Hardening gradients have been introduced to heavy-duty gears to enhance their bearing capacity, but this has led to an increase in the complexity and difficulty of fatigue analysis. To explore ways to mitigate this, in this work, a contact fatigue model of an 18CrNiMo7-6 gear pair with a hardness gradient was established, and the Brown‒Miller‒Morrow multiaxial fatigue criterion was adopted to calculate the contact fatigue lifespan under different contact pressures. The gear contact fatigue limit was then determined by fitting the stress–number of cycles (S‒N) curve. The results of this method are verified by gear contact fatigue tests. Furthermore, the effects of case hardening depth (CHD) and surface hardness (SH) on the contact fatigue lifespan and limits were explored, and we found that the contact fatigue limit of a typical carburized gear was more affected by SH than CHD. In addition, we also examined which hardness gradients were more beneficial for the fatigue performance of gears with atypical hardening gradients.
Wu J Z, Wei P T, Zhu C C, Zhang P, Liu H J. Development and application of high strength gears. Int J Adv Manuf Technol 132(7): 3123–3148 (2024)
Zhang B Y, Liu H J, Wei P T, Guagliano M, Hou S W. A modified model of Lundberg-Palmgren rolling contact fatigue formula considering the effects of surface treatments. Friction 11(10): 1922–1938 (2023)
Xia Q S, Hua D P, Zhou Q, Shi Y R, Deng X T, Lu K J, Wang H F, Liang X B, Wang Z D. Atomic-scale insights into damage mechanisms of GGr15 bearing steel under cyclic shear fatigue. Acta Metall Sin—Engl 37(7): 1265–1278 (2024)
Liu H J, Wang W, Zhu C C, Jiang C X, Wu W, Parker R G. A microstructure sensitive contact fatigue model of a carburized gear. Wear 436: 203035 (2019)
Liu P F, Li W, Nehila A, Sun Z D, Deng H L. High cycle fatigue property of carburized 20Cr gear steel under axial loading. Metals 6(10): 246 (2016)
Sirin S Y, Sirin K, Kaluc E. Effect of the ion nitriding surface hardening process on fatigue behavior of AISI 4340 steel. Mater Charact 59(4): 351–358 (2008)
Zhang Z H, Wang Z W, Shao M H, Yan J W, He Y Y, Li Y. Simulation of hollow-cathode-nitriding plasma and design of diffusion equipment with DC and RF dual discharge. Phys Scripta 98(2): 025610 (2023)
Zhang Z H, Wang Z W, Shao M H, Dou H C, He Y Y, Li Y, Luo J B. Structural and tribological properties of sulfonitrocarburizing layers prepared by plasma nitrocarburizing and low temperature ion sulfurizing. Surf Coat Tech 478: 130470 (2024)
Zhang B Y, Wei P T, Liu H J, Yan H, Guagliano M. Effect of fine particle peening on surface integrity of flexspline in harmonic drive. Surf Coat Tech 433: 128133 (2022)
Wu J Z, Wei P T, Liu H J, Zhang B Y, Tao G B. Effect of shot peening intensity on surface integrity of 18CrNiMo7-6 steel. Surf Coat Tech 421: 127194 (2021)
Liu H L, Liu H J, Bocher P, Zhu C C, Sun Z D. Effects of case hardening properties on the contact fatigue of a wind turbine gear pair. Int J Mech Sci 141: 520–527 (2018)
Lorenz S J, Sadeghi F, Wang C. Effect of spatial hardness distribution in rolling contact fatigue performance of bearing contacts. Tribol Int 171: 107550 (2022)
Wang W, Liu H J, Zhu C C, Tang J Y, Jiang C X. Evaluation of contact fatigue risk of a carburized gear considering gradients of mechanical properties. Friction 8(6): 1039–1050 (2020)
Choi Y, Liu C R. Rolling contact fatigue life of finish hard machined surfaces Part 1. Model development. Wear 261(5–6): 485–491 (2006)
Li W, Liu B S. Experimental investigation on the effect of shot peening on contact fatigue strength for carburized and quenched gears. Int J Fatigue 106: 103–113 (2018)
Gorla C, Rosa F, Conrado E, Albertini H. Bending and contact fatigue strength of innovative steels for large gears. P I Mech Eng C—J Mec 228(14): 2469–2482 (2014)
Zhang Q, Zhang J, Wu C H, Xu Z Z, Lyu S. The evaluation of contact fatigue strength for 20MnCr5 carburized gear. Int J Precis Eng Manuf 15(1): 117–121 (2014)
Lu Z H, Li Z H, Liu H J, Wei P T, Xia B, Ye M. An accelerated fatigue test method of polymer gears based on thermostress conversion relation. Eng Fract Mech 266: 108388 (2022)
