基于F-K滑移流模型的柱面微槽气浮密封浮升能力分析

doi:10.11949/0438-1157.20210464

摘要/Abstract

摘要：

由于气浮密封薄膜引发的滑移流现象频发，本文针对一种新型柱面螺旋槽气浮密封，基于线性化Boltzmann方程（F-K 模型），引入流量因子，建立稀薄气体润滑的F-K滑移流模型。采用高精度八点差分法和Newton-Raphson迭代法求解气膜压力，解决了表面槽-台阶跃、径向偏心与极薄气膜三者耦合下对求解发散和计算精度的影响。将计算结果与现有研究对比，并考察了气体滑移流效应与运行参数的内在关联，研究结果验证了新型柱面螺旋槽气浮密封在高速、低压、小膜厚和大偏心下具有较为明显的滑移流效应；此外，虽然槽深、槽数和槽长的增加提高了气膜浮力，但是增强了槽内滑移流动的响应。研究结果为拓宽动压密封应用范围提供理论了基础。

关键词: 滑移流模型, 螺旋槽, 气膜, 柱面密封, 润滑性能

Abstract:

Due to the frequent occurrence of slip flow caused by ultra-thin gas film and high-altitude rarefied gas in air-space field, a new type of cylindrical spiral groove air floating seal is designed in this paper. Based on the micro-scale characteristic size of the seal and the mechanism of airflow lubrication, the modified Reynolds equation of rarefied gas lubrication is established by simultaneously linearizing Boltzmann equation (F-K model) and introducing flow factor. The high-precision eight-point difference method and Newton-Raphson iterative method are used to solve the gas film pressure, and the F-K slip flow model is constructed, which solves the influence of the coupling of surface groove-step jump, radial eccentricity and ultra-thin gas film on the solution divergence and calculation accuracy. Then, the calculated results are compared with the existing studies, and the internal relationship between gas slip flow effect and operation parameters is investigated. The results show that the new cylindrical spiral groove air floating seal has obvious slip flow effect at high speed, low pressure, small film thickness and large eccentricity. At the same time, the dynamic pressure effect of cylindrical spiral groove air floating seal is caused by the dynamic pressure wedge caused by groove blocking effect and groove-step change, and the convergence wedge caused by eccentricity.On the other hand, the increase of groove depth, groove number and groove length increases the buoyancy of gas film but enhances the response of slip flow in the groove. The research results provide a theoretical basis for broadening the application range of dynamic seal.

Key words: slip flow model, spiral groove, gas film, cylindrical seal, lubrication performance

中图分类号:

TB 42

陆俊杰, 张炜, 马浩. 基于F-K滑移流模型的柱面微槽气浮密封浮升能力分析[J]. 化工学报, 2021, 72(8): 4267-4278.

Junjie LU, Wei ZHANG, Hao MA. Floating performance of cylindrical microgroove gas floating seal based on F-K slip flow model[J]. CIESC Journal, 2021, 72(8): 4267-4278.

图/表 13

图1 新型柱面螺旋槽气浮密封结构图

Fig.1 Schematic diagram of a new type of cylindrical spiral groove gas floating seal

图2 新型柱面螺旋槽气浮密封物理模型

Fig.2 Physical model of cylindrical spiral groove gas floating seal

图3 八点差分节点示意图

Fig.3 Schematic diagram of eight-point difference node

表1 柱面气浮密封工况参数和螺旋槽结构参数

Table 1 Initial structural and operation parameters of spiral-grooved cylindrical gas-floating seal

Parameters	Symbols	Values
outer diameter of rotating ring	R	0.025 m
length of floating ring	L	0.052 m
average gap	C	4 × 10^-6m
eccentricity	ε	0.5
rotating speed	n_r	50000 r/min
groove depth	h_c	8 × 10^-6 m
groove number	n_c	10
spiral angle	β	30°
groove length	l_c	0.025 m
gas pressure	p	0.3 MPa

图4 网格无关性验证

Fig.4 Grid independence verification

表2 文献［27］中的密封实验参数

Table 2 The experimental parameters of Ref. ［27］

Parameters	Symbols	Values
outer diameter of floating ring	R	0.0062 m
length of floating ring	L	0.0144 m
initial film thickness	C	6.5 × 10^-5 m
eccentricity	ε	0.5
depth of groove	h_c	4 × 10^-6 m
number of grooves	n_c	10
spiral angle	β	60°
length of groove	l_c	0.007 m

图5 F-K滑移流模型计算结果与文献[27]实验结果的比较

Fig.5 The comparison between the calculational result and experimental result of Ref. [27]

图6 无滑移流气膜压力(a)与F-K滑移流模型气膜压力(b)

Fig.6 Pressures of gas film in the non-slipping flow model (a) and the F-K model (b)

图7 无滑移流与F-K滑移流模型在气膜厚度4 μm和偏心率0.5下气膜浮升力随转速和压力的变化规律

Fig.7 Variations of the floating forces of the gas film with rotating speed and pressure in the non-slipping flow model and the F-K model under gas film thickness 4 μm and eccentricity 0.5

图8 无滑移流与F-K滑移流模型的气膜浮升力随膜厚与偏心率的变化规律

Fig.8 Variations of the floating forces of the gas film with eccentricity and gas film thickness in the non-slipping flow model and the F-K model

图9 无滑移流与F-K滑移流模型的气膜浮升力随槽深的变化规律

Fig.9 Variations of the floating forces with the groove depth in the non-slipping flow model and the F-K model

图10 无滑移流与F-K滑移流模型的气膜浮升力随槽数的变化规律

Fig.10 Variations of the floating forces of the gas film with the number of grooves in the non-slipping flow model and the F-K model

图11 无滑移流与F-K滑移流模型的气膜浮升力随槽长的变化规律

Fig.11 Variations of the floating forces of the gas film with the groove length in the non-slipping flow model and the F-K model

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