轴系稳定性裕度判据的理论研究

Analytical Study on the Criterion of the Stability Margin of a Rotor-Bearing System

本文提出以系统最大能量比率作为衡量轴系稳定性裕度的判据,和传统的对数衰减率与系统阻尼判据相比,该判据综合了系统所有模态的信息,考虑了特征值与特征向量的共同影响。最大能量比率较小的轴系具有较大的稳定性裕度;最大能量比率较大的轴系具有较小的稳定性裕度。探讨了特征向量在评估稳定性裕度的重要作用,指出了传统的对数衰减率与系统阻尼判据在评估轴承稳定性裕度时的局限性。作为应用实例,用最大能量比率判据考察了一模型转了轴承系统的稳定性裕度,并与用对数衰减率及系统阻尼判据所得结论进行了对比。结果表明,用本文提出的判据所得的结论与实际情况比较一致。此外,应用模型转子的计算结果,进一步阐明了对数衰减率与系统阻尼判据的共同不足是采集的信息太少。

The criterion of the maximum energy ratio is proposed to evaluate the stability margin of a rotor-bearing system. As compared with the criteria of both logarithmic decrement and system damping,the information of all the modes of the system is included ,and the influences of both the eigenvalue and the eigenvector are considered in this criterion. The system with smaller maximum energy ratio has larger stability margin,while the system with larger maximum energy ratio has smaller stability margin. The important action of eigenvector in estimating stability margin is investigated, and the limitation of both system damping and logarithmic decrement criteria is pointed out. The stability margin of a rotor-bearing system is studied by using the criterion presented in the paper,which shows that the results given by this criterion are in better accord with the actual situation than those given by the criteria of both logarithmic decrement and system damping. Furthermore,numerical calculation discloses that the reason for the limitation of the latter two criteria lies in insufficient information.