# Vibration Responses of a Coaxial Dual-Rotor System with Supporting Misalignment
## 1 Introduction
[20] applied the proper orthogonal decomposition method to the dimension reduction of a dual-rotor-bearing experimental rig and discussed the frequency behaviors of a dual-rotor-bearing coupling misalignment response. [PERSON] et al. [21] described the mechanism and influencing factors of the nonlinear properties of a misaligned inner rotor, in an aeroengine, through Lagrange equations. [PERSON] [22] and [PERSON] [23] et al. developed a multi-bearing rotor model with misalignment to investigate the dynamic response when misalignment parameters were uncertain. [PERSON] et al. [24] investigated the quantification of uncertainty effects on the dynamic responses and vibration characteristics of a multi-rotor-bearing system with the fault of angular misalignment. [PERSON] et al. [25] presented a dynamic model of a flexible rotor system with multi-supports that could be used to solve the bearing misalignment problem of a rotor system in an aeroengine. [PERSON] et al. [26] established a dynamic model of the coupling misalignment of a dual-rotor system according to the Gibbons formula [27] and the Sekhar formula [28]. [PERSON] et al. [29] proposed a dual-rotor misalignment fault quantitative identification method based on DBN and D-S evidence theory improved using the mutual information method. The results showed that the method improved the accuracy of the misalignment fault quantitative identification of the dual rotor. [PERSON] et al. [30] investigated a dual-rotor-bearing system with coupling misalignment and blade-casing rubbing and studied its nonlinear vibration characteristics. [PERSON] et al. [31] investigated the dynamic responses of a dual-rotor system with rubbing-misalignment mixed fault. Previous studies have presented detailed discussions and analyses of the effect of misalignment on a dual-rotor system of an aeroengine; however, some of the studies considered an inner rotor system instead of the total dual-rotor system. Some of the misalignment models are coupling misalignment models that only explain the impact of the coupling misalignment and do not analyze the effect of the supporting misalignment of an inner rotor which is a multi-bearing rotor system. In response to this shortcoming, in this study, we build a supporting misalignment model of a coaxial dual-rotor system and draw on the three-moment equation. The method has often been used to analyze the effects of misalignment on redundantly supported rotors. For example, [PERSON] [32] and [PERSON] [33] et al. calculated the bearing loads of a large steam turbine generator set using the three-moment equation. [PERSON] and [PERSON] [34] analyzed the influence of misalignment of the support journal bearings on the stability of a multi-rotor system. [PERSON] et al. [35] presented the vibration behavior of statically indeterminate rotor-bearing systems with hydrodynamic journal bearings. Our model based on the three-moment equation can describe misalignment caused by a bearing that is adjacent to the coupling as well as far from the coupling and it is more consistent with the real work condition of an aeroengine. In addition, the experimental results and the simulation results are in good agreement.