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

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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.

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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


PDF of theoretical distribution of stress


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


PDF of theoretical distribution of strength


PDF of two-end truncated distribution of strength


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


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 :


s (r) :

r-th order statistic

t :


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 :


δ 0 :

Initial strength


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


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

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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.

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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).

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