Skip to main content
SpringerLink
Log in

Accelerated life reliability evaluation of grating ruler for CNC machine tools based on competing risk model and incomplete data

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

Grating rulers are high-precision linear displacement sensors used in the servo control system of CNC machine tools. Due to the long lifetime of these rulers, evaluating their reliability level by using traditional methods takes huge amounts of time and resources. Meanwhile, some incomplete data are observed in the failure data, which will cause inaccurate evaluation results. In this study, an accelerated life reliability evaluation method of a grating ruler based on a competing risk model and incomplete data is proposed. Firstly, according to the characteristics of the grating ruler, the life distribution model based on competitive risk is established. The representation and conversion methods of failure data, considering incomplete data, are also proposed. Secondly, the accelerated life test (ALT) system is set up, and the 4500 h step stress ALT is conducted. Results indicate that the reliability level of the grating ruler is MTBFt = 8864.12 h, and that of each subsystem is MTBFt(MS) = 13,351.98 h, MTBFt(OS) = 14,283.48 h and MTBFt(ES) = 17,038.65 h. The advantages of the proposed method are that it is helpful in determining the subsystem with the highest failure rate in each stage and puts forward targeted suggestions for subsequent improvement designs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

Not applicable

References

  1. Fu GQ, Shi JH, Xie YP (2020) Closed-loop mode geometric error compensation of five-axis machine tools based on the correction of axes movements. J Adv Manuf Technol 110(1-2):365–382. https://doi.org/10.1007/s00170-020-05793-x

    Article  Google Scholar 

  2. Wang Y, Chen HY, Liu ZK (2016) Optical position sensor based on a digital wavelength-encoding grating ruler. Opt Eng 55(10):107103. https://doi.org/10.1117/1.OE.55.10.107103

    Article  Google Scholar 

  3. Han WN, Yu P, Li QL (2013) Design of grating displacement measuring system based on single chip microcomputer. Appl Math Mech 389:606–611. https://doi.org/10.4028/www.scientific.net/AMM.389.606

    Article  Google Scholar 

  4. Cheng Q, Feng QN, Liu ZF (2016) Sensitivity analysis of machining accuracy of multi-axis machine tool based on POE screw theory and Morris method. J Adv Manuf Technol 84(9):2301–2318. https://doi.org/10.1007/s00170-015-7791-x

    Article  Google Scholar 

  5. Merghache SM, Hamdi A (2020) Numerical evaluation of geometrical errors of three-axes CNC machine tool due to cutting forces-case: milling. J Adv Manuf Technol 111(5-6):1683–1705. https://doi.org/10.1007/s00170-020-06211-y

    Article  Google Scholar 

  6. Cheng Q, Qi BB, Liu ZF (2019) An accuracy degradation analysis of ball screw mechanism considering time-varying motion and loading working conditions. Mech Mach Theory 134:1–23. https://doi.org/10.1016/j.mechmachtheory.2018.12.024

    Article  Google Scholar 

  7. Cheng Q, Zhao HW, Zhao YS (2018) Machining accuracy reliability analysis of multi-axis machine tool based on Monte Carlo simulation. J Intell Manuf 29(1):191–209. https://doi.org/10.1007/s10845-015-1101-1

    Article  Google Scholar 

  8. Niu P, Cheng Q, Liu ZF (2021) A machining accuracy improvement approach for a horizontal machining center based on analysis of geometric error characteristics. J Adv Manuf Technol 112(9-10):2873–2887. https://doi.org/10.1007/s00170-020-06565-3

    Article  Google Scholar 

  9. Han D, Bai T (2021) Parameter estimation using EM algorithm for lifetimes from step-stress and constant-stress accelerated life tests with interval monitoring. IEEE Trans Reliab 70(1):49–64. https://doi.org/10.1109/TR.2019.2957710

    Article  Google Scholar 

  10. Wang LQ, Li YF (2017) Boundary for aviation bearing accelerated life test based on quasi-dynamic analysis. Tribol Int 116:414–421. https://doi.org/10.1016/j.triboint.2017.06.014

