Abstract
In order to consider the effects of elastohydrodynamic lubrication (EHL) on contact fatigue reliability of spur gear, an accurate and efficient method that combines with response surface method (RSM) and first order second moment method (FOSM) was developed for estimating the contact fatigue reliability of spur gear under EHL. The mechanical model of contact stress analysis of spur gear under EHL was established, in which the oil film pressure was mapped into hertz contact zone. Considering the randomness of EHL, material properties and fatigue strength correction factors, the proposed method was used to analyze the contact fatigue reliability of spur gear under EHL. Compared with the results of 1.5×105 by traditional Monte-Carlo, the difference between the two failure probability results calculated by the above mentioned methods is 2.2×10−4, the relative error of the failure probability results is 26.8%, and time-consuming only accounts for 0.14% of the traditional Monte-Carlo method (MCM). Sensitivity analysis results are in very good agreement with practical cognition. Analysis results show that the proposed method is precise and efficient, and could correctly reflect the influence of EHL on contact fatigue reliability of spur gear.
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References
PENG X Q, LIU G, WU L Y, LIU G R, LAM K Y. A stochastic finite element method for fatigue reliability analysis of gear teeth subjected to bending [J]. Computational Mechanics, 1998, 21(3):53–261.
ZHANG Y M, LIU Q L, WEN B C. Practical reliability-based design of gear paris [J]. Mechanism and Machine Theory, 2003, 38(12):1363–1370.
CHEN Tao, SUN Wei. Multi-source data fusion based small sample prediction of gear random reliability [J]. Journal of Mechanical Science and Technology, 2012, 26(8):2547–2555.
ALEMAYEHU F M, EKĞWARO-OSIR S. Uncertainty considerations in the dynamic loading and failure of spur gear pairs [J]. Journal of Mechanical Design, 2013, 135(8):1–7.
DAWSON P H. Effect of metallic contact on the pitting of lubricated rolling surface [J]. Journal of Mechanical Engineering Science, 1962, 7(1):147–155.
BHATTACHARYYA S, BOCK F C, HOWES M A H, PARIKH N M. Chemical effects of lubrication in contact fatigue, Part II: The statistical analysis, summary,and conclusions [J]. Journal of Lubricant Technology Trans ASME, 1976, 98(2):299–307.
BATTEZ A H, RICO J E F, RODRIGUEZ R C. Rolling fatigue tests of three polyglycol lubricants [J]. Wear, 2005, 258(10):1467–1470.
FAJDIGA G, GLODEŽ S, KRAMAR J. Pitting formation due to surface and subsurface initiated fatigue crack growth in contacting mechanical Elements [J]. Wear, 2007, 262(9/10):1217–1224.
LI S, KAHRAMAN A. Micro-pitting fatigue lives of lubricated point contacts: Experiments and model validation [J]. International Journal of Fatigue, 2013, 48:9–18.
LU Yao-hui, ZENG Jing, WU Ping-bo, YANG Fei, GUAN Qing-hua. Reliability and parametric sensitivity analysis of railway vehicle bogie frame based on Monte-Carlo numerical simulation [C]// High Performance Computing and Applications. Berlin: Springer, 2010:280–287.
STEFANOU G. The stochastic finite element method: Past, present and future [J]. Computer Method in Applied Mechanics and Engineering, 2009, 198(9/10/11/12):1031–1051.
LIU P L, KIUREGHIAN A D, ASCE M. Finite element reliability of geometrically nonlinear uncertain structures [J]. Journal of Engineering Mechanics, 1991, 117(8):1806–1825.
GAO Wei, WU Di, SONG Chong-min, FRANCIS T L, LI Xiao-jing. Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method [J]. Finite Elements in Analysis and Design, 2011, 47:643–652.
LIU Ji, LI Yun. An improved adaptive response surface method for structural reliability analysis [J]. Journal of Central South University, 2012, 19(4):1148–1154.
WEN Shi-zhu, YANG Pei-ran. Elastohydrodynamic lubrication [M]. Beijing: Tsinghua University Press, 1992: 100–121. (in Chinese)
HUNG Ping. Numerical calculation methods of elastohydrodynamic lubrication [M]. Beijing: Tsinghua University Press, 2013: 75–83. (in Chinese)
BAI Y C, HAN X, JIANG C, BI R G. A response surface based structural reliability analysis method by using non-probability convex model [J]. Applied Mathematical Modeling, 2014, 38:3834–3847.
LI Hua-kui. Reliability analysis of the truck rear axle and finite element analysis of the gear under the EHL [D]. Qingdao: Qingdao Technological University, 2012: 21–42. (in Chinese)
ZHANG Yan-hua. Finite element analysis of accelerating gear of wind-power-generating under the EHL [D]. Qingdao: Qingdao Technological University, 2009: 35–59. (in Chinese)
HU Yun, LIU Shao-jun, DING Sheng. Contact fatigue life on spur gear with consideration of elastohydrodynamic [J]. Journal of Central South University, 2014, 45(12): 4187–4193. (in Chinese)
SUN Zhi-li, CHEN Lang-yu. Theory and method of utility mechanical reliability design [M]. Beijing: Science Press, 2003: 78–79. (in Chinese)
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Foundation item: Project(CX2014B060) supported by Hunan Provincial Innovation for Postgraduate, China; Project(8130208) supported by General Armament Pre-research Foundation, China
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Hu, Y., Liu, Sj., Ding, S. et al. Application of response surface method for contact fatigue reliability analysis of spur gear with consideration of EHL. J. Cent. South Univ. 22, 2549–2556 (2015). https://doi.org/10.1007/s11771-015-2784-3
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DOI: https://doi.org/10.1007/s11771-015-2784-3