变截面节流器对空气静压轴承承载性能的影响
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摘要
为了分析可变截面节流器对空气静压轴承性能的影响,提出了变截面节流器的空气静压轴承模型,通过轴承承载表面弹性薄板的挠度变形实现节流器截面形状的动态变化。建立固体薄板变形和气体润滑的耦合偏微分方程,采用有限差分法和超松弛迭代法对耦合方程进行离散和数值求解。计算结果表明:节流器的截面形状直接决定了数值计算过程中喷嘴系数的大小,与刚性节流器的空气静压轴承相比,变截面节流器的空气静压轴承刚度提高了15%,在较高承载力的情况下能够获得更大的刚度。实验测试结果和理论分析基本一致,变截面节流器的设计方法能够有效提高空气静压轴承的静特性。
To analyze the effect of a variable section throttle on the performance of aerostatic bearings, an aerostatic bearing model with a variable section throttle was proposed. Furthermore, the dynamic change in the shape of the throttle cavity cross section was realized by deformation of the elastic plate of the bearing surface. First, the coupled partial differential equations of solid plate deformation and gas lubrication were established. Then, they were discretized and solved by the high-precision finite difference and over relaxation iteration methods. The results reveal that the shape of the throttle determines the value of the nozzle coefficient in the numerical calculation. Furthermore, the stiffness of aerostatic bearings with a variable section throttle is 15% higher than that of aerostatic bearings with a rigid throttle, indicating that a variable section throttle allows aerostatic bearings to achieve a greater stiffness under high bearing capacity. The results of the theoretical analysis are in good agreement with experimental results. Moreover, they indicate that a variable section throttle can effectively improve the static characteristics of aerostatic bearings.
To analyze the effect of a variable section throttle on the performance of aerostatic bearings, an aerostatic bearing model with a variable section throttle was proposed. Furthermore, the dynamic change in the shape of the throttle cavity cross section was realized by deformation of the elastic plate of the bearing surface. First, the coupled partial differential equations of solid plate deformation and gas lubrication were established. Then, they were discretized and solved by the high-precision finite difference and over relaxation iteration methods. The results reveal that the shape of the throttle determines the value of the nozzle coefficient in the numerical calculation. Furthermore, the stiffness of aerostatic bearings with a variable section throttle is 15% higher than that of aerostatic bearings with a rigid throttle, indicating that a variable section throttle allows aerostatic bearings to achieve a greater stiffness under high bearing capacity. The results of the theoretical analysis are in good agreement with experimental results. Moreover, they indicate that a variable section throttle can effectively improve the static characteristics of aerostatic bearings.
引文
[1] 周健斌, 孟光, 张文明. 微机电系统径向气体轴承特性研究[J]. 振动与冲击, 2007, 26(9):30-33.ZHOU J B, MENG G, ZHANG W M. Characteristics of micro gas journal bearing[J]. Journal of Vibration & Shock, 2007, 26(9):30-33. (in Chinese)
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[4] 夏毅敏,杨添任,张刚强,等. Nanosys-1000机床静压止推轴承流场分布规律及承载特性[J]. 光学 精密工程,2013,21(1):144-150.XIA Y M, YANG T R, ZHANG G Q, et al.. Flow field distribution and bearing characteristics of hydrostatic thrust bearing in Nanosys-1000 machine[J]. Optics and Precision Engineering, 2013, 21(1):144-150. (in Chinese)
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[9] BELFORTE G,RAPARELLI T, VIKTOROV V. Discharge coefficients of orifice-type restrictor for aerostatic bearings[J].Tribology International, 2007,40(3):512-521.
[10] 崔海龙, 岳晓斌, 张连新,等. 基于数值模拟的小孔节流空气静压轴承静动态特性研究[J]. 机械工程学报, 2016, 52(9):116-121.CUI H L, YUE X B, ZHANG L X, et al.. Static and dynamic characteristics of aerostatic bearing based on numerical simulation[J]. Journal of Mechanical Engineering, 2016,52(9):116-121. (in Chinese)
[11] 冯凯, 张俊, 王法义. 径向间隙及加工工艺对气体箔片轴承性能的影响[J]. 航空动力学报, 2016, 31(11):2773-2780.FENG K, ZHANG J, WANG F Y. Influence of radial clearance and processing technology on structural properties of gas foil bearing[J]. Journal of Aeronautical Power, 2016, 31(11):2773-2780. (in Chinese)
[12] ZHAO X L, ZHANG J A, DONG H, et al.. Numerical simulation and experimental study on the gas-solid coupling of the aerostatic thrust bearing with elastic equalizing pressure groove[J]. Shock and Vibration,2017:1-11.
