Research Papers

A New Dynamic Model of Ball-Bearing Rotor Systems Based on Rigid Body Element

[+] Author and Article Information
Hongrui Cao

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

Yamin Li, Xuefeng Chen

State Key Laboratory for Manufacturing Systems
Xi'an Jiaotong University,
Xi'an 710049, China

1Corresponding author.

Manuscript received July 22, 2015; final manuscript received December 29, 2015; published online March 8, 2016. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 138(7), 071007 (Mar 08, 2016) (10 pages) Paper No: MANU-15-1363; doi: 10.1115/1.4032582 History: Received July 22, 2015; Revised December 29, 2015

Ball-bearing rotor systems are key components of rotating machinery. In this work, a new dynamic modeling method for ball-bearing rotor systems is proposed based on rigid body element (RBE). First, the concept of RBE is given, and then the rotor is divided into several discrete RBEs. Every two adjacent RBEs are connected by imaginary springs, whose stiffness is calculated according to properties of the RBEs. Second, all the parts of rolling ball bearings (i.e., outer ring, inner ring, ball, and cage) are considered as RBEs, and Gupta's model is employed to model bearings which include radial clearance, waviness, pedestal effect, etc. Finally, the rotor and all the rolling ball bearings are coupled to develop a dynamic model of the ball-bearing rotor system. The vibration responses of the ball-bearing rotor system can be calculated by solving dynamic equations of each RBE. The proposed method is verified with both simulation and experiment. The RBE model of the rotor is compared with its finite element (FE) model first, and numerical simulation shows the validity of the RBE model. Then, experiments are conducted on a rotor test rig which is supported with two rolling ball bearings as well. Good agreements between measurement and simulation show the ability of the model to predict the dynamic behavior of ball-bearing rotor systems.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


