Reducing the vibration responses caused by the unbalance of the rotor is a crucial technology to ensure the safe and efficient operation of high-speed rotating machinery. For the flexible rotor system, the unbalance responses of rotors vary in different radial directions due to the anisotropic stiffness. The holospectrum technique using multi-sensor fusion provides ideas to solve this issue. The standard balancing method based on the holospectrum technique takes the Initial Phase Vector (IPV) as the balancing object, which could not represent the unbalance of flexible rotors correctly. In addition, the operating speed of the flexible rotor is generally higher than the first critical speed (FCS), making it necessary to fulfill the balancing of the first two modal shapes respectively in two steps. The above-mentioned procedure is not only very dangerous but also requires a large number of test runs resulting in corresponding wastages. In order to solve the issues mentioned above, a synchronous holo-balancing method for flexible rotors based on the modified initial phase vector (MIPV) is developed in this paper. Firstly, to tackle the limitation of IPV, the concept of equivalent rotating frequency circle is presented and then the MIPV is proposed as a new balancing object. MIPV could linearly represent the unbalance of the flexible rotor and increase the accuracy of holo-balancing. Secondly, the synchronous holo-balancing method is carried out to achieve the balancing at the speed below the FCS, reducing the complexity and danger of test runs at high operating speeds. And the synchronous balancing procedures based on the MIPV are further summarized in detail. Finally, two experimental results with different operating speeds and probe installations validate the feasibility and effectiveness of the proposed method. Compared with other traditional balancing methods, the proposed method can minimize the residual vibration and achieve state-of-the-art performances.

降低转子不平衡引起的振动响应是保证高速旋转机械安全高效运行的关键技术。对于柔性转子系统，由于各向异性刚度，转子的不平衡响应在不同的径向方向上有所不同。使用多传感器融合的全息技术为解决这个问题提供了思路。基于全息技术的标准平衡方法以初始相位矢量（IPV）为平衡对象，不能正确表示柔性转子的不平衡。此外，柔性转子的运行速度一般高于第一临界速度（FCS），需要分两步分别完成前两个模态形状的平衡。上述过程不仅非常危险，而且需要进行大量的试运行，造成相应的浪费。针对上述问题，本文提出了一种基于修正初始相位矢量（MIPV）的柔性转子同步全息平衡方法。首先，针对IPV的局限性，提出了等效旋转频率圆的概念，然后提出了MIPV作为一种新的平衡对象。MIPV可以线性表示柔性转子的不平衡，提高全息平衡的精度。其次，采用同步全息平衡方式，实现在FCS以下速度下的平衡，降低高运行速度下试车的复杂性和危险性。并进一步详细总结了基于 MIPV 的同步平衡程序。最后，两个不同运行速度和不同探头安装的实验结果验证了所提方法的可行性和有效性。与其他传统平衡方法相比，所提出的方法可以最大限度地减少残余振动并实现最先进的性能。