不同边界条件下高速旋转带篦齿薄壁短圆柱壳的行波共振特性研究

摘要

基于传递矩阵法研究了不同边界条件下高速旋转带周向篦齿薄壁短圆柱壳构件的行波共振特性.基于Love壳体理论,考虑离心力、科氏力和惯性力的影响,建立了旋转态薄壁圆柱壳的振动微分方程;引入传递矩阵法,通过壳体子段间的状态向量推导得到了整体结构的传递矩阵关系式;在简支-简支、固支-固支、固支-简支、固支-自由和简支-自由五种边界条件下,通过高精度的精细积分法进行求解,得到了构件的行波共振特性.算例结果表明,在固支-自由边界条件下第1阶模态振动发生在(1,3)阶,而在其它边界条件下第1阶模态振动发生在(1,4)阶,而且边界条件不同时前六阶模态分布规律也不同,但均以周向模态的振动为主;在3×104 r/min转速范围内,随着转速的逐渐增加,由于科氏力作用引起后行波频率大于前行波频率;同时,不同的边界条件对共振特性的影响不同,在工作转速附近行波频率线与激振频率线K=1或K=2相交,出现了共振裕度小于10％的共振转速点,共振裕度数值越小越容易引起对应阶次的共振,应采取措施避免共振现象的发生.%The travelling wave resonance characteristics of a high-speed rotating thin short cylindrical shell component with circumferential sealing teeth were studied in various boundary conditions based on the transfer matrix method.The vibration differential equations of the rotating thin cylindrical shell were set up based on the Love's shell theory,in which centrifugal forces,coriolis forces and inertial forces were involved.Utilizing the continuity of state vectors at the interfaces between sub-segments,the transfer matrix method was introduced to derive the transfer matrix of the overall structure.Then,its resonance characteristics were solved by the high-precise integration method in simply supported-simply supported,clamped-clamped,clamped-simply supported,clamped-free and simply supported-free boundary conditions.The examples' results show that the first-order modal vibration occurs in the (1,3) order in clamped-free boundary condition,while the first-order mode vibrations occur in the (1,4) order in other boundary conditions.The distribution of the first six order modals is also different when the boundary conditions are various,but the vibration modals are mainly presented in circumferential direction in the five boundary conditions.In the speed range of 3 × 104 r/min,the backward traveling wave frequencies are greater than the forward ones due to the coriolis force with the gradual increase of rotating speed.The influence of different boundary conditions on the resonant characteristics is different,and the traveling wave frequency lines intersect the excitation frequency lines of K =1 or K =2 in the vicinity of the operating speed.At the same time,the resonant speed points with a resonance tolerance of less than 10％ appear,and it is easier to cause the corresponding order resonance with a smaller resonant tolerance value,so it is necessary to take measures to avoid the occurrence of resonance phenomenon.