Skip to main content
Log in

The time varying reliability analysis for space focusing mechanism based on probability model

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

Compared with the ground focusing mechanism, the working environment of space focusing mechanism is more harsh and complicated. Hence the accurate prediction of its reliability is indispensable. However, it is unrealistic to obtain sample parameters of reliability analysis through repeated entity tests, due to the limitation of project cost and timetable, which lead to many existing model cannot be applied directly. We focus on a screw guide type space focusing mechanism, and propose a new time varying reliability probabilistic model that can characterize the reliability of discontinuous motion mechanisms with discrete multi-load. Its primary uncertainties and failure modes are evaluated quantitatively by failure mode effects analysis. The total damage of intermittent operation is treated as accumulative effect caused by each focusing work. And main parameters of the model are obtained by analytical calculation of mechanism wear reliability model. Finally, an integrated theoretical method are constructed and verified in this article, and the time varying reliability of proposed focusing mechanism are also discussed.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

Abbreviations

A :

Contact point of ball and nut

B :

Contact point of ball and screw

C :

Fatigue strength constant

\({C_{{\sigma _{- 1e}}}}\) :

Variation coefficient

d 0 :

Nominal diameter of screw

D ws :

Pitch radius of screw

f :

Fatigue experiment constant

F α :

Axial force on nut

F na, F nb :

Normal stress of contact point

f n(n | s):

Distribution of fatigue life under fatigue load s

f r(s (r)):

PDF of r-th order statistic

f(s):

PDF of theoretical distribution of stress

f′(s):

PDF of two-end truncated distribution of stress

f x(t)(x):

PDF of strength degradation at time t

F x(t)(x):

CDF of strength degradation at time t

F x(t)|k(x):

CDF of strength degradation when k times impacts occur within time t

f x(t)(δ 0δ, t):

PDF of strength degradation

g(δ):

PDF of theoretical distribution of strength

g′(δ):

PDF of two-end truncated distribution of strength

g(δ,t):

PDF of residual strength

g 0(δ 0):

PDF of initial strength

K :

Wear coefficient

k :

Number of impacts

\({K_\alpha}\left({{\mu _{{K_\alpha}}},{\sigma _{{K_\alpha}}}} \right)\) :

Effective stress concentration factor distribution

K f, K g :

Regularization constant

N :

Fatigue life

N(t):

Counting process describing time interval

P h :

Nominal lead

R :

Reliability probability

r b :

Radius of ball

r n :

Radius of nut raceway

r s :

Radius of screw raceway

S :

Stress

s (r) :

r-th order statistic

t :

Time

W k :

Single degradation

W (k)(x):

Stieltjes convolution of CDF of single degradation X(t): Strength degradation at time t

Z k :

Time interval

Z (k)(t):

Stieltjes convolution of CDF of time interval

α A, α B :

Contact angle of contact point

α 0 :

Initial contact angle

β(μ β,σ β):

Surface processing coefficient distribution

δ :

Strength

δ 0 :

Initial strength

δ(t):

Residual strength at time t

ε(μ ε, σ ε):

Size coefficient distribution

\({\mu _{{\sigma _{- 1e}}}}\) :

Median fatigue limit

\({\sigma _r}\left({{\mu _{{\sigma _r}}},{\sigma _{{\sigma _r}}}} \right)\) :

Fatigue limit distribution of material

\({\sigma _{re}}\left({{\mu _{{\sigma _{re}}}},{\sigma _{{\sigma _{re}}}}} \right)\) :

Fatigue limit distribution of part

φ :

Lead angle

References

  1. H.-D. Chen, Y.-H. Chen and T.-T. Shi, Error analysis for focusing mechanism of space camera, Optics and Precision Engineering, 5(21) (2013) 1349–1356.

    Article  Google Scholar 

  2. C. Gong and D. M. Frangopol, An efficient time-dependent reliability method, Structural Safety, 81(11) (2019) 101864.

    Article  Google Scholar 

  3. H. Qi, Research on mechanism reliability of space remote-sensing camera, Doctoral Dissertation, University of Chinese Academy of Sciences, China (2017).

    Google Scholar 

  4. L. Wang, J. Liu and Y. Li, The optimal controller design framework for PID-based vibration active control systems via non-probabilistic time-dependent reliability measure, ISA Transactions, 105 (2020) 129–145.

    Article  Google Scholar 

  5. L. Wang, J. Liu, C. Yang and D. Wu, Novel interval dynamic reliability computation approach for the risk evaluation of vibration active control systems based on PID controllers, Applied Mathematical Modelling, 92 (2021) 422–446.

    Article  MATH  MathSciNet  Google Scholar 

  6. L. Shi, Research on reliability modeling and evaluation methods for key components of aircraft, Master’s Thesis, Xi’an University of Technology, China (2018).

    Google Scholar 

  7. Z. Yang et al., Dynamic reliability analysis of mechanical parts under actual operation conditions, Journal of Northeastern University (Natural Science), 11 (2019) 1584–1589.

    Google Scholar 

  8. Y. Li, H. Huang and Y. Huang, Failure mode and effects analysis and time varying reliability of solar array drive assembly, Journal of Mechanical Engineering, 12 (2019) 23–26.

    Google Scholar 

  9. Y. Huang, The time varying reliability of solar array drive assembly, Master’s Thesis, University of Electronic Science and Technology of China, China (2018).

