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.

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 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.

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.

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The study is devoted to the analysis of the patterns of friction force distribution in two-roll modules. An asymmetric two-roll module is considered, in which the rolls are located 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. Friction stress models and formulas for calculating neutral angles in a two-roll module under consideration are determined. Dependencies between the forces acting on the rolls and the stresses distributed under these forces are established. It was revealed that these dependences do not change with a change in the angle of supply of the material layer to the line of centers and the angle of inclination of the upper roll relative to the vertical.

Analytical dependencies are determined that describe the patterns of change in filtration rates in the squeezing area. It was established that the fluid filtration rate along the abscissa axis at the boundaries of the compression zone is zero, and inside the zone, it takes negative values. It was found that the fluid filtration rates along the ordinate axis are zero at the beginning of the compression zone; they increase to a maximum at a point lying on the line of centers, and in the zone of strain restoration, they depend on the angle that determines the position of the point where the fluid changes direction.

The influence of factors on the width of the roller contact and the specific pressure under roller pressing of leather is analyzed in the article. As a result of experimental studies, the dependences of the width of the contact area and specific pressure on the intensity of the load, velocity, and diameter of the rollers were determined. It was revealed that the parameter of the technological specific pressure on the hide in the contact zone increases with an increase in the intensity of the load, the speed of rolls, the width of the contact area, and a decrease in the radius of rolls. An analytical dependence of the residual moisture content of leather on the specific pressure was determined. It was established that with an increase in specific pressure, the residual moisture content of leather decreases and asymptotically approaches a certain value of the function.