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A set of piston rings is used to form a dynamic gas seal between the piston and cylinder wall. Many physical phenomena are associated with the operation of the system piston-ring-cylinder (PRC), such as: inter-ring gas dynamics for the labyrinth seal, hydrodynamic lubrication and mixed friction in gaps between the rings and cylinder liner, oil flow and distribution of lubricant along the liner, twist motion of rings, liner temperature influence on the oil viscosity. The first part of the paper presents a comprehensive model of the PRC system developed by the author. Among own models it includes several models taken from literature, like: a model of viscous oil flow between rough gap surfaces formulated by Patir & Cheng and an elastic contact model of Greenwood & Tripp. The main parts of developed mathematical model and software have been experimentally verified during a research period of the author at the marine engine designing centre ”Wärtsilä” in Switzerland.