Stiffness matrix formulation for double row angular contact ball bearings: Analytical development and validation

Journal of Sound and Vibration

Volumn 332, Issue 22, 2013, Pages 5898-5916

  Gunduz, Aydin ^a   Singh, Rajendra ^a  

^a The Ohio State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AIRCRAFT APPLICATIONS; ANALYTICAL APPROACH; BEARING DISPLACEMENTS; SCIENTIFIC LITERATURE; STIFFNESS COEFFICIENTS; STIFFNESS MATRICES; STRUCTURAL ELEMENTS; TANDEM ARRANGEMENT;

ANGULAR CONTACT BALL BEARINGS; STIFFNESS;

STIFFNESS MATRIX;

EID: 84880916416     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2013.04.049     Document Type: Article

References (38)

1. T.A. Harris Rolling Bearing Analysis 2001 J. Wiley New York
2. J. Brändlein, P. Eschmann, L. Hasbargen, and K. Weigand Ball and Roller Bearings: Theory, Design and Application 1999 J. Wiley Chichester
3. A. Palmgren, Ball and Roller Bearing Engineering, SKF Industries, Philadelphia, 1959.
4. T.C. Lim, and R. Singh Vibration transmission through rolling element bearings, Part I: bearing stiffness formulation Journal of Sound and Vibration 139 2 1990 179 199
5. T.J. Royston, and I. Basdogan Vibration transmission through self-aligning (spherical) rolling element bearings: theory and experiment Journal of Sound and Vibration 215 5 1998 997 1014
6. I. Bercea, D. Nelias, and G. Cavallaro A unified and simplified treatment of the nonlinear equilibrium problem of double-row bearings. Part I: rolling bearing model Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 217 3 2003 205 212
7. D. Nelias, and I. Bercea A unified and simplified treatment of the nonlinear equilibrium problem of double-row bearings, Part II: application to taper rolling bearings supporting a flexible shaft Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 217 3 2003 213 221
8. ©, www.romaxtech.com, 2012.
9. F.P. Wardle, S.J. Lacey, and S.Y. Poon Dynamic and static characteristics of a wide speed range machine tool spindle Precision Engineering 5 4 1983 175 183
10. E.P. Gargiulo A simple way to estimate bearing stiffness Machine Design 52 1980 107 110
11. M.F. White Rolling element bearing vibration characteristics: effect of stiffness Journal of Applied Mechanics 46 1979 677 684
12. J. Kraus, J.J. Blech, and S.G. Braun In situ determination of rolling bearing stiffness and damping by modal analysis Journal of Vibration, Acoustics, Stress, and Reliability in Design, Transactions of the American Society of Mechanical Engineers 109 1987 235 240
13. M.D. Rajab, Modeling of the transmissibility through rolling element bearing under radial and moment loads, Ph.D. Dissertation, The Ohio State University, 1982.
14. K. Ishida, T. Matsuda, M. Fukui, Effect of gearbox on noise reduction of geared device, Proceedings of the International Symposium on Gearing and Power Transmissions, Tokyo, 1981, pp. 13-18.
15. J.S. Lin, Experimental analysis of dynamic force transmissibility through bearings, M.S. Thesis, The Ohio State University, 1989.
16. Y. Cao, and Y. Altintas A general method for the modeling of spindle-bearing systems Transactions of the American Society of Mechanical Engineers, Journal of Mechanical Design 126 6 2004 1089 1104
17. A.B. Jones A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions Transactions of the ASME, Journal of Basic Engineering 82 1960 309 320
18. T.C. Lim, and R. Singh Vibration transmission through rolling element bearings, Part II: system studies Journal of Sound and Vibration 139 2 1990 201 225
19. T.C. Lim, and R. Singh Vibration transmission through rolling element bearings, Part III: geared rotor system studies Journal of Sound and Vibration 151 1 1991 31 54
20. T.C. Lim, and R. Singh Vibration transmission through rolling element bearings, Part IV: statistical energy analysis Journal of Sound and Vibration 153 1 1992 37 50
21. T.C. Lim, and R. Singh Vibration transmission through rolling element bearings, Part V: effect of distributed contact load on roller bearing stiffness matrix Journal of Sound and Vibration 169 4 1994 547 553
22. J.M. De Mul, J.M. Vree, and D.A. Vaas Equilibrium and associated load distribution in ball and roller bearings loaded in five degrees of freedom while neglecting frictions I: General theory and application to ball bearings Transactions of the ASME, Journal of Tribology 111 1989 142 148
23. X. Hernot, M. Sartor, and J. Guillot Calculation of the stiffness matrix of angular contact ball bearings by using the analytical approach Transactions of the ASME, Journal of Mechanical Design 122 2000 83 90
24. P. Cermelj, and M. Boltezar An indirect approach investigating the dynamics of a structure containing ball bearings Journal of Sound and Vibration 276 1-2 2004 401 417
25. Y. Guo, and R.G. Parker Stiffness matrix calculation of rolling element bearings using a finite element/contact mechanics model Mechanism and Machine Theory 51 2012 32 45
26. © User's Manual, www.ansol.us,2012.
27. T.L.H. Walford, and B.J. Stone The measurement of the radial stiffness of rolling element bearings under oscillation conditions Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 22 4 1980 175 181
28. T.L.H. Walford, B.J. Stone, Some stiffness and damping characteristics of angular contact bearings under oscillating conditions, Proceedings of the 2nd International Conference on Vibrations in Rotating Machinery, (1980).
29. B.J. Stone The state of art in the measurement of the stiffness and damping of rolling element bearings Annals of the CIRP 31 2 1982 529 538
30. E.R. Marsh, and D.S. Yantek Experimental measurement of precision bearing dynamic stiffness Journal of Sound and Vibration 202 1 1997 55 66
31. R. Tiwari, and N.S. Vyas Estimation of nonlinear stiffness parameters of rolling element bearings from random response of rotor-bearing systems Journal of Sound and Vibration 187 1995 229 239
32. G. Pinte, S. Devos, B. Stallaert, W. Symens, J. Swevers, and P. Sas A piezo-based bearing for the active structural acoustic control of rotating machinery Journal of Sound and Vibration 329 9 2010 1235 1253
33. M. Cao, and J. Xiao A comprehensive dynamic model of double-row spherical roller bearing - model development and case studies on surface defects, preloads, and radial clearance Mechanical Systems and Signal Processing 22 2008 467 489
34. M. Cao A refined double-row spherical roller bearing model and its application in performance assessment of moving race shaft misalignments Journal of Vibration and Control 13 2007 1145 1168
35. D.H. Choi, and K.C. Yoon A design method of an automotive wheel-bearing unit with discrete design variables using genetic algorithms Journal of Tribology 123 2001 181 187
36. A. Gunduz, Multi-dimensional stiffness characteristics of double row angular contact ball bearings and their role in influencing vibration modes, Ph.D. Dissertation, The Ohio State University, 2012.
37. A. Gunduz, J.T. Dreyer, and R. Singh Effect of bearing preloads on the modal characteristics of a shaft-bearing assembly: experiments on double row angular contact ball bearings Mechanical Systems and Signal Processing 31 2012 176 195
38. W. Xu, T. Coleman, and G. Liu A secant method for nonlinear least-squares minimization Computational Optimization and Applications 51 1 2012 159 173