## 6 Conclusions  
Unbalance caused by improper assembly is the main reason for vibration faults in multi-stage rotors. A method is urgently needed to not only predict the state of a multi-stage rotor after assembly, but also to find the optimal matching relationship of a rotorat different stages to minimize the unbalance of the rotor. In this study, we developed an unbalance optimization method of a multi-stage rotor based on an assembly error propagation model. The main contributions of this study can be summarized as follows:  
1. An accurate assembly error propagation model was developed to calculate the coordinates of any point in a rotor at different stages after assembly. The alignment process and distribution of the screw holes of adjacent rotors were considered in this model for the first time. 2. A new assembly datum for unbalance optimization was proposed to ensure consistency with the actual conditions of the dynamic balance test. 3. Unbalance optimization of a multi-stage rotor was achieved using a GA. Additionally, the optimal assembly orientations of rotors at different stages were also identified. Conceptualization, Y.C. and J.C.; methodology, Y.C. ; software, Y.C. ; validation, Y.C. ; formal analysis, Y.C. ; investigation, Y.C. ; resources, J.C.; data curation, Y.C. ; writing--original draft preparation, Y.C. ; writing--review and editing, Y.C. ; visualization, Y.C. ; supervision, X.S. ; project administration, J.C.; funding acquisition, J.C. All authors have read and agreed to the published version of the manuscript. This research was funded by the Outstanding Youth Project of Natural Science Foundation of Heilongjiang Province, Grant JQ2019E002. The authors are grateful for the financial support. Not applicable. The authors acknowledge [PERSON] the College of Mechanical Engineering, Tianjin University of Science and Technology for the active support of the research. The authors declare no conflict of interest. References  
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