Controlled Process of Crystallization in Weld Pool

Abstract

In this report the problem of control of solidification crack formation in welded plates is considered. In this problem the welding source is determined in dependence on the preset configuration and curvature of the rear part weld pool. A double ellipsoid model of weld pool with preset semi-axes may be used for the first approximation of preset weld pool configuration. It is an inverse problem which may be more efficiently solved as optimal control problem. The Function of welding source as a controlling function obtained in the result of solution is determined in a class of piecewise continuous functions which is more common class and the continuous-smooth functions are special partial case of common class. Recent methods of optimal control which use for solution of optimal control problems require to present the controlling functions in class of piecewise constant functions. Laser influence, electron beam, plasma, arc and submerged arc are the welding sources with high concentrated energy. A mathematical models of these welding sources may be introduced in class of piecewise continuous function with an efficient accuracy.