Mathematical modeling of reproduction process of microgeometry of roll surface on trained strip based on similarity criteria and generalized coordinates

A mathematical model is developed based on similarity criteria and generalized coordinates, which makes it possible to adequately describe the of formation process of the surface roughness of the trained strip with an estimate of the roughness parameter Ra, taking into account disturbing production factors and the length of the trained metal. The modeling methods used in the development of technologies and research of plastic metal working processes are generalized, with the allocation of mathematical modeling based on similarity criteria and generalized coordinates, which makes it possible to obtain the most informative mathematical model and the most appropriate to the real object. The application of mathematical modeling to the process of training an annealed or galvanized strip with the formation of a negative imprint of the microgeometry of the roll surface of a training mill with its regulated parameters on its deformed surface is considered. The evolution of the use of similarity criteria is shown as they increase during the formalization of the microgeometry transferring process of the roll surface of a training mill to a deformable strip with an assessment of the adequacy of mathematical models. Using the example of the effect of disturbing production factors on the instability of the roughness formation process on a deformable strip, the possibility of extending similarity conditions not only to objects with constant, but also with variable parameters is confirmed, provided that the relative variable characteristics coincide.