Analysis of Nonlinear Motion of A Rotor System Supported by Fixed-tilting Pad Self-acting Aerodynamic Bearings

doi:10.3901/JME.2018.11.187

Abstract

Abstract: The nonlinear dynamic behaviors of a flexible rotor system with fixed-tilting pad combined aerodynamic bearings support are investigated. The compressible gas lubricated Reynolds equation is solved by the differential transformation method, and then the nonlinear gas film forces of single pad are calculated. Based on the assembly method, the pressure distribution of nonlinear gas film of the fixed-tilting pad aerodynamic bearing is obtained. Based on the Newmark integral method, the nonlinear unbalanced responses of the flexible rotor system supported by combined aerodynamic bearings are investigated using the orbit diagram, the Poincaré map diagram and the time series diagram. On this basis, the effects of different pivot ratios and preload coefficients of the pads on the stability of the rotor system are analyzed further. The numerical results show that it can be helpful to improve the stability of the rotor system when chooses the proper pivot ratios and higher preload coefficients.

Key words: fixed-tilting pad bearings, gas lubrication, nonlinear, pivot ratio, preload coefficient

CLC Number:

TH133

ZHANG Yongfang, XIAO Liangjun, LI Xianwei, ZHAO Jingqun, LI Sha. Analysis of Nonlinear Motion of A Rotor System Supported by Fixed-tilting Pad Self-acting Aerodynamic Bearings[J]. Journal of Mechanical Engineering, 2018, 54(11): 187-196.

References

[1] WANG Chengchi, JANG Mingjyi, YEH Yenliang. Bifurcation and nonlinear dynamic analysis of a flexible rotor supported by relative short gas journal bearings[J]. Chaos, Solitons & Fractals, 2007, 32(2):566-582.
[2] WANG Chengchi. Theoretical and nonlinear behavior analysis of a flexible rotor supported by a relative short herringbone-grooved gas journal-bearing system[J]. Physica D:Nonlinear Phenomena, 2008, 237(18):2282-2295.
[3] WANG Chengchi. 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.
[4] YANG Pan, ZHU Keqin, WANG Xiaoli. On the non-linear stability of self-acting gas journal bearings[J]. Tribology International, 2009, 42(1):71-76.
[5] ZHANG Jiazhong, KANG Wei, LIU Yan. Numerical method and bifurcation analysis of Jeffcott rotor system supported in gas journal bearings[J]. ASME Journal of Computational and Nonlinear Dynamics, 2009, 4(1):011007-1-9.
[6] ZHANG Xiaoqing, WANG Xiaoli, ZHANG Yuyan. Non-linear dynamic analysis of the ultra-short micro gas journal bearing-rotor systems considering viscous friction effects[J]. Nonlinear Dynamics, 2013, 73(1-2):751-765.
[7] RASHIDI M R. Bifurcation and nonlinear dynamic analysis of a rigid rotor supported by two-lobe noncircular gas-lubricated journal bearing system[J]. Nonlinear Dynamics, 2010, 61(4):783-802.
[8] RASHIDI M R, KARAMI M A, BAKHTIARI N 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.
[9] ZHANG Yongfang, HEI Di, LU Yanjun, 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.
[10] ZHANG Yongfang, ZHANG Shuai, LIU Fuxi, et al. Motion analysis of a rotor supported by self-acting axial groove gas bearing system with double time delays[J]. IMechE Part C:Journal of Mechanical Engineering Science, 2014, 228(16):2888-2899.
[11] YANG Lihua, QI Shemiao, YU Lie. Analysis on dynamic performance of hydrodynamic tilting-pad gas bearings using partial derivative method[J]. ASME Journal of Tribology, 2009, 131(1):011703-1-8.
[12] YANG Lihua, QI Shemiao, GENG Haipeng, et al. Stability analysis on rotor systems supported by self-acting tilting-pad gas bearings with frequency effects[J]. Chinese Journal of Mechanical Engineering, 2011, 24(3):380-385.
[13] DUIJNHOUWER F, NIJMEIJER H. Modelling and simulation of a compliant tilting pad air bearing[J]. IMechE Part C:Journal of Mechanical Engineering Science, 2016, 230(1):69-87.
[14] LU Yanjun, ZHANG Yongfang, SHI Xiaolei, 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.
[15] 赵家奎. 微分变换及其在电路中的应用[D]. 武汉:华中理工出版社, 1986. ZHAO Jiakui. Differential transformation and its applications for electrical circuits[D]. Wuhan:Huazhong University of Science and Technology, 1986.
[16] KHADER M, MEGAHED A. Differential transformation method for studying flow and heat transfer due to stretching sheet embedded in porous medium with variable thickness, variable thermal conductivity, and thermal radiation[J]. Applied Mathematics and Mechanics, 2014, 35(11):1387-1400.
[17] EHBRAHIMI F, GHADIRI M, SALARI E, et al. Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams[J]. Journal of Mechanical Science and Technology, 2015, 29(3):1207-1215.