Calculation Model of Multi-roll Straightening Process Based on Bilinear Hardening and Power Hardening

ObjectiveWith the development of new materials, increasing complexity in material properties has made it more difficult to define accurate straightening processes. The discrepancy between the assumptions of traditional ideal material models and actual material behavior has made accurate modeling a core issue in straightening process calculations. To more precisely describe the elastic-plastic behavior of different materials, a multi-roll straightening process model was established based on the curvature integral method, and the effects of bilinear and power hardening coefficients on the process were analyzed. The goal is to support the development of straightening techniques for new materials and provide a theoretical basis for intelligent straightening and optimal design of straightening machines.MethodsThree material models—ideal elastic-plastic, bilinear hardening, and power hardening—were selected, and the curvature-moment (M‒K) relationships for these materials during bending were derived. Using these relationships and curvature integration, a mathematical model for the multi-roll straightening process was developed. A least squares algorithm was employed to solve the nonlinear equations iteratively, enabling accurate straightening calculations. To evaluate the applicability of different material models, five straightening schemes were designed, corresponding to plasticity rates of 33.4%, 50.0%, 66.7%, 75.0%, and 80.0%. The influence of various hardening coefficients on curvature and plasticity during straightening was investigated. High-strength steel Q690 was used for experimental validation, with all three material models being imported into the multi-roll straightening model. The results were compared with both experimental data and finite element simulations to assess model accuracy.Results and DiscussionsResidual curvature was calculated under five straightening schemes and for hardening coefficients (0.1, 0.2, 0.3, 0.4, 0.5). The results show that as the bilinear and power hardening coefficients increase, the residual curvature error relative to the ideal elastic-plastic model also increases. Specifically, for bilinear hardening, the residual curvature errors were 0.253, 0.506, 0.759, 1.013, and 1.266; for power hardening, they were 0.145, 0.308, 0.489, 0.692, and 0.919. The bilinear model shows a linear increase in error, while the power model displays a nonlinear pattern. The magnitude of the hardening coefficient affects only the degree of curvature error, not the underlying behavior or material applicability. When the coefficient is fixed at 0.1, curvature changes across the five straightening schemes were analyzed. The results show that with increasing reduction, the error between hardened and ideal models increases. Particularly in schemes four and five, commonly used in practice, the residual curvature error for the ideal model is 6.06%, whereas for the power model it is 13.57%. As both the strengthening coefficient and reduction increase, differences in plasticity between hardened and ideal models become more pronounced. For example, with a coefficient of 0.5, the plasticity deviation is 14.26% for the bilinear model and 12.61% for the power model. If the target plasticity is 80% based on the ideal model, the actual plasticity of the hardened model is closer to 70%, potentially leading to insufficient bending and reduced product quality. In terms of straightening force, the ideal model yields a unidirectional force of 434.4 kN, the bilinear model 512.7 kN, and the power model 478.3 kN. The experimental result is 462.2 kN, and the theoretical value for the power model is 483.7 kN. The 4.65% error for the power model highlights the importance of selecting an accurate material model.ConclusionsThe study shows that as the bilinear and power hardening coefficients <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mi>η</mi></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/0B17B030-5E93-4f5e-9D6C-FF67444ABA6B-M005.jpg"><?fx-imagestate width="1.43933344" height="2.62466669"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/0B17B030-5E93-4f5e-9D6C-FF67444ABA6B-M005c.jpg"><?fx-imagestate width="1.43933344" height="2.62466669"?></graphic></alternatives></inline-formula> and <italic>m</italic> increase, material elastic recovery becomes more significant. Recovery has a linear relationship with the bilinear coefficient and a nonlinear one with the power coefficient. Both hardening models show reduced plastic deformation under equal pressure, leading to a weaker straightening effect. For example, the power model—more consistent with the tensile stress-strain curve—shows a 4.65% error between theory, experiment, and simulation for total straightening force. Selecting an appropriate material model based on specific material characteristics is crucial to ensure accuracy and efficiency in the straightening process. This research provides theoretical support for the development of straightening technology for new materials.