Abstract
This paper devotes to providing a dynamic reliability model for linear guideways for the whole life. Since a linear guide is always worn, the wear degradation of the linear guide is established. Moreover, the profile error of rail is considered. To get the dynamic behavior of linear guides precisely, we developed a dynamic stiffness model of the system in terms of different load conditions and operation time. The reliability model with variant stochastic parameters is proposed according to the contact characteristics of linear guides. The Monte Carlo method is adopted to solve the reliability of linear guides. The simulation results show the reliability curve agrees with the experimental results, as well as the engineering experience in practice. The proposed model can be well applied to the reliability prediction for linear guideways.
Similar content being viewed by others
References
Hwang, J., Park, C.-H., Gao, W., Kim, S.-W.: A three-probe system for measuring the parallelism and straightness of a pair of rails for ultra-precision guideways. Int. J. Mach. Tools Manuf. 47(7), 1053–1058 (2007). https://doi.org/10.1016/j.ijmachtools.2006.10.003
Zha, J., Xue, F., Chen, Y.: Straightness error modeling and compensation for gantry type open hydrostatic guideways in grinding machine. Int. J. Mach. Tools Manuf. 112, 1–6 (2017). https://doi.org/10.1016/j.ijmachtools.2016.10.002
Zha, J., Chen, Y., Wang, Z.: A tolerance design method for hydrostatic guideways motion accuracy based on error averaging effect. Procedia CIRP 75, 196–201 (2018). https://doi.org/10.1016/j.procir.2018.04.054
Wang, Z., Zhao, W., Chen, Y., Lu, B.: Prediction of the effect of speed on motion errors in hydrostatic guideways. Int. J. Mach. Tools Manuf. 64, 78–84 (2013). https://doi.org/10.1016/j.ijmachtools.2012.07.011
Majda, P.: Modeling of geometric errors of linear guideway and their influence on joint kinematic error in machine tools. Precision Eng. 36(3), 369–378 (2012). https://doi.org/10.1016/j.precisioneng.2012.02.001
Tong, V.-C., Kwon, S.-W., Hong, S.-W.: Modeling of moving table with linear roller guides subjected to geometric errors in guide rails. Int. J. Mach. Tools Manuf. 21(10), 1903–1919 (2020). https://doi.org/10.1007/s12541-020-00394-w
Fan, K.-C., Chen, H.-M., Kuo, T.-H.: Prediction of machining accuracy degradation of machine tools. Precision Eng. 36(2), 288–298 (2012). https://doi.org/10.1016/j.precisioneng.2011.11.002
Tang, H., Duan, J.-A., Zhao, Q.: A systematic approach on analyzing the relationship between straightness & angular errors and guideway surface in precise linear stage. Int. J. Mach. Tools Manuf. 120, 12–19 (2017). https://doi.org/10.1016/j.ijmachtools.2017.04.010
Yong-Sub, Y., Kim, Y.Y., Choi, J.S., Yoo, J., Lee, D.J., Lee, S.W., Lee, S.J.: Dynamic analysis of a linear motion guide having rolling elements for precision positioning devices. J. Mech. Sci. Technol. 22(1), 50–60 (2008). https://doi.org/10.1007/s12206-007-1006-9
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, 265–283 (2015). https://doi.org/10.1016/j.jsv.2015.02.021
Sakai, Y., Tanaka, T.: Influence of lubricant on nonlinear vibration characteristics of linear rolling guideway. Tribol. Int. (2019). https://doi.org/10.1016/j.triboint.2019.106124
Li, C., Xu, M., He, G., Zhang, H., Liu, Z., He, D., Zhang, Y.: Time-dependent nonlinear dynamic model for linear guideway with crowning. Tribol. Int. 151, 106413 (2020). https://doi.org/10.1016/j.triboint.2020.106413
Wang, W., Zhou, Y., Wang, H., Li, C., Zhang, Y.: Vibration analysis of a coupled feed system with nonlinear kinematic joints. Mech. Mach. Theory 134, 562–581 (2019). https://doi.org/10.1016/j.mechmachtheory.2019.01.014
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
Miura, T., Matsubara, A., Yamaji, I., Hoshide, K.: Measurement and analysis of friction fluctuations in linear guideways. CIRP Ann. 67(1), 393–396 (2018). https://doi.org/10.1016/j.cirp.2018.04.010
Oh, K.-J., Khim, G., Park, C.-H., Chung, S.-C.: Explicit modeling and investigation of friction forces in linear motion ball guides. Tribol. Int. 129, 16–28 (2019). https://doi.org/10.1016/j.triboint.2018.07.046
