转子多叶箔片轴承系统动力特性研究
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摘要
20世纪60年代末70年代初,为了满足高速透平机械,特别是航空、航天用高速透平机械对轴承稳定性和寿命的要求,ASAC(Allied Signal Aerospace Co.)在美国空军与NASA的支持下成功的开发出多叶箔片轴承,其弹性的润滑表面使其具有很多独特优良性能,自适应能力强、高转速、工作温度范围广、可靠性好等,从而在低温制冷、航空航天等领域逐渐取代了传统滚珠轴承。但其较低的承载能力和苛刻的加工要求限制了其应用范围,所以根据目前的实际情况对油润滑多叶箔片轴承进行研究具有现实意义。本文将计算和分析油润滑多叶箔片轴承的静态和动态特性,并分析其对转子系统的动力特性的影响。
首先,计算和分析油润滑全周径向轴承的静态和动态特性。引入能较好地体现油膜破裂实际情况的雷诺边界条件,运用逐点超松弛迭代法(SOR)求解差分格式的雷诺方程得到油膜压力分布,其数值积分计算轴承的承载能力,既而求得稳态运行时轴心的平衡位置。在平衡位置处运用小扰动法求解关于扰动压力的雷诺方程,得到轴承的8个动力特性系数。计算得到的轴承静态特性和动态特性与文献对比验证计算油润滑全周径向轴承静态与动态特性的方法和思路是正确可靠的。
其次,以五叶箔片对称布置的箔片轴承为例,分析其几何特征,得到最初始时油膜厚度的表达式。将箔片视为悬臂弯曲梁,且箔片间相互点接触,从而得到箔片变形方程及箔片间的相互支反力表达式,在油润滑全周径向轴承性能计算方法和思路的基础上,将箔片变形方程与稳态雷诺方程耦合求解得到油膜压力和油膜厚度分布,从而求得承载能力、起飞转速及确定轴心平衡位置。推导箔片的动态变形方程,与动态的雷诺方程耦合求解轴承的动态刚度和阻尼。分析油膜压力和厚度分布等对轴承静态特性的影响以及分析转速和扰动频率对轴承动态特性的影响。
最后,将计算得到的多叶箔片轴承的动态刚度和阻尼引入转子多叶箔片轴承系统运动方程中,运用有限元法计算转子系统的临界转速和不平衡响应,分析多叶箔片轴承的动态刚度和阻尼对转子系统动力特性的影响。
During the late 1960s and early 1970s, in support of U.S. Air Force and NASA, the Multileaf Foil Bearings has been successfully developed by ASAC (Allied Signal Aerospace Co.) to meet the requirements of turbine machine, especially in the aerospace field. The elastic lubrication surface of Multileaf Foil Bearings which make it has many unique performances, such as strong self-adaptive ability, high speed, wide working temperature range, good reliability, etc; therefore the traditional ball bearings were gradually replaced by Multileaf Foil Bearings in the low temperature refrigeration, aerospace and other fields. But the application of Multileaf Foil Bearings was limited for its low bearing capacity and strict requirements of processing, so according to the actual situation the research about oil-lubricated Multileaf Foil Bearings has practical significance. The static and dynamic characteristics of Multileaf Foil Bearings was calculated and analyzed, and also the influence on the dynamic characteristics of rotor systems.
First, the static and dynamic characteristics of oil-lubricated cylindrical bearings were calculated and analyzed. The oil film pressure distribution were obtained by considering Reynolds boundary condition and using Successive Over Relaxation Method (SOR) to solve Reynolds equation, then the bearing capacity and equilibrium position of shaft can get. The eight dynamic coefficients were obtained by using small disturbance method on balance position to solve Reynolds equation. The accuracy and reliability of compute method and mentality about bearings static and dynamic characteristic were verified by comparing to the literature.
Second, Multileaf Foil Bearings with five symmetrical arrangements leaves foil, for example, the formula of its oil film thickness were obtained by analyzing its geometric features. The foil will be regarded as cantilevered curve beam, and mutually point contact, then the foil deformation equation and formula of counterforce between each other were obtained. Based on the compute method and mentality of oil-lubricated cylindrical bearings, the oil film pressure were got by coupled solving deformation equation with Reynolds equation, and then the bearing capacity,take-off speed, axis equilibrium position etc were determined. The dynamic characteristic coefficients were obtained by coupled solving the derived dynamic deformation equation with dynamic Reynolds equation. The influence on the bearings static and dynamic characteristic were discussed by analyzing the oil film pressure and thickness distribution, rotating speed and whirl frequency.
