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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2026, Vol. 60 Issue (5): 1037-1046    DOI: 10.3785/j.issn.1008-973X.2026.05.013
    
Sensitivity analysis of hydroelectric unit parameters controlled by magnetorheological fluid dampers
Kaiwen ZHANG1,2(),Xueni WANG1,2,zhenyue MA3,Jinjian ZHANG3,Leike ZHANG1,2,*(),Lijun CHEN4
1. College of Hydro Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China
2. Shanxi Key Laboratory of Collaborative Utilization of River Basin Water Resources, Taiyuan 030024, China
3. School of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China
4. Highway School, Chang’an University, Xi’an 710064, China
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Abstract  

A rubbing dynamic model of a rotor-bearing-runner system with magnetorheological fluid damper (MRD) control was developed to address the complex shafting vibration issues in a bulb turbine generator unit. Using Sobol index analysis, a sensitivity analysis of unit parameters such as system damping, stiffness, and electromagnetic factors was conducted, with the rotor vibration amplitudes in the X and Y directions as the objective functions. Results showed that the shaft bending stiffness exerted the greatest influence on the rotor vibration amplitude in the X direction. When the bending stiffness exceeded 1.38×109 N·m2, the vibration amplitude in the X direction decreased significantly and the motion state tended to be stabilize. The average air gap between the stator and rotor had the most significant impact on the Y direction amplitude. As the average air gap increased from 1 mm to 2 mm, the system amplitude rose continuously. When the average air gap exceeded 1.73 mm, the system exhibited an unstable motion pattern. Sensitive intervals of the parameters were determined through numerical analysis, establishing an analytical pathway to enhance the efficiency and accuracy of parameter optimization.

Key words： bulb turbine generator unit      vibration control      magnetorheological fluid damper      sensitivity analysis      parameter optimization     
Received: 17 June 2025      Published: 06 May 2026
CLC:  TH 213  
  TV 734  
Fund:  国家自然科学基金资助项目（52379091）；山西省基础研究计划青年项目（202203021222112）.
Corresponding Authors: Leike ZHANG     E-mail: zkw20010303@163.com;zhangleike@tyut.edu.cn
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Kaiwen ZHANG
Xueni WANG
zhenyue MA
Jinjian ZHANG
Leike ZHANG
Lijun CHEN
Cite this article:

Kaiwen ZHANG,Xueni WANG,zhenyue MA,Jinjian ZHANG,Leike ZHANG,Lijun CHEN. Sensitivity analysis of hydroelectric unit parameters controlled by magnetorheological fluid dampers. Journal of ZheJiang University (Engineering Science), 2026, 60(5): 1037-1046.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.05.013     OR     https://www.zjujournals.com/eng/Y2026/V60/I5/1037


磁流变液阻尼器控制下的水电机组参数敏感性分析

针对贯流式水轮发电机组轴系复杂振动问题，构建基于磁流变液阻尼器(MRD)控制的转子-轴承-转轮系统碰摩动力学模型. 采用Sobol指数分析法，以转子在X和Y方向的振幅为目标函数，对系统阻尼、刚度、电磁等机组参数进行敏感性分析. 结果表明，大轴抗弯刚度对转子X方向振幅影响最大，当大轴抗弯刚度大于1.38×109 N·m2时，转子X方向的振动幅值显著降低，运动状态趋于稳定；定转子平均气隙对Y方向振幅影响最大，当定转子平均气隙从1 mm增加到2 mm时，系统振幅持续增大，当定转子平均气隙超过1.73 mm时，系统呈现非稳态运动形式. 通过数值分析确定参数的敏感性区间，构建提升参数优化效率和准确性的分析路径.


关键词： 灯泡贯流式机组,  振动控制,  磁流变液阻尼器,  敏感性分析,  参数优化 
Fig.1 Schematic cross-section of bulb turbine generator unit with magnetorheological fluid damper
Fig.2 Simplified schematic diagram of rotor-bearing-runner system structure
参数数值参数数值
σ0/(N·mV?1)8.0×105σb/(N·s·mV?1)5.1×105
σ1/(N·s·m?1)1.6×103U/V1.75
σ2/(N·s·m?1)2.0×105a0/(V·N?1)3.0×10?3
σa/(N·m?1)4.0×105——
Tab.1 Model parameters of magnetorheological fluid damper
Fig.3 Schematic diagram of blade tip rubbing force on impeller
参数取值范围
转子质量偏心e01/mm0.5~1.5
转轮质量偏心e02/mm0.5~1.5
转子阻尼c1/(N·s·m?1)0.5×105~1.5×105
转轮阻尼c2/(N·s·m?1)1.0×105~2.0×105
组合轴承阻尼c3/(N·s·m?1)0.5×105~1.5×105
水导轴承阻尼c4/(N·s·m?1)0.5×105~1.5×105
大轴抗弯刚度ke/(N·m2)0.6×109~1.6×109
组合轴承刚度k3/(N·m?1)0.6×109~1.6×109
水导轴承刚度k4/(N·m?1)0.6×109~1.6×109
转子碰摩刚度kr1/(N·m?1)0.6×109~1.6×109
转轮碰摩刚度kr2/(N·m?1)0.5×109~1.5×109
定转子平均气隙δ0/mm1.0~2.0
励磁电流If/A200~1 000
Tab.2 Parameters and value ranges of shaft system for hydroelectric generating units
Fig.4 Time domain diagram of X-direction rotor vibration before and after magnetorheological fluid damper application(ω=26 rad/s)
Fig.5 Sensitivity ranking of shaft system parameters of hydroelectric generating unit in rotor X-direction
Fig.6 Sensitivity proportion of average air gap between stator and rotor before and after considering parameter interaction
Fig.7 Bifurcation diagram of rotor X-direction displacement with main shaft bending stiffness as control parameter
Fig.8 Time domain simulation diagram of rotor X-direction displacement
Fig.9 Sensitivity ranking of shaft system parameters of hydroelectric generating unit in rotor Y-direction
Fig.10 Sensitivity proportion of water-lubricated bearing stiffness before and after considering parameter interaction
Fig.11 Bifurcation diagram of rotor Y-direction displacement with average air gap between stator and rotor as control parameter
Fig.12 Time domain simulation diagram of rotor Y-direction displacement
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