具有横向裂纹转轴耦合刚度的数值模拟和实验研究

SIMULATION AND EXPERIMENTAL INVESTIGATION ON COUPLED STIFFNESS OF ROTATING SHAFT WITH TRANSVERSE CRACK

采用有限元和实验分析研究轴向、剪切、弯曲及扭转载荷耦合作用下,含裂纹转轴刚度随各种影响因素的变化规律。采用Dimarogonas法推导6×6维裂纹转轴有限元刚度矩阵。确定网格划分方案,同时考虑d/l、a/R以及加载点与裂纹的位置关系。模拟计算结果表明,随着裂纹深度的增大,ξ向无量纲刚度的变化最快;裂纹深度在3mm～4mm时,ξ向、η向的弯曲无量纲刚度差有峰值。随着裂纹细长比的增大,弯曲和轴向的耦合刚度降低。随着裂纹深度比增大,弯曲和轴向的耦合刚度增大。结果与实验结果比较表明,文中方法是正确有效的,且接近实验结果。

Based on the finite element analysis and experimental analysis, stiffness of the cracked rotating shaft subjected to the coupling of axial, shearing, bending and torsion load is investigated, considered the influence of diversified factors. The FEM（finite element method） is used to model the cracked shaft. Six degrees of freedom are considered in each elemental node. Considering influence of coupling of sheafing and bending load, full 6 × 6 stiffness matrix of cracked element is deduced. As the model is being meshed, d/ l, a/R and the location relationship of loading point and crack position should be considered. Series responding curves have been calculated, which include both non-dimension stiffness and coupling stiffness by bending and axial load, the curves describe that, with the increase of depth of the crack shaft, the variation of non-dimensional stiffness of ξ direction is the most quickly; the peak D-value of the two non-dimensional stiffness for ξ and η directions occur at the depth of transverse crack varying in the small range of about 3 mm and 4 mm. With the increase of depth ratio of the crack shaft, the coupling stiffness by bending and axial load decrease; with the increase of slenderness ratio of the crack shaft, the coupling stiffness by bending and axial load increase. Simply supported rotating shaft with a middle transverse crack is used in the experiment. The 3-point bending experimental investigation is carried out, in order to obtain the stiffness data. Comparing the non-dimension stiffness curves of simulation calculation and experimental result , the simulation calculation tallied with experiment calculation preferably.