Last, the dynamic stiffness and damping obtained by calculating were introduced into the movement equation of rotor system, the critical speed and unbalance response were computed by using finite element method (FEM). The influence on dynamic characteristics of rotor system was discussed by analyzing the dynamic stiffness and damping of Multileaf Foil Bearings.
首先,计算和分析油润滑全周径向轴承的静态和动态特性。引入能较好地体现油膜破裂实际情况的雷诺边界条件,运用逐点超松弛迭代法(SOR)求解差分格式的雷诺方程得到油膜压力分布,其数值积分计算轴承的承载能力,既而求得稳态运行时轴心的平衡位置。在平衡位置处运用小扰动法求解关于扰动压力的雷诺方程,得到轴承的8个动力特性系数。计算得到的轴承静态特性和动态特性与文献对比验证计算油润滑全周径向轴承静态与动态特性的方法和思路是正确可靠的。
其次,以五叶箔片对称布置的箔片轴承为例,分析其几何特征,得到最初始时油膜厚度的表达式。将箔片视为悬臂弯曲梁,且箔片间相互点接触,从而得到箔片变形方程及箔片间的相互支反力表达式,在油润滑全周径向轴承性能计算方法和思路的基础上,将箔片变形方程与稳态雷诺方程耦合求解得到油膜压力和油膜厚度分布,从而求得承载能力、起飞转速及确定轴心平衡位置。推导箔片的动态变形方程,与动态的雷诺方程耦合求解轴承的动态刚度和阻尼。分析油膜压力和厚度分布等对轴承静态特性的影响以及分析转速和扰动频率对轴承动态特性的影响。
最后,将计算得到的多叶箔片轴承的动态刚度和阻尼引入转子多叶箔片轴承系统运动方程中,运用有限元法计算转子系统的临界转速和不平衡响应,分析多叶箔片轴承的动态刚度和阻尼对转子系统动力特性的影响。
During the late 1960s and early 1970s, in support of U.S. Air Force and NASA, the Multileaf Foil Bearings has been successfully developed by ASAC (Allied Signal Aerospace Co.) to meet the requirements of turbine machine, especially in the aerospace field. The elastic lubrication surface of Multileaf Foil Bearings which make it has many unique performances, such as strong self-adaptive ability, high speed, wide working temperature range, good reliability, etc; therefore the traditional ball bearings were gradually replaced by Multileaf Foil Bearings in the low temperature refrigeration, aerospace and other fields. But the application of Multileaf Foil Bearings was limited for its low bearing capacity and strict requirements of processing, so according to the actual situation the research about oil-lubricated Multileaf Foil Bearings has practical significance. The static and dynamic characteristics of Multileaf Foil Bearings was calculated and analyzed, and also the influence on the dynamic characteristics of rotor systems.
First, the static and dynamic characteristics of oil-lubricated cylindrical bearings were calculated and analyzed. The oil film pressure distribution were obtained by considering Reynolds boundary condition and using Successive Over Relaxation Method (SOR) to solve Reynolds equation, then the bearing capacity and equilibrium position of shaft can get. The eight dynamic coefficients were obtained by using small disturbance method on balance position to solve Reynolds equation. The accuracy and reliability of compute method and mentality about bearings static and dynamic characteristic were verified by comparing to the literature.
Second, Multileaf Foil Bearings with five symmetrical arrangements leaves foil, for example, the formula of its oil film thickness were obtained by analyzing its geometric features. The foil will be regarded as cantilevered curve beam, and mutually point contact, then the foil deformation equation and formula of counterforce between each other were obtained. Based on the compute method and mentality of oil-lubricated cylindrical bearings, the oil film pressure were got by coupled solving deformation equation with Reynolds equation, and then the bearing capacity,take-off speed, axis equilibrium position etc were determined. The dynamic characteristic coefficients were obtained by coupled solving the derived dynamic deformation equation with dynamic Reynolds equation. The influence on the bearings static and dynamic characteristic were discussed by analyzing the oil film pressure and thickness distribution, rotating speed and whirl frequency.
Last, the dynamic stiffness and damping obtained by calculating were introduced into the movement equation of rotor system, the critical speed and unbalance response were computed by using finite element method (FEM). The influence on dynamic characteristics of rotor system was discussed by analyzing the dynamic stiffness and damping of Multileaf Foil Bearings.
