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Fuzzy comprehensive performance evaluation method of rolling linear guide based on improved analytic hierarchy process

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Abstract

Aiming at the problem that the multi-objective evaluation of performance and the weighting coefficients of indexes is difficult to find, a fuzzy comprehensive performance evaluation method of rolling linear guide (RLG) is proposed. Considering the static and dynamic indexes, a structure model containing nine weighting coefficients was constructed. The performance evaluation function was established by the compromise programming method and the average power method, while weighting coefficients were determined by the improved analytic hierarchy process (I-AHP); the mathematical model was obtained to evaluate the RLG in a certain application. The evaluation results show that the confidence of the static, dynamic and comprehensive performance of the RLG is 59.21 %, 81.97 %, and 63.34 %, respectively. The feasibility of the method was verified by numerical simulation. This method indicates the pros and cons of the performance of the RLG and also indicates the direction for its optimized design.

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Abbreviations

C :

Basic rated dynamic load [N]

Cij :

Important relationship between factors i and j

CI :

Average random consistency index

CR :

Consistency comparison coefficient

D w :

Diameter of roller [mm]

E1, E2 :

Elastic modulus of carriage, rail, and ball [GPa]

f:

Maximum operating frequency of the machine tool [Hz]

f 0 :

Given parameter

f 2j :

J-th order natural frequency [Hz]

fmax,fmin :

Maximum and minimum natural frequencies [Hz]

F1, F2 :

Any applied load and previous load [N]

I :

Unit matrix

m :

Total number of stiffness considered

n :

Number of low-order natural frequencies considered

n max :

Maximum speed of the machine tool spindle [r/min]

nn :

Number of the roller in a groove

N :

Total number of roller

p :

Penalty coefficient

P m :

Base point

P :

Comparative matrix

q :

Given parameter

r i :

Ranking index (i = 1,2,…, n)

rmax, rmin :

Maximum and minimum stiffness of ranking index

S1i(k):

Vertical and horizontal stiffness (i = 1,2) [N/um]

Smax, Smin :

Maximum and minimum stiffness [N/um]

V1, V2 :

Poisson’s ratio of carriage, rail, and ball

ZB :

Middle preload [N]

β :

Contact angle [°]

δ1,δ2 :

Deformation at a certain load [um]

λ max :

Maximum eigenvalue

ω :

Corresponding eigenvector

ω i :

Weighting coefficients

ωij :

Weighting coefficients

ΔF :

Relative load

Δδ :

Relative deformation

References

  1. S. Shimizu, Load distribution and accuracy-rigidity of linear motion ball guides system: Theoretical verification for accuracy average effect, J. of the Japan Society for Precision Engineering, 57(10) (1991) 1814–1819.

    Article  Google Scholar 

  2. H. Ohta, Sound of linear guideway type recirculating linear ball bearings, J. of Tribology-transactions of the ASME, 121(4) (1999) 678–685.

    Article  Google Scholar 

  3. S. Shimizu, Stiffness analysis of precision machinery elements: Stiffness analysis of linear motion rolling guide, J. of the Japan Society for Precision Engineering, 64(11) (1998) 1573–1576.

    Article  Google Scholar 

  4. H. Ohta and K. Tanaka, Vertical stiffnesses of preloaded linear guideway type ball bearings incorporating the flexibility of the carriage and rail, J. of Tribology-transactions of the ASME, 132(1) (2010) 011102.

    Article  Google Scholar 

  5. W. Sun et al., Statics modeling and analysis of linear rolling guideway considering rolling balls contact, Proceedings of the Institution of Mechanical Engineers, Part C: J. of Mechanical Engineering Science, 229(1) (2015) 168–179.

    Google Scholar 

  6. J. S. Dhupia et al., Experimental identification of the nonlinear parameters of an industrial translational guide for machine performance evaluation, J. of Vibration and Control, 14(5) (2008) 645–668.

    Article  Google Scholar 

  7. H. Ohta and E. Hayashi, Vibration of linear guideway type recirculating linear ball bearings, J. of Sound and Vibration, 235(5) (2000) 847–861.

    Article  Google Scholar 

  8. J. F. Li et al., Dynamic characteristics of linear rolling guide joint based on contact stiffness, Advanced Materials Research (2012) 1342–1347.

  9. J. S. Wu, J. C. Chang and J. P. Hung, The effect of contact interface on dynamic characteristics of composite structures, Mathematics and Computers in Simulation, 74(6) (2007) 454–467.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. S. Wu et al., The effect of bending loads on the dynamic behaviors of a rolling guide, Journal of Mechanical Science and Technology, 26(3) (2012) 671–680.

    Article  Google Scholar 

  11. J. P. Hung, Load effect on the vibration characteristics of a stage with rolling guides, Journal of Mechanical Science and Technology, 23(1) (2009) 89–99.

    Article  Google Scholar 

  12. L. D. Zhu et al., Modeling and simulation of dynamic characteristics of the linear rolling guide in turn-milling center, Key Engineering Materials, 464 (2011) 358–361.

    Article  Google Scholar 

  13. S. W. Kwon, V. C. Tong and S. W. Hong, Five degrees of freedom model for static analysis of linear roller bearing subjected to external loading, Proceedings of the Institution of Mechanical Engineers, Part C: J. of Mechanical Engineering Science, 233(8) (2019) 2920–2938.

