DOI QR코드

DOI QR Code

A hybrid method for dynamic stiffness identification of bearing joint of high speed spindles

  • Zhao, Yongsheng (Key Laboratory of advanced manufacturing technology, Beijing University of Technology) ;
  • Zhang, Bingbing (Key Laboratory of advanced manufacturing technology, Beijing University of Technology) ;
  • An, Guoping (Key Laboratory of advanced manufacturing technology, Beijing University of Technology) ;
  • Liu, Zhifeng (Key Laboratory of advanced manufacturing technology, Beijing University of Technology) ;
  • Cai, Ligang (Key Laboratory of advanced manufacturing technology, Beijing University of Technology)
  • Received : 2014.01.01
  • Accepted : 2015.12.15
  • Published : 2016.01.10

Abstract

Bearing joint dynamic parameter identification is crucial in modeling the high speed spindles for machining centers used to predict the stability and natural frequencies of high speed spindles. In this paper, a hybrid method is proposed to identify the dynamic stiffness of bearing joint for the high speed spindles. The hybrid method refers to the analytical approach and experimental method. The support stiffness of spindle shaft can be obtained by adopting receptance coupling substructure analysis method, which consists of series connected bearing and joint stiffness. The bearing stiffness is calculated based on the Hertz contact theory. According to the proposed series stiffness equation, the stiffness of bearing joint can be separated from the composite stiffness. Then, one can obtain the bearing joint stiffness fitting formulas and its variation law under different preload. An experimental set-up with variable preload spindle is developed and the experiment is provided for the validation of presented bearing joint stiffness identification method. The results show that the bearing joint significantly cuts down the support stiffness of the spindles, which can seriously affects the dynamic characteristic of the high speed spindles.

Keywords

Acknowledgement

Supported by : Beijing Natural Science Foundation, National Natural Science Foundation of China