    Article  Google Scholar 

  11. You DZ, Pham H (2016) Self-adaptive stress accelerated life testing scheme. J Braz Soc Mech Sci 39(6):2095–2103. https://doi.org/10.1007/s40430-016-0683-7

    Article  Google Scholar 

  12. Zhou W, Wang M, Wu Q (2021) Accelerated life testing method of metallized film capacitors for inverter applications. IEEE Trans Transp Electr 7(1):37–49. https://doi.org/10.1109/TTE.2020.3021614

    Article  Google Scholar 

  13. Charki A, Laronde R, Guérin F (2011) Robustness evaluation using highly accelerated life testing. J Adv Manuf Technol 56(9):1253–1261. https://doi.org/10.1007/s00170-011-3264-z

    Article  Google Scholar 

  14. Ozturk UE (2016) A novel approach for accelerated life testing of ground vehicle components. Exp Tech 41(2):171–178. https://doi.org/10.1007/s40799-016-0166-x

    Article  Google Scholar 

  15. Park M, Rhee S (2018) A study on life evaluation & prediction of railway vehicle contactor based on accelerated life test data. J Mech Sci Technol 32(10):4621–4628. https://doi.org/10.1007/s12206-018-0909-y

    Article  Google Scholar 

  16. Wang L, Shi Y (2017) Estimation for constant-stress accelerated life test from generalized half-normal distribution. J Syst Eng Electron 28(4):810–816. https://doi.org/10.21629/JSEE.2017.04.21

    Article  Google Scholar 

  17. Lee JH, Cho HY (2018) An experimental study of the lifetime of a tripod shaft with torsional fatigue using an accelerated life test method. Int J Precis Eng Manuf 19(9):1399–1404. https://doi.org/10.1007/s12541-018-0165-1

    Article  Google Scholar 

  18. Dang C, Cote J, Leblanc P (2018) Accelerated aging test and life expectancy of reduced-wall high-stress MV TRXLPE cables. IEEE Trans Dielectr Electr Insul 25(3):1039–1046. https://doi.org/10.1109/TDEI.2018.006856

    Article  Google Scholar 

  19. Kalaiselvan C, Rao LB (2016) Accelerated life testing of nano ceramic capacitors and capacitor test boards using non-parametric method. Measurement 88:58–65. https://doi.org/10.1016/j.measurement.2016.03.035

    Article  Google Scholar 

  20. Rodriguez-Picon LA, Flores-Ochoa VH (2017) Estimation of a log-linear model for the reliability assessment of products under two stress variables. Int J Syst Assur Eng Manag 8(2):1026–1040. https://doi.org/10.1007/s13198-016-0564-6

    Article  Google Scholar 

  21. Liang QW, Wand DD (2018) Influence study of Weibull distribution parameter on double stress down-step accelerated life test. Indian J Mar Sci 47(1):46–52

    Google Scholar 

  22. Zhao XJ, Xu JY, Liu B (2018) Accelerated degradation tests planning with competing failure modes. IEEE Trans Reliab 67(1):142–155. https://doi.org/10.1109/TR.2017.2761025

    Article  Google Scholar 

  23. Yu ZY, Ren ZQ, Tao JY (2014) Accelerated testing with multiple failure modes under several temperature conditions. Math Probl Eng 2014:1–8. https://doi.org/10.1155/2014/839042

    Article  Google Scholar 

  24. Zhang CF, Shi YM, Wu M (2016) Statistical inference for competing risks model in step-stress partially accelerated life tests with progressively Type-I hybrid censored Weibull life data. J Comput Appl Math 297:65–74. https://doi.org/10.1016/j.cam.2015.11.002

    Article  MATH  Google Scholar 

  25. Luo W, Zhang C, Chen X (2015) Tan Y (2015) Accelerated reliability demonstration under competing failure modes. Reliab Eng Syst Saf 136:75–84. https://doi.org/10.1016/j.ress.2014.11.014

    Article  Google Scholar 

  26. Zhang CF, Shi YM, Bai XC (2017) Inference for constant-stress accelerated life tests with dependent competing risks from bivariate Birnbaum–Saunders distribution based on adaptive progressively hybrid censoring. IEEE Trans Reliab 66(1):111–122. https://doi.org/10.1109/TR.2016.2639583

