Reliability Optimization Design for Large Aerospace Planetary Mechanism Based on Hierarchical Finite Element

doi:10.3901/JME.2023.01.059

Abstract

Abstract: As the foundation and core of various heavy aircraft transmission systems, the reliability level of large-scale aviation planetary mechanism restricts the economic affordability and service safety for the aircraft to a great extent. A model of heavy helicopter planetary mechanism as the object of study, and aims to improve the fatigue reliability level of the system. The fatigue load history of the gear teeth under the coupling of global elastic behavior of the system is calculated using a hierarchical finite element method, and the probabilistic fatigue strength of gear teeth is fitted based on the gear low circumference fatigue test with the minimum order statistics transformation method to provide cost-effective load and strength input variables for the system reliability prediction model. Based on this, a mapping path from the key structural elements of large-scale aviation planetary mechanism to the system reliability indexes is established, and then a new method of reliability-driven multi-objective optimization design for planetary mechanism structural dimensions is proposed. Finally, the influence law of ring gear rim thickness and planet carrier baseplate thickness on the fatigue reliability of the planetary gear train is analyzed, and the results of the best stiffness matching between the rim and baseplate dimensions for the specified type of large aviation planetary mechanism can be obtained. The stiffness potential of the core structural elements is maximized as a way to balance the contradiction between reliability and lightweight requirements of large aviation planetary equipment.

Key words: planetary transmission, hierarchical analysis, finite element method, reliability modeling, fatigue test

CLC Number:

TH132

LI Ming, LUO Yuan, XIE Liyang. Reliability Optimization Design for Large Aerospace Planetary Mechanism Based on Hierarchical Finite Element[J]. Journal of Mechanical Engineering, 2023, 59(1): 59-70.

