Research Papers

A General Method for the Dynamic Modeling of Ball Bearing–Rotor Systems

[+] Author and Article Information
Yamin Li

State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: huishita.liyamin@stu.xjtu.edu.cn

Hongrui Cao

Associate Professor
State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: chr@mail.xjtu.edu.cn

Linkai Niu

State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: niulinkai@stu.xjtu.edu.cn

Xiaoliang Jin

Assistant Professor
School of Mechanical and
Aerospace Engineering,
Oklahoma State University,
Stillwater, OK 74078-5016
e-mail: xiaoliang.jin@okstate.edu

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received May 24, 2014; final manuscript received November 28, 2014; published online February 4, 2015. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 137(2), 021016 (Apr 01, 2015) (11 pages) Paper No: MANU-14-1293; doi: 10.1115/1.4029312 History: Received May 24, 2014; Revised November 28, 2014; Online February 04, 2015

A general dynamic modeling method of ball bearing–rotor systems is proposed. Gupta's bearing model is applied to predict the rigid body motion of the system considering the three-dimensional motions of each part (i.e., outer ring, inner ring, ball, and rotor), lubrication tractions, and bearing clearances. The finite element method is used to model the elastic deformation of the rotor. The dynamic model of the whole ball bearing–rotor system is proposed by integrating the rigid body motion and the elastic vibration of the rotor. An experiment is conducted on a test rig of rotor supported by two angular contact ball bearings. The simulation results are compared with the measured vibration responses to validate the proposed model. Good agreements show the accuracy of the proposed model and its ability to predict the dynamic behavior of ball bearing–rotor systems. Based on the proposed model, vibration responses of a two bearing–rotor system under different bearing clearances were simulated and their characteristics were discussed. The proposed model may provide guidance for structural optimization, fault diagnosis, dynamic balancing, and other applications.

