Abstract
The dynamics of ball bearings are important to fatigue breakage, dynamic performance and motion precision of mechanisms connected by ball bearings joints with multi-clearances. In this study, a new method is proposed for multibody dynamics analysis on mechanisms under the effects of radial internal clearances and impact of balls/cage pockets interactions of ball bearings. Including balls/rings interactions and balls/cage pockets interactions, the three dimensional dynamics models of the crank slider mechanism are established and calculated by generalized-α algorithms on the basis of Hertzian contact theory and penalty function method. The rules of eccentric trajectories of inner and outer ring center for one ball bearing joint are verified with the results calculated by XU’s references. The results of dynamic errors, motion trajectories, dynamic forces are achieved under different speeds, radial clearances and number of ball bearings. The speeds and radial clearances are critical to the dynamic performances and motion precision of mechanisms, especially the number of ball bearings. The number of ball bearings is important to impact force and motion stability of the mechanism.
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References
L. X. Xu et al., Effects of bearing clearance and flexibility on the dynamic errors of mechanisms, Journal of Mechanical Engineering, 42 (7) (2012) 30–36.
G. X. Wang and H. Z. Liu, Research progress of joint effects model in multibody system dynamics, Chinese Journal of Theoretical and Applied Mechanics, 47 (1) (2015) 31–50.
D. S. Shah and V. N. Patel, A review of dynamic modeling and fault identifications methods for rolling element bearing, Procedia Technology, 14 (2014) 447–456.
S. Erkaya and İ. Uzmay, Modeling and simulation of joint clearance effects on mechanisms having rigid and flexible links, Journal of Mechanical Science and Technology, 28 (8) (2014) 2979–2986.
Y. C. Liu and Y. Q. Yu, A survey of mechanism and robot with clearances, Mechanical Science and Technology, 23 (4) (2004) 454–460.
T. A. Harris and M. N. Kotzalas, Rolling Bearing Analysis, Fifth Ed., Wiley, New York, USA (2006).
A. B. Jones, A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions, Journal of Basic Engineering, 82 (2) (1960) 309–320.
P. K. Gupta, Advanced Dynamics of Rolling Elements, Springer Verlag, New York, USA (1984).
M. Tiwari, P. K. Gupta and O. Prakash, Effect of radial internal clearance of a ball bearing on the dynamics of a balanced horizontal rotor, Journal of Sound and Vibration, 238 (5) (2000) 723–726.
S. P. Harsha, Nonlinear dynamic analysis of a high-speed rotor supported by rolling element bearings, Journal of Sound and Vibration, 290 (1–2) (2006) 65–100.
S. P. Harsha, K. Sandeep and R. Prakash, Dynamic response of an unbalanced rotor supported on nonlinear vibration associated with ball bearings, Int. Mech. Scienece, 45 (4) (2003) 723–756.
S. P. Harsha and K. Sandeep, Stability analysis of a ball bearing rotor system due to surface waviness and number balls, International Journal of Mechanical Sciences, 46 (7) (2004) 1057–1081.
C. Bai and Q. Xu, Dynamic model of ball bearing with internal clearance and waviness, Journal of Sound and Vibration, 294 (1–2) (2006) 23–48.
S. E. Deng et al., Flexible-body dynamics analysis on cage of high-speed angular contact ball bearing, Acta Armamentarii, 32 (5) (2011) 225–231.
G. C. Chen, P. J. Ping and J. Q. He, Effects of geometric parameters on static load capacity of a double-row four-point contact ball bearing, Journal of Mechanical Science and Technology, 27 (4) (2013) 1053–1061.
T. Q. Yao et al., Research on multibody contact dynamics of ball bearings, Journal of Aerospace Power, 28 (7) (2013) 1624–1637.
W. G. Zhang et al., Nonlinear analysis for a machine-tool spindle system supported with ball bearing, Journal of Vibration and Shock, 27 (9) (2008) 72–75.
A. Ashtekar and F. Sadeghi, Experimental and analytical investigation of high speed turbocharger ball bearings, Journal of Engineering for Gas Turbines and Power, 133 (12) (2011) 1201–1228.
G. X. Wang and H. Z. Liu, Dynamics modeling of parallel mechanism with spherical joint clearance, Journal of Vibration and Shock, 33 (10) (2014) 43–49.
P. Ravn, A continuous analysis method for planar multibody systems with joint clearance, Multibody System Dynamics, 2 (1) (1998) 1–24.
P. Flores et al., Dynamic behavior of planar rigid multibody systems including revolute joints with clearance, Proc. Inst. Mech. Eng., Part K, J. Multi-body Dyn., 221 (2) (2007) 161–174.
Q. Tian et al., A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems, Nonlinear Dynamics, 64 (1–2) (2011) 25–47.
Z. H. Qi, G. Wang and T. Li, Contact analysis of deep groove ball bearing joint in multibody systems, Chinese Journal of Theoretical and Applied Mechanics, 45 (3) (2013) 426–431.
Z. H. Qi, G. Wang and Z. G. Zhang, Contact analysis of deep groove ball bearing joint in multibody systems, Multibody Syst. Dyn., 33 (2015) 115–141.
L. X. Xu and Y. H. Yang, Modeling a non-ideal rolling ball bearing joint with localized defects in planar multibody systems, Multibody System Dynamics, 35 (4) (2015) 409–426.
L. X. Xu et al., Dynamic analysis of a slider-crank mechanism with two types of non-ideal revolute joints, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics (2015).
L. X. Xu et al., Modeling and analysis of planar multibody systems containing deep groove ball bearing with clearance, Mechanism and Machine Theory, 56 (2012) 69–88.
L. X. Xu and Y. G. Li, An approach for calculating the dynamic load of deep groove ball bearing joints in planar multibody systems, Nonlinear Dynamics, 70 (3) (2012) 2145–2161.
L. X. Xu, A general method for impact dynamic analysis of a planar multi-body system with a rolling ball bearing joint, Nonlinear Dynamics, 78 (2) (2014) 857–879.
L. X. Xu and Y. G. Li, Modeling of a deep-groove ball bearing with waviness defects in planar multibody system, Multibody System Dynamics, 33 (3) (2014) 1–30.
T. Q. Yao, Y. L. Chi and Y. Y. Huang, A new generalized-α algorithms for multibody dynamics, Chinese Journal of Mechanical Engineering, 45 (10) (2009) 53–60.
J. A. Wensing, On the dynamics of ball bearings, Ph.D. Thesis, University of Twente, Netherlands (1998).
Y. H. Wijnant, Contact dynamics in the field of elastohydrodynamic lubrication, Ph.D. Thesis, University of Twente, Netherlands (1998).
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Recommended by Associate Editor Junhong Park
Tingqiang Yao is a Associate Professor at Kunming University of Science and Technology of China. He obtained his B.S., M.S. and Ph.D. in Mechanical Engineering from Kunming University of Science and Technology. He worked at Kunming University of Science and Technology of China (2009-). His research interests include multibody systems dynamics in rolling element bearing and mechanical systems.
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Yao, T., Xian, L., Wang, L. et al. Multibody contact dynamics on mechanisms with deep groove ball bearing joints. J Mech Sci Technol 31, 4119–4135 (2017). https://doi.org/10.1007/s12206-017-0808-7
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DOI: https://doi.org/10.1007/s12206-017-0808-7