Received: March 01, 2024
Revised: March 03, 2024
Accepted: March 08, 2024
Lviv Polytechnic National University
Department of Robotics and Integrated Technologies of Mechanical Engineering, Lviv Polytechnic National University
Department of Robotics and Integrated Technologies of Mechanical Engineering, Lviv Polytechnic National University
EPAM Digital

The goal of the work is to develop a mathematical model of a workpiece bending process by copier to determine the necessary parameters of the process and increase its efficiency. Significance. The quality of the process of workpiece bending by copier depends on many factors and is accompanied by both elastic and plastic deformations. Therefore, a mathematical description and analysis of the workpieces is an urgent issue, because it will allow to justify the parameters of the process and increase its efficiency. Method. The dependence between stresses and strains was used for an analysis of the bending process, instead of Hooke's law. Since there is a linear stressed and a volumetric deformed state for the narrow workpiece, then, according to the assumption of the flat cross-sections, a relative deformation of the arbitrary fiber is a linear function of its movement from a neutral layer. It was determined a bending moment in the section of the workpiece having the curvature radius of the neutral layer and considered the equilibrium of the workpiece bent element from the last point of contact with the copier to the point of a force application. As a result, a system of equations was obtained that eliminates the task of elastic-plastic deformation of the workpiece. Results. Using the mathematical model of the workpiece bending process by copier allows to determine the necessary parameters of the process, in particular, the clamping force, the size of which, in addition to other factors, is significantly influenced by the gap, with the increase of which the value of the clamping force will decrease. Scientific novelty. Mathematical dependencies have been established to determine the main parameters of the workpiece bending process by copier. Practical significance. The results of mathematical modelling will allow to increase the efficiency and quality of that process

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