The article is devoted to the analytical description of contact curves leather squeezing machines. The expressions for the ratio of strain rates during roller squeezing of the skin are determined when the deformation of the leather and the cloth is given as a power function. It has been established that changes in skin moisture during the squeezing process do not affect the model of contact curves when the deformation of the skin and cloth are given by power functions.

The study is devoted to mathematical modeling of the shape of the roll contact curves in two-roll modules. A two-roll module is considered, in which the rolls are positioned relative to the vertical with a tilt to the right, have unequal diameters and elastic coatings from the materials of different stiffness and friction coefficients, the material layer is fed with a tilt downward relative to the center line. The equations of the curves of roll contact in the considered two-roll module are derived. It is revealed that the obtained models are general in the sense that they are applicable for particular cases of interaction in a two-roll module.

A study on deformation and filtration properties of a leather semi-finished product after chrome tanning are presented. The analytical dependences of compressive load on compressive (recovery) strain and moisture content of a leather semi-finished product are obtained. The empirical dependences of hydraulic gradient on filtration rates are determined for various compression ratios of the leather semi-finished product. It was revealed that with an increase in compressive load and moisture content of the leather semi-finished product, the compressive deformation increases. The shoulder section is subject to the greatest deformation, then the belly section and the least deformation is observed in the butt section. A linear relationship has been established between the hydraulic gradient and the rate of moisture filtration through the leather semi-finished product in the directions perpendicular and parallel to its surface. Graphical abstract

The basic problems of the theory of contact interaction in a symmetric two-roll module are solved. Mathematical models of roll contact curves, friction stresses and distribution patterns of contact stresses in a symmetric two-roll module are obtained. Expressions that determine the indices of the roll contact curves in a symmetric two-roll module are derived. It was revealed that the neutral point in the drive roll is to the left of the centerline, and the maximum point of the diagrams of normal contact stresses does not coincide with the neutral point and is either in the no-slip zone or in the backward slip zone.