Sensitivity Analysis of Foil Geometrical Parameters for the Third-Generation CO<sub>2</sub> Gas Foil Bearings Based on Design of Experiments Method

LI Zhuocong; LI Zhigang; LI Jun

doi:10.7652/xjtuxb202607015

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

更新时间：2026-07-09

- Sensitivity Analysis of Foil Geometrical Parameters for the Third-Generation CO₂ Gas Foil Bearings Based on Design of Experiments Method
- Journal of Xi'an Jiaotong University Vol. 60, Issue 7, Pages: 159-172(2026)
- 作者机构：
  
  西安交通大学叶轮机械研究所，710049，西安
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202607015
  CLC： TH133.3;TH117.2
- Received：09 October 2025，
  
  Published：10 July 2026
- 稿件说明：
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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：

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.

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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

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