Mathematical modeling of plasma preheating of a cylindrical workpiece

The article considers a problem of mathematical modeling of the plasma-mechanical processing of circular cylindrical workpieces for the case of stationary and non-stationary modes. Workpiece preheating by a plasma arc can considerably reduce the strength characteristics of the processed material and significantly increase the productivity of shaping operations. When constructing the thermophysical model, the author's technique is used, based on the effect of fictitious near-surface internal heat sources. The modeling is based on partial differential equations of heat transfer under the assumption of anisotropy and temperature invariance of the physical and mechanical properties of the processed materials. The initial and boundary conditions consider both convective heat exchange with the environment and heat transfer by radiation in the infrared band. For stationary and non-stationary modes, the temperature fields are calculated by the Fourier method, what makes it possible to determine the value and the gradient pattern in the near-surface layer of the workpiece that is subjected to the greatest heating. The obtained relations are presented in an engineering form, which is convenient for carrying out practical calculations. A distinctive feature of the constructed models is the possibility of constructing temperature fields regardless of the workpiece sizes, since all the relations are derived in a dimensionless form with a unified characteristic size - the radius of the processed shaft. The conducted numerical experiment showed the limits of applicability and the need to use relations, considering the nonstationarity of the mode at the level of half of the characteristic size. When processing shafts longer than the workpiece radius, the effect of time becomes insignificant and the process can be considered stationary. In addition, the calculations made it possible to get the optimal distance between the cutter and the plasma burner in a dimensionless form from the point of view of the duration of non-overheating operation of the tool.