FORCE ANALYSIS OF THE BENDING PROCESS OF THE WORKPIECE BY COPIER

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

[1] J. Liu, Sh. Li et al "Machine learning (ML) based models for predicting the ultimate bending moment resistance of high strength steel welded I-section beam under bending", Thin-Walled Structures, vol. 191, p. 111051, October, 2023.
https://doi.org/10.1016/j.tws.2023.111051
[2] E.P. 1. Hinchy, C. Carcagno et al. "Using finite element analysis to develop a digital twin of a manufacturing bending operation", in 53rd CIRP Conference on Manufacturing Systems, Chicago, 2020, pp. 568-574.
https://doi.org/10.1016/j.procir.2020.03.031
[3] Sh.-Ch. Chen, J. Liu et al. "Investigations into the local buckling and post-buckling behaviour of fixed-ended hybrid I-section stub columns with slender web", Thin-Walled Structures, vol. 184, p. 110174, March, 2023.
https://doi.org/10.1016/j.tws.2022.110174
[4] X. Yun, Yu. Zhuet et al. "Welded steel I-section columns: Residual stresses, testing, simulation and design", Engineering Structures, vol. 282, p. 115631, May, 2023.
https://doi.org/10.1016/j.engstruct.2023.115631
[5] L. Schaper, T. Tankova et al. "A novel residual stress model for welded I-sections", Journal of Constructional Steel Research, vol. 188, p. 107017, January, 2022.
https://doi.org/10.1016/j.jcsr.2021.107017
[6] Sh. Chen, Jun-zhi Liu et al. "Material properties and residual stresses of welded high strength steel and hybrid I-sections", Engineering Structures, vol. 276, p. 115293, February, 2023.
https://doi.org/10.1016/j.engstruct.2022.115293
[7] Jun-zhi Liu, H. Fang et al. "Numerical investigation and design for the local buckling behaviour of high strength steel hexagonal hollow section stub columns under axial compression", Thin-Walled Structures, vol. 186, p. 110717, May, 2023.
https://doi.org/10.1016/j.tws.2023.110717
[8] Jun-zhi Liu, Sh. Chen et al. "Testing, numerical modelling and design of Q690 high strength steel welded T-section stub columns", Engineering Structures, vol. 259, p. 114142, May, 2023.
https://doi.org/10.1016/j.engstruct.2022.114142
[9] Yu. N. Rabotnykov, Polzuchest elementov konstruktsii. Lviv, Ukraine: Vishcha shkola, 1966. [in Ukrainian].
[10] K. N. Rusynko, Teoriya plastichnosti i neustanovivsheisya polzuchesti. Lviv, Ukraine: Vishcha shkola, 1981. [in Ukrainian].