Original Article

Correlation analysis between coiling tension and the sleeve's hoop stress

Department of Mechanical Engineering, Sunmoon University, Asan, Chungnam, Republic of Korea

^* e-mail: yonghuipark@sunmoon.ac.kr

Received: 6 July 2024
Accepted: 6 November 2024

Abstract

The coiling process, crucial for winding long sheets of consistent thickness, often encounters challenges due to deformation induced by pressure and frictional forces on the inner mandrel and sleeve. This necessitates precise stress calculations to ensure operational safety within elastic deformation limits. This study proposes a novel mathematical model to accurately predict stress distribution in the sleeve's hoop direction. The mathematical model is modified by applying a correction factor, derived from an enhanced analytical solution based on the Lame equation, specifically tailored to address coiling stress during prior elastic deformation. Validation of the proposed analytical solution was carried out using finite element analysis through the ABAQUS model. This validation process revealed variations in stress within the sleeve's hoop direction corresponding to different coiling tensions. Furthermore, parametric analysis highlighted a correlation between increased coiling tension and higher frictional forces exerted by the first layer of the steel coil on the sleeve, resulting in discernible variations in hoop stress based on sleeve radius and coiling tension. The key innovation lies in the application of the correction factor to the Lame equation, enabling the derivation of stress results consistent with finite element analysis, even under arbitrary coiling tension and sleeve radius inputs. This analytical solution not only holds promise for predicting the behavior of various thick-walled cylinders produced through different manufacturing processes involving coiling but also facilitates integration with monitoring systems to mitigate slumping during steel rolling operations, all while minimizing computational burden.