    Google Scholar 

  10. H. Zhang, Surface precision measurement, space thermal, reliability and clearance effect analysis of deployable space antennas, Doctoral Dissertation, Zhejiang University, China (2010).

    Google Scholar 

  11. T. B. André and E. M. Robert, On the ensemble crossing rate approach to time variant reliability analysis of uncertain structures, Probabilistic Engineering Mechanics, 1(19) (2004) 9–19.

    Google Scholar 

  12. M. Ebrahimian, A. Pirouzmand and A. Rabiee, Developing a method for time-variant reliability assessment of passive heat removal systems in nuclear power plants, Annals of Nuclear Energy, 10(160) (2021) 108365.

    Article  Google Scholar 

  13. SAE International S-18 Committee, ARP4754A, Guidelines for Development of Civil Aircraft and Systems, Society of Automotive Engineers, Warrendale (2010).

  14. SAE International S-18 Committee, ARP4761, Guidelines and Methods for Conducting the Safety Assessment Process on Civil Airborne System and Equipment, Society of Automotive Engineers, Warrendale (1996).

    Google Scholar 

  15. K. Durga Rao et al., Dynamic fault tree analysis using Monte Carlo simulation in probabilistic safety assessment, Reliability Engineering and System Safety, 94 (2009) 872–883.

    Article  Google Scholar 

  16. X. Jia et al., Design and experiment research on precision focusing mechanism of space remote sensor, Journal of Mechanical Engineering, 7(52) (2016) 25–30.

    Article  Google Scholar 

  17. P. Cheng and M. Wu, Research on dynamic characteristics of space camera focusing platform, Opt. Precision Eng., 3 (2019) 602–609.

    Article  Google Scholar 

  18. Z. Wang, L. Xie and B. Li, Time-dependent reliability models of systems with common cause failure, International Journal of Performability Engineering, 3(4) (2007) 419–432.

    Google Scholar 

  19. Z. Zhou et al., Study on dynamic characteristics of wind turbine planetary gear system coupled with bearing at varying wind speed, Applied Mechanics and Materials, 1414 (2011) 653–657.

    Article  Google Scholar 

  20. Y. Dai, Z. Han and H. Zhu, FMEA Theories and methodsreview on research progress, China Quality, 10 (2007) 23–26.

    Google Scholar 

  21. C. Su et al., A time-dependent probabilistic fatigue analysis method considering stochastic loadings and strength degradation, Advances in Mechanical Engineering, 10 (2018) 1–9.

    Article  Google Scholar 

  22. W. Huang and R. G. Askin, A generalized SSI reliability model considering stochastic loading and strength aging degradation, IEEE T. Reliab., 53 (2004) 77–82.

    Article  Google Scholar 

  23. J. Li and G. Thompson, A method to take account of inhomogeneity in mechanical component reliability calculation, IEEE Transaction on Reliability, 54(3) (2005) 159–168.

    Article  Google Scholar 

  24. O. Ditlevsen, Stochastic model for joint wave and wind loads on offshore structures, Strutural Safety, 24 (2002) 139–163.

    Article  Google Scholar 

  25. X. Yuan, Stochastic modeling of deterioration in nuclear power plant components, Doctoral Dissertations, University of Waterloo, Canada (2007).

    Google Scholar 

  26. Z. Xu and W. Xie, A modified residual strength prediction method for aluminum alloy plates with MSD, Mechanics Research Communications, 109(10) (2020) 103584.

    Article  Google Scholar 

  27. X. Xu et al., Wear prediction of ball screw using archard’s model, Modular Machine Tool and Automatic Manufacturing Technique, 2(2) (2016) 54–59.

    Google Scholar 

  28. D. Straub, R. Schneider, E. Bismuta and H.-J. Kim, Reliability analysis of deteriorating structural systems, Structural Safety, 82 (2020) 101877.

    Article  Google Scholar 

  29. H. Qi, J. Guo and M. Shao, Design of focusing mechanism of space camera with high reliability and high precision, Revista de la Facultad de Ingeniería, 31(9) (2016) 176–185.

    Google Scholar 

Download references

Acknowledgments

The study is supported partially by the National Natural Science Foundation of China (Grant Nos.: 61427811). The support is gratefully acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Mengyuan Wu or Chuang Li.

Additional information

Cheng Penghui received the Ph.D. degree from the University of Chinese Academy of Sciences in 2022. His main research areas have been within space mechanical design, dynamic analysis, reliability analysis, and space camera design.

Wu Mengyuan, a Senior Engineer and Master’s Supervisor, received his Ph.D. degree from the University of Chinese Academy of Sciences in 2012. He is working at the Xian Institute of Optics and Precision Mechanics, Chinese Academy of Sciences. His main research areas have been within space optical remote sensor design, mechanical design and analysis, dynamics of transmission mechanism, etc. He has been responsible for or participated in a number of important research projects of national ministries.

Li Chuang, a Senior Engineer, Ph.D. Supervisor, received his Ph.D. degree from the Xi’an Jiaotong University in 2005. His main research areas have been within precision structure and mechanism of space camera, space optical detection and imaging. In recent years, he has been responsible for or participated in more than 10 important research projects of national ministries. He has published more than 40 academic papers and obtained more than 30 patents.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheng, P., Wu, M. & Li, C. The time varying reliability analysis for space focusing mechanism based on probability model. J Mech Sci Technol 36, 5587–5597 (2022). https://doi.org/10.1007/s12206-022-1022-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-022-1022-9

Keywords

Navigation