On the Repeated Natural Frequencies for Torsional Vibration of Shafts
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摘要: 借助于传递矩阵法研究了两轴系扭振的重频条件。必要条件为:存在节点啮合对(JEC);充要条件为:四个边界传递系数(fB)等于零的个数不少于3个。给出了两轴系存在重频时的振型选择。多级轴系重频的必要条件与两轴系的必要条件相同,而如果所有的相邻JEC之间的传递系数(fI)等于零时,频率重数等于独立的fB为零的个数减1.若存在fI≠0,可将它所对应的连接部分删除,从而把整个轴系的JEC分成内部不含fI≠0的几组,该阶频率的总重数等于各组独立解个数之和。Abstract: To investigate the repeated frequency condition (RFC) for torsional vibration of shafts' system, the transfer matrix method was adopted. Firstly, the transfer relationship from the boundary to engaging disks of double shafts' system(DSS) was constructed. Secondly, the RFC of DSS was deduced out and the methods to select mode shape were presented. Finally, the relationship was extended to multilevel transmission system (MTS), and the RFC of this system was explored. The conclusions is this:1) the necessary RFC requires the existence of joint engaging couple (JEC);2) for DSS, the sufficient is the number of boundary transfer factors (fB) larger than 2;3) the whole system can be split into independent groups, the total multiplicity is the sum of independent solution number of every group, the latter is the number of independent fB=0 inside the group minus 1.
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Key words:
- vibration /
- natural frequency /
- torsional vibration
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