    Article  Google Scholar 

  27. Yang ZJ, Li XX, Chen CH (2018) Reliability assessment of the spindle systems with a competing risk model. Proc Inst Mech Eng O J Risk Reliab 233(2):226–234. https://doi.org/10.1177/1748006X18770343

    Article  Google Scholar 

  28. Jiang L, Feng Q, Coit DW (2012) Reliability and maintenance modeling for dependent competing failure processes with shifting failure thresholds. IEEE Trans Reliab 61(4):932–948. https://doi.org/10.1109/TR.2012.2221016

    Article  Google Scholar 

  29. Gurauskis D, Kilikevicius A (2021) Thermal and geometric error compensation approach for an optical linear encoder. Sensors-Basel 21(2):360. https://doi.org/10.3390/s21020360

    Article  Google Scholar 

  30. Lin CT, Hsu YY, Lee SY (2019) Inference on constant stress accelerated life tests for log-location-scale lifetime distributions with type-I hybrid censoring. J Stat Comput Simul 89(4):720–749. https://doi.org/10.1080/00949655.2019.1571591

    Article  MATH  Google Scholar 

  31. Fan TH, Wang WL (2011) Accelerated life tests for Weibull series systems with masked data. IEEE Trans Reliab 60(3):557–569. https://doi.org/10.1109/TR.2011.2134270

    Article  Google Scholar 

  32. Ranjan R, Upadhyay SK (2016) Classical and Bayesian estimation for the parameters of a competing risk model based on minimum of exponential and gamma failures. IEEE Trans Reliab 65(3):1522–1535. https://doi.org/10.1109/TR.2016.2575439

    Article  Google Scholar 

  33. Chen WZ, Yang ZJ, Chen CH (2019) Load-dependent rotating performance of motorized spindles: measurement and evaluation using multi-zones error map. IEEE Access 7:180482–180490. https://doi.org/10.1109/ACCESS.2019.2957599

    Article  Google Scholar 

  34. Nassar M, Dey S (2018) Different estimation methods for exponentiated Rayleigh distribution under constant-stress accelerated life test. Qual Reliab Eng Int 34(8):1633–1645. https://doi.org/10.1002/qre.2349

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (51905209); Free Exploration Key Project of Natural Science Foundation of Jilin Province Science and Technology Development Plan, China (2020122332JC); Jilin Province Youth Scientific and Technological Talent Support Project (QT202114); and Science and Technology Research Project of Education Department of Jilin Province, China (Grant No. 42180).

Code availability

Not applicable

Author information

Authors and Affiliations

  1. Key Laboratory of CNC Equipment Reliability, Ministry of Education, Jilin University, Changchun, 130025, China

    Haiji Yang, Guofa Li, Jialong He, Liding Wang & Wei Zhang

  2. School of Mechanical and Aerospace Engineering, Jilin University, Changchun, 130025, China

    Haiji Yang, Guofa Li, Jialong He, Liding Wang & Wei Zhang

  3. School of Reliability and Systems Engineering, Beihang University, Beijing, 100191, China

    Yupeng Ma

Authors
  1. Haiji Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guofa Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jialong He
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yupeng Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Liding Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Wei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Haiji Yang: background research, data curation, software, validation, writing – original draft, editing

Guofa Li: methodology, review and editing, supervision

Jialong He: supervision, project administration, funding acquisition

Yupeng Ma: review and editing, supervision.

Liding Wang: supervision

Wei Zhang: assist in experiment, data curation

All authors read and approved the final manuscript.

Corresponding author

Correspondence to Jialong He.

Ethics declarations

Ethics approval and consent to participate

Not applicable

Consent for publication

Not applicable

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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, H., Li, G., He, J. et al. Accelerated life reliability evaluation of grating ruler for CNC machine tools based on competing risk model and incomplete data. Int J Adv Manuf Technol 124, 3725–3736 (2023). https://doi.org/10.1007/s00170-021-07627-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-021-07627-w

Keywords

Search

Navigation