[13] CHEN Y S, CHIU C C, CHENG Y D. Influences of operational conditions and geometric parameters on the stiffness of aerostatic journal bearings[J]. Precision Engineering, 2010, 34(4):722-734.
[14] 赵晓龙, 董皓, 方舟,等. 小孔节流空气静压止推轴承节流孔出口流场特性研究[J]. 润滑与密封, 2016, 41(12):37-40.ZHAO X L, DONG H, FANG ZH, et al.. Research on orifice exit flow field characteristics of aerostatic bearings with small hole throttle[J]. Lubrication Engineering, 2016, 41(12):37-40. (in Chinese)
[15] NAGHDI P M. The theory of shells and plates[J]. Mechanics of Solids,1973:425-640.
[2] 陈琦,陈斌,蔡黎明. 均压槽对空气静压轴承微振动的影响[J]. 光学 精密工程,2014,22(12):3354-3359.CHEN Q,CHEN B,CAI L M. Effect of equalizing groove on small vibration of aerostatic bearings[J]. Optics and Precision Engineering,2014,22(12):3354-3359.(in Chinese)
[3] RAPARELLI T, VIKTOROV V, COLOMBO F, et al.. Aerostatic thrust bearings active compensation: Critical review[J]. Precision Engineering, 2016, 44:1-12.
[4] 夏毅敏,杨添任,张刚强,等. Nanosys-1000机床静压止推轴承流场分布规律及承载特性[J]. 光学 精密工程,2013,21(1):144-150.XIA Y M, YANG T R, ZHANG G Q, et al.. Flow field distribution and bearing characteristics of hydrostatic thrust bearing in Nanosys-1000 machine[J]. Optics and Precision Engineering, 2013, 21(1):144-150. (in Chinese)
[5] GAO S, CHENG K, CHEN S, et al.. CFD based investigation on influence of orifice chamber shapes for the design of aerostatic thrust bearings at ultra-high speed spindles[J]. Tribology International, 2015, 92:211-221.
[6] LI Y, YIN Y, YANG H, et al.. Modeling for optimization of circular flat pad aerostatic bearing with a single central orifice-type restrictor based on CFD simulation[J]. Tribology International, 2017, 109:206-216.
[7] NISHIO U, SOMAYA K, YOSHIMOTO S. Numerical calculation and experimental verification of static and dynamic characteristics of aerostatic thrust bearings with small feedholes[J]. Tribology International, 2011, 44(12):1790-1795.
[8] 李一飞,尹益辉. 小孔节流静压支承轴承力学性能的数值建模[J]. 光学 精密工程,2017,25(2):417-424.LI Y F, YIN Y H. Numerical modeling of mechanical performances of aerostatic bearing with orifice-type restrictor[J]. Optics and Precision Engineering, 2017, 25(2):417-424. (in Chinese)
[9] BELFORTE G,RAPARELLI T, VIKTOROV V. Discharge coefficients of orifice-type restrictor for aerostatic bearings[J].Tribology International, 2007,40(3):512-521.
[10] 崔海龙, 岳晓斌, 张连新,等. 基于数值模拟的小孔节流空气静压轴承静动态特性研究[J]. 机械工程学报, 2016, 52(9):116-121.CUI H L, YUE X B, ZHANG L X, et al.. Static and dynamic characteristics of aerostatic bearing based on numerical simulation[J]. Journal of Mechanical Engineering, 2016,52(9):116-121. (in Chinese)
[11] 冯凯, 张俊, 王法义. 径向间隙及加工工艺对气体箔片轴承性能的影响[J]. 航空动力学报, 2016, 31(11):2773-2780.FENG K, ZHANG J, WANG F Y. Influence of radial clearance and processing technology on structural properties of gas foil bearing[J]. Journal of Aeronautical Power, 2016, 31(11):2773-2780. (in Chinese)
[12] ZHAO X L, ZHANG J A, DONG H, et al.. Numerical simulation and experimental study on the gas-solid coupling of the aerostatic thrust bearing with elastic equalizing pressure groove[J]. Shock and Vibration,2017:1-11.
[13] CHEN Y S, CHIU C C, CHENG Y D. Influences of operational conditions and geometric parameters on the stiffness of aerostatic journal bearings[J]. Precision Engineering, 2010, 34(4):722-734.
[14] 赵晓龙, 董皓, 方舟,等. 小孔节流空气静压止推轴承节流孔出口流场特性研究[J]. 润滑与密封, 2016, 41(12):37-40.ZHAO X L, DONG H, FANG ZH, et al.. Research on orifice exit flow field characteristics of aerostatic bearings with small hole throttle[J]. Lubrication Engineering, 2016, 41(12):37-40. (in Chinese)
[15] NAGHDI P M. The theory of shells and plates[J]. Mechanics of Solids,1973:425-640.