    Google Scholar 

  14. S. Maniraj and R. Thanigaivelan, Optimization of electrochemical micromachining process parameters for machining of amcs with different compositions of GGBS using Taguchi and TOPSIS methods, Transactions of The Indian Institute of Metals (2019) 1–10.

  15. K. L. Cheung et al., Optimizing usability of an economic decision support tool: Prototype of the equipt tool, International J. of Technology Assessment in Health Care, 34(1) (2018) 1–10.

    Article  Google Scholar 

  16. S. Evtiukov et al., Methods of accident reconstruction and investigation given the parameters of vehicle condition and road environment, Transportation Research Procedia, 20 (2017) 185–192.

    Article  Google Scholar 

  17. T. L. Saaty, How to make a decision: The analytic hierarchy process, Interfaces, 24(6) (1994) 19–43.

    Article  Google Scholar 

  18. T. L. Saaty and V. Ramanujam, An objective approach to faculty promotion and tenure by the analytic hierarchy process, Research in Higher Education, 18(3) (1983) 311–331.

    Article  Google Scholar 

  19. J. Hu et al., Risk assessment of seismic hazards in hydraulic fracturing areas based on fuzzy comprehensive evaluation and AHP method (FAHP): A case analysis of Shangluo area in Yibin City, Sichuan Province, China, J. of Petroleum Science and Engineering, 170 (2018) 797–812.

    Article  Google Scholar 

  20. L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965) 338–353.

    Article  MathSciNet  MATH  Google Scholar 

  21. Q. Xu et al., Optimum selection of tool materials for machining of high-strength steels based on fuzzy comprehensive evaluation method, Proceedings of the Institution of Mechanical Engineers, Part B: J. of Engineering Manufacture, 233(1) (2019) 145–153.

    Article  Google Scholar 

  22. F. Liu and Z. Y. Ma, Fuzzy comprehensive evaluation method for symmetry degree of mechanical structure symmetry, Transactions of the Canadian Society for Mechanical Engineering, 41(3) (2017) 337–353.

    Article  Google Scholar 

  23. Y. Guo et al., Reliability assessment for multi-source data of mechanical parts of civil aircraft based on the model, Journal of Mechanical Science and Technology, 33(7) (2019) 3205–3211.

    Article  Google Scholar 

  24. E. Ballestero, Utility functions: A compromise programming approach to specification and optimization, J. of Multi-criteria Decision Analysis, 6(1) (1997) 11–16.

    Article  MATH  Google Scholar 

  25. Z. D. Ma, N. Kikuchi and H. C. Cheng, Topological design for vibrating structures, Computer Methods in Applied Mechanics and Engineering, 121(1–4) (1995) 259–280.

    Article  MathSciNet  MATH  Google Scholar 

  26. J. Kreji, Fuzzy eigenvector method for obtaining normalized fuzzy weights from fuzzy pairwise comparison matrices, Fuzzy Sets and Systems, 315 (2017) 26–43.

    Article  MathSciNet  Google Scholar 

  27. T. L. Saaty and G. Hu, Ranking by eigenvector versus other methods in the analytic hierarchy process, Applied Mathematics Letters, 11(4) (1998) 121–125.

    Article  MathSciNet  MATH  Google Scholar 

  28. P. Pawelko, S. Berczynski and Z. Grzadziel, Modeling roller guides with preload, Archives of Civil and Mechanical Engineering, 14(4) (2014) 691–699.

    Article  Google Scholar 

  29. J. S. Wu et al., Characterization of the dynamic behavior of a linear guideway mechanism, Structural Engineering and Mechanics, 25(1) (2007) 1–20.

    Article  Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge the support of the National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2015ZX04014-021-03).

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Authors and Affiliations

  1. School of Mechanical Engineering, Dalian University of Technology, Dalian, Liaoning Province, 116024, China

    Yali Ma, Jiayong Wei, Cancan Li, Chen Liang & Guochao Liu

Authors
  1. Yali Ma
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  2. Jiayong Wei
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  3. Cancan Li
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  4. Chen Liang
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  5. Guochao Liu
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Corresponding author

Correspondence to Yali Ma.

Additional information

Recommended by Editor Seungjae Min

Yali Ma obtained her B.D., M.D., and Ph.D. in Mechanical Engineering from Dalian University of Technology, Liaoning, P.R. China. She is a Professor of Mechanical Engineering at Dalian University of Technology, and a member of China Mechanical Design Institute Committee. Her research interests include intelligent design, performance and structure collaborative optimization design.

Jiayong Wei, M.D., is affiliated in School of Mechanical Engineering, Dalian University of Technology, Liaoning, P.R. China. His research interests are structural optimization design and performance evalua-tion.

Cancan Li, M.D., is affiliated in School of Mechanical Engineering, Dalian University of Technology, Liaoning, P.R. China. His research interests are structural optimization design, digital design of mechanical equipment.

Chen Liang, M.D., is affiliated in School of Mechanical Engineering, Dalian University of Technology, Liaoning, P.R. China. His research interests are structural optimization design, digital design of mechanical equipment.

Guochao Liu, M.D., is affiliated in School of Mechanical Engineering, DLUT, Liaoning, P.R. China. His research interests are structural optimization design and performance evaluation.

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Ma, Y., Wei, J., Li, C. et al. Fuzzy comprehensive performance evaluation method of rolling linear guide based on improved analytic hierarchy process. J Mech Sci Technol 34, 2923–2932 (2020). https://doi.org/10.1007/s12206-020-0624-3

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  • DOI: https://doi.org/10.1007/s12206-020-0624-3

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