Abstract
High-speed ball bearings are widely used in aerospace, high-speed machining tool and other complex mechanical systems. And the stiffness is one of most critical parameter of bearings to decide the machine performance. This paper attempts to construct a 5-DOF stiffness matrix based on quasi-dynamic model of high-speed ball bearings to analyze the variation of stiffness with different work condition precisely, and the variation of stiffness with structural parameter and manufacturing errors are calculated for the optimization of tolerance. In this method, the effect of combined loads and lubrication effect are considered, which can achieve high precision analysis of the relationship between contact load and displacement. And then a 5-DOF stiffness matrix can be calculated precisely. The results can be used to optimize the design bearing for improving stiffness.
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Abbreviations
- D b :
-
Ball diameter
- d :
-
Bearing raceway diameter
- F :
-
Force
- f :
-
Raceway groove curvature coefficient
- i :
-
Inner
- K :
-
stiffness matrix
- k :
-
stiffness
- M :
-
Torque
- o :
-
Outer
- r :
-
Raceway groove curvature radius
- ω :
-
Rotational speed
References
Harris, T. A. and Kotzalas, M. N., “Advanced Concepts of Bearing Technology: Rolling Bearing Analysis,” Taylor & Francis, 5th Ed., 2007.
Harris, T. A. and Kotzalas, M. N., “Rolling Bearing Analysis, Essential Concepts of Bearing Technology,” Taylor & Francis, 2007.
Jones, A. B., “New Departure Engineering Data: Analysis of Stresses and Deflections,” New Departure Division, 1946.
Palmgren, A., “Ball and Roller Bearing Engineering,” Philadelphia: SKF Industries Inc., 3rd Ed., 1959.
Brandlein, J., Eschmann, P., Hasbargen, L., and Weigand, K., “Ball and Roller Bearings: Theory, Design and Application,” Wiley, 3rd Ed., 1999.
De Mul, J., Vree, J. M., and Maas, D. A., “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, Vol. 111, No. 1, pp. 149–155, 1989.
Hagiu, G. and Gafitanu, M., “Dynamic Characteristics of High Speed Angular Contact Ball Bearings,” Wear, Vol. 211, No. 1, pp. 22–29, 1997.
Hernot, X., Sartor, M., and Guillot, J., “Calculation of the Stiffness Matrix of Angular Contact Ball Bearings by using the Analytical Approach,” Journal of Mechanical Design, Vol. 122, No. 1, pp. 83–90, 2000.
Houpert, L., “A Uniform Analytical Approach for Ball and Roller Bearings Calculations,” Journal of Tribology, Vol. 119, No. 4, pp. 851–858, 1997.
Gargiulo, E. P., “A Simple Way to Estimate Bearing Stiffness,” Machine Design, Vol. 52, No. 17, pp. 107–110, 1980.
Lim, T. and Singh, R., “Vibration Transmission through Rolling Element Bearings, Part I: Bearing Stiffness Formulation,” Journal of Sound and Vibration, Vol. 139, No. 2, pp. 179–199, 1990.
Guo, Y. and Parker, R. G., “Stiffness Matrix Calculation of Rolling Element Bearings using a Finite Element/Contact Mechanics Model,” Mechanism and Machine Theory, Vol. 51, pp. 32–45, 2012.
Bourdon, A., Rigal, J. F., and Play, D., “Static Rolling Bearing Models in a CAD Environment for the Study of Complex Mechanisms: Part I -Rolling Bearing Model,” Journal of Tribology, Vol. 121, No. 2, pp. 205–214, 1999.
Liew, H.-V. and Lim, T. C., “Analysis of Time-Varying Rolling Element Bearing Characteristics,” Journal of Sound and Vibration, Vol. 283, No. 3, pp. 1163–1179, 2005.
Noel, D., Ritou, M., Furet, B., and Le Loch, S., “Complete Analytical Expression of the Stiffness Matrix of Angular Contact Ball Bearings,” Journal of Tribology, Vol. 135, No. 4, Paper No. 041101, 2013.
Du Y. H., Qiu M., and Jiang, X. Q., “Stiffness Calculation of High-Speed Precision Angular Contact Ball Bearings,” Bearing, No. 10, pp. 5–8, 2001.
Li, S., Chen, X., Zhang, G., Wang, C., Yang, L., and Chen, C., “Analyses of Dynamic Supporting Stiffness about Spindle Bearings at Extra High-Speed in Electricspindles,” Chinese Journal of Mechanical Engineering, Vol. 42, No. 11, pp. 60–65, 2006.
Liu, Y. H., Li. Z. Y., and Zhang, C. H., “Analysis and Calculation on Static Stiffness of High Speed Angular Contact Ball Bearings,” Bearing, No. 8, pp. 1–3, 2005.
Hwang, Y.-K. and Lee, C.-M., “Development of a Simple Determination Method of Variable Preloads for High Speed Spindles in Machine Tools,” Int. J. Precis. Eng. Manuf., Vol. 16, No. 1, pp. 127–134, 2015.
Wang, S.-G. and Xia, Y.-M., “Effect of the Interference Fit and Axial Preload in the Stiffness of the High-Speed Angular Contact Ball Bearing,” Journal of University of Science and Technology of China, Vol. 36, No. 12, pp. 1314–1320, 2006.
Zhang, X. L., Shao, F. C., and Cao C. Z., “Static Stiffness Precise Compuataion of Angular Contact Ball Bearings,” Bearing, No. 5, pp. 2–5, 1995.
Fang, B., Zhang, L., Qu, X.-T., and Zhao, J., “Theoretical and Experimental Research of Stiffness of Angular Contact Ball Bearing,” Journal of Jilin University (Engineering and Technology Edition), Vol. 42, No. 4, pp. 840–844, 2012.
Harsha, S. P., Sandeep, K., and Prakash, R., “Non-Linear Dynamic Behaviors of Rolling Element Bearings due to Surface Waviness,” Journal of Sound and Vibration, Vol. 272, No. 3, pp. 557–580, 2004.
Lin, C.-W., Lin, Y.-K., and Chu, C.-H., “Dynamic Models and Design of Spindle-Bearing Systems of Machine Tools: A Review,” Int. J. Precis. Eng. Manuf., Vol. 14, No. 3, pp. 513–521, 2013.
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Yang, Z., Li, B. & Yu, T. Influence of structural parameters and tolerance on stiffness of high-speed ball bearings. Int. J. Precis. Eng. Manuf. 17, 1493–1501 (2016). https://doi.org/10.1007/s12541-016-0175-9
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DOI: https://doi.org/10.1007/s12541-016-0175-9