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| Adaptive Multi-Objective Optimization Design of Active Magnetic Bearings System Based on Multi-Physics |
| Xu Yuhao1, Wang Xiaoyuan1, Liu Mingxin2, Li Na1, Yu Tian1 |
1. School of Electrical and information Engineering Tianjin University Tianjin 300072 China;
2. State Grid Tianjin Electric Power Company Tianjin 300010 China |
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Abstract Active magnetic bearing is a widely used supporting component in the industrial field. With the arrival of the wave of economic recovery, the trend of “high-speed” and “high-efficiency” in the industrial field has become increasingly apparent, which undoubtedly puts higher requirements on the performance of supporting components such as active magnetic bearings. Among numerous active magnetic bearing optimization design methods, traditional finite element methods generally suffer from high model complexity and slow calculation speed. On the other hand, although traditional multi-objective optimization methods have improved computational speed, they are prone to convergence issues due to the algorithm being trapped in local optima. Therefore, after careful consideration, an adaptive multi-objective optimization method based on the multi-physics field is proposed.
Firstly, the electromagnetic design process of a high-speed permanent magnet synchronous motor provides the basic design process of an active magnetic bearings system. In addition, taking the twelve-pole radial active magnetic bearing and the concentric single-ring axial active magnetic bearing as examples, specific formulas related to the design process are provided.
Secondly, comprehensive optimization is carried out on NSGA-Ⅱ, and the optimized NSGA-Ⅱ is combined with multi-physics fields to achieve a cyclic optimization process of real-time variable range correction. During the sorting process, the improved “super dominated” sorting method is chosen. Different adaptive rules with non-dominated levels and iteration times as variables are proposed in the selection process, crossover and mutation process, and retention process to ensure population diversity and adaptability in optimization.
Then, based on the operating conditions of the active magnetic bearings system, four main constraint forms were proposed: volume constraint, stiffness constraint, rotor strength constraint of radial active magnetic bearing, and thrust disc strength constraint of axial active magnetic bearing. Furthermore, the electromagnetic force density, total loss of the active magnetic bearings system, and critical speed are regarded as optimization objectives.
Then, using hypervolume and inverted general distance as performance indicators, the two optimization methods are compared, taking the ZDT problem as an example. The results show that compared with traditional NSGA-Ⅱ, the adaptive multi-objective optimization method not only converges faster but also reduces the time complexity from O(3×1002) to O(300×lg300).
Finally, the results before and after optimization are compared through multi-physics field simulation, and an experimental platform is built to compare the parameter changes of each optimization objective. Taking radial active magnetic bearing as an example, the optimized displacement stiffness coefficient increases by 105.4% from 459 N/mm to 943 N/mm. At the same time, the current stiffness coefficient increases from 80.4 N/A to 146 N/A with an increase of 81.6%. The error between the measured and calculated values after optimizing the displacement stiffness coefficient is 5.8%, and the error after optimizing the current stiffness coefficient is 7.3%. The simulation and experimental results demonstrate that the proposed adaptive multi-objective optimization method can ensure global optimization and fast convergence in active magnetic bearings systems.
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Received: 30 January 2024
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2025, Vol. 40 
