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Effects of nonlinear behaviour of linear ball guideway on chatter frequency of lathe machine tool

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Abstract

Linear ball guideways (LBGs) have several advantages for the precise positioning control of machine tools. However, the ball-groove contact behaviour leads to poor dynamic compliance, which induces a significant nonlinear behaviour of the guideway and a poor chatter stability. The nonlinearity complicates the chatter prediction due to the dependence of the contact stiffness. This approach aims to offer an industrially orientated method of estimation of chatter stability for structures based on LBG. Consequently, the present study first employs Hertzian contact theory to describe the ball-groove contact behaviour in the LBG of a lathe machine. Two static models are presented, both predict the LBG stiffness under different cutting loads. The first model describes is simplified, ignores the effects of the contact force on the deformation of the guideway components, even with that limitation depicts the main behaviour of the system. The second model is more precise and adopts a dynamic substructuring cosimulation method to incorporate the effects of structural deformation into the analysis. For both models, a linearisation approach is employed to analyse the dynamic behaviour of the system under static loading and define the dynamic compliance. The chatter frequencies of the LBG are estimated using the second model and are shown to be in good agreement with the experimental results. In general, the results of the analysis show that fundamental shifts in the frequency response of the LBG occur under specific values of the cutting force and gravity load. In other words, the results confirm that this method provides sufficient estimation of nonlinear behaviour of machine tool based on the LBG.

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References

  1. Wang W, Li C, Zhou Y, Wang H, Zhang Y (2018) Nonlinear dynamic analysis for machine tool table system mounted on linear guides. Nonlinear Dyn 94(3):2033–2045. https://doi.org/10.1007/s11071-018-4473-x

    Article  Google Scholar 

  2. Xu M et al (2021) Model and nonlinear dynamic analysis of linear guideway subjected to external periodic excitation in five directions. Nonlinear Dynamics, vol 105. https://doi.org/10.1007/s11071-021-06796-3

  3. Kong X, Sun W, Wang B, Wen B (2015) 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. https://doi.org/10.1016/j.jsv.2015.02.021

    Article  Google Scholar 

  4. Shaw D, Su WL (2013) Stiffness analysis of linear guideways without preload. J Mech 29 (2):281–286. https://doi.org/10.1017/jmech.2012.136

    Article  Google Scholar 

  5. Ohta H, Tanaka K (2010) Vertical stiffnesses of preloaded linear guideway type ball bearings incorporating the flexibility of the carriage and rail. J Tribol 132(1):1–9. https://doi.org/10.1115/1.4000277

    Article  Google Scholar 

  6. Wu JSS, Chang JC, Tsai GA, Lin CY, Ou FM (2012) The effect of bending loads on the dynamic behaviors of a rolling guide. J Mech Sci Technol 26(3):671–680. https://doi.org/10.1007/s12206-011-1228-8

    Article  Google Scholar 

  7. Rahmani M, Bleicher F (2016) Experimental and analytical investigations on normal and angular stiffness of linear guides in manufacturing systems. Procedia CIRP 41:795–800. https://doi.org/10.1016/j.procir.2015.12.033

    Article  Google Scholar 

  8. Yuan Lin C, Pin Hung J, Liang Lo T (2010) Effect of preload of linear guides on dynamic characteristics of a vertical column–spindle system. Int J Mach Tools Manuf 50(8):741–746. https://doi.org/10.1016/j.ijmachtools.2010.04.002

    Article  Google Scholar 

  9. Hung JP, Lai YL, Lin CY, Lo TL (2011) 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. https://doi.org/10.1016/j.ijmachtools.2011.05.002

    Article  Google Scholar 

  10. Yang L, Wang L, Zhao W (2020) Hybrid modeling and analysis of multidirectional variable stiffness of the linear rolling guideway under combined loads. Proc Inst Mech Eng C J Mech Eng Sci 234:095440622090889. https://doi.org/10.1177/0954406220908894

    Article  Google Scholar 

  11. Anoopnath P, Babu V, Vishwanath A (2018) Hertz contact stress of deep groove ball bearing. Materials Today: Proceedings 5:3283–3288. https://doi.org/10.1016/j.matpr.2017.11.570

    Google Scholar 

  12. Altintas Y, Brecher C, Weck M, Witt S (2005) Virtual Machine Tool. CIRP Ann 54 (2):115–138. https://doi.org/10.1016/S0007-8506(07)60022-5

