采用试验设计方法的第三代CO<sub>2</sub>气体箔轴承箔片几何参数敏感性分析

李卓聪; 李志刚; 李军

doi:10.7652/xjtuxb202607015

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采用试验设计方法的第三代CO₂气体箔轴承箔片几何参数敏感性分析

更新时间：2026-07-09

- 采用试验设计方法的第三代CO₂气体箔轴承箔片几何参数敏感性分析
- Sensitivity Analysis of Foil Geometrical Parameters for the Third-Generation CO₂ Gas Foil Bearings Based on Design of Experiments Method
- 西安交通大学学报 2026年60卷第7期页码：159-172
- 作者机构：
  
  西安交通大学叶轮机械研究所，710049，西安
- 作者简介：
  
  作者简介：李卓聪（1996—），男，博士生；
  李志刚（通信作者），男，教授，博士生导师。
- 基金信息：
  
  国家自然科学基金资助项目(52422602)
- DOI：10.7652/xjtuxb202607015
  中图分类号： TH133.3;TH117.2
- 收稿：2025-10-09，
  
  纸质出版：2026-07-10
- 稿件说明：
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李卓聪, 李志刚, 李军. 采用试验设计方法的第三代CO₂气体箔轴承箔片几何参数敏感性分析[J]. 西安交通大学学报, 2026,60(7):159-172. DOI: 10.7652/xjtuxb202607015.

LI Zhuocong, LI Zhigang, LI Jun. Sensitivity Analysis of Foil Geometrical Parameters for the Third-Generation CO₂ Gas Foil Bearings Based on Design of Experiments Method[J]. Journal of Xi'an Jiaotong University, 2026, 60(7): 159-172. DOI: 10.7652/xjtuxb202607015.
李卓聪, 李志刚, 李军. 采用试验设计方法的第三代CO₂气体箔轴承箔片几何参数敏感性分析[J]. 西安交通大学学报, 2026,60(7):159-172. DOI: 10.7652/xjtuxb202607015. DOI：

LI Zhuocong, LI Zhigang, LI Jun. Sensitivity Analysis of Foil Geometrical Parameters for the Third-Generation CO₂ Gas Foil Bearings Based on Design of Experiments Method[J]. Journal of Xi'an Jiaotong University, 2026, 60(7): 159-172. DOI: 10.7652/xjtuxb202607015. DOI：

摘要

针对CO

气体箔轴承多场耦合静、动态特性数值评估方法缺失、参数影响规律尚不明确的问题，开展了第三代波箔型CO

气体箔轴承箔片几何参数敏感性分析研究。基于全三维非定常共轭传热方法，构建了气体箔轴承气膜对转子和顶箔的对流换热数学模型，通过耦合求解Reynolds方程，三维能量方程和转子、轴承结构三维导热方程，建立了第三代波箔型CO

气体箔轴承静、动态特性多场耦合数值预测方法；利用空气箔轴承极限承载能力、动态刚度和阻尼系数试验数据，完成了数值方法的有效性验证；基于中心组合设计方法，开展了波箔高度、波箔半长、波箔厚度和顶箔厚度等箔片几何参数敏感性分析研究。采用所建立的数值预测方法求解25种箔片几何参数组合下第三代波箔型CO

气体箔轴承在高温（315 ℃）、高压（2.0 MPa）环境下的静、动态特性，获得以静

态载荷、直接刚度和能量耗散系数为响应的主效应图。计算结果表明：静态载荷和直接刚度随波箔高度增大和波箔半长减小而增大；当偏心率

为0.5时，静态载荷和直接刚度随波箔厚度先增大后减小，并在波箔厚度分别为30%水平和20%水平时取得最大值；在重载（

=0.8）工况下，波箔厚度对静态载荷和直接刚度影响最大，影响幅度分别为35.1%和76.4%；箔片几何参数对两类性能指标的调控规律呈反向耦合特征，因此应以直接刚度和能量耗散系数为响应开展多目标优化，获取使轴承综合动态性能最优的箔片几何参数。该研究结果可为第三代波箔型CO

气体箔轴承性能分析和结构设计提供参考。

Abstract

To address the lack of multiphysics coupled numerical evaluation methods and the unclear influence law of parameters on the static and dynamic characteristics of CO

gas foil bearings（GFBs），a sensitivity analysis was conducted on the foil geometrical parameters of the third-generation bump-type CO

GFBs.Based on a full three-dimensional（3 D）unsteady conj ugate heat transfer（CHT）method，a mathematical model for the convective heat transfer between the GFB gas film and the shaft and top foil was developed.Through the coupled solution of the Reynolds equation，the 3D energy equation，and the 3D structural heat conduction equations for the shaft and bearing，a multiphysics coupled numerical prediction method for the static and dynamic characteristics of the third-generation bump-type CO

