Characteristics analysis of multi-leaf foil bearing with bump-foil support considering slip boundary
-
摘要:
为探究滑移边界和轴承参数对轴承特性的影响，将考虑滑移边界的雷诺方程应用至具有波箔支撑的多叶式箔片轴承中。依次借助Newton-Raphson法和小扰动法线性化压力控制方程，并利用弯曲梁模型描述箔片径向变形，结合有限差分法建立该类型轴承的流-固耦合求解模型，数值结果与试验结果吻合较好。研究了轴承数、偏心率、长径比、间隙比、平箔片数目以及平箔片厚度对该类型轴承特性参数的影响规律，研究结果表明：对于八叶轴承，当轴承数或间隙比较小时，滑移边界会导致承载力普遍下降3%，此时应考虑其影响，但该影响对长径比和平箔片厚度的变化不敏感。此外，该类型轴承稳定性整体较好，当轴承数较小时滑移边界会导致轴承稳定性下降。
Abstract:To investigate the effect of slip boundary and bearing parameters on bearing characteristics, the Reynolds equation considering slip boundary was introduced to the multi-leaf foil bearing with bump-foil support. The Newton-Raphson iterative method and the perturbation method were successively employed to linearize the pressure governing equation, and the curved beam model was used to describe the radial foil deformation. The finite difference method was adopted to help establish the fluid-structure coupling solution model of this type of bearing, and the numerical results agreed well with the experimental results. The influences of bearing number, eccentricity ratio, length-diameter ratio, clearance ratio, the number and thickness of top foil on characteristic parameters were studied. The results indicated that slip boundary caused a general decrease of 3% in the load capacity of eight-leaf bearing when the bearing number and length-diameter ratio were small, meaning that the effect of slip boundary should be taken into consideration. Nevertheless, this effect was not sensitive to the change in the length-diameter ratio and thickness of the top foil. Besides, this type of bearing had a better stability. When the bearing number was small, the slip boundary led to the decline of bearing stability.
-
Key words:
- slip boundary /
- multi-leaf foil bearing /
- bump-foil support /
- static characteristics /
- stability
-
图 4 弯曲梁单元刚度矩阵验证结果
Figure 4. Verification results of stiffness matrix of curved beam element
图 10 轴向中截面上的气膜压力、气膜厚度和Kn分布
Figure 10. Film pressure, film thickness and Kn distribution on axial midsection
图 11 偏心率和轴承数对承载力的影响
Figure 11. Influence of eccentricity and bearing number on bearing capacity
图 12 不同轴承数和偏心率下的气膜压力和Kn分布
Figure 12. Film pressure, Kn distribution for different bearing number and eccentricity ratio
图 13 无量纲长径比和间隙比对承载力的影响
Figure 13. Influence of dimensionless length-diameter ratio and clearance ratio on bearing capacity
图 14 不同长径比和间隙比下的气膜压力和Kn分布
Figure 14. Film pressure, Kn distribution for different length-diameter ratio and clearance ratio
图 15 无量纲平箔片厚度和平箔片数目对承载力的影响
Figure 15. Influence of dimensionless thickness of top foil and foil number on bearing capacity
图 16 不同平箔片数目下的Kn和气膜压力分布
Figure 16. Kn, film pressure distribution for different foil numbers
表 1 不同滑移模型对应的系数
Table 1. Coefficients of different slip models
系数 滑移模型 无滑移 1阶 1.5阶 2阶 Wu c1 0 a a a 2a/3 c2 0 0 2/9 1/2 1/4 
下载: 导出CSV
参数 数值 轴颈半径R/10−2 m 5.71500 轴瓦半径Rb/10−2 m 5.79628 内切圆半径Rt/10−2 m 5.74548 平箔片半径Rf/10−2 m 5.95000 轴承轴向长度L/10−1 m 1.52400 弹性模量Eb/1011 Pa 2.06850 平箔片厚度tf/10−4 m 2.54000 平箔片数量N 8 气体动力黏度μ /10−5 （Pa·s） 2.95300 转速Ω/（r/min） 33000
下载: 导出CSV
表 3 多叶波箔式轴承的计算参数
Table 3. Parameters of multi-leaf foil bearing with bump-foil support
参数 数值 轴颈半径R/10−2 m （2.34900） 轴瓦半径Rb/10−2 m 2.62500 内切圆半径Rt/10−2 m 2.35000 平箔片半径Rf/10−2 m （2.75000） 轴承长度L/10−2 m （4.69800） 弹性模量Eb/1011 Pa 2.14000 泊松比νb 0.3 平箔片厚度tf/10−4 m （1.01600） 平箔片数量N （8） 波箔片跨距s/10−3 m 4.20000 波箔片厚度tb/10−4 m 1.01600 波箔片半长度l/10−3 m 1.75000 气体动力黏度μ /10−5 （Pa·s） 1.93200 转速Ω/（r/min） （50000） 偏心率 ε （0.5）
下载: 导出CSV
-
