固定瓦-可倾瓦微气体轴承-转子系统的非线性运动分析

张永芳1,2,吕烨迪1,2, 肖良君1,2, 赵晶群1,2, 刘 成1,2

振动与冲击 ›› 2017, Vol. 36 ›› Issue (11) : 65-72.

PDF(1044 KB)
PDF(1044 KB)
振动与冲击 ›› 2017, Vol. 36 ›› Issue (11) : 65-72.
论文

固定瓦-可倾瓦微气体轴承-转子系统的非线性运动分析

  • 张永芳1,2 , 吕烨迪1,2, 肖良君1,2, 赵晶群1,2, 刘 成1,2
作者信息 +

Nonlinear dynamic analysis of a rotor system supported by micro fixed-tilting pad gas-lubricated bearings

  •  ZHANG Yong-fang1,2, LÜ Ye-di1,2, XIAO Liang-jun1,2, ZHAO Jing-qun1,2, LIU Cheng1,2
Author information +
文章历史 +

摘要

针对固定瓦-可倾瓦微气体轴承,考虑气体稀薄效应,给出了具有Burgdorfer一阶滑移速度边界的Reynolds方程,运用微分变换法结合有限差分法求解方程,得到了各瓦块在单块瓦坐标系中的非线性气膜力,然后通过组装技术获得了固定瓦-可倾瓦微气体轴承的气膜力。针对固定瓦-可倾瓦微气体轴承支撑的刚性Jeffcott转子系统,运用转子中心轨迹图、Poincaré映射图和时间历程图分析了转子的不平衡响应,比较了努森数、转速等对转子系统非线性特性的影响。数值结果表明:稀薄效应对转子中心的运动轨迹有较大影响,转子系统的不平衡响应表现为周期一运动、周期三运动和周期四运动。

Abstract

By considering gas rarefaction effect, Reynolds equation with Burgdorfer 1st-order slip velocity boundary in the lubrication of micro fixed-tilting pad gas-lubricated bearing was derived. The modified Reynolds equation was solved by the differential transformation method coupled with the finite difference method, and then the nonlinear gas film forces of single pad were calculated. Based on the assembly method, the gas film forces of the micro fixed-tilting pad gas-lubricated bearing were obtained. For a rigid rotor system supported by micro fixed-tilting pad gas-lubricated bearings, the unbalanced responses of the rotor were investigated by the orbit diagram, the Poincaré map diagram and the time series diagram. In addition, the comparisons of influences of Knudsen number and rotational speed on the nonlinear dynamic characteristics of the rotor were made. The results show that the gas rarefaction effect has a great influence on the orbits of the center of the rotor. And the unbalance responses of the rotor system characterized as period-1, period-3, period-4 motions.

关键词

微气体轴承 / 固定瓦-可倾瓦 / 转子系统 / 非线性

Key words

 micro gas-lubricated bearing / fixed-tilting pad / rotor system / nonlinear

引用本文

导出引用
张永芳1,2,吕烨迪1,2, 肖良君1,2, 赵晶群1,2, 刘 成1,2. 固定瓦-可倾瓦微气体轴承-转子系统的非线性运动分析[J]. 振动与冲击, 2017, 36(11): 65-72
ZHANG Yong-fang1,2, Lü Ye-di1,2, XIAO Liang-jun1,2, ZHAO Jing-qun1,2, LIU Cheng1,2. Nonlinear dynamic analysis of a rotor system supported by micro fixed-tilting pad gas-lubricated bearings[J]. Journal of Vibration and Shock, 2017, 36(11): 65-72