References

  1. Altintas, Y. and Cao, Y.Z. (2005), "Virtual design and optimization of machine tool spindles", CIRP Ann. Manuf. Tech., 54 (1), 379-382. https://doi.org/10.1016/S0007-8506(07)60127-9
  2. Aydin, G., Jason, T.D. and Singh, R. (2012), "Effect of bearing preloads on the modal characteristics of a shaft-bearing assembly: Experiments on double row angular contact ball bearings", Mech. Syst. Signal Pr., 31, 176-195. https://doi.org/10.1016/j.ymssp.2012.03.013
  3. Cao, Y.Z. and Altintas, Y. (2004), "A general method for the modeling of spindle-bearing systems", ASME J. Mech. Des., 126 (6), 1089-1104. https://doi.org/10.1115/1.1802311
  4. Cao, Y.Z. and Altintas, Y. (2007), "Modeling of spindle-bearing and machine tool systems for virtual simulation of milling operations", Int. J. Mach. Tool. Manuf., 47 (9), 1342-1350. https://doi.org/10.1016/j.ijmachtools.2006.08.006
  5. Celic, D. and Boltezar, M. (2009), "The influence of the coordinate reduction on the identification of the joint dynamic properties", Mech. Syst. Signal Pr., 23(4), 1260-1271. https://doi.org/10.1016/j.ymssp.2008.11.002
  6. Chen, J.S. and Chen, K.W. (2005), "Bearing load analysis and control of a motorized high speed spindle", Int. J. Mach. Tool. Manuf., 45(12-13), 1487-1493. https://doi.org/10.1016/j.ijmachtools.2005.01.024
  7. DeMul, J.M., Vree, J.M. and Mass, D.A. (1989), "Equilibrium and association load distribution in ball and roller bearings loaded in five degrees of freedom while neglecting friction, Part I: General theory and application to ball bearings", ASME J. Tribology, 111 (1), 142-148. https://doi.org/10.1115/1.3261864
  8. Guo, Y. and Robert, G.P. (2012), "Stiffness matrix calculation of rolling element bearings using a finite element / contact mechanics model", Mech. Mach. Theory, 51, 32-45. https://doi.org/10.1016/j.mechmachtheory.2011.12.006
  9. Hagiu, G.D. and Gafitanu, M.D. (1992), "Dynamic characteristics of high speed angular contact ball bearings", Wear, 211(1), 22-29. https://doi.org/10.1016/S0043-1648(97)00076-8
  10. Hamid, A. and Mostafa, N. (2010), "Tool point dynamics prediction by a three-component model utilizing distributed joint interfaces", Int. J. Mach. Tool. Manuf., 50(11), 998-1005. https://doi.org/10.1016/j.ijmachtools.2010.07.003
  11. Hernot, X., Sartor, M. and Guillot, J. (2000), "Calculation of the stiffness matrix of angular contact ball bearings by using the analytical approach", Tran. ASME, 122(3), 83-90. https://doi.org/10.1115/1.533548
  12. Hu, F., Wu, B., Hu, Y. and Shi, T. (2009), "Identification of dynamic stiffness matrix of bearing joint region", Front. Mech. Eng. China, 4(3), 289-299.
  13. Houpert, L. (1997), "A uniform analytical approach for ball and roller bearings calculations", ASME J. Tribology, 119(4), 851-858. https://doi.org/10.1115/1.2833896
  14. Jalali, H., Ahmadian, H. and Mottershead, J.E. (2007), "Identification of nonlinear bolted lap-joint parameters by force-state mapping", Int. J. Solid. Struct., 44(25-26), 8087-8105. https://doi.org/10.1016/j.ijsolstr.2007.06.003
  15. Jeng, Y.R. and Gao, C.C. (2001), "Investigation of the ball-bearing temperature rise under an oil-air lubrication system", Proc. Inst. Mech. Eng. Part J: J. Eng. Tribology, 215(2), 139-148. https://doi.org/10.1243/1350650011541783
  16. Jiang, S.Y. and Mao, H.B. (2010), "Investigation of variable optimum preload for a machine tool spindle", Int. J. Mach. Tool. Manuf., 50(1), 19-28. https://doi.org/10.1016/j.ijmachtools.2009.10.001
  17. Jones, A.B. (1960), "A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions", ASME J. Basic Eng., 82(2), 309-320. https://doi.org/10.1115/1.3662587
  18. Kashani, H. and Nobari, A.S. (2010), "Identification of dynamic characteristics of nonlinear joint based on the optimum equivalent linear frequency response function", J. Sound Vib., 329(9), 1460-1479. https://doi.org/10.1016/j.jsv.2009.11.007
  19. Kim, S.M. and Lee, S.K. (2001), "Prediction of thermo-elastic behavior in a spindle bearing system considering bearing surroundings", Int. J. Mach. Tool. Manuf., 41 (6), 809-831. https://doi.org/10.1016/S0890-6955(00)00103-6
  20. Kim, S.M., Lee, K.J. and Lee, S.K. (2002), "Effect of bearing support structure on the high-speed spindle bearing compliance", Int. J. Mach. Tool. Manuf., 42 (3), 365-373. https://doi.org/10.1016/S0890-6955(01)00126-2
  21. Li, H.Q. and Shin, Y.C. (2004), "Analysis of bearing configuration effects on high speed spindles using an integrated dynamic thermo-mechanical spindle model", Int. J. Mach. Tool. Manuf., 44(4), 347-364. https://doi.org/10.1016/j.ijmachtools.2003.10.011
  22. Lim, T.C. and Singh, R. (1990), "Vibration transmission through rolling element bearings, Part I: Bearing stiffness formulation", J. Sound Vib., 139(2), 179-199. https://doi.org/10.1016/0022-460X(90)90882-Z
  23. Majid, M., Eldon, G. and Simon, S.P. (2013), "FRF based joint dynamics modeling and identification", Mech. Syst. Signal Pr., 39(1-2), 265-279. https://doi.org/10.1016/j.ymssp.2013.03.022
  24. Mao, K.M., Li, B., Wu, J. and Shao, X.Y. (2010), "Stiffness influential factors-based dynamic modeling and its parameter identification method of fixed joints in machine tools", Int. J. Mach. Tool. Manuf., 50(2), 156-164. https://doi.org/10.1016/j.ijmachtools.2009.10.017
  25. Michael, H., Stefan, O. and Lothar, G. (2002), "Identification of a bolted-joint model with fuzzy parameters loaded normal to the contact interface", Mech. Res. Commun., 29(2-3), 177-187. https://doi.org/10.1016/S0093-6413(02)00245-8
  26. Rivin, E.I. (2000), "Tooling structure: interface between cutting edge and machine tool", Ann. CIPP, 49(2), 591-634.
  27. Royston, T.J. (2008), "Leveraging the equivalence of hysteresis models from different fields for analysis and numerical simulation of jointed structures", J. Comput. Nonlin. Dyn., 3, 1-8.
  28. Schmitz, T.L. and Smith, K.S. (2009), Machining Dynamics: Frequency Response to Improved Productivity, Springer Science + Business Media, New York, NY, USA.
  29. Shamine, D.M., Hong, S.W. and Shin, Y.C. (1998), "Experimental identification of dynamic parameters of rolling element bearings in machine tools", J. Dyn. Syst. Measur. Control Tran., ASME, 122(1), 95-101.
  30. Yang, T.C., Fan, S.H. and Lin, C.S. (2003), "Joint stiffness identification using FRF measurements", Comput. Struct., 81(28-29), 2549-2556. https://doi.org/10.1016/S0045-7949(03)00328-6

Cited by

  1. Vibration performance evaluation of planar flexible multibody systems with joint clearance vol.39, pp.12, 2017, https://doi.org/10.1007/s40430-017-0855-0
  2. Reconstruction of structured models using incomplete measured data vol.62, pp.3, 2017, https://doi.org/10.12989/sem.2017.62.3.303
  3. Characterization of the effect of joint clearance on the energy loss of flexible multibody systems with variable kinematic structure vol.63, pp.5, 2016, https://doi.org/10.12989/sem.2017.63.5.691
  4. Investigation of Gas Foil Bearings With an Adaptive and Non-Linear Structure vol.13, pp.1, 2016, https://doi.org/10.2478/ama-2019-0001