O. B. Kovalev

Mathematical modelling of striation formation in oxygen laser cutting of mild steel

A physicomathematical model is proposed for the phenomenon of formation of periodic striations in oxygen laser cutting of mild steel sheets. The mechanism of roughness origination is assumed to be caused by a cyclic reaction of iron–oxygen oxidation. The mathematical description is based on solving the adjoint problems of heat and mass transfer in the liquid phase and in the solid metal with nonlinear moving interfaces between the substances and phase changes. The motion of the boundaries occurs owing to metal melting under the action of focused laser radiation and the heterogeneous chemical reaction of iron oxidation in oxygen. The main feature of iron oxidation is the loss of protective properties of its oxide film due to melting. The general statement of the problem for the nonlinear heat-conduction equation with variable coefficients is formulated by the type of the Stefan problem solved with the use of the difference method with smoothing coefficients at the melting point and the fictitious domain method, which allows obtaining of the solution without explicit identification of the cut boundary and the phase-transition front. Results of numerical simulations of the shape and linear size of roughness as functions of the cutting velocity, purity of oxygen and thickness of the film of the iron oxide being formed are presented.

Simulation of surface profile formation in oxygen laser cutting of mild steel due to combustion cycles

A physicomathematical model of cyclic iron combustion in an oxygen flow during oxygen laser cutting of metal sheets is developed. The combustion front is set into motion by focused laser radiation and a heterogeneous oxidation reaction in oxygen. The burning rate is limited by oxygen supply from the gas phase towards the metal surface, and the interface motion depends on the local temperature. A 3D numerical simulation predicts wavy structures on the metal surface; their linear sizes depend on the scanning speed of the laser beam, the thickness of the produced liquid oxide film and the parameters of the oxygen jet flow. Simulation results help in understanding the mechanism of striation formation during oxygen gas-laser cutting of mild steel and are in qualitative agreement with experimental findings.

Formation of a vortex flow at the laser cutting of sheet metal with low pressure of assisting gas

Specific features of subsonic jet gas flows in narrow channels geometrically similar to the laser cut are studied experimentally and theoretically. Such flows are visualized by a technique based on prior application of a viscous liquid film onto the side walls of the channel made of transparent glass. The gas flow inside the channel induces a liquid flow on the glass wall in the form of extremely small filaments, which coincide with the streamlines of the gas flow. Filming of these filaments by a CCD camera allows one to capture the specific features of these gas-dynamic flows. Mathematical modelling of the dynamics of a viscous compressible heat-conducting gas was performed by solving full three-dimensional Navier–Stokes equations. Numerical calculations and experiments reveal vortex structures in the flow at the entrance and exit of the channel, which may directly affect the surface quality in real gas-laser cutting of metals. The largest vortex, which arises at the channel exit, collects and accumulates the liquid flowing down the channel walls. Jet flows are generated by sonic nozzles with conical or cylindrical exit sections or by a double coaxial nozzle. The double nozzle includes the central conical nozzle and the side concentric nozzle, which allows additional side injection of the gas to be organized. The study with the double nozzle shows that the vortices disappear as the pressure in the external nozzle is increased, and a stable vortex-free attached gas flow is formed.

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.

Presence of Plagiotrochus Mayr, 1881 in the Himalayan area, with redescription of Plagiotrochus semicarpifoliae (Cameron, 1902) COMB. N. (Hymenoptera: Cynipidae)

Plagiotrochus semicarpifoliae comb n. is transferred to Plagiotrochus Mayr from Callirhytis Foerster, 1869, and adults of the agamic form are redescribed and compared with other species of the genus. The plesiomorphic traits of P. semicarpifoliae suggest a Southeast Asian origin for Plagiotrochus, which could have migrated with their hosts to the Mediterranean area, where the most derived forms are present.

Modeling of the random packing of a loose layer of polydisperse spherical particles

A method for calculating the loose packing structure of polydisperse spherical particles with a predetermined size distribution function is proposed. The coordinates of the particle centers in the loose layer are determined as the result of random fall of single spheres on a substrate under the action of gravity, assuming the inelastic collision of the spheres and considering the force of their adhesive interaction, and also assuming that the motion of one sphere on the surface of the other is pure slip. Numerical simulation is used to obtain the pattern of arrangement of polydisperse spherical particles in the loose powder layer, whose porosity depends on the particle size distribution function. The results are compared with experimental data.

Effect of the recoil pressure induced by evaporation on motion of powder particles in the light field during laser cladding

A model is proposed, which takes into account acceleration of powder particles by a force induced by recoil of material vapors from the irradiated region of the particle surface. Results of a numerical analysis of heat and mass transfer in the case of motion of individual stainless steel powder particles in a gas flow and in a light field of laser radiation under conditions of laser cladding are presented. Acceleration of particles is found to depend on their diameter, carrier gas velocity, powder material properties, laser radiation power, and degree of attenuation of the power density in the laser beam in the direction of its action on the substrate. The calculated results are compared with experimental data on light-propulsion acceleration of individual particles (of aluminum, aluminum oxide, and graphite) under the action of pulsed laser radiation.

Numerical simulation and experimental investigation of three-dimensional gas-jet transportation of powder particles in direct material deposition

This paper presents experimental and theoretical results of studies the DMD processes. Three-dimensional physical and mathematical analysis of gas-jet transportation of powder particles has been developed. A detailed research of gas and powder stream parameters for coaxial nozzle is performed. The distribution of the 3D mass-flow and the density of powder flow are calculated and the positions of the local powder focus area in the space between the nozzle and the substrate are determined. A dedicated device has been designed and implemented in order to measure the 3D powder jet profiles of existing nozzles. A laser plane from a diode laser He-NE source is placed perpendicularly to the powder jet and creates a 2D slice of the powder flow by lighting it at a given height. Comparisons of numerical simulation results with experimental data are presented. It gives more complete understanding of the physical mechanisms of the processes.This paper presents experimental and theoretical results of studies the DMD processes. Three-dimensional physical and mathematical analysis of gas-jet transportation of powder particles has been developed. A detailed research of gas and powder stream parameters for coaxial nozzle is performed. The distribution of the 3D mass-flow and the density of powder flow are calculated and the positions of the local powder focus area in the space between the nozzle and the substrate are determined. A dedicated device has been designed and implemented in order to measure the 3D powder jet profiles of existing nozzles. A laser plane from a diode laser He-NE source is placed perpendicularly to the powder jet and creates a 2D slice of the powder flow by lighting it at a given height. Comparisons of numerical simulation results with experimental data are presented. It gives more complete understanding of the physical mechanisms of the processes.