A mathematical model of the offset ink printing system has been developed, which describes the operation modes of all its components. A simulator of the serialparallel structure ink printing system has been constructed, which reproduces the technological process of imprints replication. The simulation and research of the influence of the ink splitting factor at the contact places of the rollers and cylinders on the process of its transfer to the paper with different values of the form filling

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... efficients by the printing elements have been carried out. As a result of model experiments, a significant influence of the ink splitting factor value at the contact places of the rollers and cylinders on the ink thickness at the output of the ink printing system has been established. It has been found that this effect in the replication of imprints with different form filling coefficients by the printing elements has an Sshaped dependence. The high sensitivity of the offset ink printing system to the change of the ink splitting factors is established, which increases with the decrease in the density of the image elements on the surface of the imprints. A significant difference in the influence of the ink splitting factors on the dynamics of the ink printing system when replicating imprints with different fill density of their image elements is revealed. Problem statement. Offset ink printing system is a system consisting of an ordered set of metal cylinders and elastic rollers interconnected. In it, there are processes of supplying, rolling, and circulation of direct and reverse ink flows, the formation of a uniform thin ink flow with technologically defined properties. And also there is rolling this ink flow to the surface of the printing plate and transfer it through the blanket cylinder to the paper [1]. The physical processes that take place in ink printing systems are quite complex. Being in the distributing system the ink must be continuously transmitted from one system's element to another, well wetting the surfaces of the rollers and contact cylinders at the same time. Structural-mechanical ink properties are the basic technological properties that determine its deformation behavior in the ink printing system during printing, as well as the conditions of the interaction of ink with paper. Structural-mechanical properties mean rheological, cohesive, and adhesive properties of ink [2]. The printing process can only be realized if the adhesion of the ink to the paper and the printing elements of the form are greater than its cohesion. The ink