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 and Francis, Boca Raton, FL.
Harris, T. A. , and Kotzalas, M. N. , 2007, Rolling Bearing Analysis: Advanced Concepts of Bearing Technology, Taylor and Francis, Boca Raton, FL.
Walters, C. T. , 1969, “ Study of the Behavior of High-Speed Angular-Contact Ball Bearings Under Dynamic Load,” Final Report on Contract Report No. NAS 8-21255, May 12.
Walters, C. T. , 1971,“ The Dynamics of Ball Bearings,” ASME J. Lubr. Technol., 93(1), pp. 1–10. [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.
Weinzapfel, N. , and Sadeghi, F. , 2009, “ A Discrete Element Approach for Modeling Cage Flexibility in Ball Bearing Dynamics Simulations,” ASME J. Tribol., 131(2), p. 021102. [CrossRef]
Ashtekar, A. , and Sadeghi, F. , “ A New Approach for Including Cage Flexibility in Dynamic Bearing Models by Using Combined Explicit Finite and Discrete Element Methods,” ASME J. Tribol., 134(4), p. 041502. [CrossRef]
Jain, S. , and Hunt, H. , 2011, “ A Dynamic Model to Predict the Occurrence of Skidding in Wind-Turbine Bearings,” J. Phys.: Conf. Ser., 350, p. 012027. [CrossRef]
Tu, W. , Shao, Y. , and Mechefske, C. K. , 2012, “ An Analytical Model to Investigate Skidding in Rolling Element Bearings During Acceleration,” J. Mech. Sci. Technol., 26(8), pp. 2451–2458. [CrossRef]
Singh, S. , Köpke, U. G. , Howard, C. Q. , and Petersen, D. , 2014, “ Analyses of Contact Forces and Vibration Response for a Defective Rolling Element Bearing Using an Explicit Dynamics Finite Element Model,” J. Sound Vib., 333(21), pp. 5356–5377. [CrossRef]
Kogan, G. , Klein, R. , Kushnirsky, A. , and Bortman, J. , 2015, “ Toward a 3D Dynamic Model of a Faulty Duplex Ball Bearing,” Mech. Syst. Sig. Process., 54–55, pp. 243–258. [CrossRef]
Liu, J. , and Shao, Y. , 2015, “ A New Dynamic Model for Vibration Analysis of a Ball Bearing Due to a Localized Surface Defect Considering Edge Topographies,” Nonlinear Dyn., 79(2), pp. 1329–1351. [CrossRef]
Ahmadi, A. M. , Petersen, D. , and Howard, C. , 2015, “ A Nonlinear Dynamic Vibration Model of Defective Bearings–The Importance of Modelling the Finite Size of Rolling Elements,” Mech. Syst. Sig. Process., 52–53, pp. 309–326. [CrossRef]
Vakharia, V. , Gupta, V. K. , and Kankar, P. K. , 2015, “ Nonlinear Dynamic Analysis of Ball Bearings Due to Varying Number of Balls and Centrifugal Force,” 9th IFToMM International Conference on Rotor Dynamics Mechanisms and Machine Science, Vol. 21, pp. 1831–1840.
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.
He, C. , Xu, H. Y. , and Zhang, Y. Q. , 2015, “ Analysis of the Nonlinear Dynamic Response of Gyroscope Rotor System Considered Elasto-Hydrodynamic Lubrication,” 3rd International Conference on Mechatronics, Robotics and Automation, pp. 727–731.
Hou, L. , Chen, Y. S. , Cao, Q. J. , and Zhang, Z. Y. , 2015, “ Turning Maneuver Caused Response in an Aircraft Rotor-Ball Bearing System,” Nonlinear Dyn., 79(1), pp. 229–240. [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]
Babu, C. K. , Tandon, N. , and Pandey, R. K. , 2014, “ Nonlinear Vibration Analysis of an Elastic Rotor Supported on Angular Contact Ball Bearings Considering Six Degrees of Freedom and Waviness on Balls and Races,” ASME J. Vib. Acoust., 136(4), p. 044503. [CrossRef]
Gupta, T. C. , Gupta, K. , and Sehgal, 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.
Gupta, T. C. , and Gupta, K. , 2014, “ Modeling of Flexible Coupling to Connect Misaligned Flexible Rotors Supported on Ball Bearings,” ASME Paper No. GT2014-26891.
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.
Kurvinen, E. , Sopanen, J. , and Mikkola, A. , 2015, “ Ball Bearing Model Performance on Various Sized Rotors With and Without Centrifugal and Gyroscopic Forces,” Mech. Mach. Theory, 90, pp. 240–260. [CrossRef]
Li, Y. , Cao, H. , Niu, L. , and Jin, X. , 2015, “ A General Method for the Dynamic Modeling of Ball-bearing Rotor Systems,” ASME J. Manuf. Sci. Eng., 137(2), p. 021016. [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]


Grahic Jump Location
Fig. 2

The discretization of the rotor

Grahic Jump Location
Fig. 3

The geometrical interaction between two adjacent rotor RBEs

Grahic Jump Location
Fig. 4

The geometrical interaction between the kth bearing and the jth rotor RBE

Grahic Jump Location
Fig. 5

Traction model of lubricant [30]

Grahic Jump Location
Fig. 12

The bearing–rotor test rig

Grahic Jump Location
Fig. 13

The dynamic model of the test rig

Grahic Jump Location
Fig. 6

The interaction between the pedestal and the outer raceway

Grahic Jump Location
Fig. 11

The trajectory of different nodes at the speed of 10,000 r/min

Grahic Jump Location
Fig. 10

The relative error of displacements at different nodes

Grahic Jump Location
Fig. 9

Displacements of different nodes

Grahic Jump Location
Fig. 8

Models of the rotor: (a) RBE model and (b) FE model

Grahic Jump Location
Fig. 7

The flow chart of numerical computation

Grahic Jump Location
Fig. 16

Frequency spectra of vibration responses of P1 in y direction: (a) experiment and (b) simulation

Grahic Jump Location
Fig. 14

Orbits of the rotor at different nodes (speed: 2000 r/min): (a) experiment and (b) simulation

Grahic Jump Location
Fig. 15

Orbits of the rotor at different nodes (speed: 7500 r/min): (a) experiment and (b) simulation



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In