# Frontiers of Mechanical Engineering

 Front. Mech. Eng.    2019, Vol. 14 Issue (4) : 461-473     https://doi.org/10.1007/s11465-019-0525-2
 RESEARCH ARTICLE
New analysis model for rotor-bearing systems based on plate theory
Zhinan ZHANG1, Mingdong ZHOU2(), Weimin DING3, Huifang MA4
1. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
2. State Key Laboratory of Mechanical System and Vibration, Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures, Shanghai Jiao Tong University, Shanghai 200240, China
3. Ningbo Donly Co., Ltd., Ningbo 315000, China
4. AECC Commercial Aircraft Engine Co., Ltd. Shanghai 200240, China
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 Abstract The purpose of this work is to develop a new analysis model for angular-contact, ball-bearing systems on the basis of plate theory instead of commonly known approaches that utilize spring elements. Axial and radial stiffness on an annular plate are developed based on plate, Timoshenko beam, and plasticity theories. The model is developed using theoretical and inductive methods and validated through a numerical simulation with the finite element method. The new analysis model is suitable for static and modal analyses of rotor-bearing systems. Numerical examples are presented to reveal the effectiveness and applicability of the proposed approach. Corresponding Authors: Mingdong ZHOU Online First Date: 09 October 2018    Issue Date: 02 December 2019
 Cite this article: Zhinan ZHANG,Mingdong ZHOU,Weimin DING, et al. New analysis model for rotor-bearing systems based on plate theory[J]. Front. Mech. Eng., 2019, 14(4): 461-473. URL: http://journal.hep.com.cn/fme/EN/10.1007/s11465-019-0525-2 http://journal.hep.com.cn/fme/EN/Y2019/V14/I4/461
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 Fig.1  Illustration of concentrated load applied to an annular plate [27]. (a) Concentrated load is applied to the rigid shaft; (b) equivalent axial load; (c) equivalent radial load Fig.2  (a) Illustration of the deformation of an annular plate; (b) illustration of an infinitesimal element Fig.3  Deformation of the annular plate under (a) axial load and (b) radial load Tab.1  Calculation of axial and radial deformation parameters Fig.4  Application procedure for the proposed method [27] Fig.5  3D model of the rotor-bearing system in a water ring vacuum pump Fig.6  Results of comparison of the first bending mode for the rotor bearing system. (a) Using the spring element-based approach; (b) using the plate theory-based approach Tab.2  spring element-based approach and plate theory-based approach Fig.7  Calculating displacement during acceleration Fig.8  Comparison of the results of displacement during acceleration. (a) Using the spring element-based method; (b) using the plate theory-based method Tab.3  Datasheet for displacement parameters $α$ and $β$ Fig.9  Flowchart for database development Fig.10  Plate theory-based model and potential new models Schematic of the coordinate system Table A1 Maximum axial displacement under different boundary conditions or loads
 1 J S Rao. History of Rotating Machinery Dynamics. Berlin: Springer Netherlands, 2011 2 J P Jing, G Meng, S Yi. On the non-linear dynamic behavior of a rotor-bearing system. Journal of Sound and Vibration, 2004, 274(3–5): 1031–1044 https://doi.org/10.1016/S0022-460X(03)00663-1 3 T Zheng, N Hasebe. Nonlinear dynamic behaviors of a complex rotor-bearing system. Journal of Applied Mechanics, 2000, 67(3): 485–495 https://doi.org/10.1115/1.1286208 4 T A Harris, M N Kotzalas. Rolling Bearing Analysis: Essential Concepts of Bearing Technology. 5th ed. Boca Raton: CRC Press, 2007 5 T A Harris, M N Kotzalas. Rolling Bearing Analysis: Advanced Concepts of Bearing Technology. 