The challenges of the inverse problems solution in welding technology: a review and a practice

Abstract

Methods for solving the inverse technological problem, which consists in determining the welding parameters by the desired properties of the welded joint, are discussed. The quality criteria of welds have been developed, which can be used to solve the inverse problems of welding technology. In the simplest case, weld sizes and their ratios may be the quality criteria. The time and space are considered discrete during the modeling thus the equations describing welding process are transcendental equations. The transcendental equations included in the systems colligate welding parameters such as current, arc voltage, travel speed, electrode diameter, its extension, physical properties of welding metal from one hand and quality criteria from another hand. One of the methods of solving the inverse technological problems is the solving of systems of transcendental equations. The mathematical support is discussed and the application of the graphical method for determining the welding parameters is shown. The possibility of determining the optimal welding parameters using methods of nonlinear programming is shown also. According the method of Lagrange multipliers one have formed the expression in which the most important weld quality criteria are used as an object function. Other quality criteria were accepted as constraints. Solving the expression obtained in the space of restrictions on welding parameters, welding parameters are obtained that deliver the local conditional optimum of the subject function.