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Jones, A. B., 1960, “A General Theory of Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions,” ASME J. Basic Eng., 82(21), pp. 309–320. [CrossRef]
Harris, T. A., and Kotzalas, M. N., 2007, Rolling Bearing Analysis: Essential Concepts of Bearing Technology, Taylor & Francis, Boca Raton, FL.
Harris, T. A., and Kotzalas, M. N., 2007, Rolling Bearing Analysis: Advanced Concepts of Bearing Technology, Taylor & Francis, Boca Raton, FL.
Sopanen, J., and Mikkola, A., 2003, “Dynamic Model of a Deep-Groove Ball Bearing Including Localized and Distributed Defects. Part 1: Theory,” Proc. Int. Mech. Eng., Part K, 217(3), pp. 201–211. [CrossRef]
Harsha, S. P., Sandeep, K., and Prakash, R., 2004, “Non-Linear Dynamic Behaviors of Rolling Element Bearings due to Surface Waviness,” J. Sound Vib., 272(3–5), pp. 557–580. [CrossRef]
Bai, C., and Xu, Q., 2006, “Dynamic Model of Ball Bearings With Internal Clearance and Waviness,” J. Sound Vib., 294(1–2), pp. 23–48. [CrossRef]
Tadina, M., and Boltežar, M., 2011, “Improved Model of a Ball Bearing for the Simulation of Vibration Signals due to Faults During Run-Up,” J. Sound Vib., 330(17), pp. 4287–4301. [CrossRef]
Ahmadi, A. M., Petersen, D., and Howard, C., 2015, “A Nonlinear Dynamic Vibration Model of Defective Bearings—The Importance of Modeling the Finite Size of Rolling Elements,” Mech. Syst. Signal Process., 52–53, pp. 309–326. [CrossRef]
Pandya, D. H., Upadhyay, S. H., and Harsha, S. P., 2014, “Nonlinear Dynamic Behavior of Balanced Rotor Bearing System Due to Various Localized Defects,” Proceedings of the International Conference on Advances in Tribology and Engineering Systems, Lecture Notes in Mechanical Engineering, pp. 345–357. [CrossRef]
Gupta, P. K., 1979, “Dynamics of Rolling-Element Bearings Part III: Ball Bearing Analysis,” ASME J. Lubr. Technol., 101(3), pp. 312–318. [CrossRef]
Gupta, P. K., 1984, Advanced Dynamic of Rolling Elements, Springer, New York. [CrossRef]
Niu, L., Cao, H., He, Z., and Li, Y., 2014, “Dynamic Modeling and Vibration Response Simulation for High Speed Rolling Ball Bearings With Localized Defects in Raceways,” ASME J. Manuf. Sci. Eng., 136(4), p. 041015. [CrossRef]
Sunnersjö, C. S., 1978, “Varying Compliance Vibrations of Rolling Bearings,” J. Sound Vib., 58(3), pp. 363–373. [CrossRef]
Harsha, S. P., 2006, “Rolling Bearing Vibrations—The Effects of Surface Waviness and Radial Internal Clearance,” Int. J. Comput. Methods Eng. Sci. Mech., 7(2), pp. 91–111. [CrossRef]
Kankar, P. K., Sharma, S. C., and Harsha, S. P., 2012, “Vibration Based Performance Prediction of Ball Bearing Caused by Localized Defects,” J. Nonlinear Dyn., 69(3), pp. 847–875. [CrossRef]
Tomovic, R., Miltenovic, V., Banic, M., and Miltenovic, A., 2010, “Vibration Response of Rigid Rotor in Unloaded Rolling Element Bearing,” Int. J Mech. Sci., 52(9), pp. 1176–1185. [CrossRef]
Wang, L., Cui, L., Gu, L., and Zheng, D.-Z., 2008, “Study on Dynamic Characteristics of Angular Ball Bearing With Non-Linear Vibration of Rotor System,” Proc. Int. Mech. Eng., Part C, 222(9), pp. 1800–1819. [CrossRef]
Cheng, M., Meng, G., and Wu, B., 2011, “Nonlinear Dynamics of a Rotor–Ball Bearing System With Alford Force,” J. Vib. Control, 18(1) pp. 1–11. [CrossRef]
Hu, Q. H., Deng, S., and Teng, H., 2011 “A 5-DOF Model for Aeroengine Spindle Dual-Rotor System Analysis,” Chin. J. Aeronaut., 24(2), pp. 224–234. [CrossRef]
Jang, G. H., and Jeong, S. W., 2002, “Nonlinear Excitation Model of Ball Bearing Waviness in a Rigid Rotor Supported by Two or More Ball Bearings Considering Five Degrees of Freedom,” ASME J. Tribo.124(1), pp. 82–90. [CrossRef]
Jang, G. H., and Jeong, S. W., 2003, “Analysis of a Ball Bearing With Waviness Considering the Centrifugal Force and Gyroscopic Moment of the Ball,” ASME J. Tribol., 125(3), pp. 487–498. [CrossRef]
Babu, C. K., Tandon, N., and Pandey, R. K., 2012, “Vibration Modeling of a Rigid Rotor Supported on the Lubricated Angular Contact Ball Bearings Considering Six Degrees of Freedom and Waviness on Balls and Races,” ASME J. Vib. Acoust., 134(1), p. 011006. [CrossRef]
Chen, G., 2009, “A New Rotor–Ball Bearing–Stator Coupling Dynamics Model for Whole Aero-Engine Vibration,” ASME J. Vib. Acoust., 131(1), p. 061009. [CrossRef]
Zhang, X., Han, Q., Peng, Z., and Chu, F., 2013, “Stability Analysis of a Rotor–Bearing System With Time-Varying Bearing Stiffness due to Finite Number of Balls and Unbalanced Force,” J. Sound Vib., 332(25), pp. 6768–6784. [CrossRef]
Zhang, X., Han, Q., Peng, Z., and Chu, F., 2014, “A New Nonlinear Dynamic Model of the Rotor-Bearing System Considering Preload and Varying Contact Angle of the Bearing,” Commun. Nonlinear Sci. Numer. Simul., 22(1–3), pp. 821–841. [CrossRef]
Karacay, T., and Akturk, N., 2008, “Vibration of a Grinding Spindle Supported by Angular Contact Ball Bearing,” Proc. Int. Mech. Eng., Part K, 222(1), pp. 61–75. [CrossRef]
Zhou, H., Feng, G., Luo, G., Ai, Y., and Sun, D., 2014, “The Dynamic Characteristics of a Rotor Supported on Ball Bearings With Different Floating Ring Squeeze Film Dampers,” Mech. Mach. Theory, 80, pp. 200–213. [CrossRef]
Bai, C., Zhang, H., and Xu, Q., 2010, “Experimental and Numerical Studies on Nonlinear Dynamic Behavior of Rotor System Supported by Ball Bearings,” ASME J. Eng. Gas Turbines Power, 132(8), p. 082502 [CrossRef]
Bai, C., Zhang, H., and Xu, Q., 2013, “Subharmonic Resonance of a Symmetric Ball Bearing–Rotor System,” Int. J. Nonlinear Mech., 50, pp. 1–10. [CrossRef]