GFBs was developed.The numerical method is validated against experimental data for the load-carrying capacity（LCC），dynamic stiffness，and damping coefficients of air-lubricated GFBs.Subsequently，a sensitivity analysis on foil geometrical parameters—including the bump foil's height，half-length，and thickness，as well as the top foil' s thickness—was performed using the central composite design（CCD）method.The static and dynamic characteristics under high-temperature and high-pressure conditions（315 ℃，2.0 Pa）were calculated for 25 foil geometrical parameter combinations.Main effect diagrams were obtained with static load，direct stiffness，and the energy dissipation factor as responses.The calculation results indicate that the static load and direct stiffness increase as the bump foil's height increases and the bump foil's

half-length decreases.At an eccentricity ratio of

=0.5，the static load and direct stiffness initially increase and then decrease with increasing bump foil thickness，peaking at thickness levels of 30% and 20%，respectively.Under heavy-load conditions（

=0.8），both static load and direct stiffness are most sensitive to the bump foil's thickness，with influence magnitudes of 35.1% and 76.4%，respectively.Since the regulation laws of foil geometrical parameters on two kinds of performance indicators exhibit inverse coupling characteristics，multi-objective optimization with direct stiffness and the energy dissipation factor as responses should be implemented to obtain foil geometrical parameters that make the overall dynamic performance of GFBs optimal.The findings serve as a reference for the performance analysis and structural design of the third-generation bump-type CO

GFBs.

关键词

Keywords

references

Dellacorte C, Valco M J.Load capacity estimation of foil air journal bearings for oil-free turbomachinery applications [J].Tribology Transactions, 2000, 43 (4):795-801.

Mohawk Innovative Technology, Inc..High load capacity compliant foil hydrodynamic journal bearing:5902049 [P].1999-05-11.

李昊, 耿海鹏, 孙岩桦, 等.箔片安装位置对气体轴承性能影响的仿真分析[J].西安交通大学学报, 2019, 53(3):81-87.

Li Hao, Geng Haipeng, Sun Yanhua, et al.Simulation analysis for influence of installation position on gas bearing performances [J].Journal of Xi'an Jiaotong University, 2019, 53(3):81-87.

李昊, 耿海鹏, 孙岩桦, 等.拱箔成型工艺对箔片轴承性能影响的仿真分析[J].西安交通大学学报, 2019, 53(4):9-14.

Li Hao, Geng Haipeng, Sun Yanhua, et al.Simulation analysis for influence of bump forming process on gas bearing performances [J].Journal of Xi'an Jiaotong University, 2019, 53(4):9-14.

Feng Kai, Kaneko S.Analytical model of bump-type foil bearings using a link-spring structure and a finiteelement shell model [J].Journal of Tribology, 2010, 132(2):021706.

Feng Kai, Kaneko S.Prediction of dynamic coefficients of bump-type foil bearings with bumps considered as link-spring structures [J].Tribology Online, 2011, 6(1):10-18.

Bi Chunxiao, Han Dongjiang, Yang Jinfu.The frequency perturbation method for predicting dynamic coefficients of supercritical carbon dioxide lubricated bearings [J]. Tribology International, 2020, 146:106256.

Han Dongjiang, Bi Chunxiao.The partial derivative method for dynamic stiffness and damping coefficients of supercritical CO 2 foil bearings [J ] . Lubricants, 2022, 10(11):307.

Gu Yongpeng, Ren Gexue, Zhou Ming. A novel method for calculating the dynamic force coefficients of gas foil bearings and its application in the rotordynamic analysis [J].Journal of Sound and Vibration, 2021, 515:116466.

Feng Kai, Kaneko S.A thermohydrodynamic sparse mesh model of bump-type foil bearings [J].Journal of Engineering for Gas Turbines and Power, 2013, 135(2):022501.

San Andrés S L, Kim T H.Thermohydrodynamic analysis of bump type gas foil bearings: a model anchored to test data [J].Journal of Engineering for Gas Turbines and Power, 2010, 132(4):042504.

Rieken M, Mahner M, Schweizer B.Thermal optimization of air foil thrust bearings using different foil materials [J].Journal of Turbomachinery, 2020, 142(10):101003.

Mahner M, Bauer M, Schweizer B.Numerical analyzes and experimental investigations on the fully-coupled thermo-elasto-gasdynamic behavior of air foil journal bearings [J].Mechanical Systems and Signal Processing, 2021, 149:107221.

Michel H, Liebich R.Challenges in validating a thermo-hydrodynamic gas foil bearing model [J].Journal of Engineering for Gas Turbines and Power, 2021, 143(4):041029.

Kim D, Ki J, Kim Y, et al.Extended three-dimensional thermo-hydrodynamic model of radial foil bearing:case studies on thermal behaviors and dynamic characteristics in gas turbine simulator [J].Journal of Engineering for Gas Turbines and Power, 2012, 134(5):052501.

Gad A M, Kaneko S.Fluid flow and thermal features of gas foil thrust bearings at moderate operating temperatures [C]//Proceedings of the 9th IFTOMM international conference on rotor dynamics.Cham: Springer International Publishing, 2015:1223-1233.