参考文献

[1] Dessornes O O,Landais S S,Valle R R,et al. Advances in the development of a microturbine engine [ J ]. ASME Journal of Engineering for Gas Turbines and Power,2014,136(7):1 – 9.
[2] Demiria S,Boedob S,Holsenb L S. Wear characteristics of large aspect ratio silicon microbearing systems [ J ]. Wear,2014,312(1–2):58 – 69.
[3] Ise T,Arita N,Asami T,et al. Development of externally pressurized small-size conical-shaped gas bearings for micro rotary machines [ J ]. Precision Engineering,2014,38(3):506 – 511.
[4] Dai X Y,Li H,Shen S N,et al. Numerical simulation of bearing force over bit-patterned media using 3-D DSMC method [ J ]. IEEE Transactions on Magnetics,2015,51(11):7209804 –7209807.
[5] Wang W Z,Liu Y Z,Jiang P N. Numerical investigation on influence of real gas properties on nonlinear behavior of labyrinth seal-rotor system [ J ]. Applied Mathematics and Computation,2015,263:12-24.
[6] Zhang Y F,Hei D,Lu Y J,et al. Bifurcation and chaos analysis of nonlinear rotor system with axial-grooved gas-lubricated journal bearing support [ J ]. Chinese Journal of Mechanical Engineering,2014,27(2):358 – 368.
[7] Meybodi R R,Mohammadi A K,Bakhtiari-Nejad F. Numerical analysis of a rigid rotor supported by aerodynamic four-lobe journal bearing system with mass unbalance [ J ]. Communications in Nonlinear Science and Numerical Simulation,2012,17(1):454 – 471.
[8] Wang C C. Bifurcation and nonlinear analysis of a flexible rotor supported by a relative short spherical gas bearing system [ J ]. Communications in Nonlinear Science and Numerical Simulation,2010,15(9):2659 – 2671.
[9] Hassini M,Arghir M. A simplified and consistent nonlinear transient analysis method for gas bearing:extension to flexible rotors [ J ]. ASME Journal of Engineering for Gas Turbines and Power,2015,137(9):092502 – 092511.
[10] Zhang Y F,Zhang S,Liu F X,et al. Motion analysis of a rotor supported by self-acting axial groove gas bearing system with double time delays [ J ]. Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science,2014,228(16):2888 – 2899.
[11] White J. Combined effects of surface roughness and rarefaction in the region between high wave number-limited and high bearing number-limited lubricant flows [ J ]. ASME Journal of Tribology. 2015,137(1):012001 – 012010.
[12] Zhang X Q,Wang X L, Liu R. Modeling and analysis of micro hybrid gas spiral-grooved thrust bearing for microengine [ J ]. ASME Journal of Engineering for Gas Turbines and Power. 2013,135(12):122508 – 122515.
[13] Zhang X Q,Wang X L,Zhang Y Y. Non-linear dynamic analysis of the ultra-short micro gas journal bearing-rotor systems considering viscous friction effects [ J ]. Nonlinear Dynamics,2013,73(1):751 – 765.
[14] Zhang W M,Meng G,Peng Z K. Gaseous slip flow in micro-bearings with random rough surface [ J ]. International Journal of Mechanical Sciences,2013,68:105 – 113.
[15] 杨琴,刘宇陆,张海军,等. 气体稀薄效应对微机电系统(MEMS)气体轴承-转子系统不平衡响应的影响 [ J ]. 西安交通大学学报,2015,49(7):134 – 139.
YANG Qin,LIU Yu-lu,ZHANG Hai-jun,et al. Influence of gas rarefaction effect on unbalance response of micro-electro-mechanical (MEMS) gas bearing-rotor system [ J ]. Journal of Xi’an Jiaotong University,2015,49(7):134 – 139.
[16] Lu Y J,Zhang Y F,Shi X L,et al. Nonlinear dynamic analysis of a rotor system with fixed-tilting-pad self-acting gas-lubricated bearings support [ J ]. Nonlinear Dynamics,2012,69(3):877 – 890.
[17] Shen S,Chen G,Crone R M. A kinetic-theory based first order slip boundary condition for gas flow [ J ]. Physics of Fluids,2007,19(8):086101 – 086106.
[18] 赵家奎. 微分变换及其在电路中的应用 [ M ]. 武汉:华中理工大学出版社,1988.

PDF(1044 KB)

Accesses

Citation

Detail

段落导航
相关文章

/