Gao, S., Long, X., and Meng, G., 2008, “Nonlinear Response and Nonsmooth Bifurcations of an Unbalanced Machine-Tool Spindle-Bearing System,” Nonlinear Dyn., J. Nonlinear Dyn.54(4), pp. 365–377. [CrossRef]
Yuan, X., Zhu, Y., and Zhang, Y., 2014, “Multi-Body Vibration Modeling of Ball Bearing–Rotor System Considering Single and Compound Multi-Defects,” Proc. Int. Mech. Eng., Part K, 228(2), pp. 199–212. [CrossRef]
Ma, H., Li, H., Zhao, X., Niu, H., and Wen, B., 2013, “Effects of Eccentric Phase Difference Between Two Discs on Oil-Film Instability in a Rotor-Bearing System,” Mech. Syst. Signal Process., 41(1–2), pp. 526–545. [CrossRef]
Young, T. H., Shiau, T. N., and Kuo, Z. H., 2007, “Dynamic Stability of Rotor-Bearing Systems Subjected to Random Axial Forces,” J. Sound Vib., 305(3), pp. 467–480. [CrossRef]
Villa, C., Sinou, J. J., and Thouverez, F., 2008, “Stability and Vibration Analysis of a Complex Flexible Rotor Bearing System,” Commun. Nonlinear Sci., 13(4), pp. 804–821. [CrossRef]
Sinou, J. J., 2009, “Non-Linear Dynamic and Contacts of an Unbalanced Flexible Rotor Supported on Ball Bearings,” Mech. Mach. Theory, 44(9), pp. 1713–1732. [CrossRef]
Gupta, T. C., Gupta, K., and Sehgal, D. K., 2008, “Nonlinear Vibration Analysis of an Unbalanced Flexible Rotor Supported by Ball Bearings With Radial Internal Clearance,” ASME Paper No. GT2008-51204. [CrossRef]
Gupta, T. C., Gupta, K., and Sehgal, and D. K., 2011, “Instability and Chaos of a Flexible Rotor Ball Bearing System: An Investigation on the Influence of Rotating Imbalance and Bearing Clearance,” ASME J. Eng Gas Turbines Power, 133(8), p. 082501. [CrossRef]
Gupta, T. C., and Gupta, K., 2013, “Correlation of Parameters to Instability and Chaos of a Horizontal Flexible Rotor Ball Bearing System,” ASME Paper No. GT2013-95308. [CrossRef]
Lin., C. W., Tu, J. F., and Kamman, J., 2003, “An Integrated Thermo-Mechanical-Dynamic Model to Characterize Motorized Machine Tool Spindles During Very High Speed Rotation,” Int. J. Mach. Tool Manu., 43(10), pp. 1035–1050. [CrossRef]
Cao, Y., and Altintas, Y., 2004, “A General Method for the Modeling of Spindle-Bearing System,” ASME J. Mech. Des., 126(6), pp. 1089–1104. [CrossRef]
Cao, H., Holkup, T., and Altintas, Y., 2011, “A Comparative Study on the Dynamics of High Speed Spindles With Respect to Different Preload Mechanisms,” Int. J. Adv. Manuf. Technol., 57(9–12), pp. 871–883. [CrossRef]
Cao, H., Niu, L., and He, Z., 2012, “Method for Vibration Response Simulation and Sensor Placement Optimization of a Machine Tool Spindle System With a Bearing Defect,” Sensors, 12(7), pp. 8732–8754. [CrossRef] [PubMed]
Cao, H., Holkup, T., Chen, X., and He, Z., 2012, “Study on Characteristic Variations of High-Speed Spindles Induced by Centrifugal Expansion Deformations,” J. Vibroeng., 14(3), pp. 1278–1291.
Gagnol, V., Bouzgarrou, C. B., Ray, P., and Barra, C., 2005, “Modelling Approach for a High Speed Machine Tool Spindle-Bearing System,” ASME Paper No. DETC2005-84681. [CrossRef]
Gagnol, V., Bougarrou, B. C., Ray, P., and Barra, C., 2007, “Stability-Based Spindle Design Optimization,” ASME J. Manuf. Sci. Eng., 129(2), pp. 407–415. [CrossRef]
Li, H., and Shin, Y. C., 2004, “Integrated Dynamic Thermo-Mechanical Modeling of High Speed Spindles, Part 1: Model Development,” ASME J. Manuf. Sci. Eng., 126(1), pp. 148–158. [CrossRef]
Li, H., and Shin, Y. C., 2009, “Integration of Thermo-Dynamic Spindle and Machining Simulation Models for a Digital Machining System,” Int. J. Adv. Manuf. Technol., 40(7–8), pp. 648–661. [CrossRef]
Matthew, D. B., Farshid, S., Ankur, A., and Archer, J., 2014, “Combined Explicit Finite and Discrete Element Methods for Rotor Bearing Dynamic Modeling,” Tribol. Trans. [CrossRef]


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Fig. 1

Geometrical interactions of a bearing–rotor system

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Fig. 2

Ball/raceway interaction

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Fig. 3

Finite element model of the rotor

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Fig. 4

Flow chart of numerical computation

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Fig. 5

The bearing–rotor test rig

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Fig. 6

Simplified assembly drawing of the test rig

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Fig. 7

The finite element model of the rotor

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Fig. 8

Traction model of lubricant in simulation

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Fig. 9

The comparison of vibration response at node 8 between simulation and experiment

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Fig. 10

Frequency spectra of experiment and simulation: (a) spectrum of experiment, (b) spectrum of F–M, and (c) spectrum of R–M

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Fig. 11

The peak value of vibration response of the rotor at each node

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Fig. 12

Time domain response of node 3: (a) clearance = 0 μm, (b) clearance = 5 μm, (c) clearance = 10 μm, (d) clearance = 15 μm, (e) clearance = 20 μm, and (f) clearance = 25 μm

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Fig. 13

Frequency spectrum of vibration for different clearances

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Fig. 14

(a) and (b) Contact force between a ball and the inner raceway for different clearances

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Fig. 15

Average peak value of contact force for different clearances




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