往复弯曲统一曲率定理及其试验验证

辊式矫直工艺和辊式矫圆工艺均通过往复弯曲方式达到统一曲率的目的,辊式矫形过程中的往复弯曲变形规律是确定矫形工艺参数的理论依据。针对往复弯曲变形过程,建立一套符号系统,将弯曲曲率和弯矩矢量化。基于小曲率平面弯曲弹复方程和应变叠加原理,引入初始当量应变和当量应变的概念,采用图解法对往复弯曲弹复过程进行分析,在考虑稳定金属材料往复弯曲过程中的形变硬化、Baushinger效应和循环软化,分三种情形证明往复弯曲可以湮灭初始曲率的差异,最终使曲率统一到同一方向、同一数值,提出往复弯曲统一曲率定理。进而,设计模压往复弯曲试验装置,选用不同初始形状、不同材料的板坯进行往复弯曲试验,讨论残余曲率半径和拟合圆弧偏差随弯曲次数的变化规律,验证往复弯曲统一曲率定理的正确性,为辊式矫直和辊式矫圆工艺方案和控制策略的制定奠定了理论基础。

Uniform Curvature Theorem by Reciprocating Bending and Its Experimental Verification

In the roller-type straightening process and setting round process, the initial curvature is unified by means of the reciprocating bending. The deformation law of reciprocating bending is the theoretical basis for determining the process parameters. In the reciprocating bending process, a set of symbol system is established, and the bending curvature and moment are both vector. The small curvature plane bending springback equation and strain superposition principle are the theoretical basis. The initial equivalent strain and equivalent strain are introduced. Considering the deformation hardening, Baushinger effect and cyclic softening, the reciprocating bending springback process is analyzed by using the graphic method. It shows that the reciprocating bending eliminates the difference of initial curvatures and makes the curvatures be in the same direction and have same value. The uniform curvature theorem by reciprocating bending is presented. The bending test device is designed. The different material plates that has different initial shape are used to carry out the reciprocating bend test. The variation of residual curvature and the deviation of fitting arc are discussed. The correctness of the uniform curvature theorem is proved. It lays the theoretical foundation for the development of process plan and control strategy in the roller-type straightening and setting round process.