Abstract
This paper presents a dynamic reliability analysis method of rolling linear guide considering the uncertainty of geometric parameters. A three degree of freedom (DOF) dynamic motion model of rolling linear guide that considers the complexity of the actual load is established. In order to improve the accuracy of reliability evaluation, interval model is used to express the uncertainty of geometric parameters. The reliability range of dynamic response is determined according to the accuracy grade of rolling linear guide. The interval reliability calculation method is used to analyze and calculate the horizontal and vertical dynamic reliability of rolling linear guide. Then, the comprehensive dynamic reliability of rolling linear guide is obtained. Finally, the dynamic reliability of the SHS-45R rolling linear guide is analyzed by using the reliability evaluation method described in this paper. And the validity and accuracy of the result is demonstrated by comparing with the Monte Carlo simulation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Albertelli, N. Cau, G. Bianchi and M. Monno, The effects of dynamic interaction between machine tool subsystems on cutting process stability, The International Journal of Advanced Manufacturing Technology, 58(9–12) (2012) 923–932.
C. Y. Lin, J. P. Hung and T. L. Luo, Effect of preload of linear guides on dynamic characteristics of a vertical column-spindle system, International Journal of Machine Tools and Manufacture, 50(8) (2010) 741–746.
J. P. Hung, Y. L. Lai, C. Y. Lin and T. Z. Luo, Modeling the machining stability of a vertical milling machine under the influence of the preloaded linear guide, International Journal of Machine Tools and Manufacture, 51(9) (2011) 731–739.
Y. S. Yi, Y. Y. Kim, J. S. Choi, J. Yoo, D. J. Lee, S. W. Lee and S. J. Lee, Dynamic analysis of a linear motion rolling guide having rolling elements for precision positioning devices, Journal of Mechanical Science and Technology, 22(1) (2008) 50–60.
H. T. Zou and B. L. Wang, Investigation of the contact stiffness variation of linear rolling guides due to the effects of friction and wear during operation, Tribology International, 92 (2015) 472–484.
W. Tao, Y. Zhong, H. Feng and Y. Wang, Model for wear prediction of roller linear guides, Wear, 305(1–2) (2013) 260–266.
X. P. Li, Y. M. Liang, H. T. Yang, X. Ju and G. H. Zhao, Influence of bolt joint on dynamic characteristic of linear rolling guide, Applied Mechanics and Materials, 307 (2013) 182–185.
X. X. Kong, W. Sun, B. Wang and B. C. Wen, Dynamic and stability analysis of the linear guide with time-varying, piece-wise-nonlinear stiffness by multi-term incremental harmonic balance method, Journal of Sound and Vibration, 346(1) (2015) 265–283.
V. C. Tong, G. Khim, S. W. Hong and C. H. Park, Construction and validation of a theoretical model of the stiffness matrix of a linear ball rolling guide with consideration of carriage flexibility, Mechanism and Machine Theory, 140 (2019) 123–143.
G. I. Schuëller and H. A. Jensen, Computational methods in optimization considering uncertainties - an overview, Computer Methods in Applied Mechanics and Engineering, 198(1) (2008) 2–13.
S. S. Rao and P. K. Bhatti, Probabilistic approach to manipulator kinematics and dynamics, Reliability Engineering and System Safety, 72(1) (2001) 47–58.
C. Li, W. Wang, Y. Zhang, S. Guo, Z. Li and C. Qiao, Indexing accuracy reliability sensitivity analysis of power tool turret, Eksploatacja i Niezawodnosc-Maintenance and Reliability, 17(1) (2015) 27–34.
D. Zhou, X. Zhang and Y. Zhang, Dynamic reliability analysis for planetary gear system in shearer mechanisms, Mechanism and Machine Theory, 105 (2016) 244–259.
W. Wang, Y. M. Zhang and C. Y. Li, Dynamic reliability analysis of linear guides in positioning precision, Mechanism and Machine Theory, 116 (2017) 451–464.
S. Q. Qiu and H. X. G. Ming, Reliability analysis of multi-state series systems with performance sharing mechanism under epistemic uncertainty, Quality and Reliability Engineering International, 35(7) (2019) 1998–2015.
R. X. Wang, X. Gao, Z. Y. Gao, S. Q. Li, J. M. Gao, J. J. Xu and W. Deng, Comprehensive reliability evaluation of multistate complex electromechanical systems based on similarity of cloud models, Quality and Reliability Engineering International, 36(3) (2020) 1048–1073.
B. Möller and M. Beer, Engineering computation under uncertainty-capabilities of non-traditional models, Computers & Structures, 86(10) (2008) 1024–1041.
