Abstract In practical engineering, gravitational acceleration cannot be scaled (λg = 1), which is not considered in the existing similitude studies of rotor systems. In this paper, a restriction in scaling procedure caused by λg = 1 is first demonstrated analytically. Aiming at this issue, a method to derive the scaling laws of rotor systems is proposed based on the generalized equations of subsystems, where gravitational acceleration, geometric and material distortion are considered. The derived scaling law for the vibration response is different from that of previous literatures because λg = 1 is considered. On this basis, this paper presents a method for designing scaled models that can reduce the difficulty and costs of the model test. The accuracy and effectiveness of the proposed methods are verified by predicting the dynamic characteristics of a rotor system. Moreover, the effect of gravitational acceleration is discussed and the predicted results are compared with the previous literature. The results show that neglecting the gravitational acceleration leads to a certain error when predicting the vibration responses in the vertical direction.

中文翻译：

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考虑重力加速度的转子系统动态特性的部分相似

摘要 在实际工程中，重力加速度不能被标度（λg = 1），这在现有的转子系统相似性研究中没有考虑。在本文中，首先通过分析证明了由 λg = 1 引起的缩放程序的限制。针对这个问题，提出了一种基于子系统广义方程的推导转子系统标度定律的方法，其中考虑了重力加速度、几何畸变和材料畸变。由于考虑了 λg = 1，因此推导出的振动响应标度律与以前的文献不同。在此基础上，本文提出了一种可以降低模型试验难度和成本的比例模型设计方法。通过预测转子系统的动态特性，验证了所提出方法的准确性和有效性。此外，讨论了重力加速度的影响，并将预测结果与以前的文献进行了比较。结果表明，在预测垂直方向的振动响应时，忽略重力加速度会导致一定的误差。