Global sensitivity analysis of design variables for porous hydrostatic gas bearings considering uncertainty考虑不确定性下多孔静压气体轴承设计变量全局灵敏度分析
Wu YH, Cao LX, Tang JC, Tian MQ, 2025. Global sensitivity analysis of design variables for porous hydrostatic gas bearings considering uncertainty. Probabilistic Engineering Mechanics, 79: 103722.DOI: 10.1016/j.probengmech.2024.103722
多孔静压气体轴承 (porous hydrostatic gas bearing, PHGB) 利用多孔材料作为节流器，因其出色的稳定性和承载力而在机械设备和科学仪器中得到广泛认可。目前，多孔静压气体轴承的设计依赖于确定性模型来计算承载力和刚度，而气源压力和轴承间隙等参数的调整主要依赖于经验。然而，实际应用中不可避免地会引入与压缩机性能、材料特性和制造误差相关的不确定性，这会显著影响多孔静压气体轴承的设计性能。为解决这些挑战，本文进行了全局灵敏度分析来识别导致多孔静压气体轴承力学性能变化的敏感因素。首先，基于 Darcy 方程和连续性方程建立了多孔静压气体轴承模型，并验证了其对轴承特性的预测精度。随后，引入采用稀疏混沌多项式展开的全局灵敏度分析方法来定量评估供给压力、轴承长度、直径、间隙和偏心率等不确定性对承载力和质量流量的影响。本研究确定了影响多孔静压气体轴承机械性能的最关键不确定性参数，研究结果将使设计人员能够全面了解不确定性条件下轴承的机械性能，同时降低计算成本，为多孔静压气体轴承分析和设计提供宝贵的理论基础。关键词: 多孔静压气体轴承, 全局灵敏度分析, 不确定性, 力学性能, 混沌多项式展开Porous hydrostatic gas bearing (PHGB) utilizes porous materials as restrictors and is widely recognized in mechanical equipment and scientific instruments due to their exceptional stability and load capacity. At present, the design of PHGB relies on deterministic models to calculate bearing capacity and stiffness, and the adjustment of parameters such as air supply pressure and bearing clearance mainly depends on experience. However, uncertainties related to compressor performance, material properties, and manufacturing errors are inevitably introduced in the practical applications, which can significantly affect the design performance of PHGBs. To address these challenges, this paper presents a global sensitivity analysis to identify the sensitive factors causing variations in the mechanical properties of PHGBs. First, a PHGB model is developed based on the Darcy and continuity equations, and its predictive accuracy for bearing characteristics is validated. Subsequently, a global sensitivity analysis method employing sparse polynomial chaos expansion is introduced to quantitatively assess the impact of uncertainties such as supply pressure, bearing length, diameter, clearance, and eccentricity on load capacity and mass flow rate. This analysis identifies the most critical uncertain parameters influencing the mechanical performance of PHGBs. The insights gained from this study will enable designers to comprehensively understand the mechanical performance of bearings under uncertainty while reducing computational costs, thus providing a valuable theoretical foundation for PHGB analysis and design.Keywords: PHGB; Global sensitivity analysis; Uncertainty; Mechanical performance; Polynomial chaos expansion.Fig. 1. Photograph of a PHGB
Fig. 2. Schematic view of the PHGB
Fig. 3. Mass flow rate in a small control volume
Fig. 4. Comparison of predicted load capacity with air bushing made by New Way® Air Bushings
Fig. 5. Pressure distribution of the gas flow in bearing clearance
图 6: 多孔静压气体轴承的预测承载力与质量流量随供应压力比的变化Fig. 6. Predicted load capacity and mass flow rate of the PHGB versus supply pressure ratio (Ps/Pa)
图 7: 多孔静压气体轴承的预测承载力与质量流量随轴承间隙的变化Fig. 7. Predicted load capacity and mass flow rate of the PHGB versus bearing clearance (Ps/Pa)
Fig. 8. Precision comparison of SPCE models
Fig. 9. Probability distribution of PHGB performance
Fig. 10. GSA results for the load capacity
Fig. 11. GSA results for the mass flow rate
作者信息 | Authors
Yi-Hua Wu湖南大学 (Hunan University) 设计艺术学院
曹立雄 Li-Xiong Cao, 通讯作者 (Corresp.)湖南大学 (Hunan University) 设计艺术学院Email: lixiongc@hnu.edu.cn, clx_328@hnu.edu.cn
唐嘉昌 Jia-Chang Tang湖南工业大学 (Hunan University of Technology) 机械工程系
湖南省计量测试研究院 (Hunan Institute of Metrology & Test)
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