5th ed. Boca Raton: CRC Press, 2007 6 E P Gargiulo. A simple way to estimate bearing stiffness. Machine Design, 1980, 107–110 https://doi.org/10.1097/00004424-198103000-00016 7 H F Ma, G J Liu, R M Nan. et al. Measurement of dynamics radial stiffness of bearings in rotor system by resonance method. Bearing, 2012, (11): 38–41 (in Chinese) 8 X N Zhang, Q K Han, Z K Peng, et al. Stability analysis of a rotor-bearing system with time-varying bearing stiffness due to finite number of balls and unbalanced force. Journal of Sound and Vibration, 2013, 332(25): 6768–6784 https://doi.org/10.1016/j.jsv.2013.08.002 9 R Tiwari, A W Lees, M I Friswell. Identification of dynamic bearing parameters. Shock and Vibration Digest, 2004, 36(2): 99–124 https://doi.org/10.1177/0583102404040173 10 J M de Mul, J M Vree, D A Maas. Equilibrium and associated load distribution in ball and roller bearings loaded in five degrees of freedom while neglecting friction-Part II: Application to roller bearings and experimental verification. Journal of Tribology, 1989, 111(1): 149–155 https://doi.org/10.1115/1.3261865 11 J M de Mul, J M Vree, D A Maas. Equilibrium and associated load distribution in ball and roller bearings loaded in five degrees of freedom while neglecting friction-Part I: General theory and application to ball bearings. Journal of Tribology, 1989, 111(1): 142–148 https://doi.org/10.1115/1.3261864 12 T L H Walford, B J Stone. The measurement of the radial stiffness of rolling element bearings under oscillating conditions. Journal of Mechanical Engineering Science, 1980, 22(4): 175–181 https://doi.org/10.1243/JMES_JOUR_1980_022_035_02 13 J Kraus, J J Blech, S G Braun. In situ determination of rolling bearing stiffness and damping by modal analysis. Journal of Vibration, Acoustics, Stress, and Reliability in Design, 1987, 109(3): 235–240 https://doi.org/10.1115/1.3269426 14 E R Marsh, D S Yantek. Experimental measurement of precision bearing dynamic stiffness. Journal of Sound and Vibration, 1997, 202(1): 55–66 https://doi.org/10.1006/jsvi.1996.0793 15 H F Ma. Application of radial stiffness of rolling bearings in calculation of critical speed of rotors. Bearing, 2013, 4: 33–35 (in Chinese) 16 B J Stone. The state of the art in the measurement of the stiffness and damping of rolling element bearings. CIRP Annual-Manufacture Technology, 1982, 31(2): 529–538 https://doi.org/10.1016/S0007-8506(07)60175-9 17 A B Jones. A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions. Journal of Basic Engineering, 1960, 82(2): 309–320 https://doi.org/10.1115/1.3662587 18 Y Kang, C C Huang, C S Lin, et al. Stiffness determination of angular-contact ball bearings by using neural network. Tribology International, 2006, 39(6): 461–469 https://doi.org/10.1016/j.triboint.2005.02.005 19 T C Lim, R Singh. Vibration transmission through rolling element bearings Part I: Bearing stiffness formulation. Journal of Sound and Vibration, 1990, 139(2): 179–199 https://doi.org/10.1016/0022-460X(90)90882-Z 20 A Gunduz, R Singh. Stiffness matrix formulation for double row angular contact ball bearings: Analytical development and validation. Journal of Sound and Vibration, 2013, 332(22): 5898–5916 https://doi.org/10.1016/j.jsv.2013.04.049 21 H V Liew, T C Lim. Analysis of time-varying rolling element bearing characteristics. Journal of Sound and Vibration, 2005, 283(3–5): 1163–1179 https://doi.org/10.1016/j.jsv.2004.06.022 22 Y Guo, R G Parker. Stiffness matrix calculation of rolling element bearing using a finite element/contact mechanics model. Mechanism and Machine Theory, 2012, 51: 32–45 https://doi.org/10.1016/j.mechmachtheory.2011.12.006 23 S J Jiang, S F Zheng. A modeling approach for analysis and improvement of spindle-drawbar-bearing assembly dynamics. International Journal of Machine Tools and Manufacture, 2010, 50(1): 131–142 https://doi.org/10.1016/j.ijmachtools.2009.08.010 24 X N Zhang, Q K Han, Z K Peng, et al. Stability analysis of a rotor-bearing system with time-varying bearing stiffness due to finite number of balls and unbalanced force. Journal of Sound and Vibration, 2013, 332(25): 6768–6784 https://doi.org/10.1016/j.jsv.2013.08.002 25 X Sheng, B Z Li, Z P Wu, et al. Calculation of ball bearing speed-varying stiffness. Mechanism and Machine Theory, 2014, 81: 166–180 https://doi.org/10.1016/j.mechmachtheory.2014.07.003 26 S Timoshenko, S Woinowsky-Krieger. Theory of plates and shells. New York: McGraw-Hill, 1959 27 Z N Zhang, W M Ding, H F Ma. Simplified model for bearing stiffness based on plate theory. Bearing, 2015, (4): 7–11 (in Chinese) 28 H W Liu, J X Lin, M L Cao. Theory of Plates and Shells. Hangzhou: Zhejiang University Press, 1987 (in Chinese) 29 W U Hao, J W Wang, Q An. Study on the calculating method of radial stiffness of tapered roller bearing. Lubrication Engineering, 2008, 33(7): 39–43 (in Chinese)
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