Skip to main content
SpringerLink
Log in

Time domain load extrapolation method for CNC machine tools based on GRA-POT model

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

Abstract

The load extrapolation is to obtain load data that may occur during the whole life cycle of product based on the limited measured load data, especially extreme load. Aiming at the two problems of traditional time domain extrapolation: without considering the interval time between extreme adjacent values and the high sensitivity of the peak over threshold (POT) model to the extreme threshold, a time domain load extrapolation method for computerized numerical control (CNC) machine tools based on Gray relational analysis-peak over threshold model (GRA-POT) is proposed. Firstly, for the first problem, an improved Markov chain Monte Carlo (MCMC) time domain load reconstruction method is proposed and analysis of reconstructed time domain load; secondly, according to the mean excess function (MEF) method, the extreme threshold range of POT model is determined and divided into multiple sets. The generalized Pareto distribution (GPD) fitting is performed for multiple sets of candidate load extreme samples. Finally, the Gray relational degrees (GRD) between each group of GPD and the median rank distribution are calculated by the Gray relational analysis (GRA), and the extreme threshold corresponding to the maximum GRD is selected as the optimal threshold of the POT model. The dynamic cutting force signal of CNC machine tool under constant speed cutting condition was reconstructed and extrapolated using the proposed method, and the dynamic cutting force spectrum of CNC machine tool was compiled. Case analysis results show that the POT extrapolation model with high fitting precision can be obtained using the proposed method. Furthermore, the precision of load spectrum of CNC machine tool is improved.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Klemenc J, Fajdiga M (2008) Improved modelling of the loading spectra using a mixture model approach. Int J Fatigue 30(7):1298–1313

    Article  MATH  Google Scholar 

  2. Liu C, Wu J, Li G, Tan G (2013) Frequency–spectrum characteristics of force in end milling with tool wear and eccentricity. Int J Adv Manuf Technol 67(1–4):925–938

    Article  Google Scholar 

  3. He J, Wang S, Li G, Yang Z, Hu L, Wu K (2018) Compilation of NC lathe dynamic cutting force spectrum based on two-dimensional mixture models. Int J Adv Manuf Technol 98(1–4):251–262

    Article  Google Scholar 

  4. Chen C, Yang Z, He J, Tian H, Li Z, Wang D (2017) Load spectrum generation of machining center based on rainflow counting method. J Vibroeng 19(8):5767–5779

    Article  Google Scholar 

  5. Roquet P, Javier G, Castilla R, Raush G, Codina E (2018) A simplified methodology to evaluate the design specifications of hydraulic components. Appl Sci 8(9):1–12

    Article  Google Scholar 

  6. He J, Yang Z, Chen C, Li G, Li Z, Jia H (2018) Improved multi-wavelet denoising with neighboring coefficients of cutting force for application in the load spectrum of computer numerical control lathe. Adv Mech Eng 10(2):1–11

    Article  Google Scholar 

  7. Wang J, Chen H, Li Y, Wu Y, Zhang Y (2016) A review of the extrapolation method in load Spectrum compiling. Stroj Vestn-J Mech E 62(1):60–75

    Article  Google Scholar 

  8. Johannesson P (2006) Extrapolation of load histories and spectra. Fatigue Fract Eng Mater Struct 29(3):209–217

    Article  Google Scholar 

  9. Cook NJ (1982) Towards better estimation of extreme winds. J Wind Eng Ind Aerodyn 9(3):295–323

    Article  Google Scholar 

  10. Carboni M, Cerrini A, Johannesson P, Guidetti M, Beretta S (2010) Load spectra analysis and reconstruction for hydraulic pump components. Fatigue Fract Eng Mater Struct 31(3–4):251–261

    Google Scholar 

  11. Fogle J, Agarwal P, Manuel L (2010) Towards an improved understanding of statistical extrapolation for wind turbine extreme loads. Wind Energy 11(6):613–635

    Article  Google Scholar 

  12. Ragan P, Manuel L (2008) Statistical extrapolation methods for estimating wind turbine extreme loads. J Sol Energ Eng 130(3):031011

    Article  Google Scholar 

  13. Balkema AA, Haan LD (1974) Residual life time at great age. Ann Probab 2(5):792–804

    Article  MathSciNet  MATH  Google Scholar 

  14. James P (1975) Statistical inference using extreme order statistics. Ann Stat 3(1):119–131

    Article  MathSciNet  MATH  Google Scholar 

  15. Gonzalez J, Rodriguez D, Sued M (2013) Threshold selection for extremes under a semiparametric model. Stat Methods Appl 22(4):481–500

    Article  MathSciNet  MATH  Google Scholar 

  16. Ghosh S, Resnick S (2010) A discussion on mean excess plots. Stoch Process Appl 120(8):1492–1517

    Article  MathSciNet  MATH  Google Scholar 

  17. Dumouchel W, Duncan G (1983) Using sample survey weights in multiple regression analyses of stratified samples. J Am Stat Assoc 78(383):535–543

    Article  MATH  Google Scholar 

  18. Wang J, Hu J, Wang N, Yao M, Wang Z (2012) Multi-criteria decision-making method-based approach to determine a proper level for extrapolation of Rainflow matrix. P I Mech Eng B: J Mec 226(5):1148–1161

    Article  Google Scholar 

  19. He J (2017) Compilation of cutting force spectrum of CNC lathe and its application in reliability test. Jilin University, Changchun (in Chinese)

    Google Scholar 

  20. Conover J, Jaeckel H, Kippola W (1967) Simulation of field loading in fatigue texting. SAE Trans 75(1):543–556

    Google Scholar 

  21. Abhang L, Hameedullah M (2012) Determination of optimum parameters for multi-performance characteristics in turning by using grey relational analysis. Int J Adv Manuf Technol 63(1–4):13–24

    Article  Google Scholar 

  22. Grimmett GR, Stirzaker DR (1992) Probability and random processes, 2nd edn. Oxford University Press

  23. Wang J, Wang N, Wang Z, Zhang Y, Liu L (2012) Determination of the minimum sample size for the transmission load of a wheel loader based on multi-criteria decision-making technology. J Terrramech 49(3–4):147–160

    Article  Google Scholar 

Download references

Funding

This work was supported by the Scientific and Technological Development Project of Jilin Province (Grant No. 20170204007G X), Industrial Technology Research and Development Project of Jilin Province (Grant No. 2019C040-2), Jilin Scientific and Technological Development Program (20180312042ZG), and Program for JLU Science and Technology Innovative Research Team (JLUSTIRT).

Author information

Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Jilin University, Changchun, 130022, Jilin, People’s Republic of China

    Jialong He, Xinyue Zhao, Guofa Li, Chuanhai Chen, Zhaojun Yang & Zhang Xinge

  2. Key Laboratory of Reliability Technology for CNC Equipment in Machinery Industry, Jilin University, Changchun, Jilin, People’s Republic of China

    Jialong He, Xinyue Zhao, Guofa Li, Chuanhai Chen, Zhaojun Yang & Zhang Xinge

  3. College of Computer Science and Technology, Jilin University, Changchun, 130022, Jilin, People’s Republic of China

    Jialong He & Liang Hu

Authors
  1. Jialong He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xinyue Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guofa Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chuanhai Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhaojun Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Liang Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Zhang Xinge
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Guofa Li or Chuanhai Chen.

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

He, J., Zhao, X., Li, G. et al. Time domain load extrapolation method for CNC machine tools based on GRA-POT model. Int J Adv Manuf Technol 103, 3799–3812 (2019). https://doi.org/10.1007/s00170-019-03774-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-019-03774-3

Keywords

Search

Navigation