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http://dx.doi.org/10.7736/KSPE.2015.32.2.117

Dynamic Analysis of Spindle Supported by Multiple Bearings of Different Types  

Tong, Van-Canh (Graduate School, Department of Mechatronics, Kumoh National Institute of Technology)
Bae, Gyu-Hyun (Graduate School, Department of Mechatronics, Kumoh National Institute of Technology)
Hong, Seong-Wook (Department of Mechatronics, Kumoh National Institute of Technology)
Publication Information
Abstract
This paper presents a dynamic modeling method for the indeterminate spindle-bearing system supported by multiple bearings of different types. A spindle-bearing system supported by ball and cylindrical roller bearings is considered. The de Mul's bearing model is extended for calculating ball and cylindrical roller bearing stiffness matrices with inclusion of centrifugal force and gyroscopic moment. The dependence between spindle shaft reaction forces and bearing stiffness is effectively resolved using an iterative approach. The spindle rotor dynamics is established with the Timoshenko beam theory based finite elements. The spindle reaction forces, bearings stiffness and spindle natural frequencies are obtained with taking into account spindle radial load, ball bearing axial preload and rotational speed effects. The developed method is verified by comparing the simulation results with those from a commercial program.
Keywords
Spindle-bearing system; Angular contact ball bearing; Cylindrical roller bearing; Stiffness matrix; Natural frequency;
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Times Cited By KSCI : 3  (Citation Analysis)
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1 SKF Group, "Bearing Arrangements," http://www.skf.com/group/products/bearings-units-housings/superprecision-bearings/principles/design-considerations/ bearing-arrangements/index.html (Accessed DEC. 7, 2014).
2 Nelson, H. D. and McVaugh, J. M., "The Dynamics of Rotor-Bearing Systems using Finite Elements," J. Manuf. Sci. and Eng., Trans. ASME, Vol. 98, No. 2, pp. 593-600, 1976.
3 Hong, S. W. and Park, J. H., "An Efficient Method for the Unbalance Response Analysis of Rotor-Bearing Systems," J. Sound & Vibration, Vol. 200, No. 4, pp. 491-504, 1997.   DOI
4 Bae, G. H., Lee, C. H., Hwang, J., and Hong, S. W., "Estimation of Axial Displacement in High-Speed Spindle due to Rotational Speed," J. Korean Soc. Precis. Eng., Vol. 29, No. 6, pp. 671-679, 2012.   과학기술학회마을   DOI
5 Chen, L. K. and Ku, D. M., "Finite Element Analysis of Natural Whirl Speeds of Rotating Shafts," Computers and Structures, Vol. 40, No. 3, pp. 741-747, 1991.   DOI
6 Hong, S. W., Choi, C. S., and Lee, C. H., "Effects of Bearing Arrangement on the Dynamic Characteristics of High-Speed Spindle," J. Korean Soc. Precis. Eng., Vol. 30, No. 8, pp. 854-863, 2013.   과학기술학회마을   DOI   ScienceOn
7 Noel, D., Ritou, M., Furet, B., and Loch, S. L.,"Complete Analytical Expression of the Stiffness Matrix of Angular Contact Ball Bearings," J. Tribol. Trans. ASME, Vol. 135, No. 4, Paper No. 041101, 2013.
8 Tong, V. C. and Hong, S. W., "Characteristics of Tapered Roller Bearing Subjected to Combined Radial and Moment Loads," Int. J. Precis. Eng. Manuf.-Green Tech., Vol. 1, No. 4, pp. 323-328, 2014.   DOI
9 Jorgensen, B. R. and Shin, Y. C., ''Dynamics of Spindle-Bearing Systems at High Speeds including Cutting Load Effects,'' J. Manuf. Sci. Eng., Trans. ASME, Vol. 120, Vol. 2, pp. 387-394, 1998.   DOI   ScienceOn
10 Hong, S. W., Kang, J. O., and Shin, Y. C., "Dynamic Characteristics of Indeterminate Rotor Systems with Angular Contact Ball Bearings Subject to Axial and Radial Loads," Int. J. Precis. Eng. Manuf., Vol. 3, No. 2, pp. 61-71, 2002.
11 Cao, Y. and Altintas, Y., "A General Method for the Modeling of Spindle-Bearing Systems," J. Mechanical Design, Trans. ASME, Vol. 126, No. 6, pp. 1089-1104, 2005.
12 Harris, T. A. and Kotzalas, M. N., "Advanced Concept of Bearing Technology," New York, Taylor & Francis, 5th Ed., pp. 68-93, 2007.
13 Schaeffler Technologies, "BEARINX$^{(R)}$-online Shaft Calculation," http://www.schaeffler.de/content.schaeffler.de/en/products_services/inafagproducts/calculating/bearinxonline/bearinx_online.jsp/ (Accessed DEC. 05 2014)
14 de Mul, J. M., 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 I-II," J. Tribol., Trans. ASME, Vol. 111, pp. 149-155, 1989.   DOI