Zhang X H, Wei P T, Parker R G, Liu G L, Liu H J, Wu S J. Study on the relation between surface integrity and contact fatigue of carburized gears. Int J Fatigue 165: 107203 (2022)
Schijve J. Fatigue of structures and materials in the 20th century and the state of the art. Int J Fatigue 39(3): 307–333 (2003)
Li W, Deng S, Liu B S. Experimental study on the influence of different carburized layer depth on gear contact fatigue strength. Eng Fail Anal 107: 104225 (2020)
Wu J Z, Liu H J, Wei P T, Lin Q J, Zhou S S. Effect of shot peening coverage on residual stress and surface roughness of 18CrNiMo7-6 steel. Int J Mech Sci 183: 105785 (2020)
Pavlina E J, Van Tyne C J. Correlation of yield strength and tensile strength with hardness for steels. J Mater Eng Perform 17(6): 888–893 (2008)
Lang D O R, Kernen i R. Dimensionierung komplizierter bauteile aus stahl im bereich der zeit- und dauerfestigkeit. Mater Und Werkstofftech 10(1): 24–29 (1979)
Tao Q, Wang J, Fu L M, Chen Z, Shen C J, Zhang D K, Sun Z. Ultrahigh hardness of carbon steel surface realized by novel solid carburizing with rapid diffusion of carbon nanostructures. J Mater Sci Technol 33(10): 1210–1218 (2017)
Brown M W, Miller K J. A theory for fatigue failure under multiaxial stress-strain conditions. Proc Inst Mech Eng 187(1): 745–755 (1973)
Kim K. Estimation methods for fatigue properties of steels under axial and torsional loading. Int J Fatigue 24(7): 783–793 (2002)
Roessle M. Strain-controlled fatigue properties of steels and some simple approximations. Int J Fatigue 22(6): 495–511 (2000)
Zhang X H, Liu H J, Wu S J, Li G M, Wei P T. Experimental investigation on the effect of barrel finishing processes on surface integrity of 18CrNiMo7-6 carburized rollers. P I Mech Eng E—J Pro 236(5): 2095–2105 (2022)
Boschetto A, Bottini L, Veniali F. Microremoval modeling of surface roughness in barrel finishing. Int J Adv Manuf Technol 69(9): 2343–2354 (2013)
Lesyk D A, Mordyuk B N, Martinez S, Dzhemelinskyi V V, Grzesiak D, Grochała D, Lamikiz A. Laser-based additive manufacturing and mechanical surface post-processing: Comparison of barrel finishing, shot and ultrasonic peening for corrosion resistance improvement of superalloy. Lasers Manuf Mater Process 10(4): 702–734 (2023)
Zhang B Y, Liu H J, Bai H Y, Zhu C C, Wu W. Ratchetting–multiaxial fatigue damage analysis in gear rolling contact considering tooth surface roughness. Wear 428: 137–146 (2019)
Zhang B Y, Liu H J, Zhu C C, Li Z. Numerical simulation of competing mechanism between pitting and micro-pitting of a wind turbine gear considering surface roughness. Eng Fail Anal 104: 1–12 (2019)
Rajinikanth V, Soni M K, Mahato B, Rao M A. Microstructural investigation of rolling contact fatigue (RCF) on a failed planetary gear of a windmill gearbox. Eng Fail Anal 121: 105167 (2021)
Vukelic G, Pastorcic D, Vizentin G, Bozic Z. Failure investigation of a crane gear damage. Eng Fail Anal 115: 104613 (2020)
Zhang B Y, Liu H J, Zhu C C, Ge Y B. Simulation of the fatigue-wear coupling mechanism of an aviation gear. Friction 9(6): 1616–1634 (2021)
Flodin A, Andersson S. A simplified model for wear prediction in helical gears. Wear 249(3–4): 285–292 (2001)
Liu H L, Liu H J, Zhu C C, Tang J Y. Study on gear contact fatigue failure competition mechanism considering tooth wear evolution. Tribol Int 147: 106277 (2020)
Tong Y L, Hua K, Xie H Y, Cao Y, Huang Z B, Liang Z P, Li X L, Wu H X, Wang H F. Subsurface deformation mechanism and the interplay relationship between strength-ductility and fretting wear resistance during fretting of a high-strength titanium alloy. Friction 12(10): 2259–2280 (2024)
Yan Y T, Jiang C, Li W D. Simulation on coupling effects between surface wear and fatigue in spur gear. Eng Fail Anal 134: 106055 (2022)
Zhou Q, Jiao Z C, Huang Z B, Shi Y R, Li Y L, Yin C H, Wang H F, Pinto H C, Greiner C, Liu W M. Wear-resistant CrCoNi nanocrystalline film via friction-driven surface segregation. Acta Mater 279: 120299 (2024)
Zhou Q, Luo D W, Hua D P, Ye W T, Li S, Zou Q G, Chen Z Q, Wang H F. Design and characterization of metallic glass/graphene multilayer with excellent nanowear properties. Friction 10(11): 1913–1926 (2022)