References

[1] 冯海生, 王黎钦, 彭波, 等. 高速大功率密度齿轮传动系统的干摩擦阻尼环减振特性研究[J]. 机械工程学报, 2017, 53(21):37-45. FENG Haisheng, WANG Liqin, PENG Bo, et al. Vibration damping characteristics of dry friction damping ring of high speed large power density gear transmission[J]. Journal of Mechanical Engineering, 2017, 53(21):37-45.
[2] 郝允志, 孙冬野, 林毓培, 等. 无级变速传动系统整体优化控制策略[J]. 机械工程学报, 2013, 49(12):84-91. HAO Yunzhi, SUN Dongye, LIN Yupei, et al. Overall optimization control strategy of continuously variable transmission system[J]. Journal of Mechanical Engineering, 2013, 49(12):84-91.
[3] LI M, XIE L, DING L. Load sharing analysis and reliability prediction for planetary gear train of helicopter[J]. Mechanism and Machine Theory, 2017, 115:97-113.
[4] XUE H L, LIU G, YANG X H, et al. Key technologies research of helicopter transmissions[J]. Applied Mechanics and Materials, 2015, 743:55-60.
[5] MCFARLAND J M, RIHA D S. Uncertainty quantification methods for helicopter fatigue reliability analysis[C]//65th Annual Forum Proceedings-AHS International, May 27-29, 2009. Grapevine, TX:American Helicopter Society. 2009, 2730-2737
[6] LI T, ZHAO Z, SUN C, et al. Adaptive channel weighted cnn with multisensor fusion for condition monitoring of helicopter transmission system[J]. IEEE Sensors Journal, 2020, 20(15):8364-8373.
[7] NEJAD A R, GAO Z, MOAN T. On long-term fatigue damage and reliability analysis of gears under wind loads in offshore wind turbine drivetrains[J]. International Journal of Fatigue, 2014, 61:116-128.
[8] 刘波, 安宗文. 考虑零件寿命相关的风电齿轮箱可靠性分析[J]. 机械工程学报, 2015, 51(10):164-171. LIU Bo, AN Zongwen. System reliability analysis of wind turbine gearbox considering component life dependency[J]. Journal of Mechanical Engineering, 2015, 51(10):164-171.
[9] LI Y F, VALLA S A, ZIO E. Reliability assessment of generic geared wind turbines by GTST-MLD model and Monte Carlo simulation[J]. Renewable Energy, 2015, 83:222-233.
[10] HUANG X, HU S, ZHANG Y, et al. A method to determine kinematic accuracy reliability of gear mechanisms with truncated random variables[J]. Mechanism and Machine theory, 2015, 92:200-212.
[11] CHEN J, CHEN L, QIAN L, et al. Time-dependent kinematic reliability analysis of gear mechanism based on sequential decoupling strategy and saddle-point approximation[J]. Reliability Engineering & System Safety, 2022, 220:108292.
[12] OLATUBOSUN S A, ZHANG Z. Dependency consideration of passive system reliability by coupled stress-strength interference/functional relations of parameters approach[J]. Reliability Engineering & System Safety, 2019, 188:549-560.
[13] CUI D, WANG G, LU Y, et al. Reliability design and optimization of the planetary gear by a GA based on the DEM and Kriging model[J]. Reliability Engineering & System Safety, 2020, 203:107074.
[14] NIU X P, ZHU S P, HE J C, et al. Fatigue reliability design and assessment of reactor pressure vessel structures:Concepts and validation[J]. International Journal of Fatigue, 2021, 153:106524.
[15] XIE L, LIU J, WU N, et al. Backwards statistical inference method for P-S-N curve fitting with small-sample experiment data[J]. International Journal of Fatigue, 2014, 63:62-67.
[16] ZHANG G, WANG G, LI X, et al. Global optimization of reliability design for large ball mill gear transmission based on the Kriging model and genetic algorithm[J]. Mechanism and Machine Theory, 2013, 69:321-336.
[17] 周志刚, 徐芳. 考虑强度退化和失效相关性的风电齿轮传动系统动态可靠性分析[J]. 机械工程学报, 2016, 52(11):80-87. ZHOU Zhigang, XU Fang. Dynamic reliability analysis of gear transmission system of wind turbine considering strength degradation and dependent failure[J]. Journal of Mechanical Engineering, 2016, 52(11):80-87.
[18] SUSMEL L. NOTCHES, Nominal stresses, fatigue strength reduction factors and constant/variable amplitude multiaxial fatigue loading[J]. International Journal of Fatigue, 2022:106941.
[19] AI Y, ZHU S P, LIAO D, et al. Probabilistic modeling of fatigue life distribution and size effect of components with random defects[J]. International Journal of Fatigue, 2019, 126:165-173.
[20] STRZELECKI P. Determination of fatigue life for low probability of failure for different stress levels using 3-parameter Weibull distribution[J]. International Journal of Fatigue, 2021, 145:106080.
[21] LI M, XIE L Y, LI H Y, et al. Life distribution transformation model of planetary gear system[J]. Chinese Journal of Mechanical Engineering, 2018, 31(1):1-8.
[22] CHEN J, LI W, SHENG L, et al. Study on reliability of shearer permanent magnet semi-direct drive gear transmission system[J]. International Journal of Fatigue, 2020, 132:105387.
[23] WANG H, ZHANG Y M, YANG Z. A reliability allocation method of CNC lathes based on copula failure correlation model[J]. Chinese Journal of Mechanical Engineering, 2018, 31(1):1-9.
[24] 周金宇, 韩文钦, 邱睿, 等. 结构系统疲劳失效相关机理与可靠性模型[J]. 机械工程学报, 2018, 54(16):220-226. ZHOU Jinyu, HAN Wenqin, QIU Rui, et al Dependence mechanism of fatigue failure and reliability model for structure systems[J]. Journal of Mechanical Engineering, 2018, 54(16):220-226.
[25] 苏长青, 张义民, 杜劲松. 具有相关失效模式转子系统的频率可靠性研究[J]. 机械工程学报, 2012, 48(6):175-179 SU Changqing, ZHANG Yimin, DU Jinsong. Frequency reliability analysis of rotor system with correlation failure modes[J]. Journal of Mechanical Engineering, 2012, 48(6):175-179.
[26] YAN Y. Load characteristic analysis and fatigue reliability prediction of wind turbine gear transmission system[J]. International Journal of Fatigue, 2020, 130:105259.
[27] WANG X, YANG Y, WANG W, et al. Simulating coupling behavior of spur gear meshing and fatigue crack propagation in tooth root[J]. International Journal of Fatigue, 2020, 134:105381.
[28] ZORKO D. Investigation on the high-cycle tooth bending fatigue and thermo-mechanical behavior of polymer gears with a progressive curved path of contact[J]. International Journal of Fatigue, 2021, 151:106394.
[29] VUČKOVIĆ K, ČULAR I, MAŠOVIĆ R, et al. Numerical model for bending fatigue life estimation of carburized spur gears with consideration of the adjacent tooth effect[J]. International Journal of Fatigue, 2021, 153:106515.
[30] CONRADO E, GORLA C, DAVOLI P, et al. A comparison of bending fatigue strength of carburized and nitrided gears for industrial applications[J]. Engineering Failure Analysis, 2017, 78:41-54.
[31] PENG C, XIAO Y, WANG Y, et al. Effect of laser shock peening on bending fatigue performance of AISI 9310 steel spur gear[J]. Optics and Laser Technology, 2017, 94:15-24.
[32] BLAIS P, TOUBAL L. Single-gear-tooth bending fatigue of HDPE reinforced with short natural fiber[J]. International Journal of Fatigue, 2020, 141:105857.
[33] BROWN M A, CHANG J H. Analytical techniques for helicopter component reliability[C]//Proceedings of the American Helicopter Society 64th Annual Forum. Montreal, April 29-May 1, 2008, Canada:American Helicopter Society International, 2008:563-573.