Life Prediction of Planetary Gearbox Based on Competing Failure Mechanisms and Experimental Study

doi:10.3901/JME.2025.03.284

Abstract

Abstract: Gears are designed to carry out alternating loads during the transmission process, and the special structure of their involutes causes changes in the sliding/rolling ratio during the meshing process as well as changes in the friction performance caused by the morphology characteristics of the tooth surfaces, ultimately leading to contact fatigue or tooth root bending fatigue. The service life of planetary gear trains depends on the minimum life of various types of gears such as gear rings, planetary gears and sun gears under the competition of contact fatigue and bending fatigue. A finite element model is built up for a spur planetary geartrain, and the time-varying friction coefficient is taken into account. Critical plane methods based on the multi-axial fatigue criteria, such as Brown-Miller method, Fatemi-Socie method, Morrow method and Smith-Waston-Topper method are used to evaluate the fatigue crack initiation location and life distribution of competitive failure in planetary gear train. The residual stress from surface to core is fitted based on the experimentally measured hardness, and the fatigue parameters are then modified accordingly. Finally, fatigue tests are conducted for planetary gear trains under the same operating conditions to investigate the evolution process of surface pits on failed gears and verify the effectiveness and accuracy of the developed model. The results show that the contact fatigue strength of the gearbox is much lower than the bending fatigue strength. The Fatemi-Socie method has higher accuracy in evaluating the contact fatigue life of gears. The sun gear more likely suffers from contact fatigue compared with other gears due to its teeth meshing with different planetary gears in sequence, and pitting first occurs on the subsurface near the tooth root of the pitch line. The contact fatigue life and location considering residual stress are consistent with the experimental results. The modeling method developed in this study can provide insight into the life prediction of planetary gearboxes based on competitive failure fatigue, and the method can be used for the fatigue properties of other types of transmission components.

Key words: spur planetary gearbox, multi-axial fatigue, competing failure mechanism, residual stress, life prediction

CLC Number:

TH131

WANG Hanming, DONG Qingbing, CHEN Zhuang, ZHAO Bo, SHI Xiujiang. Life Prediction of Planetary Gearbox Based on Competing Failure Mechanisms and Experimental Study[J]. Journal of Mechanical Engineering, 2025, 61(3): 284-298.

