平面应力下薄壁管材连续矫直压弯量力学模型与数值解法

Numerical solution and mechanical modeling of the intermesh for continuous straightening a thin-walled tube in plane stress

薄壁管材在连续矫直过程中,各矫直辊组的压弯量作为核心工艺参数直接决定了薄壁管材的矫直精度。而目前现场仍沿用经验图表结合人工经验和反复试矫对其进行估定,亟待建立针对性的压弯量数学模型以指导生产。为此从薄壁管材的结构特点和矫直辊系组成出发,构建了针对压弯量计算的简化悬臂结构模型,基于相关假设和弹塑性相关理论,分别确定了平面应力状态下弹性区和弹塑性区管材横截面的弯矩模型,运用虚功原理建立了矫直辊压弯量力学模型,并给出了数值计算方法,完成了程序开发。经有限元动态仿真试验证明了模型的正确性和适用性,通过对典型管材数据的计算绘制了一系列工艺参数曲线,得到管材轴线弯曲半径和压弯量随管材直径、壁厚和屈服极限的变化关系,为现场压弯量的调整提供理论依据。

The straightening intermesh as the main straightening technical parameter, decides the preci- sion for continuous straightening thin-walled tubes, however, it is usually carried out based on the expe- riential data and chart by skilled laborers, whose art is based on experience and experiments, the special mathematical model of the straightening intermesh is immediately necessary. Therefore, firstly, a new simplified cantilever unit model for calculating the intermesh is presented based on the structural features of the thin-walled tube and the multi-roll straightener,and then the bending-moment of the cross section in plane stress is subsequently obtained in the elastic zone and also in the elastic-plastic zone based on the elastic-plastic theory and relevant hypothesis. Finally, the mechanical model of the straightening in- termesh is presented using the principle of virtual work,and it is also shown how to solve by numerical method and how to develop calculating program synchronously. In order to certify whether the model is correct,we have done some dynamic simulations by FEA, the results have shown that it is correct and suitable, so a series of technical parameter curves can be plotted by the datum calculated with the program,which can indicate the relationships between the intermesh,the bending-radius of the tube axis and the diameter,the wall thickness,the yield stress of the tube. It can provide the theoretical basis for adjusting the straightening intermeshes for the local production.