引文
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3 DellaCorte C., K.C. Radil, R.J. Bruckner. Design, Fabrication, and Performance of Open Source Generation I and II Compliant Hydrodynamic Gas Foil Bearings. 2008, 51(3): 11.
4许怀锦.转子—箔片轴承系统动力学特性理论及实验研究.哈尔滨工业大学博士学位论文. 2009: 2.
5 Block H.,J.J. VanRossum. The foli bearing-A new depature in Hydrodynamic Lubrication. ALSE J.Lubr.Eng., 1953(9): 316~330.
6 Agrawal G.L. Foil AIir/Gas Bearing Technology ~ An Overview. ASME Paper NO.97-GT-347, 1997.
7 Hayashi K. Development of aerodynamic foil bearings for hight speed rotor. 21st Leeds-Lyon Symposium on Tribology, 1994: 291~299.
8 Xiong L.-Y., G. Wu, Y. Hou. Development of aerodynamic foil journal bearings for a high speed cryogenic turboexpander. Cryogenics, 1997, 37(4): 221~230.
9 Y.Hou, Z.H.Zhu, C.Z.Chen. Comparative test on two kinds of new compliant foil bearing for small cryogenic turbo-expander. Cryogenics, 2004, 44(1): 69~72.
10 Howard S.A.,C. DellaCorte. Gas Foil Bearings for Space Propulsion Nuclear Electric Power Generation. NASA TM-2006-214115, 2006.
11刘占生,许怀锦.波箔型动压气体径向轴承的应用与研究进展.轴承, 2008(1): 39~43.
12 Song J.-h.,D. Kim. Foil Gas Bearing With Compression Springs: Analyses and Experiments. ASME J. of Tribology, 2007, 129(1): 628~639.
13 Walowit J. Gas lubricated foil bearing technology development for propulsion and power system. Technical report,Air Force Aero Propulsion Laboratory,Ohio, 1973.
14 Walowit J.,J. Anno. Modern developments in lubrication mechanics. Applied Sicence Publishers LTD, 1975: 214~221.
15 Ku C.-P.R.,H. Heshmat. Compliant foil bearing structural stiffness analysis: part I - theoretical model including strip and variable bump foil geometry. Journal of Tribology, Transactions of the ASME, 1992, 114(2): 394~400.
16 Ku C.-P.R.,H. Heshmat. Structural stiffness and coulomb damping in compliant foil journal bearings: parametric studies. STLE Tribology Transactions, 1994, 37(4): 455~462.
17 Ku C.-P.R.,H. Heshmat. Structural stiffness and coulomb damping in compliant foil journal bearings: theoretical considerations. STLE Tribology Transactions, 1994, 37(3): 525~533.
18 Heshmat H., J.A. Walowit, O. Pinkus. Analysis of gas-lubricated foil journal bearings. ASME J. of Lubrication Tribology, 1982, 105(10): 647~655.
19 Heshmat H. Analysis of Compliant Foil Bearings With Spatially Variable Stiffness. AIAA/SAE/ASME/ASEE 27th Joint Propulsion Conference. CA.AIAA-91-2102-CP, 1991.
20 Heshmat H.,C.-P.R. Ku. Structural damping of self-acting compliant foil journal bearings. Journal of Tribology, Transactions of the ASME, 1994, 116(1): 76~82.
21 Heshmat H. Operation of foil bearings beyond the bending critical mode. Journal of Tribology, 2000, 122(1): 192-198.
22 Salehi M., H. Heshmat, J.F. Walton. Advancements in the structural stiffness and damping of a large compliant foil journal bearing: An experimental study. Journal of engineering for gas turbines and power, 2007, 129(1): 154~161.
23 Heshmat H., P. Hryniewicz, J.F. Walton. Low-friction wear-resistant coatings for high-temperature foil bearings. Tribology international, 2005, 38(11-12): 1059-1075.
24 Jahanmir S., H. Heshmat, C. Heshmat. Evaluation of DLC Coatings for High-Temperature Foil Bearing Applications. Journal of Tribology, 2009, 131(1).
25 DellaCorte C.,M. Valco. Load capacity estimation of foil air journal bearings for oil-free turbomachinery applications. Tribology Transactions, 2000, 43(4): 795~801.
26 Dellacorte C., A. Zaldana, K. Radll. A systems approach to the solid lubrication of foil air bearings for oil-free turbomachinery. Journal of Tribology, 2004, 126(1): 200~207.
27 Kim T.,L. San Andres. Limits for high-speed operation of gas foil bearings. Journal of Tribology, 2006, 128(3): 670~673.
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