Design and investigation on static and dynamic characteristics of aerostatic bearings with non-coplanar orifice and groove

Abstract

Aerostatic bearings are extensively applied in the motion stage systems of cutting-edge equipment such as lithography machines. In this paper, a novel aerostatic bearing with non-coplanar orifice and groove (NCOG) is proposed, which effectively addresses the issue that the air supply tubes affect the high-speed motion accuracy of aerostatic guideways. Based on the gas lubrication theory, a three-dimensional computational fluid dynamics (CFD) model is established to analyze the pressure distribution and flow field status of the aerostatic bearing with NCOG. This reveals the lubrication mechanism as well as the static and dynamic characteristics of the aerostatic bearing with such a structure. The results indicate that the aerostatic bearing with NCOG can achieve the same functionality as traditional bearings with identical structural dimensions. The research on static characteristics shows that increasing the orifice diameter and the groove depth can enhance the pressure within the groove. The results of the dynamic characteristics study demonstrate that increasing the orifice diameter can reduce the micro-vibrations of the bearing. Additionally, when the groove depth is less than 0.04 mm, the turbulent kinetic energy (TKE) of the bearing increases with the increase in groove depth, while when it is greater than 0.04 mm, the TKE decreases with the deepening of the groove. Notably, when the groove depth exceeds 0.1 mm, the TKE of the bearing decreases sharply. The effectiveness of the CFD model and the accuracy of the conclusions regarding the static and dynamic characteristics are verified through experiments.

Graphical abstract

Keywords

aerostatic bearing / non-coplanar orifice and groove / static-dynamic characteristics / turbulent kinetic energy / numerical and experimental analysis

References

[1] Gao Q , Chen W , Lu L , Huo D , Cheng K . Aerostatic bearings design and analysis with the application to precision engineering: State-of-the-art and future perspectives. Tribology International, 2019, 135: 1–7

[2] Vainio V , Miettinen M , Majuri J , Theska R , Viitala R . Manufacturing and static performance of porous aerostatic bearings. Precision Engineering, 2023, 84: 177–190

[3] Cheng C , Zhao M , Zhao Z , Liu Z , Hou W , Yan L , Li Z , Chen S , Xu L . Study on micro-vibration mechanism and flow characteristics of aerostatic bearings based on proper orthogonal decomposition. Physics of Fluids, 2024, 36(8): 087104

[4] Hwang J , Park C H , Kim S W . Estimation method for errors of an aerostatic planar XY stage based on measured profiles errors. International Journal of Advanced Manufacturing Technology, 2010, 46(9–12): 877–883

[5] Raghunathan S. A study of reticle non-flatness induced image placement error in extreme ultraviolet lithography. Doctoral Dissertation. Albany: University at Albany, State University of New York, 2010

[6] Zhang Y , Wu J , Xing K , Wen Z , Tan J . Evaluation of measurement uncertainty of the high-speed variable-slit system based on the Monte Carlo method. Frontiers of Mechanical Engineering, 2020, 15(4): 517–537

[7] Wen Z , Wu J , Zhang Y , Cui J , Tan J . Improving the rotational stiffness of compact aerostatic guideway by micro-structures optimization. IEEE Access: Practical Innovations, Open Solutions, 2019, 7: 55780–55787

[8] Li S , Cui W . Research on the influence of supersonic phenomena on the gas film flow field of micron-groove-orifice aerostatic journal bearings under high gas supply pressure. Advances in Mechanical Engineering, 2022, 14(8): 1–16

[9] Qiu S , Ke C , Li K , Zhang X , Peng N , Liu L . Nonlinear dynamic analysis of a novel tangentially supplied aerostatic bearing-rotor system: Theory and experiment. Mechanical Systems and Signal Processing, 2025, 224: 112221

[10] Wen Z , Chi Y , Gu H , Qu H , Shi Z . CFD research for air bearing with gradient-depth recesses. Applied Sciences, 2024, 14(17): 7710

[11] Wu Y , Li C , Li J , Du J . Lubrication mechanism and characteristics of aerostatic bearing with close-spaced micro holes. Tribology International, 2024, 192: 109278

[12] Zheng J , Wu J , Liu H , Wang J , Zhao P . An analytical model for aerostatic thrust bearings based on the average pressure of the area surrounded by orifice. Lubricants, 2025, 13(3): 110

[13] Wen Z , Gu H , Shi Z . Key technologies and design methods of ultra-precision aerostatic bearings. Lubricants, 2023, 11(8): 315

