开闭裂纹转轴刚度的解析研究

Analysis on stiffness of rotor system with a switching crack

根据材料力学的中性轴理论,解析求解了开闭扩展裂纹转轴刚度,得到了裂纹扩展方向、裂纹垂直方向及耦合方向刚度的解析表达式,进而得到了固定坐标系下的对应刚度,并与传统的余弦刚度模型和高-朱刚度模型进行了对比分析。结论表明:裂纹扩展方向刚度呈现曲边梯形形状,裂纹扩展垂直方向刚度呈现为对称的阶梯形状,而耦合刚度表现为正弦曲线形状;固定坐标系下三个方向的刚度均表现为复杂的波动曲线,且在一个周期内水平刚度和纵向刚度以二分之一周期为分界存在一定的对称性,而偶和刚度存在一定的反对称性等。

Based on the neutral axis theory in material mechanics,the shaft stiffness with a switching crack was solved analytically.The analytic expressions of the stiffnesses in the direction of crack growth,in its vertical direction and in their coupling direction were obtained and the corresponding stiffnesses in the fixed coordinate system were achieved.The stiffness model in the paper was compared with the cosine model and the Zhu-Gao model.The conclusion indicates that:the stiffness curve is of a trapezoidal shape in crack growth direction,a symmetrical ladder shape in its vertical direction and a sinusoid shape in coupling direction.In the fixed coordinate system,the stiffnesses in three directions appear as complicated oscillating curves.The horizontal stiffness and vertical stiffness are of certain symmetry in one period,while the coupling stiffness has certain inversion symmetry.