## 6 Conclusions  
Aiming at the mass imbalance problem of AMB rotor, a dynamic balance correction method based on ANF and ICM is proposed in this paper. Firstly, the improved ANF algorithm is used to track the displacement signal of the AMB rotor, and the amplitude and phase of the displacement signal are calculated. Then, the ICM is used to solve the counterweight mass of the rotor dynamic balance, and the dynamic balance of the rotor is  
Figure 16: Comparison diagram of rotor vibration displacement under reduced rotation speed.  
Figure 15: Rotor displacement spectrum before and after dynamic balance.  
corrected. Finally, the feasibility of the method is verified by simulation and experiment. The following conclusions can be drawn.  
1. The improved ANF algorithm adds an adaptive module to the input signal, which can modify the parameters according to the amplitude and frequency of the signal so as to realize the accurate tracking of the displacement signal and calculate the amplitude and phase information. Therefore, the displacement signal of the rotor can be transformed into the displacement vector used in the ICM.
2. With the help of ANF algorithm and fiber optical sensor, the linear relationship between the rotor counterweight mass and rotor displacement response is calculated by ICM, and the counterweight mass of rotor balance is solved. The dynamic balance correction of the rotor can be effectively realized by a double-sided counterweight.
3. The dynamic balance correction method of the AMB rotor based on ANF and ICM proposed in this paper can reduce the displacement unbalance of the rotor ends of the test rig used in this paper by 56.6%, 62.8%, 49.2% and 63.7%, respectively. The dynamic balance effect can be further improved after improving the counterweight phase accuracy and counterweight quality accuracy.  
The dynamic balancing method presented in this paper can also be applied to rotating components supported by conventional bearings. The on-site dynamic balancing of rotating components can be achieved by deploying displacement sensors.  
Finally, although the method in this paper can greatly reduce the imbalance caused by the rotor mass eccentricity, there are still some shortcomings. Due to the need to repeatedly test weights and adjust counterweights, the machine's start-stop problem cannot be avoided; a phase detector is required to mark the initial phase. Aiming at the above problems, the next step is to study the virtual test weight of the rotor. In addition, an algorithm should be found in order to identify the phase of the rotor, replacing the hardware with software.  
Conceptualization, X.G. and H.P.; methodology, X.G. and H.P.; software, H.P.; validation, X.G., H.P. and J.Z.; formal analysis, X.G.; investigation, H.P.; resources, X.G.; data curation, H.P.; writing--original draft preparation, H.P.; writing--review and editing, X.G., H.P., H.L. and J.Z.; visualization, H.P.; supervision, X.G.; project administration, H.P.; funding acquisition, X.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (52205050), Changzhou Science and Technology Plan Project (CJ20242057), The Natural Science Foundation of the Jiangsu Higher Education Institutions of China (22 KJB460011), CNPC-CZU Innovation Alliance (CCIA2023-03) and Postgraduate Research & Practice Innovation Program of Jiangsu Province (SJCX23_1496).  
Not applicable.  
Data Availability Statement: Data is contained within the article.  
The authors declare no conflicts of interest.