Mathematical model of bead profile in high deposition welds

Mathematical models of reinforcement and penetration profile in high deposition welds produced by multiple-wire processes are presented. A practical approach for assessment of shape and size of weld bead is introduced wherein characteristic coefficients (αi) of parametric equations y = f(αi, x) are expressed as functions of process parameters such as welding current, speed, and voltage, and they are determined by calibration of model with experimental observations using a heuristic technique. The validity of new model is demonstrated through a case study presentation on twin-wire welding. Compared to a semi-elliptical reinforcement and a cosine/parabolic penetration profiles in single-wire welds, an elliptical segment and a composite trigonometric function, respectively, are found more appropriate to represent multiple-wire welds. The effects of process parameters on bead profile and weld bead dilution for straight and reverse polarities over a wide range of process parameters are evaluated. The developed models explain effect of welding parameters on weld bead shape and weld cooling time, thus, apt for determining dimensions of heat source in modeling of welding processes.