Optimisation of the thermal conditions of laser welding small‐diameter circular joints

Modelling of the optimum thermal conditions of laser welding circumferential joints of small diameter

“…The algorithm of the solution of the optimisation problem [1]- [4] will be examined and the results of solving this problem will be analysed in comparison with the results of solution of the optimisation problem for the boundary conditions of the first type, examined in Ref. 4 and presented in Fig.…”

“…where the unknown quantities ξ 0 , ξ 1 ,... are determined from the solution of the system of nonlinear algebraic equations: 4,11 ( …”

“…After substitution of the equations [4] and [5] in the form of a series in respect of the Bessell function and transformations, equality [6] has the form of the integral equation in relation to the unknown function q(r, t) whose solution is determined by the equation: 11 …”

“…These methods make it possible to formulate the problems of optimum control of the welding processes and obtain new schemes of the sources and the conditions of their effect. 7 These solutions cannot be obtained in the calculations based on the solution of the direct problem. The problem of determination of the welding conditions relates to the inverse problems and can be solved most efficiently in the linear formulation using the method of the theory of optimum control.…”

“…[1][2] In welding cylindrical components with a small diameter, the highquality formation of the welded joint depends greatly on the effective power q i , the welding source and welding speed v. These two main parameters of the welding process determined to heat input i q v , which in the first approximation characterises the penetrating capacity of the welding process and the cross-sectional area of the welded joint. 3,4 With increase of the speed of movement of the welding source and the proportional increase of the power of the source, the thermal process in the welded material tends to the limiting state in which the heat propagates mainly in the direction normal to the direction of displacement of the source. The source, determining this limiting state, is a powerful rapidly moving source.…”