内齿圈的轮缘柔性会显著影响行星传动在轮齿啮合层面和系统功率分流层面上的力学性能,是决定大型航空行星系统服役可靠性水平的关键设计因素之一。为了分析内齿圈的轮缘柔性对行星系统疲劳可靠性的影响方式及程度,在应力-强度干涉理论框架下,基于全概率公式计算原理构建了行星系统可靠性评估模型,并利用集中质量有限元法和轮齿概率寿命转化试验分别为可靠性模型提供载荷和强度输入变量。最终,建立了从轮缘厚度到行星系统可靠性指标的映射关系,准确地确定了在质量约束下可靠性增益效果最优的内齿圈轮缘厚度尺寸,为大型航空行星系统的疲劳可靠性设计提供了技术储备。
The flexibility of the ring gear plays a crucial role in the mechanical properties of planetary transmission. It affects both the tooth meshing level and the system power split level, making it one of the most important design factors in ensuring the service reliability of large aerospace planetary mechanisms. In order to analyze the way and extent to which the rim flexi-bility of the ring gear affects the fatigue reliability of the planetary system. In this study, a planetary system reliability as-sessment model is developed using the stress-strength interference theory and the full probability formula calculation. The model incorporates load and strength input variables obtained through the lumped mass finite element method and probabilistic life transformation test of the gear teeth. Finally, the mapping relationship between rim thickness and the reli-ability index of the planetary system is established, and the thickness range of the ring gear rim with the best reliability gain effect under the mass constraint is accurately determined, which provides a technical reserve for the fatigue reliabil-ity design of large aviation planetary systems.
[1]ASTRIDGE D G.Helicopter transmissions—design for safety and reliability[J].Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2016, 203(2):123-38
[2]许华超, 秦大同.内激励下弹性边界柔性直齿内齿圈振动响应研究[J].机械工程学报, 2018, 54(09):161-167
[3]XU H C,QIN D T.Vibration Response of FlexibleSpur Ring Gear with Elastic Foundation under Internal Excitation[J].Journal of Mechanical Engineering, 2018, 54(16):161-167
[4]WANG C, ZHANG X, ZHOU J, et al.Calculation method of dynamic stress of flexible ring gear and dynamic characteristics analysis of thin-walled ring gear of planetary gear train[J].Journal of Vibration Engineering & Technologies, 2020, 9(5):751-66
[5]李铭, 罗源, 谢里阳.基于层级有限元法的大型航空行星机构可靠性优化设计[J].机械工程报, 2023, 59(01):59-70
[6]LI M,LUO Y,XIE L Y.Reliability optimizationdesign for large aerospace planetary mechanism base d on hierarchical finite element[J].Journal of Mech anical Engineering, 2023, 59(01):59-70
[7]Duan T, Zhang A, Wei J, et al.Effects of crack and structural flexibility on planetary gear[J].Journal of Sound and Vibration, , :-
[8]system faultfeature considering ring gear boundary condition[J].Engineering Failure
[9]Analysis, 2023, 149:107245.
[10]Guan X, Tang J, Hu Z, et al.Dynamic analysis of spur gear pair established by flexible ring and time-varying mesh model[J]. Journal of the Brazilian Society of Mechanical Sciences and
[11]Engineering, 2022, 44(4):159.
[12]KAHRAMAN A, KHARAZI A A, UMRANI M.A deformable body dynamic analysis of planetary gearswith thin rims[J].Journal of Sound and Vibration, 2003, 262(3):752-68
[13]ABOUSLEIMAN V, VELEX P, BECQUERELLE S.Modeling of spur and helical gear planetary drives with flexible ring gears and planet carriers[J].Journal of Mechanical Design, 2007, 129(1):95-106
[14]ABOUSLEIMAN V, VELEX P.A hybrid 3D finite elementlumped parameter model for quasi-static and dynamic analyses of planetaryepicyclic gear sets[J].Mechanism and Machine Theory, 2006, 41(6):725-48
[15]HU Y, TALBOT D, KAHRAMAN A.A gear load distribution model for a planetary gear set with a flexible ring gear having external splines[J]. Journal of Mechanical Design, 2019, 141(5).
[16]CHEN Z, SHAO Y.Mesh stiffness of an internal spur gear pair with ring gear rim deformation[J]. Mechanism and Machine Theory, 2013, 69:1-12.
[17]CHEN Z, SHAO Y, SU D.Dynamic simulation of planetary gear set with flexible spur ring gear[J].Journal of Sound and Vibration, 2013, 332(26):7191-204
[18]CHEN Z, ZHU Z, SHAO Y.Fault feature analysis of planetary gear system with tooth root crack and flexible ring gear rim[J]. Engineering Failure Analysis, 2015, 49:92-103.
[19]YAN Y.Load characteristic analysis and fatigue reliability prediction of wind turbine gear transmission system[J]. International Journal of Fatigue, 2020, 130:9.
[20]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(Complete):321-36
[21]王正, 王增全.基于应力-强度干涉的车用发动机机械零部件寿命计算方法[J].机械工程学报, 2014, 50(16):47-53
[22]WANG Z,WANG Z Q.Method for calculating the B10 reliable life of mechanical components of vehicle engine based on the stress-strength interference[J].Journal of Mechanical Engineering, 2014, 50(16):47-53
[23]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.
[24]洪东跑, 马小兵, 赵宇, 等.基于容差分析的结构非概率可靠性模型[J].机械工程学报, 2010, 46(04):157-162
[25]HONG D P, MA X B, ZHAO Y, et al.Structural non probabilistic reliability model based on
[26]toleranceanalysis [j].Journal of mechanical engineering, 2010, 46 (04): 157-162(in Chinese).
[27]黄土地, 彭兆春, 柏松, 等.概率双线性累积损伤模型与机械结构时变可靠性分析[J].机械工程学报, 2023, 59(16):117-127
[28]HUAND T D, PENG Z C, BAI S, et al.Probabilistic bilinear cumulative damage model and time-varying reliability analysis of mechanical structures [j][J].Journal of mechanical engineering, 2023, 59(16):117-127
[29]冯振宇, 柴崇博, 邹君, 等.含多裂纹对接板应力强度因子三维有限元分析[J].航空学报, 2021, 42(05):242-249
[30]FENG Z Y, CHAI C B, ZOU J, et al.Three dimensional finite element analysis of stress intensity factors of butt plates with multiple cracks [j][J].Acta Aeronautica Sinica, 2021, 42(05):242-249