(A) study on the optimization of process parameters using a semi-analytical finite element method in circumferential gas tungsten arc welding of a aluminum pipe

Abstract

The heat flow during circumferential welding of a small diameter aluminum pipe, which cannot be assumed to be in the quasi-stationary state because of the heat accumulation, was analyzed by employing a semi-analytical finite element method. The circumferential distributions of the arc heat flux and the temperature were simulated in the forms of an expanded series to calculate the 3-dimensional heat flow with a 2-dimensional solution domain. The arc heat distribution, assumed as a Gaussian form, was expressed in several circumferential line heat sources by using the Fourier series expansion. The solution domain was divided into two subdomains to apply the two types of series with two different numbers of the expanding term, which results in the reduction of the calculation time. The thermal cycles and isotherms in the r-z plane clculated by using the proposed semi-analytical finite element method agreed fairly well with the experimental results adopted from a reference. Due to the heat build-up the fusion zone increases in its size as the welding proceeds. The temperature near the heat source rises also as the welding proceeds, but the shape of the circumferential temperature distribution of a ring element was maintained almost unchanged during the entire welding process except for the welding start. Both the increment of the fusion zone and the rise of the temperature were chiefly caused by the rise of the coefficient of constant terms in series for the temperature distribution. The proposed semi-analytical finite element method could be considered as very useful for analyzing the heat flow in circumferential welding of small diameter pipes because of its simple formulation and short computing time. When the material properties are dependent on the temperature in the circumferential welding of a pipe, the orthogonality in integration of harmonics may not be obtained in the formulation of the semi-analytical finite element method for the heat flow analysis. When...