The article summarises the modelling of the technological process of Mannesmann piercing in the configuration of the GreatMannesmann rolling mill in the Tube Mill of Třinecké Železárny using the approach of both mathematical modelling and numerical simulation. In accordance with the mathematical model of the given process, the formation of the cavity during the rolling in the numerical range is replaced by pre-drilling a billet of a specific size given by the mathematical model. The numerical simulations have shown an absolutely fundamental effect of the distribution of the initial temperature field of the billet on the actual piercing process. The billet with the initial inhomogeneous temperature field was subject to very strong transverse oscillations and significant spiral structures appeared in the distribution of all physical quantities. When simulating the piercing process on the Mannesmann piercer in the Tube Mill of Třinecké Železárny, parameterised by a mathematical model so as to take into account in the best possible approximation the influence of the cavity initiation sequence during the actual piercing, the simulation results were completely consistent with the predictions of the mathematical model of the submitted process calibration.

The paper presents laboratory physical modeling of the seamless tubes production, specifically the first step of the Mannesmann production process, the so-called punching. A "Universal rolling mill" at MATERIAL & METALLURGICAL RESEARCH Ltd. was used for experiments. The experimental material was micro-alloyed steel. The tests were carried out at four different heating temperatures and at different rpm speeds of the working rolls. The other settings of the rolling mill remained the same. In terms of the geometrical parameters, the biggest necking of the punched sample (preferably at both ends) was observed with increasing temperature and strain rate. The torque decreased with increasing temperature and with lower speed of working rolls. The punching time and the total current power consumption decreased with increasing temperature and with a higher deformation rate.

At the studying the Mannesmann piercing process, we unify two approaches to the problem solving. Namely, the commercial FEM software procedure and the mathematical model of the process via the mathematical model of the considered FEM-simulation bound by certain unifying symmetries. Such phenomenon seemingly exists only if the FE-mesh is initiated to be physically interpreted. We shortly outline, how to come to the slightly modified Cahn-Hilliard equation as to the mathematical model of the FE-simulation possessing quasi-symmetry given by a lattice of colloidal assembly formed by the chosen FE-mesh. Separation of two cylindrical surfaces of the pierced product together with the inpainting role of the piercing plug are described with respect to the background given by the Navier-Stokes equations related to the flow between the both surfaces. Influence of the involved groups related to the considered quasi-symmetry is illustrated by the convergence/divergence of the Newton-Raphson number in the CPU-time.