Abstract
The contact state and stiffness of linear guide are affected by the complex external loads, and the vibrations in different directions are coupled with each other. However, existing dynamic models are inaccurate because they ignore displacement coupling and do not consider the position deviation of guide rail. This paper presents a five degree-of-freedom dynamic model for table system that incorporates the effects of the displacement coupling and position deviation of guide rail. The ball-to-groove contact model and position deviation model are established by using the Hertz contact theory and homogeneous coordinate transformation, respectively. Dynamic equations are solved by combining the Monte Carlo and Newmark methods to determine the displacements of table system, and the accuracy of proposed dynamic model is verified through experimental method. The results show that the vibrations of table system are coupled with each other, and the position deviation of guide rail only affects the vibration amplitudes in the region other than the resonance regions. Proposed model is thus suitable for improving the machining accuracy and stability of machine tools.
Similar content being viewed by others
Data availability
It declares that no data or materials are available for this research.
Code availability
It declares that codes are not available for this research.
References
Al-Bender F, Symens W (2005) Characterization of frictional hysteresis in ball-bearing guideways. Wear 258:1630–1642
He GY, Sun GM, Zhang HS, Huang C, Zhang D (2017) Hierarchical error model to estimate motion error of linear motion bearing table. Int J Adv Manuf Technol 93:1915–1927
Fujita T, Matsubara A, Yamazaki K (2011) Experimental characterization of disturbance force in a linear drive system with high-precision rolling guideways. Int J Mach Tools Manuf 51:104–111
Yang XJ, Lu D, Zhao WH (2018) Decoupling and effects of the mechanical vibration on the dynamic precision for the direct-driven machine tool. Int J Adv Manuf Technol 95:3243–3258
Li B, Luo B, Mao XY, Cai H, Peng FY, Liu HQ (2012) A new approach to identifying the dynamic behavior of CNC machine tools with respect to different worktable feed speeds. Int J Mach Tools Manuf 72:73–84
Yang HJ, Wang ZH, Zhang T, Du F (2020) A review on vibration analysis and control of machine tool feed drive systems. Int J Adv Manuf Technol 107:503–525
Kwon SW, Tong VC, Hong SW (2018) Five-degrees-of-freedom model for static analysis of linear roller bearing subjected to external loading. Proc Inst Mech Eng Part C-J Mech Eng Sci 0(0):1–19
Soleimanian P, Mohammadpour M, Ahmadian H (2020) Coupled tribo-dynamic modelling of linear guideways for high precision machining application. Proc Inst Mech Eng Part J-J Eng Tribol 0(0):1–27
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):011102
Pawełko P, Berczyński S, Grządziel Z (2014) Modeling roller guides with preload. Arch Civ Mech Eng 14(4):691–699
Dunaj P, Berczyński S, Pawełko P, Grządziel Z, Chodźko M (2019) Static condensation in modeling roller guides with preload. Arch Civil Mech Eng 19:1072–1082
Tong VC, Khim G, Hong SW, Park CH (2019) 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
Yang L, Wang L, Zhao WH (2020) Hybrid modeling and analysis of multidirectional variable stiffness of the linear rolling guideway under combined loads. Proc Inst Mech Eng Part C-J Mech Eng Sci 0(0):1–12
Sakai Y, Tanaka T (2020) Influence of lubricant on nonlinear vibration characteristics of linear rolling guideway. Tribol Int 144:106124
Zou HT, Wang BL (2015) 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
Wang W, Zhang YM, Li CY, Wang H, Zhou YX (2017) Effects of wear on dynamic characteristics and stability of linear guides. Meccanica 52:2899–2913
Wang W, Zhang YM, Li CY (2017) Dynamic reliability analysis of linear guides in positioning precision. Mech Mach Theory 116:451–464
Ohta H, Hayashi E (2000) Vibration of linear guideway type recirculating linear ball bearings. J Sound Vib 235(5):847–861
Ohta H, Kitajima Y, Kato S, Igarashi Y (2006) Effects of ball groupings on ball passage vibrations of a linear guideway type ball bearing (pitching and yawing ball passage vibrations). J Tribol 129:525–532
Kong XX, Sun W, Wang B, Wen BC (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 346:265–283
Li CY, Xu M, He G, Zhang H, Liu Z, He D, Zhang Y (2020) Time-dependent nonlinear dynamic model for linear guideway with crowning. Tribol Int 151:106413
Hung JP (2009) Load effect on the vibration characteristics of a stage with rolling guides. J Mech Sci Technol 23(1):89–99
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
Powałka B, Okulik T (2012) Dynamics of the guideway system founded on casting compound. Int J Adv Manuf Technol 59:1–7
Deng CY, Yin GF, Fang H, Meng ZY (2015) Dynamic characteristics optimization for a whole vertical machining center based on the configuration of joint stiffness. Int J Adv Manuf Technol 76:1225–1242
Deng CY, Liu Y, Zhao J, Wei B, Yin GF (2017) Analysis of the machine tool dynamic characteristics in manufacturing space based on the generalized dynamic response model. Int J Adv Manuf Technol 92:1411–1424
Wang W, Li CY, Zhou YX, Wang H, Zhang YM (2018) Nonlinear dynamic analysis for machine tool table system mounted on linear guides. Nonlinear Dyn 94:2033–2045
Li J, Xie FG, Liu XJ, Li WD, Zhu SW (2016) Geometric error identification and compensation of linear axes based on a novel 13-line method. Int J Adv Manuf Technol 87:2269–2283
Tang H, Duan JA, Zhao QC (2017) 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
Sun GM, He GY, Zhang DW, Sang YC, Zhang XL, Ding BH (2018) Effects of geometrical errors of guideways on the repeatability of positioning of linear axes of machine tools. Int J Adv Manuf Technol 98:2319–2333
Majda P (2012) Modeling of geometric errors of linear guideway and their influence on joint kinematic error in machine tools. Precis Eng 36(3):369–378
Deng YJ, Jin X, Zhang ZJ (2015) A macro–micro compensation method for straightness motion error and positioning error of an improved linear stage. Int J Adv Manuf Technol 80:1799–1806
Ma JX, Lu D, Zhao WH (2016) Assembly errors analysis of linear axis of CNC machine tool considering component deformation. Int J Adv Manuf Technol 86:281–289
Funding
This research was supported by National Natural Science Foundation of China (Grant No. 51775094).
Author information
Authors and Affiliations
Contributions
Chang Liu is responsible for the idea conception, algorithm implementation and validation, and manuscript writing; Chunyu Zhao and Bangchun Wen help analyze through constructive discussions.
Corresponding author
Ethics declarations
Ethics approval and consent to participate
The authors claim that there are no ethical issues involved in this research. All the authors consent to participate in this research and contribute to the research.
Consent for publication
This work is approved by all authors for publication.
Conflict of interest
The authors declare no competing interests.
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
Liu, C., Zhao, C. & Wen, B. Investigation on coupled vibration of machine tool table system with position deviations. Int J Adv Manuf Technol 114, 2321–2337 (2021). https://doi.org/10.1007/s00170-021-06874-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-021-06874-1