    Article  Google Scholar 

  13. Sun W., Kong X, Wang B (2013) Precise finite element modeling and analysis of dynamics of linear rolling guideway on supporting direction. J Vibroengineering 15(3):1330–1340

    Google Scholar 

  14. Klerk D, Rixen D, Voormeeren S (2008) General framework for dynamic substructuring: history, review, and classification of techniques. Aiaa Journal - AIAA J 46:1169–1181. https://doi.org/10.2514/1.33274

    Article  Google Scholar 

  15. Law M, Phani AS, Altintas Y (2013) Position-dependent multibody dynamic modeling of machine tools based on improved reduced order models. J Manuf Sci Eng 135(2):021–008. https://doi.org/10.1115/1.4023453

    Article  Google Scholar 

  16. Ksica F, Hadas Z (2017) Position-dependent response simulation of machine tool using state-space models. MM Science Journal 2017:2120–2127. https://doi.org/10.17973/MMSJ.2017_12_201799

    Article  Google Scholar 

  17. Brecher C, Chavan P, Spierling R, Fey MA (2018) substructuring approach for simulation of time dependent workpiece dynamics during milling. MM Science Journal 12:2625–2632. https://doi.org/10.17973/MMSJ.2018_12_2018105

    Article  Google Scholar 

  18. Roettgen D, Allen MS, Kammer D, Mayes RL, Allen MS, Mayes RL, Rixen DJ (eds) (2017) Substructuring of a nonlinear beam using a modal iwan framework, part ii: nonlinear modal substructuring. Dynamics of Coupled Structures, vol 4, pp 179–197. Springer International Publishing, Cham

  19. Hadraba P, Wang J, Lin H, Hadas Z (2022) Theoretical study of nonlinear chatter stability analysis based on synthesis of linearizations in operating points for different turning conditions. MM Science Journal

  20. Gegg B, Suh C, Luo A (2011) Machine tool vibrations and cutting dynamics SpringerLink: Bücher. Springer, New York

    Book  Google Scholar 

  21. Tlusty J. (2000) Manufacturing processes and equipment Prentice Hall Upper Saddle River

  22. Wang J, Uhlmann E, Oberschmidt D, Sung C, Perfilov I (2016) Critical depth of cut and asymptotic spindle speed for chatter in micro milling with process damping. CIRP Ann 65(1):113–116. https://doi.org/10.1016/j.cirp.2016.04.088

    Article  Google Scholar 

  23. Johnson KL (1985) Contact mechanics. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  24. Krampert D, Ziegler M, Unsleber S, Reindl L, Rupitsch SJ (2021) On the stiffness hysteresis of profiled rail guides. Tribol Int 160:107019. https://doi.org/10.1016/j.triboint.2021.107019

    Article  Google Scholar 

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Acknowledgements

The authors are grateful to Tajmac-ZPS a.s. for providing the machine tool for the experiment.

Funding

This work was supported by the Ministry of Science and Technology of Taiwan (Grant no: MOST 111-2221-E-006-142) and Faculty of Mechanical Engineering, Brno University of Technology (Grant no. FSI-S-20-6335).

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Brno University of Technology, Technicka 2896/2, Brno, 616 69, Czech Republic

    Petr Hadraba & Zdenek Hadas

  2. Department of Mechanical Engineering, National Cheng Kung University, No. 1 University Road, Tainan, 701, Taiwan

    Jiunn-Jyh Wang

Authors
  1. Petr Hadraba
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  2. Jiunn-Jyh Wang
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  3. Zdenek Hadas
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Contributions

Petr Hadraba provided the analysis, experiment, and wrote the manuscript. Zdenek Hadas designed and supervised the experiment and manuscript preparation. Jiunn-Jyh Wang supervised the simulations and provide revision of the manuscript. The authors discussed together main ideas for this manuscript.

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Correspondence to Petr Hadraba.

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Hadraba, P., Wang, JJ. & Hadas, Z. Effects of nonlinear behaviour of linear ball guideway on chatter frequency of lathe machine tool. Int J Adv Manuf Technol 126, 225–240 (2023). https://doi.org/10.1007/s00170-023-11079-9

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  • DOI: https://doi.org/10.1007/s00170-023-11079-9

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