The unbalance-induced vibration of a high-speed rotor directly affects the manufacturing accuracy. To effectively suppress this undesired vibration and avoid the complicated process of using trial weights during the balancing adjustment, a modal-based balancing method for a high-speed rotor without trial weights is proposed. First, the matrix sweep operation is employed to acquire the unbalance equivalent plane (EP). Next, the equivalent concentration methods, using the vector feedback principle (VFP) and modal equivalent principle (MEP), respectively, are studied and compared, while the equivalent transfer of the continuous unbalance vector to the EP is realized. Then, through modal analysis and the MEP, a balancing method, without trial weights required, is proposed for the high-speed rotor, which only needs to collect vibration data below critical speed. Finally, the rotor model and the presented method are validated on a rotor test platform, where the simulation and experiment results show that the unbalance-induced vibration has been effectively suppressed, ensuring smooth and safe operation of the rotor at high speed.

As a ubiquitous phenomenon in rotor systems, anisotropic stiffness generally causes the response of an unbalanced rotor to vary across radial directions. The standard holospectrum-based balancing method, which adopts the initial phase vector as a balancing object, cannot be used in rotor systems with anisotropic stiffness. To tackle the limitations of the standard holospectrum-based balancing method, an improved holospectrum-based balancing method with increased accuracy and a greater scope of application is presented in this article. First, a dynamic model of an unbalanced rotor system with anisotropic stiffness is developed, the theoretical expression of the deviation between the initial phase vector and the unbalance is examined, and the effects of anisotropic stiffness on the initial phase vector are analysed. Second, based on the analysis of the precession characteristics of the rotor, a modified initial phase vector that compensates for the negative influence of anisotropic stiffness is presented as the new balancing object. An improved holospectrum-based balancing method is proposed based on this modified initial phase vector, and the balancing procedures are summarised in detail. Finally, the initial phase vector induced error in the identification of the unbalance is simulated for different initial conditions, and the feasibility of the modified initial phase vector is verified on a rotor test rig. Both the numerical analysis and the empirical test validate the effectiveness and accuracy of this new method.