L. Zhang, J. G. Zhang, L. F. You and S. Zhou, Reliability analysis of structures based on a probability-uncertainty hybrid model, Quality and Reliability Engineering International, 35(4) (2019) 263–279.
Y. Ben-Haim, Convex Models of Uncertainty in Applied Mechanics, Elsevier Science Publishers, New York, USA (1990) 151–157.
J. Cheng, M. Y. Tang, Z. Y. Liu and J. R. Tan, Direct reliability-based design optimization of uncertain structures with interval parameters, Journal of Zhejiang University-Science A: Applied Physics & Engineering, 17(11) (2016) 841–854.
Z. Qiu, Comparison of static response of structures using convex models and interval analysis method, International Journal for Numerical Methods in Engineering, 56(12) (2003) 1735–1753.
C. Jiang, X. Han and G. R. Liu, Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval, Computer Methods in Applied Mechanics and Engineering, 196(49) (2007) 4791–4800.
J. L. Wu, Z. Luo, N. Zhang and Y. Q. Zhang, A new interval uncertain optimization method for structures using Chebyshev surrogate models, Computers & Structures, 146 (2015) 185–196.
J. Cheng, Z. Y. Liu, M. Y. Tang and J. R. Tan, Robust optimization of uncertain structures based on normalized violation degree of interval constraint, Computers & Structures, 182 (2017) 41–54.
X. G. Yu, X. Wang, X. T. Liu and Y. S. Wang, Reliability reallocation for cost uncertainty of fuel cell vehicles via improved differential evolution algorithm, Quality and Reliability Engineering International, 36 (2020) 303–314.
W. Wang, C. Y. Li, Y. X. Zhou, H. Wang and Y. M. Zhang, Nonlinear dynamic analysis for machine tool table system mounted on linear guides, Nonlinear Dynamics, 94(7) (2018) 2033–2045.
Z. T. Fu, X. M. Zhang, X. L. Wang and W. Y. Yang, Analytical modeling of chatter vibration in orthogonal cutting using a predictive force model, International Journal of Mechanical Sciences, 88(6) (2014) 145–153.
B. Li, X. Wang, Y. Hu and C. Li, Analytical prediction of cutting forces in orthogonal cutting using unequal division shear-zone model, The International Journal of Advanced Manufacturing Technology, 54(5–8) (2011) 431–443.
J. Gu, J. S. Agapiou and S. Kurgin, CNC machine tool work offset error compensation method, Journal of Manufacturing Systems, 37 (2015) 576–585.
H. Ohta and K. Tanaka, Vertical stiffnesses of preloaded linear guideway type ball bearings incorporating the flexibility of the carriage and rail, Journal of Tribology, 132(1) (2010) 547–548.
T. Harris, Rolling Bearing Analysis, Wiley, New York, USA (1991).
L. Bizarre, F. Nonato and K. L. Cavalca, Formulation of five degrees of freedom ball bearing model accounting for the nonlinear stiffness and damping of elastohydrodynamic point contacts, Mechanism and Machine Theory, 124 (2018) 179–196.
W. Wang, Y. M. Zhang, C. Y. Li, H. Wang and Y. X. Zhou, Effects of wear on dynamic characteristics and stability of linear guides, Meccanica, 52(111–12) (2017) 2899–2913.
R. E. Moore, Methods and Applications of Interval Analysis, SIAM, Philadelphia, USA (1979).
Z. P. Qiu and L. Wang, The need for introduction of non-probabilistic interval conceptions into structural analysis and design, Science China Physics, Mechanics & Astronomy, 59(11) (2016) 90–92.
C. M. Fu, Y. X. Liu and Z. Xiao, Interval differential evolution with dimension-reduction interval analysis method for uncertain optimization problems, Applied Mathematical Modelling, 69 (2019) 441–452.
Acknowledgments
This work was supported by the National Natural Science Foundation of China [Grant numbers 51705048 and 51835001].
Author information
Authors and Affiliations
Corresponding author
Additional information
Li Jian is currently pursuing the Ph.D. degree in Mechanical Engineering with Chongqing University. His research interests include reliability technology, failure analysis of CNC machine tool, and advanced manufacturing technology.
Ran Yan is currently a lecturer at Chongqing University, a fixed researcher at the State Key Laboratory of Mechanical Transmission, Chongqing University, a member of the Chongqing Science and Technology Association and a member of the National Association of Basic Research on Interchangeability and Measurement Technology. Her research interests include mechatronic product reliability technology and modern quality engineering.
Rights and permissions
About this article
Cite this article
Li, J., Ran, Y., Wang, H. et al. Dynamic performance reliability analysis of rolling linear guide under parameter uncertainty. J Mech Sci Technol 34, 4525–4536 (2020). https://doi.org/10.1007/s12206-020-1012-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-020-1012-8