Modeling of Velocities and Accelerations in Sliding Processes

Abstract This study aims to develop a mathematical model of the stick-slip phenomenon for various materials employed in sliding tribosystems. Specifically, it focuses on modeling the slip phase of a sliding cylinder, determining its velocity and acceleration. The methodology is illustrated through an example involving the first slip event in a steel-on-steel tribosystem. The modeling framework is based on extensive experimental investigations conducted in the Tribology Laboratory of the IMMR Department at the Faculty of Mechanics. Existing literature provides an overview of different tribosystems and experimental setups used to analyze stick-slip behavior. In this study, a simple sliding tribosystem was utilized, comprising a weight (oscillating mass) on a flat surface moving at a constant translational velocity. The weight was connected to a force sensor via a tensile helical spring. The system was integrated with a CETR UMT-2 Tribometer, enabling controlled variation of translational speed (0.02–8 mm/s) and real-time data acquisition of tangential force, time, velocity, and displacement.