Abstract
In this paper, a three-degree-of-freedom dynamic model of a machine tool table system considering nonlinear contact behaviors is established to obtain vibration characteristics. The relationship between contact deformation and force is derived via Hertz contact theory, and piecewise nonlinear interaction forces are obtained. Then, dynamic differential equations of the three-degree-of-freedom system are constructed. The numerical simulations are solved by Runge–Kutta integration method to investigate the dynamic behaviors of the dynamic system. When the system is under a small excitation force, it exhibits softening nonlinear behavior in the primary resonance region. With excitation amplitude increasing to a larger value, the system exhibits hardening nonlinear behavior. In order to better investigate the effects of excitation amplitude, excitation angle, installation distance and height of work piece on the vibration characteristics, frequency–amplitude curves, 3-D frequency spectrum, time history, frequency domain, phase diagram and Poincare section are employed. Jump discontinuity phenomenon, super-harmonic resonance and varied frequency components are dependent on the key parameters. Some conclusions are drawn to suppress the vibration of machining process and improve the quality of work piece.
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Zhang, G.P., Huang, Y.M., Shi, W.H., Fu, W.P.: Predicting dynamic behaviours of a whole machine tool structure based on computer-aided engineering. Int. J. Mach. Tools Manuf. 43(7), 699–706 (2003). https://doi.org/10.1016/S0890-6955(03)00026-9
Hung, J.-P., Lai, Y.-L., Lin, C.-Y., Lo, T.-L.: Modeling the machining stability of a vertical milling machine under the influence of the preloaded linear guide. Int. J. Mach. Tools Manuf. 51(9), 731–739 (2011). https://doi.org/10.1016/j.ijmachtools.2011.05.002
Wu, J.S.-S., Chang, J.-C., Hung, J.-P.: The effect of contact interface on dynamic characteristics of composite structures. Math. Comput. Simul. 74(6), 454–467 (2007). https://doi.org/10.1016/j.matcom.2006.07.003
Sun, W., Kong, X., Wang, B., Li, X.: Statics modeling and analysis of linear rolling guideway considering rolling balls contact. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 229(1), 168–179 (2015). https://doi.org/10.1177/0954406214531943
Kong, X., Sun, W., Wang, B., Wen, B.: Dynamic and stability analysis of the linear guide with time-varying, piecewise-nonlinear stiffness by multi-term incremental harmonic balance method. J. Sound Vib. 346(1), 265–283 (2015)
Ohta, H., Nakagawa, T.: Using ceramic balls to reduce noise in a linear guideway type recirculating linear ball bearing. J. Tribol. Trans. ASME 125(3), 480–486 (2003). https://doi.org/10.1115/1.1537264
Ohta, H., Iwasaki, S., Kazama, T., Hoshino, K.: Sound of a ball spline operated at a certain linear velocity. Arch. Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol. 1994–1996 (vols. 208–210) 223(1), 17–25 (2009)
Shimizu, S., Saito, E., Uchida, H., Sharma, C.S., Taki, Y.: Tribological studies of linear motion ball guide systems. Tribol. Trans. 41(1), 49–59 (1998)
Shimizu, S., Sharma, C.S., Shirai, T.: Life prediction for linear rolling element bearings: a new approach to reliable life assessment. J. Tribol. 124(1), 121–128 (2002)
Shimizu, S., Shimoda, H., Tosha, K.: Study on the life distribution and reliability of roller-based linear bearing. Tribol. Trans. 51(4), 446–453 (2008)
Wei, W., Yimin, Z., Changyou, L., Hao, W., Yanxun, Z.: Effects of wear on dynamic characteristics and stability of linear guides. Meccanica 52(11), 2899–2913 (2017). https://doi.org/10.1007/s11012-016-0605-x
Zou, H.T., Wang, B.L.: Investigation of the contact stiffness variation of linear rolling guides due to the effects of friction and wear during operation. Tribol. Int. 92, 472–484 (2015)
