Abstract Similitude theory is used to establish the necessary conditions between the enlarged or reduced model and the original structure, and has been widely applied to vibration and impact tests of large structures. However, several limitations and difficulties still persist in partial similitude for complex structures. In this paper, a partial similitude method to obtain scaling laws is proposed. The powers in scaling laws are variables against the scaling factors, and the coupling effect among design parameters is considered in the powers. The accuracy and applicability of the proposed method are demonstrated in two case studies. The first case study discusses the partial similitude of a single rotor-bearing system. The single rotor-bearing system is scaled with distortion in the geometrical dimension and boundary conditions. It is found that the proposed method predicts the critical speeds and unbalance responses with good accuracy. Furthermore, the proposed method can improve the prediction accuracy by comparing with the methods in current literatures. The second case study comprises a dual-rotor system to demonstrate the accuracy and applicability of the proposed method for more complex rotor-bearing system. The speed ratio, excitation position, co-rotation, and counter-rotation are discussed in predicting the critical speeds as well as unbalance responses. It is also found that the proposed method can improve the prediction accuracy.

中文翻译：

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一种考虑标度律变幂并应用于转子轴承系统的偏相似法

摘要 相似理论用于建立放大或缩小模型与原始结构之间的必要条件，已广泛应用于大型结构的振动和冲击试验。然而，复杂结构的部分相似仍然存在一些限制和困难。在本文中，提出了一种获得标度律的部分相似方法。缩放定律中的幂是相对于缩放因子的变量，并且在幂中考虑了设计参数之间的耦合效应。在两个案例研究中证明了所提出方法的准确性和适用性。第一个案例研究讨论了单个转子轴承系统的部分相似性。单转子轴承系统在几何尺寸和边界条件上随着变形进行缩放。结果表明，所提出的方法能够以良好的精度预测临界速度和不平衡响应。此外，通过与现有文献中的方法进行比较，所提出的方法可以提高预测精度。第二个案例研究包括一个双转子系统，以证明所提出的方法对更复杂的转子轴承系统的准确性和适用性。在预测临界速度和不平衡响应时讨论了速比、励磁位置、同向旋转和反向旋转。还发现所提出的方法可以提高预测精度。第二个案例研究包括一个双转子系统，以证明所提出的方法对更复杂的转子轴承系统的准确性和适用性。在预测临界速度和不平衡响应时讨论了速比、励磁位置、同向旋转和反向旋转。还发现所提出的方法可以提高预测精度。第二个案例研究包括一个双转子系统，以证明所提出的方法对更复杂的转子轴承系统的准确性和适用性。在预测临界速度和不平衡响应时讨论了速比、励磁位置、同向旋转和反向旋转。还发现所提出的方法可以提高预测精度。