Algorithm Based on Convex Programming Method for Optimum Heat Input Control in Arc Welding

A simple mathematical method for the estimation of the optimum heat inputs in arc welding has been developed in the present work, the optimization problem is to make the temperature field coincide with the requirement during welding. In the expression of the problem, an analytical solution of heat flow equation is applied for the calculation of the temperature field in welding, and the objective function is defined as the difference between calculated and required temperatures. The problem is expressed as the quadratic function of heat inputs and it results in the convex programming problem, and it is clarified that the global optimum is certainly obtained by using Kuhn-Tucker conditions in the non-linear programming method. Furthermore, the propriety of the optimizing algorithm is evaluated experimentally by a bead-on-plate welding test, and it is concluded that the algorithm proposed in the present work is reliable and useful enough to determine the optimum heat input pattern in arc welding process.