横向裂纹轴耦合刚度分析

基于断裂力学理论和局部柔度理论，推导了横向裂纹轴在轴力、剪力、弯矩及扭矩共同作用时的刚度矩阵，分析了裂纹深度比和转轴细长比等参数对转轴刚度的影响。结果表明：当裂纹深度小于转轴半径的一半时，可以仅考虑垂直裂纹方向的刚度变化；但当裂纹深度大于转轴半径的一半时，裂纹轴的轴向、剪切、弯曲及扭转刚度的影响都要考虑。同时在分析计算含裂纹转子系统动力特性时应对部分耦合刚度有所考虑。三点弯曲试验研究说明，所得的理论结果比以往的理论值更接近实验值，且转轴细长比越大、裂纹深度比越小,结果越精确。

Analysis of Coupled Rigidity of the Shaft with a Transverse Crack

Based on the fracture mechanics theory and local flexibility theorem, the coupled rigidity of the cracked shaft with fixed or simple ends in studied. The stiffness matrix is analysed by use of MATLAB. The results show that the rigidity of the cracked shaft decreases along with the increase of the depth ratio and the slenderness ratio. The coupled stiffness of most of cracked shafts can be completely neglected, but it should be considered, in such cases, for example, when the axial stiffness has effect on the shear rigidity parallel to the crack, and so on. Based on the 3-points bending experiment , the theoretical values obtained in former literatures and in the paper are compared with the result of the experiment. It is shown that the errors in the new results are less than those by the theory used before. The larger the slender-ness and the smaller the depth ratio, the preciser the results for the cracked shaft. The method presented in verified to be effective and feasible.