Ohta, H., Tanaka, K.: Vertical stiffnesses of preloaded linear guideway type ball bearings incorporating the flexibility of the carriage and rail. J. Tribol. 132(1), 547–548 (2010)
Lynagh, N., Rahnejat, H., Ebrahimi, M., Aini, R.: Bearing induced vibration in precision high speed routing spindles. Int. J. Mach. Tools Manuf. 40(4), 561–577 (2000). https://doi.org/10.1016/S0890-6955(99)00076-0
Harsha, S.P., Sandeep, K., Prakash, R.: Nonlinear dynamic response of a rotor bearing system due to surface waviness. Nonlinear Dyn. 37(2), 91–114 (2004). https://doi.org/10.1023/B:NODY.0000042916.10351.ff
Bai, C., Zhang, H., Xu, Q.: Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotor-bearing system. Nonlinear Dyn. 53(3), 173 (2007). https://doi.org/10.1007/s11071-007-9306-2
Han, Q., Chu, F.: Nonlinear dynamic model for skidding behavior of angular contact ball bearings. J. Sound Vib. 354, 219–235 (2015). https://doi.org/10.1016/j.jsv.2015.06.008
Zhou, W.Y., Li, D.X.: Design and analysis of an intelligent vibration isolation platform for reaction/momentum wheel assemblies. J. Sound Vib. 331(13), 2984–3005 (2012)
Wang, W., Zhang, Y., Li, C.: Dynamic reliability analysis of linear guides in positioning precision. Mech. Mach. Theory 116, 451–464 (2017). https://doi.org/10.1016/j.mechmachtheory.2017.06.011
Al-Bender, F., Symens, W.: Characterization of frictional hysteresis in ball-bearing guideways. Wear 258(11–12), 1630–1642 (2005). https://doi.org/10.1016/j.wear.2004.11.018
Xi, Y., Zhou, Y., Zhang, W., Mao, J.: An experimental method for measuring friction behaviors of linear rolling guides. Chin. Sci. Bull. 59(29–30), 3912–3918 (2014)
Ohta, H., Kitajima, Y., Kato, S., Igarashi, Y.: Effects of ball groupings on ball passage vibrations of a linear guideway type ball bearing (pitching and yawing ball passage vibrations). J. Tribol. 129(1), 525–532 (2006)
Ohta, H., Kato, S., Matsumoto, J., Nakano, K.: A design of crowning to reduce ball passage vibrations of a linear guideway type recirculating linear ball bearing. J. Tribol. 127(2), 749–755 (2004)
Hung, J.P.: Load effect on the vibration characteristics of a stage with rolling guides. J. Mech. Sci. Technol. 23(1), 89–99 (2009). https://doi.org/10.1007/s12206-008-0925-4
Lin, C.Y., Hung, J.P., Lo, T.L.: Effect of preload of linear guides on dynamic characteristics of a vertical column-spindle system. Int. J. Mach. Tools Manuf. 50(8), 741–746 (2010). https://doi.org/10.1016/j.ijmachtools.2010.04.002
Li, B., Wang, X., Hu, Y., Li, C.: Analytical prediction of cutting forces in orthogonal cutting using unequal division shear-zone model. Int. J. Adv. Manuf. Technol. 54(5), 431–443 (2011). https://doi.org/10.1007/s00170-010-2940-8
Fu, Z., Zhang, X., Wang, X., Yang, W.: Analytical modeling of chatter vibration in orthogonal cutting using a predictive force model. Int. J. Mech. Sci. 88, 145–153 (2014). https://doi.org/10.1016/j.ijmecsci.2014.08.005
Harris, T.: Rolling Bearing Analysis, pp. 13–21. Wiley, New York (1991).
Bizarre, L., Nonato, F., Cavalca, K.L.: Formulation of five degrees of freedom ball bearing model accounting for the nonlinear stiffness and damping of elastohydrodynamic point contacts. Mech. Mach. Theory 124, 179–196 (2018)
Funding
This study is funded by National Natural Science Foundation of China (Grant No. 51575095), China Postdoctoral Science Foundation (Grant No. 2017M610180) and Major State Basic Research Development Program of China (973 Program) (Grant No. 2014CB046303).
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Wang, W., Li, C., Zhou, Y. et al. Nonlinear dynamic analysis for machine tool table system mounted on linear guides. Nonlinear Dyn 94, 2033–2045 (2018). https://doi.org/10.1007/s11071-018-4473-x
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DOI: https://doi.org/10.1007/s11071-018-4473-x