Adjoint problems of mechanics of continuous media in gas-laser cutting of metals

A mathematical model of gas-laser cutting of metal plates in an inert gas is proposed. The formation and flow of the liquid metal melt film at the cutting front is considered within the framework of incompressible boundary-layer equations. Based on the resultant analytical solution, a local law of energy conservation on the cutting surface is derived, which takes into account the melt-film thickness and the temperature dependence of thermophysical parameters of the metal. The problem of the cutting shape and depth is solved in the two-dimensional formulation. A comparison with experimental data is made in terms of the cutting depth and maximum cutting velocity for carbon and alloy steel.