Belief reliability modeling and analysis for planetary reducer considering multi-source uncertainties and wear

doi:10.23919/JSEE.2021.000106

Journal of Systems Engineering and Electronics ›› 2021, Vol. 32 ›› Issue (5): 1246-1262.doi: 10.23919/JSEE.2021.000106

• RELIABILITY • Previous Articles

Belief reliability modeling and analysis for planetary reducer considering multi-source uncertainties and wear

Yun LI¹(), Kaige JIANG^2,³(), Ting ZENG¹(), Wenbin CHEN^2,^3,*(), Xiaoyang LI^2,³(), Deyong LI¹(), Zhiqiang ZHANG¹()

¹ Beijing Spacecraft Manufacturing Co., Ltd, China Academy of Space Technology, Beijing 100094, China
² School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
³ Science and Technology on Reliability and Environmental Engineering Laboratory, Beijing 100191, China

Received:2020-08-28 Online:2021-10-18 Published:2021-11-04
Contact: Wenbin CHEN E-mail:handanliyun@126.com;jiangkaige@buaa.edu.cn;zitty@sina.com;chenwenbin@buaa.edu.cn;leexy@buaa.edu.cn;lideyong120@126.com;zhiqianglesurmoi@163.com
About author:|LI Yun was born in 1979. He received his B.S. degree in mechanical engineering from Hebei Normal University of Science & Technology, Qinhuangdao, China, in 2003, M.S. degree in mechanical engineering from Beijing University of Technology, Beijing, China, in 2011, and Ph.D. degree in mechanical engineering from Beijing University of Technology, Beijing, China, in 2014. From 2001 to 2009, he was an engineer with the China HI-TECH Group Corporation. Since 2014, he has been a senior engineer with Beijing Spacecraft Manufacturing Co., Ltd, China Academy of Space Technology. He is the author of more than 30 articles, and more than 10 inventions. His research interests are reliability technology of space mechanism system and precision assembly technology of space mechanism. E-mail: handanliyun@126.com||JIANG Kaige was born in 1998. She received her B.S. degree in quality and reliability engineering from Beihang University, Beijing, China in 2020. She is currently pursuing her M.S. degree at the School of Reliability and Systems Engineering, Beihang University, Beijing, China. Her research interest is reliability modeling. E-mail: jiangkaige@buaa.edu.cn||ZENG Ting was born in 1981. He received his M.S. degree in mechanical design and automation from Wuhan University of Technology, Hubei, China in 2009. He is currently a senior engineer with Beijing Spacecraft Manufacturing Co., Ltd, China Academy of Space Technology. His research interests are space mechanism design and advanced manufacturing technology. E-mail: zitty@sina.com||CHEN Wenbin was born in 1993. He received his B.S. degree in quality and reliability engineering from Beihang University, Beijing, China in 2016. He is currently pursuing his Ph.D. degree at the School of Reliability and Systems Engineering, Beihang University, Beijing, China. His research interests are belief reliability theory, reliability modeling in complex physical systems, and accelerated degradation testing. E-mail: chenwenbin@buaa.edu.cn||LI Xiaoyang was born in 1980. She is currently a professor at the School of Reliability and Systems Engineering, Beihang University. She received her Ph.D. degree in systems engineering from Beihang University in 2007 and visited the Intelligent Maintenance Systems Center of University of Cincinnati from 2010 to 2011. Her research interests are reliability experiment modeling and resilience modeling and evaluation. E-mail: leexy@buaa.edu.cn||LI Deyong was born in 1987. He received his M.S. degree in engineering from Beihang University, Beijing, China in 2014. He is currently a senior engineer with Beijing Spacecraft Manufacturing Co., Ltd, China Academy of Space Technology. His research interests are assembly test of large space deployable mechanism and simulation development direction of microgravity. E-mail: lideyong120@126.com||ZHANG Zhiqiang was born in 1993. He received his B.S. degree in engineering from Beijing Institute of Technology in 2015 and Ph.D. degree in engineering from Beijing Institute of Technology in 2020. He is currently an engineer with Beijing Spacecraft Manufacturing Co., Ltd, China Academy of Space Technology. His research interests are analysis of assembly accuracy and assembly of space mechanism. E-mail: zhiqianglesurmoi@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (51775020; 51875019) and the Fundamental Research Funds for the Central Universities (YWF-20-BJ-J-515).

Abstract

Abstract:

The planetary reducer is a common type of transmission mechanism, which can provide high transmission accuracy and has been widely used, and it is usually required with high reliability of transmission characteristics in practice. During the manufacturing and usage stages of planetary reducers, uncertainties are ubiquitous and wear is inevitable, which affect the transmission characteristics and the reliability of planetary reducers. In this paper, belief reliability modeling and analysis considering multi-uncertainties and wear are proposed for planetary reducers. Firstly, based on the functional principle and the influence of wear, the performance margin degradation model is established using the hysteresis error as the key performance parameter, where the degradation is mainly caused by the accumulated wear. After that, multi-source uncertainties are analyzed and quantified separately, including manufacturing errors, uncertainties in operational and environmental conditions, and uncertainties in performance thresholds. Finally, the belief reliability model is established based on the performance margin degradation model. A case study of a planetary reducer is applied and the reliability sensitivity analysis is implemented to show the practicability of the proposed method. The results show that the proposed method can provide some suggestions to the design and manufacturing phases of the planetary reducer.

