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工程设计学报
Chin J Eng Design  2023, Vol. 30 Issue (2): 226-236    DOI: 10.3785/j.issn.1006-754X.2023.00.010
Modeling, Simulation, Analysis and Decision     
Effect of calculation model on effectiveness of characteristics analysis of aerostatic bearings
Xiaocheng XIN1(),Wei LONG1(),Hao GAO1,Ping WANG1,Jilin LEI2
1.Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China
2.Yunnan Province Key Laboratory of Internal Combustion Engines, Kunming University of Science and Technology, Kunming 650500, China
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Abstract  

Aerostatic bearings have the characteristics of high precision, low friction and long life, which are widely used in aerospace and other fields. The bearing area and thickness of gas film of different aerostatic bearings are very different, resulting in extremely complex flow field inside the gas film. However, the traditional N-S (Navier-Stokes) equation based on the laminar flow hypothesis can not accurately predict the working characteristics of the bearing. Therefore, taking the disk-shaped center air supply orifice throttle aerostatic bearing as the research object, a mathematical model of its gas film flow field was established based on the gas lubrication and turbulence theory, and the development motion of turbulent spots in the gas film flow field after forming vortices and the transition process to smooth laminar flow were analyzed. Under the same operating conditions, the k-? model was adopted for the characteristic flow field when the gas film thicknss was smaller (<10 μm), the large eddy simulation (LES) model was adopted for the characteristic flow field when the gas film thickness was medium (10?20 μm), and the k-? model and the laminar flow model were adopted for the characteristic flow field when the gas film thicknss was larger (20?30 μm). Then, the static characteristics test platform of aerostatic bearing was designed and built to verify the accuracy of the calculation model. The results showed that selecting appropriate calculation model according to different operating conditions could improve the calculation accuracy of gas film flow field of aerostatic bearings. When the gas film thickness was less than 10 μm, the turbulence in the gas cavity was relatively large, and it was appropriate to describe it using the k-? model. When the gas film thickness increased to 10?20 μm, the large vortices in the gas cavity diffused and transported energy along the radius at a certain speed, which should be described by the LES model. When the gas film thickness increased to 20?30 μm, the capacitance effect of the gas film increased, which made the rear half of the gas cavity present laminar flow characteristics, and the hybrid calculation model should be used to describe it. The research results provide reference data for the design of aerostatic bearings under different operating conditions, and the accurate selection of calculation model is conducive to shortening the development cycle.

Key words： aerostatic bearing      turbulence theory      k-? model      large eddy simulation (LES) model      hybrid calculation model     
Received: 08 June 2022      Published: 06 May 2023
CLC:  TH 133.3  
Corresponding Authors: Wei LONG     E-mail: xiao_cheng_xin@163.com;daifor@163.com
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Xiaocheng XIN
Wei LONG
Hao GAO
Ping WANG
Jilin LEI
Cite this article:

Xiaocheng XIN,Wei LONG,Hao GAO,Ping WANG,Jilin LEI. Effect of calculation model on effectiveness of characteristics analysis of aerostatic bearings. Chin J Eng Design, 2023, 30(2): 226-236.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2023.00.010     OR     https://www.zjujournals.com/gcsjxb/Y2023/V30/I2/226


计算模型对空气静压轴承特性分析有效性的影响

空气静压轴承具有精度高、摩擦小和寿命长的特点，被广泛应用于航空航天等领域。不同空气静压轴承气膜的承载面积和厚度的差距悬殊，导致气膜内部的流场极为复杂，传统的基于层流假设的N-S（Navier-Stokes）方程已无法精确预测该轴承的工作特性。为此，以圆盘形中心供气小孔节流空气静压轴承为研究对象，基于气体润滑和湍流理论建立其气膜流场数学模型，分析了气膜流场内湍流斑形成涡旋后的发展运动以及向平滑层流过渡的过程。在相同工况下，针对气膜厚度较小（<10 μm）时的特征流场采用k-?模型，针对气膜厚度中等（10~20 μm）时的特征流场采用大涡模拟（large eddy simulation, LES）模型，针对气膜厚度较大（20~30 μm）时的特征流场采用“k-?模型+层流模型”。然后，设计并搭建空气静压轴承静态特性测试实验台，以验证所采用计算模型的准确性。结果表明：根据不同工况选择适宜的计算模型，可提高空气静压轴承气膜流场的计算精度。当气膜厚度小于10 μm时，气腔内湍动程度较大，宜采用k-?模型进行描述；当气膜厚度增大到10~20 μm时，气腔内大涡旋以一定速度沿半径方向扩散并输运能量，宜采用LES模型进行描述；当气膜厚度增大至20~30 μm时，气膜的容性效应增强，使得气腔内后半部分呈现层流特征，宜采用混合计算模型进行描述。研究结果为不同工况下空气静压轴承的设计提供了参考数据，准确选择计算模型有利于缩短研发周期。


关键词： 空气静压轴承,  湍流理论,  k-?模型,  大涡模拟（LES）模型,  混合计算模型 
Fig.1 Structure diagram of aerostatic bearing
参数数值
轴承直径D/mm100
气腔直径Dq/mm3
供气孔直径d/mm0.2
气膜厚度h/μm5~30
供气压力ps /MPa0.2~0.6
Table 1 Structure dimensions and working parameters of aerostatic bearing
Fig.2 Grid independence verification results of numerical calculation of gas film flow field characteristics
Fig.3 Test bench for static characteristics of aerostatic bearing
Fig.4 Bearing capacity of aerostatic bearing under different gas film thicknesses
Fig.5 Characteristics of gas film flow field with gas film thickness of 5 μm
Fig.6 Characteristics of gas film flow field with gas film thickness of 15 μm
Fig.7 Characteristics of gas film flow field with gas film thickness of 25 μm
Fig.8 Air consumption of aerostatic bearing under different gas film thicknesses
Fig.9 Static stiffness of aerostatic bearing under different air supply pressures
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