The factors describing the gripping conditions and the deformed state of sheet material (for example, leather) between the rotating rollers are considered in the article. The pull-in condition and horizontal motion of sheet material in a roll module, the upper and lower rollers of which rotate at the same linear velocity, are mathematically described. The dependence of the motion of internal particles (fibers) of sheet material on the process of its deformation is determined. The parameters characterizing the deformation properties of the processed sheet material are considered. The dependence of the motion of internal particles of sheet material on the angle of gripping at the inlet, during motion and at the outlet from rotating rollers during the process of its deformation is determined. A mathematical model is obtained to determine the parameters of strain and stress in the deformation zone of sheet material moving between rotating rollers.

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