[14] Chakraborty B , Chakraborti P . Design and development of different applications of PATB (porous aerostatic thrust bearing): A review. Tribologia – Finnish Journal of Tribology, 2023, 40(1–2): 18–28

[15] Marinescu A , Cicone T , Fatu A . The evaluation of two analytical solutions for a compliant single-recess hydrostatic thrust bearing. Tribology International, 2024, 196: 109672

[16] Belforte G , Raparelli T , Viktorov V , Trivella A . Discharge coefficients of orifice-type restrictor for aerostatic bearings. Tribology International, 2007, 40(3): 512–521

[17] Zhou Y , Chen X , Cai Y , Chen H , Han B . Measurement of gas pressure distribution in aerostatic thrust bearings using pressure-sensitive film. Tribology International, 2018, 120: 9–15

[18] Li W , Cai S , Zhang P , Ping Y , Feng K . Numerical and experimental study on the novel active aerostatic bearings with the controllable throttling effect for obtaining high static stiffness. Mechanical Systems and Signal Processing, 2024, 216: 111469

[19] Belforte G , Colombo F , Raparelli T , Trivella A , Viktorov V . Comparison between grooved and plane aerostatic thrust bearings: static performance. Meccanica, 2011, 46(3): 547–555

[20] Zheng L , Li J , Sun Y , Chen W , Zhang X . Design, analysis, and implementation of a compound restrictor aerostatic bearing system. Tribology International, 2025, 204: 110489

[21] Wen Z , Wu J , Xing K , Zhang Y , Li J , Tan J . Design of microstructure parameters on a small multi-throttle aerostatic guideway in photolithography. Engineering, 2021, 7(2): 226–237

[22] Du J , Zhang G , Liu T , To S . Improvement on load performance of externally pressurized gas journal bearings by opening pressure-equalizing grooves. Tribology International, 2014, 73: 156–166

[23] Chen X D , He X M . The effect of the recess shape on performance analysis of the gas-lubricated bearing in optical lithography. Tribology International, 2006, 39(11): 1336–1341

[24] Gao S , Cheng K , Chen S , Ding H , Fu H . CFD based investigation on influence of orifice chamber shapes for the design of aerostatic thrust bearings at ultra-high speed spindles. Tribology International, 2015, 92: 211–221

[25] Feng K , Wang G , An C , Chen R , Li W , Huang S , Jiang J . Design and analysis of biomimetic micro-groove aerostatic bearing inspired by Populus euphratica veins for enhanced load capacity and stiffness. Precision Engineering, 2025, 93: 18–36

[26] Li W , Wang G , Feng K , Zhang Y , Wang P . CFD-based investigation and experimental study on the performances of novel back-flow channel aerostatic bearings. Tribology International, 2022, 165: 107319

[27] Zhou Y , Chen X , Chen H . A hybrid approach to the numerical solution of air flow field in aerostatic thrust bearings. Tribology International, 2016, 102: 444–453

[28] Wen Z , Wu J , Tan J . An adaptive modeling method for multi-throttle aerostatic thrust bearing. Tribology International, 2020, 149: 105830

[29] Aoyama T , Kakinuma Y , Kobayashi Y . Numerical and experimental analysis for the small vibration of aerostatic guideways. CIRP Annals, 2006, 55(1): 419–422

[30] Long W , Bao G . Entrance effect on load capacity of orifice compensated aerostatic bearing with feeding pocket. Chinese Journal of Mechanical Engineering, 2010, 23(4): 451–459

[31] Wang F S , Bao G . Characteristics of supersonic flow in new type externally pressurized spherical air bearings. Journal of Central South University, 2012, 19(1): 128–134

[32] Yoshimoto S , Yamamoto M , Toda K . Numerical calculations of pressure distribution in the bearing clearance of circular aerostatic thrust bearings with a single air supply inlet. ASME. Journal of Tribology, 2007, 129(2): 384–390

[33] Eleshaky M E . CFD investigation of pressure depressions in aerostatic circular thrust bearings. Tribology International, 2009, 42(7): 1108–1117

[34] Chen M F , Huang W L , Chen Y P . Design of the aerostatic linear guideway with a passive disk-spring compensator for PCB drilling machine. Tribology International, 2010, 43(1–2): 395–403

[35] Belforte G , Colombo F , Raparelli T , Trivella A , Viktorov V . Performance of externally pressurized grooved thrust bearings. Tribology Letters, 2010, 37(3): 553–562

RIGHTS & PERMISSIONS

Higher Education Press