A comprehensive analytical model for tensile-bending straightening in strip processing by coupling residual stress and buckling deformation

Abstract

Tensile-bending straightening machines improve strip quality by optimizing the residual stress distribution within the strip and eliminating plate defects. Straightening involves multiple roller groups and various initial defect shapes. However, previous research has mainly focused on single roller group analyses and finite element models. These approaches cannot fully address the entire straightening process for strips with initial defects, hindering their practical application and reducing straightening accuracy. Therefore, this paper proposes for the first time an analytical mechanistic model for the whole process of strip tensile-bending straightening. Elastoplastic mechanics and symplectic geometry mechanics were applied to reveal the complete mechanism of the stress changes from the initial defect to straightening. First, an offline "coordinated-uncoordinated-recoordinated" model is proposed, providing a universal residual stress formula that is adaptable to various defect types. Second, unlike traditional methods, the Hamiltonian approach is used to derive critical buckling load solutions for defective strips. Furthermore, based on pre-straightening residual stress and compressive layer plastic deformation, a comprehensive analytical model is developed to encompass the stress distribution, evolution, buckling, and mechanical changes during straightening. The analytical model predictions closely matched three-dimensional finite element simulation results, outperforming traditional methods in accuracy and efficiency. The model is applicable for various strip defects, enabling the straightening parameters to be optimized, bridging the gap between traditional assumptions and practical applications, and offering precise control, with broad applicability and potential.