value of 0.86% for the comparison of the weld penetration is obtained. However, calculated weld pool depth is less than that obtained from the experiment especially for the case of welding practice done at the upper domain as in the case 3 in which computed penetration size of the molten pool is 31.4% smaller than that obtained from experience. 5. Conclusion According to results presented in this paper, the following observations and conclusions can be made: 1. Method for heat source modeling, i.e. the Goldak model, was successfully implemented to simulate the weld bead shape in SAW process. Model parameters of the Goldak heat source model were determined by multiple linear regression method basing on several welding schedules. Case 1 Case 3 Case 5 Case 9 Case 13 Case 15 Fig. 11 Comparison of geometry of fusion zone obtained from computational and experimental results

8 Validation made in terms of weld penetration and width was in a good agreement for both DCEP and AC welding modes in the lower domain of weldability or low-energy input welding as in the case 1 and 13 for DCEP and AC welding procedure, respectively. Generally, it can be concluded that computational result of this model is accurate and reliable in particular for welding parameters of the lower domain of weldability.. Geometric parameters of the Goldak heat source model can be accurately approximated by using proposed multiple linear regression model along with a set of welding experiments. 3. For an effective weld prediction in SAW process, the optimal size fraction values of 1.4 for DCEP and that of 1.63 for AC welding operation have been statistically determined from a series of modeling cases. These values are beneficial for a successful correlation between calculated molten pool and that obtained from welding experiment. 6. Acknowledgement The authors would like to gratefully thank the M.S.C. Steel Public Co., Ltd. for providing the welding facilities and carrying out the experiments. Also, the authors would like to express their gratitude to Materials Science Laboratory, Faculty of Engineering, King Mongkut s University of Technology North Bangkok for macroscopic examination of weld specimens and The Graduate College, King Mongkut's University of Technology North Bangkok for partially funding this research program. 7. References [1] Rosenthal, D., (1949). The theory of moving sources of heat and its application to metal treatments, Transactions of American Society of Mechanical Engineers, 1946, Vol. 68, pp [] Rykalin, R.R., (1974). Energy sources for welding, Welding in the world, 1974, Vol. 1, No. 9/10, pp [3] Goldak, J., Chakravarti, A. and Bibby, M. (1984). A new finite element model for welding heat sources, Metallurgical Transactions B, Vol. 15B, pp [4] Li, P. and Lu, H. (01), Hybrid heat source model designing and parameter prediction on tandem submerged arc welding, International journal of advanced manufacturing technology, 01, Vol. 6, pp [5] Xiaolei, J., Jie, X., Zhaoheng, L., Shaojie, H., Yu, F. and Zhi, S. (014), A new method to estimate heat source parameters in gas metal arc welding simulation process, Fusion engineering and design, 014, Vol. 89, pp [6] Structural Welding Code - Steel (010), the American Welding Society, AWS -D1.1/D1.1 M:010, 010.