Abstract
One of the controversial provisions the rolling theory is the question of the possibility the stable process of cold rolling with lubrication at a complete lag of the strip’s metal in the deformation zone, i.e. in conditions of negative advancing.
 The equilibrium state in the zone of deformation with negative advance can be maintained due to the change in the thickness of the lubricating film. This is evidenced by experimental data from the study of the dependence of the advancing and the thickness of the lubricant layer on the grip angle during cold rolling with castor oil the copper samples in sizes 5x60 mm. Rolling was carried out on a duo 180 laboratory mill in steel rolls with a diameter of 190 mm. The rolling speed was 0.35 m/s.
 Then stress state modeling is used to theoretically substantiate the possibility of a stable process with single-zone sliding of metal in rolls during cold rolling with effective technological lubricants. According to Newton's law, the frictional forces acting in the zone of deformation depend on the sliding speed of the metal on the rolls and on the thickness of the lubricating film.
 Substituting the chooses model of specific friction forces into T. Karman's differential equation of equilibrium and solving it under known boundary conditions, expressions for the distribution of contact stresses were obtained.
 The results of calculations in the conditions of contact-hydrodynamic friction prove that the maximum of normal pressure shifts closer to the entrance to the deformation zone. In the case of rolling with a negative advancing, the longitudinal normal tensile stresses occur near the cross-section at the exit of the metal from the rolls. The average pressure in the deformation zone is always greater than the forced yield strength for the rolling strip.
 With an increase in the lag of the metal from the rolls at the exit from the zone of deformation, the average pressure decreases. Rolling with single-zone strip sliding is an energy-efficient process.
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