journal article·2026-07-10Open access

Modeling and Analysis Method for Error Motion of Precision Aerostatic Rotary Stage and Experimental Verification

Xiaofeng Zheng, Xiangyu Zhao, Deqiang Mu, Tianhao Zheng, Daowei Zhang, Lei Zhang, Cheng Li, Tianyang Dong

Applied Sciences· Volume 16· Issue 14

Abstract

The rotational error motion of precision aerostatic rotary stages substantially affects the accuracy of machining and measuring equipment. A comprehensive and flexible error modeling method is absent. This paper develops an analytical model for the error motion of an aerostatic rotary stage bearing, utilizing linear superposition and spatial force equilibrium principles. The error motion of an orifice-restricted rotary stage is computed using this approach. The impact of bearing manufacturing inaccuracies (e.g., journal roundness, thrust plate profile) and micro-vibrations caused by internal turbulence is analyzed. Finally, the model was validated experimentally using the reversal method. The results indicate that bearing manufacturing errors positively correlate with error motion, and micro-vibration considerably influences errors at the sub-100 nm level. The relative error between the predicted and measured values is less than 15%, confirming the validity and applicability of this modeling and analytical approach. This research enhances error motion analysis methods and offers a novel constructive reference for predicting and optimizing error motion in precision aerostatic rotary stages.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Advanced Measurement and Metrology Techniques · Iterative Learning Control Systems · Tribology and Lubrication Engineering

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China

University of Chinese Academy of Sciences, Beijing 100049, China

Chang Guang Satellite Technology Co., Ltd., Changchun 130102, China

Department of Precision Instrument, Tsinghua University, Beijing 100084, China

Funding

Jilin Province Science and Technology Development Plan Project of China

References (30)

Show source-provided references
1. Potential fields in hydrostatic bearing spindle: Review and recent advances of rotational accuracy10.1007/s00170-025-15914-z ↗
2. A study on run-out characteristics of externally pressurized gas journal bearing: Rotor run-out characteristics
3. Design and optimization of fluid lubricated bearings operated with extreme working performances—A comprehensive review10.1088/2631-7990/ad1825 ↗
4. An analytical study on the rotational accuracy of aerostatic journal bearing
5. Effects of part accuracy on rotational accuracy in hydrostatic bearing
6. Estimation of rotational motion accuracy for rotary units10.7736/KSPE.2015.32.2.127 ↗
7. Dynamic accuracy model of porous journal air bearing considering rotational speed10.1016/j.triboint.2021.107064 ↗
8. Research on the Dynamic Performance of Aerostatic Radial Bearings with Elastic Throttles10.3901/JME.2025.05.074 ↗
9. Research on the Mechanism of Improving Hydrostatic Spindle Rotating Accuracy with Controllable Restrictor10.3901/JME.2019.11.160 ↗
10. The Laws and Ultimate Prediction of Rotation Accuracy for Hydrostatic Spindle10.3901/JME.2021.13.070 ↗
11. Meng, S. (2016). Research on the Rotary Accuracy of the Hydrostatic-dynamic Spindle Affected by Journal Geometric Error and Electromagnetic Eccentricity. [Ph.D. Thesis, Hunan University].
12. Identification of nonlinear dynamic coefficients in plain journal bearings10.1016/j.triboint.2008.01.002 ↗
13. Reducing the radial error motion of an aerostatic journal bearing to a nanometre level: Theoretical modelling10.1007/s11249-013-0241-8 ↗
14. An analytical study on the rotational accuracy of externally pressurized air journal bearing
15. Wang, W., Song, P., Yu, H., and Zhang, G. (2022). Study on Static Characteristics of Ultra-Precision Aerostatic Motorized Spindle under Gas–Magnetic Field Coupling. Electronics, 11.10.3390/electronics11091434 ↗
16. Numerical analysis and experimental investigation into the effects of manufacturing errors on the running accuracy of the aerostatic porous spindle10.1016/j.triboint.2017.09.020 ↗
17. Influence of shape errors and inertia effects on the error motion of the aerostatic spindle10.1177/13506501231211393 ↗
18. Influence of angular misalignment and triangular surface waviness on the performance of hybrid air journal bearings10.1108/ILT-12-2024-0457 ↗
19. Jia, S., Jia, C., and Lu, Y. (2024). Dynamic Modeling of 5-DOF Aerostatic Bearing Rotor System with Adjustable Gas Film Gap. Lubricants, 12.10.3390/lubricants12120424 ↗
20. Performance of inherently compensated flat pad aerostatic bearings subject to dynamic perturbation forces10.1016/j.precisioneng.2012.01.002 ↗
21. Large eddy simulation of vortex shedding and pressure fluctuation in aerostatic bearings10.1016/j.jfluidstructs.2013.03.012 ↗
22. Numerical analysis and experimental study on the microvibration of an aerostatic thrust bearing with a pocketed orifice-type restrictor10.1177/1350650114556556 ↗
23. Li, Y. (2018). Mechanical Performances Analysis and Parameters Design Optimization of the Aerostatic Bearing with Orifice Type Restrictor. [Ph.D. Thesis, China Academy of Engineering Physics].
24. A study on the running accuracy of an externally pressurized gas thrust bearing: Rotor run-out characteristics
25. Yin, J. (2013). Separated Aerostatic Bearings and Its Mechanism of Error Averaging. [Master’s Thesis, China Jiliang University].
26. Jin, S. (2022). Modeling and Experimental Study on Rotation Error of Aerostatic Bearing. [Master’s Thesis, Harbin Institute of Technology].
27. A statistical approach to tolerance evaluation for circles and cylinders10.1080/07408170490458616 ↗
28. Liu, T., Liu, Y., and Chen, S. (1990). Hydrostatic Gas Lubrication, Harbin Institute of Technology Press.
29. Self-calibration: Reversal, redundancy, error separation, and ‘absolute testing’10.1016/S0007-8506(07)60515-0 ↗
30. A simple method for separating spindle error from test ball roundness error