[1] HOU Yu,ZHAO Qi,GUO Yu,et al. Application of gas foil bearings in China[J]. Applied Sciences,2021,11(13): 6210.1-6210.13. [2] BRUCKNER R J. An assessment of gas foil bearing scalability and the potential benefits to civilian turbofan engines[C]//Proceedings of the ASME Turbo Expo 2010: Power for Land, Sea, and Air. Glasgow, UK: ASME, 2010: 29-35. [3] 赵晓荣. 多叶波箔型气体动压轴承静特性及气动加热数值研究[D]. 南京: 南京航空航天大学, 2016.ZHAO Xiaorong. Numerical research on the static and aerodynamic heating characteristics of multi-leaf compliant foil bearings[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2016. (in Chinese) [4] 李旺. 动压气体轴承周向变截面间隙内流动特性研究[D]. 南京: 南京航空航天大学, 2019.LI Wang. Research on flow characteristics of aerodynamic bearings with variable cross sectional clearance[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2019. (in Chinese) [5] OH K P,ROHDE S M. A theoretical investigation of the multileaf journal bearing[J]. Journal of Applied Mechanics,1976,43(2): 237-242. doi: 10.1115/1.3423816 [6] ARAKERE N K,NELSON H D. An analysis of gas-lubricated foil-journal bearings[J]. Tribology Transactions,1992,35(1): 1-10. doi: 10.1080/10402009208982082 [7] ZHANG Guanghui,XIE Liang,WANG Yu,et al. Performance analysis of oil lubricated foil bearing with flexible supported back spring structure: Part Ⅰ model development and numerical investigation[J]. Journal of Engineering for Gas Turbines and Power,2014,136(11): 112501.1-112301.10. [8] ZHANG Guanghui,XIE Liang,WANG Yu,et al. Performance analysis of oil lubricated foil bearing with flexible supported back spring structure: Part Ⅱ comparison of predictions and measured test data[J]. Journal of Engineering for Gas Turbines and Power,2014,136(11): 112502.1-112502.10. [9] DU Jianjun,ZHU Jianjun,LI Bing,et al. The effect of area contact on the static performance of multileaf foil bearings[J]. Tribology Transactions,2015,58(4): 592-601. doi: 10.1080/10402004.2014.997907 [10] LI Changlin,DU Jianjun,ZHU Jianjun,et al. Effects of structural parameters on the load carrying capacity of the multileaf gas foil journal bearing based on contact mechanics[J]. Tribology International,2018,131: 318-331. [11] SHAHDHAAR M A,YADAWAD S S,KHAMARI D S,et al. Numerical investigation of slip flow phenomenon on performance characteristics of gas foil journal bearing[J]. SN Applied Sciences,2020,2(10): 1-18. [12] 燕震雷,伍林. 稀薄效应对可倾瓦动压气体轴承性能的影响[J]. 航空动力学报,2020,35(7): 1496-1505. doi: 10.13224/j.cnki.jasp.2020.07.018YAN Zhenlei,WU Lin. Effect of rarefied effect on the performance of tilting pad dynamic pressure gas bearings[J]. Journal of Aerospace Power,2020,35(7): 1496-1505. (in Chinese) doi: 10.13224/j.cnki.jasp.2020.07.018 [13] ZHANG Xiangbo,DING Shuiting,DU Farong,et al. Investigation into gas lubrication performance of porous gas bearing considering velocity slip boundary condition[J]. Friction,2022,10(6): 891-910. doi: 10.1007/s40544-021-0503-7 [14] SZERI A Z. Fluid film lubrication[M]. New York, US: Cambridge University Press, 2010: 466-510. [15] 池长青. 流体力学润滑[M]. 北京: 国防工业出版社, 1998: 485-487. [16] PILKEY W D. Formulas for stress, strain, and structural matrices[M]. Hoboken, US: John Wiley and Sons, Incorporation, 1994: 878-879. [17] 黄钟文. 基于多重网格法的表面微织构气体箔片轴承特性研究[D]. 哈尔滨: 哈尔滨工业大学, 2019.HUANG Zhongwen. Research on micro-textured gas foil bearing characteristics based on multigrid method[D]. Harbin: Harbin Institute of Technology, 2019. (in Chinese) [18] WANG Nenzi,CHANG Chinyuan. An application of Newton’s method to the lubrication analysis of air-lubricated bearings[J]. Tribology Transactions,1999,42(2): 419-424. doi: 10.1080/10402009908982237 [19] HU Hongyang,FENG Ming,REN Tianming. Study on the performance of gas foil journal bearings with bump-type shim foil[J]. Journal of Engineering Tribology,2021,235(3): 509-523. [20] KOEPSEL W F. Gas lubricated foil bearing development for advanced turbomachines[R]. AFAPL-TR-76-114, 1977. [21] HIRANI H,SUH N P. Journal bearing design using multiobjective genetic algorithm and axiomatic design approaches[J]. Tribology International,2005,38(5): 481-491. doi: 10.1016/j.triboint.2004.10.008 -
点击查看大图
计量
- 文章访问数: 195
- HTML浏览量: 43
- PDF量: 47
- 被引次数: 0