References

[1] ZHANG Ning，GUO Shuo，HE Guoning，et al. Failure analysis of the carburized 20MnCr5 gear in fatigue working condition[J]. International Journal of Fatigue，2022，161:106938.
[2] SHARIF K，EVANS H，SNIDLE R. Modelling of elastohydrodynamic lubrication and fatigue of rough surfaces:The effect of lambda ratio[C]. ARCHIVE Proceedings of the Institution of Mechanical Engineers Part J Journal of Engineering Tribology 1994-1996(vols 208-210)，2012，226(12):1039-1050.
[3] AL-MAYALI M F，HUTT S，SHARIF K J，et al. Experimental and numerical study of micropitting initiation in real rough surfaces in a micro- elastohydrodynamic lubrication regime[J]. Tribology Letters，2018，66(4):1-14.
[4] MALLIPEDDI D，NORELL M，SOSA M，et al. The effect of manufacturing method and running-in load on the surface integrity of efficiency tested ground，honed and superfinished gears[J]. Tribology International，2019，131:277-287.
[5] KLEIN M，HÖHN B R，MICHAELIS K，et al. Theoretical and experimental investigations about flank breakage in bevel gears[J]. Industrial Lubrication and Tribology，2011，63(1):5-10.
[6] WARHADPANDE A，SADEGHI F，KOTZALAS M N，et al. Effects of plasticity on subsurface initiated spalling in rolling contact fatigue[J]. International Journal of Fatigue，2012，36(1):80-95.
[7] 周长江，王豪野，靳广虎，等. 考虑残余应力的螺旋锥齿轮接触疲劳裂纹萌生-扩展寿命计算方法研究[J]. 机械工程学报，2022，58(23):28-38. ZHOU Changjiang，WANG Haoye，JIN Guanghu，et al. Calculation method of contact fatigue life of spiral bevel gears considering residual stress[J]. Journal of Mechanical Engineering，2022，58(23):28-38.
[8] KAROLCZUK A，MACHA E. A review of critical plane orientations in multiaxial fatigue failure criteria of metallic materials[J]. International Journal of Fracture，2005，134:267-304.
[9] BROWN M W，MILLER K J. Initiation and growth of cracks in biaxial fatigue[J]. Fatigue & Fracture of Engineering Materials & Structures，1979，1:231-246.
[10] FATEMI A，SOCIE D F. A critical plane approach to multiaxial fatigue damage including out-of-phase loading[J]. Fatigue & Fracture of Engineering Materials & Structures，1988，11(3):149-165.
[11] SOCIE D F，MORROW J. Review of contemporary approaches to fatigue damage analysis [M]//BURKE J J， WEISS V. Risk and failure analysis for improved performance and reliability. Boston:Springer. 1980:141-194.
[12] SMITH K N，TOPPER T，WATSON P. A stress–strain function for the fatigue of metals[J]. J Materials，1970，5:767-778.
[13] HE Peiyu，HONG Rongjing，WANG Hua，et al. Fatigue life analysis of slewing bearings in wind turbines[J]. International Journal of Fatigue，2018，111:233-242.
[14] NESLÁDEK M，PACETTI L，PAPUGA J. Validation of fatigue criteria under fretting fatigue conditions[J]. International Journal of Fatigue，2022，161:106895.
[15] SPRINGER M，PETTERMANN H E. Fatigue life predictions of metal structures based on a low-cycle，multiaxial fatigue damage model[J]. International Journal of Fatigue，2018，116:355-365.
[16] BASAN R，MAROHNIĆ T. Multiaxial fatigue life calculation model for components in rolling-sliding line contact with application to gears[J]. Fatigue & Fracture of Engineering Materials & Structures，2019，42(7):1478-1493.
[17] SUM W S，WILLIAMS E J，LEEN S B. Finite element，critical-plane，fatigue life prediction of simple and complex contact configurations[J]. International Journal of Fatigue，2005，27(4):403-416.
[18] 王雄，董庆兵，史修江，等. 基于多轴疲劳准则的齿轮点蚀寿命预测[J]. 摩擦学学报，2023，43(1):92-103. WANG Xiong，DONG Qingbing，SHI Xiujiang，et al. Gear pitting life prediction based on multi-axial fatigue criterion[J]. Tribology，2023，43(1):92-103.
[19] GHAFFARI M A，PAHL E，XIAO S. Three dimensional fatigue crack initiation and propagation analysis of a gear tooth under various load conditions and fatigue life extension with boron/epoxy patches[J]. Engineering Fracture Mechanics，2015，135:126-146.
[20] OOI G T C，ROY S，SUNDARARAJAN S. Investigating the effect of retained austenite and residual stress on rolling contact fatigue of carburized steel with XFEM and experimental approaches[J]. Materials Science and Engineering:A，2018，732:311-319.
[21] FLEURY R M N，SALVATI E，NOWELL D，et al. The effect of surface damage and residual stresses on the fatigue life of nickel superalloys at high temperature[J]. International Journal of Fatigue，2019，119:34-42.
[22] VUKOVIĆ K，ULAR 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.
[23] GIORDANI T，CLARKE T R，KWIETNIEWSKI C E F，et al. Mechanical and metallurgical evaluation of carburized，conventionally and intensively quenched steels[J]. Journal of Materials Engineering and Performance，2013，22:2304-2313.
[24] 中华人民共和国国家质量监督检验检疫总局，中国国家标准化管理委员会. GB/T 3480.2-2021，直齿轮和斜齿轮承载能力计算第2部分:齿面接触强度(点蚀)计算[S]. 北京:中国标准出版社，2021. General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China，Standardization Administration of the People’s Republic of China. GB/T 3480.2-2021. Calculation of load capacity of spur and helical gears-Part 2:Calculation of surface durability (pitting)[S]. Beijing:Standards Press of China，2021.
[25] ISO 6336-2:2019(E). Calculation of load capacity of spur and helical gears—Part 2:Calculation of surface durability (pitting)[R]. 2019.
[26] XU H，KAHRAMAN A，ANDERSON N E，et al. Prediction of mechanical efficiency of parallel-axis gear pairs[J]. Journal of Mechanical Design，2007，129(1):58-68.
[27] LI Jing，ZHANG Zhongping，SUN Qiang，et al. Multiaxial fatigue life prediction for various metallic materials based on the critical plane approach[J]. International Journal of Fatigue，2011，33(2):90-101.
[28] MADGE J J，LEEN S B，SHIPWAY P H. The critical role of fretting wear in the analysis of fretting fatigue[J]. Wear，2007，263(1-6):542-551.
[29] SUN Xianshun，ZHAO Jun，HU Youbin，et al. The prediction and experimental study of bending fatigue Life of carburized gears[J]. Journal of Materials Engineering and Performance，2023:1-9.
[30] SHAMSAEI N，FATEMI A. Effect of hardness on multiaxial fatigue behaviour and some simple approximations for steels[J]. Fatigue & Fracture of Engineering Materials & Structures，2009，32(8):631-646.
[31] 王天鹏，张建仁，王磊，等. 桥梁缆索钢丝裂纹扩展速率预测及疲劳寿命计算[J]. 湖南大学学报，2021，48(03):24-33. WANG Tianpeng，ZHANG Jianren，WANG Lei，et al. Crack growth rate prediction and fatigue life calculation of bridge cable steel wires[J]. Journal of Hunan University，2021，48(03):24-33.
[32] GLODEŽ S，WINTER H，STÜWE H P. A fracture mechanics model for the wear of gear flanks by pitting[J]. Wear，1997，208(1-2):177-183.
[33] LIN Xinhao，XU Yazhou. An equivalent damage model to fretting fatigue initiation life considering wear[J]. International Journal of Fatigue，2022，163:107048.
[34] WANG Can，LI Chao，LING Yong，et al. Investigation on fretting fatigue crack initiation in heterogenous materials using a hybrid of multiscale homogenization and direct numerical simulation[J]. Tribology International，2022，169:107470.
[35] ZHANG Qi，ZHANG Jing，WU Changhong，et al. The evaluation of contact fatigue strength for 20MnCr5 carburized gear[J]. International Journal of Precision Engineering and Manufacturing，2014，15:117-121.