稳定金属材料往复弯曲使材料纤维受到多次拉压循环加载，是一个十分复杂的弹塑性弯曲及弹复变形过程。本项目考虑形变硬化、Bauschginer效应和循环软化（硬化）因素建立便于工程应用的材料本构模型；进而基于小曲率平面弯曲弹复理论，利用数学归纳法推导曲梁往复弯曲残余曲率方程和残余曲率统一方程，证明曲梁经多次往复弯曲湮灭各微梁段初始曲率的差异，最终曲率统一到同一方向、同一数值，即往复弯曲统一曲率定理，并采用往复弯曲实验和有限元模拟相结合的方法对其验证；以上述理论为基础，建立现有型材多辊矫直工艺和管材三辊矫圆工艺的理论解析模型，研究多辊矫直和三辊矫圆的变形规律及控制策略，揭示上述矫形工艺的机理；在此基础上，提出并验证四种新型高效、高精度的矫形工艺方法。本项目成果的工程应用不仅能够带动相关机械行业的技术革新，而且可以大大提高我国型材及管材的品质，使我国在矫形技术领域达到国际先进水平。

Reciprocating bending about stable metal materials is a very complex bending springback process of elastic-plastic deformation, which makes the material fibers receive multiple tension-compression cyclic loading. Considering the deformation hardening, Bauschginer effect and cyclic softening (hardening), the material constitutive model is established. And then based on the theory of small curvature plane bending springback, the mathematical induction is used to derive the residual curvature equation and the unified residual curvature equation, which can prove that by repeatedly reciprocating bending initial curvature difference of each micro-beam is annihilated, finally unified in the same direction, the same numerical, namely the unify curvature theorem by reciprocating bending. It is verified by combining with experiment and finite element simulation. On the basis of above theory, the analytic models of multi-roller straightening process and three-roller setting round process are established, deformation laws and control strategies are obtained, and the mechanism of straightening process is revealed. On this basis, four new methods of straightening process, high efficiency, high precision, are proposed and verified. The achievements of this project not only to technical innovation of related machinery industry, but also greatly improve steel and pipe quality, make our country reach the international advanced level in the technical field of straightening.