Closed-form analytical model for large differential variable-pitch straightening
摘要
Conventional straighteners often struggle to process high-strength or thick plates, and the theoretical basis for large-differential variable-pitch straightening remains insufficient. This study develops an analytical framework tailored to straighteners with large differential roller spacing. A non-asymmetric three-point bending model is established, and closed-form equations for reduction and straightening force are derived by incorporating the elastoplastic deformation behavior of plate leveling. The analytical model and the “Variable-Pitch MATLAB Calculation Program” are validated using industrial production data, demonstrating high predictive accuracy. Comparisons with ABAQUS simulations show strong agreement in post-leveling flatness and force evolution across different straightening schemes, confirming the robustness of the approach. The results reveal that increasing roller pitch can markedly decrease straightening force when the plastic deformation level is constant, while reducing the number of work rollers, although lowering overall system forces, tends to increase the residual stress remaining in the leveled plate. The proposed framework provides a more complete theoretical foundation for large-differential variable-pitch straightening and practical guidance for designing high-capacity straightening systems, particularly for applications involving high-strength and thick-gauge plates where improved efficiency and reduced equipment load are essential.