Key words: belief reliability, planetary reducer, performance margin, wear, multi-source uncertainty

Yun LI, Kaige JIANG, Ting ZENG, Wenbin CHEN, Xiaoyang LI, Deyong LI, Zhiqiang ZHANG. Belief reliability modeling and analysis for planetary reducer considering multi-source uncertainties and wear[J]. Journal of Systems Engineering and Electronics, 2021, 32(5): 1246-1262.

Figures/Tables 22

Fig 1

Fig 2

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Fig 4

Table 1

Distributions of the manufacturing errors"

Parameter	Distribution	Parameter	Distribution
$ {j_{tEM - a}} $	$ N\left( {\dfrac{1}{2} \left( {{E_{sns - a}} + {E_{sni - a}}} \right),{{\left[ {\dfrac{1}{6} \left( {{E_{sns - a}} - {E_{sni - a}}} \right)} \right]}^2}} \right) $	$ {j_{tKea - c}} $	$ N\left( {0,{{\left[ {\dfrac{1}{3} {t_{Kea}}\tan \alpha } \right]}^2}} \right) $
$ {j_{tEM - b}} $	$ N\left( {\dfrac{1}{2} \left( {{E_{sns - b}} + {E_{sni - b}}} \right),{{\left[ {\dfrac{1}{6} \left( {{E_{sns - b}} - {E_{sni - b}}} \right)} \right]}^2}} \right) $	$ {j_{t\Delta r}} $	$ N\left( {\left( {{\Delta _{r\max }} - {\Delta _{r\min }}} \right)\tan \alpha ,{{\left[ {\dfrac{1}{3} \left( {{\Delta _{r\max }} - {\Delta _{r\min }}} \right)\tan \alpha } \right]}^2}} \right) $
$ {j_{tEM - c}} $	$ N\left( {\dfrac{1}{2} \left( {{E_{sns - c}} + {E_{sni - c}}} \right),{{\left[ {\dfrac{1}{6} \left( {{E_{sns - c}} - {E_{sni - c}}} \right)} \right]}^2}} \right) $	$ {j_{t\Delta rcp}} $	$ N\left( {\dfrac{{\text{1}}}{{\text{2}}}\left( {{T_D} + {T_d} - 2es} \right)\tan \alpha ,{{\left[ {\dfrac{1}{6} \sqrt {T_D^2 + T_d^2} \tan \alpha } \right]}^2}} \right) $
$ {e_{g - a}} $	$ N\left( {{\text{0 }},{\text{ }}{{\left( {\dfrac{1}{6}{F_{r - a}}} \right)}^2}} \right) $	$ {\alpha _{T - a}} $	$ N\left( {{\mu _{\alpha T - a}}{\text{,}}{{\left( {{c_{\alpha T - a}} \cdot {\mu _{\alpha T - a}}} \right)}^2}} \right) $
$ {e_{g - b}} $	$ N\left( {{\text{0 }},{\text{ }}{{\left( {\dfrac{1}{6}{F_{r - b}}} \right)}^2}} \right) $	$ {\alpha _{T - b}} $	$ N\left( {{\mu _{\alpha T - b}},{{\left( {{c_{\alpha T - b}} \cdot {\mu _{\alpha T - b}}} \right)}^2}} \right) $
$ {\varphi _a} $	$ U\left( {0,2{\rm{{\text{π}}}} } \right) $	$ {\alpha _{T - c}} $	$ N\left( {{\mu _{\alpha T - c}},{{\left( {{c_{\alpha T - c}} \cdot {\mu _{\alpha T - c}}} \right)}^2}} \right) $
$ {\varphi _b} $	$ U\left( {0,2{\rm{{\text{π}}}} } \right) $	$ {\alpha _{T - H}} $	$ N\left( {{\mu _{\alpha T - H}},{{\left( {{c_{\alpha T - H}} \cdot {\mu _{\alpha T - H}}} \right)}^2}} \right) $

Table 1

Table 2

Table 3

Table 4

Fig 5

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Fig 7

Fig 8

Fig 9

Fig 10

Fig 11

Fig 12

Fig 13

Fig 14

Fig 15

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Fig 17

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Parameter	Distribution
$ T $	$ N\left( {{\mu _T},{{\left( {{c_T} \cdot {\mu _T}} \right)}^2}} \right) $
$ w $	$ N\left( {{\mu _w},{{\left( {{c_w} \cdot {\mu _w}} \right)}^2}} \right) $

Physical parameter	Z_a	Z_b	Z_c	α/(°)	m/mm	$i_{aH}^b $
Value	26	76	25	20	0.5	3.923

Belief reliability modeling and analysis for planetary reducer considering multi-source uncertainties and wear

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