Ku C P R, Heshmat H.Compliant foil bearing structural stiffness analysis: part Ⅰ theoretical model including strip and variable bump foil geometry [J]. Journal of Tribology, 1992, 114(2):394-400.

Feng Kai, Kaneko S.Parametric studies on static performance and nonlinear instability of bump-type foil bearings [J].Journal of System Design and Dynamics, 2010, 4(6):871-883.

许浩杰, 高磊, 安琦.波箔型气体箔片推力轴承润滑性能的数值研究[J].华东理工大学学报(自然科学版), 2021, 47(1):101-109.

Xu Haojie, Gao Lei, An Qi.Numerical study on the lubrication performance of bump-type gas foil thrust bearing [J].Journal of East China University of Science and Technology (Natural Science Edition), 2021, 47(1):101-109.

邵聪鹏, 许浩杰, 李双敏, 等.考虑平箔综合弹性变形的空气箔片轴承性能[J].华东理工大学学报(自然科学版), 2025, 51(1):119-128.

Shao Congpeng, Xu Haojie, Li Shuangmin, et al.Performance of air foil bearings with considering comprehensive elastic deformation of flat foil [J].Journal of East China University of Science and Technology(Nat ural Science Edition), 2025, 51(1):119-128.

Kim D.Design space of foil bearings for closed-loop supercritical CO 2 power cycles based on three-dimensional thermohydrodynamic analyses [J ] .Journal of Engineering for Gas Turbines and Power, 2016, 138(3):032504.

Walker M S, Kruizenga A M, Weck K P F, et al. Progress in overcoming materials challenges with supercritical CO 2 recompression closed Brayton Cycles: SAND-2016-8126 [R ] .USA: Sandia, 2016.

Xu Fangcheng, Liu Zhansheng, Zhang Guanghui, et al. Effects of shear stiffness in top foil structure on gas foil bearing performance based on thick plate theory [J]. Proceedings of the Institution of Mechanical Engineers: Part J Journal of Engineering Tribology, 2013, 227(7):761-776.

Lehn A, Mahner M, Schweizer B.A contribution to the thermal modeling of bump type air foil bearings:analysis of the thermal resistance of bump foils [J]. Journal of Tribology, 2017, 139(6):061702.

Timoshenko S, Goodier J N.Theory of elasticity [M]. New York, USA:McGraw-Hill, 1951.

Yovanovich M M, Jafarpur K.Bounds on laminar natural convection from isothermal disks and finite plates of arbitrary shape for all orientations and Prandtl numbers [C]//ASME Winter Annual Meeting.New York, USA:ASME, 1993:93.

Seghir-ouali S, Saury D, Harmand S, et al.Convective heat transfer inside a rotating cylinder with an axial air flow [J].International Journal of Thermal Sciences, 2006, 45(12):1166-1178.

Mills A F.Heat transfer [M].Upper Saddle River NJ, USA:Prentice Hall, 1999.

Childs D.Turbomachinery rotordynamics: phenomena, modeling, and analysis [M].Hoboken, NJ, USA:John Wiley & Sons, Inc., 1993.

Aksoy S.Coupled thermo-elastohydrodynamic analysis of a bump-type compliant foil journal bearing [D]. Istanbul: Sabanci University, 2014.

王法义.空气箔片轴承设计、制造及其静态和动态特性实验研究[D].长沙:湖南大学, 2014.

Dellacorte C, Radil K C, Bruckner R J, et al.Design, fabrication, and performance of open source generationⅠandⅡ compliant hydrodynamic gas foil bearings [J]. Tribology Transactions, 2008, 51(3):254-264.

Bruckner R J, Puleo B J.Compliant foil journal bearing performance at alternate pressures and temperatures [C]//ASME Turbo Expo2008:Power for Land, Sea, and Air. New York, USA: ASME, 2008:587-594.

Rudloff L, Arghir M, Bonneau O, et al.Experimental analyses of a first generation foil bearing: startup torque and dynamic coefficients [J].Journal of Engineering for Gas Turbines and Power, 2011, 133 (9):092501.

Hoffmann R, Munz O, Pronobis T, et al.A valid method of gas foil bearing parameter estimation: a model anchored on experimental data [J].Proceedings of the Institution of Mechanical Engineers: Part C Journal of Mechanical Engineering Science, 2018, 232(24):4510-4527.

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采用试验设计方法的第三代CO2气体箔轴承箔片几何参数敏感性分析

Sensitivity Analysis of Foil Geometrical Parameters for the Third-Generation CO2 Gas Foil Bearings Based on Design of Experiments Method

DOI：10.7652/xjtuxb202607015

摘要

Abstract

关键词

Keywords

references

采用试验设计方法的第三代CO₂气体箔轴承箔片几何参数敏感性分析

Sensitivity Analysis of Foil Geometrical Parameters for the Third-Generation CO₂ Gas Foil Bearings Based on Design of Experiments Method