Xz, W., Xu, X., Li, X., He, X., Tian Hongliang, K.: Mixed lubrication of a linear motion rolling guideway pair. J. Vib. Shock 39(09), 260–266 (2020)
Gu, J., Zhang, Y.: Dynamic analysis of a ball screw feed system with time-varying and piecewise-nonlinear stiffness. Proc. Inst. Mech. Eng. Part C J Mech. Eng. Sci. 233(18), 6503–6518 (2019). https://doi.org/10.1177/0954406219865923
Tong, V.-C., Khim, G., Hong, S.-W., Park, C.-H.: Construction and validation of a theoretical model of the stiffness matrix of a linear ball guide with consideration of carriage flexibility. Mech. Mach. Theory 140, 123–143 (2019). https://doi.org/10.1016/j.mechmachtheory.2019.05.021
Yuan Lin, C., Pin Hung, J., Liang Lo, T.: 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
Jiang, S., Wang, Y., Wang, Y.: Modeling of static stiffness for linear motion roller guide. J. Tribol. (2019). https://doi.org/10.1115/1.4044292
Wang, W., Li, C.Y., Zhou, Y.X., Wang, H., Zhang, Y.M.: Nonlinear dynamic analysis for machine tool table system mounted on linear guides. Nonlinear Dyn. 94(3), 2033–2045 (2018). https://doi.org/10.1007/s11071-018-4473-x
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
Tao, W., Zhong, Y., Feng, H., Wang, Y.: Model for wear prediction of roller linear guides. Wear 305(1), 260–266 (2013). https://doi.org/10.1016/j.wear.2013.01.047
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). https://doi.org/10.1016/j.triboint.2015.07.005
Gu, J., Agapiou, J.S., Kurgin, S.: CNC machine tool work offset error compensation method. J. Manuf. Syst. 37, 576–585 (2015). https://doi.org/10.1016/j.jmsy.2015.04.001
Kuanmin, M.A.O., Can, G.O.N.G., Bing, L.I., Ming, Z.: Dynamic modeling research of linear motion ball guide considering surface waviness. J. Huazhong Univ. Sci. Technol. 42(6), 1–5 (2014)
Chengwei, W., Linqing, Z.: Effect of waviness and roughness on lubricated wear related to running-in. Wear 147(2), 323–334 (1991). https://doi.org/10.1016/0043-1648(91)90189-2
Liu, J., Wu, H., Shao, Y.: A comparative study of surface waviness models for predicting vibrations of a ball bearing. Sci. China Technol. Sci. 60(12), 1841–1852 (2017). https://doi.org/10.1007/s11431-017-9110-3
Li, M., Yu, H., Li, D., Wang, B., Zhang, G.: Modeling for dynamic contact angle of ball screw mechanism aimed to structural parameters. Nongye Gongcheng Xuebao/Transactions of the Chinese Society of Agricultural Engineering 32(4), 98–104 (2016). https://doi.org/10.11975/j.issn.1002-6819.2016.04.014
Yu, H., Ran, Y., Zhang, G., Li, X., Li, B.: A time-varying comprehensive dynamic model for the rotor system with multiple bearing faults. J. Sound Vib. 488, 115650 (2020). https://doi.org/10.1016/j.jsv.2020.115650
Zhang, Y., Wen, B., Liu, Q.: First passage of uncertain single degree-of-freedom nonlinear oscillators. Comput. Methods Appl. Mech. Eng. 165(1), 223–231 (1998). https://doi.org/10.1016/S0045-7825(98)00042-5
Guida, M., Pulcini, G.: Reliability analysis of mechanical systems with bounded and bathtub shaped intensity function. IEEE Trans. Reliab. 58(3), 432–443 (2009). https://doi.org/10.1109/TR.2009.2026690
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 (2014). https://doi.org/10.1177/0954406214531943
Tu, G., Tao, W., Feng, H., Yin, A.: Reliability test method of overloaded linear rolling guide vice based on stepping loading [J]. Mach. Tool Hydraul. 40(05), 47 (2012)
Funding
This work was financially supported by the National Natural Science Foundation of China (Grant No. 51835001) and the National Major Scientific and Technological Special Project for “High-grade CNC and Basic Manufacturing Equipment” of China (Grant No. 2018ZX04032-001).
Author information
Authors and Affiliations
Contributions
Hui Yu conceived the study and wrote the manuscript; Yan Ran and Genbao Zhang supervised and reviewed the manuscript; Guangqi Ying helped to collect and analyze the data. All authors read and approved the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Yu, H., Ran, Y., Zhang, G. et al. A dynamic time-varying reliability model for linear guides considering wear degradation. Nonlinear Dyn 103, 699–714 (2021). https://doi.org/10.1007/s11071-020-06139-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-020-06139-8