Study on Contact Fatigue Crack Modeling and Propagation Law of Rolling Bearings

doi:10.3969/j.issn.1004-132X.2023.16.001

Abstract

Abstract: Aiming at the damage evolution problems of rolling bearings, fatigue crack propagation mechanism was studied via XFEM. The reliability of the XFEM was verified by an example. An XFEM model of rolling contact fatigue with subsurface initial crack was proposed through fracture mechanics theory. The influencing mechanism of initial crack angle, depth and length on the propagation life and growth path of cracks in subsurfaces were analysed. Crack propagation mechanism was studied through analyzed the variation of stress intensity factors. Results show that sliding mode is the main growth mode of initial cracks in subsurface. The crack angle has a great influence on the fatigue crack growth path. The initial cracks with angle in the 15~45 degree range are easy to change the grow direction to surface which lead to fatigue spall. The crack size and depth have little effects on the morphology of the crack propagation path, but will affect the difficulty of crack propagation.

Key words: extended finite element method(XFEM), crack propagation, rolling contact fatigue, mechanism

摘要： 针对滚动轴承的疲劳剥落损伤演化问题，采用扩展有限元方法研究疲劳裂纹扩展机理，通过算例验证了扩展有限元方法的可靠性。运用断裂力学理论建立了包含次表面初始裂纹的滚动接触疲劳扩展有限元模型，分析了初始裂纹倾斜角度、所处深度和初始裂纹长度对次表面裂纹生长到表面的扩展路径影响机制，通过分析应力强度因子变化研究了裂纹扩展机理。研究结果表明，次表面疲劳裂纹以滑开型裂纹扩展模式为主；初始裂纹角度对疲劳裂纹扩展路径影响较大，初始裂纹角度在15°~45°时裂纹会转向表面发展而形成疲劳剥落；初始裂纹尺寸和深度对裂纹扩展路径形貌的影响较小，但会影响裂纹扩展的难易程度。

关键词: 扩展有限元方法, 裂纹扩展, 滚动接触疲劳, 机理

CLC Number:

TH133.33

GUO Wei, CAO Hongrui, ZI Yanyang, WEI Xunkai. Study on Contact Fatigue Crack Modeling and Propagation Law of Rolling Bearings[J]. China Mechanical Engineering, 2023, 34(16): 1891-1899.

郭伟, 曹宏瑞, 訾艳阳, 尉询楷. 滚动轴承接触疲劳裂纹建模与扩展规律研究[J]. 中国机械工程, 2023, 34(16): 1891-1899.

References

［1］赵传国. 滚动轴承失效分析概论［J］. 轴承，1996(1)：39-46.
ZHAO Chuanguo. Introduction to Failure Analysis of Rolling Bearings［J］. Bearing, 1996(1):39-46.
［2］LANGUEH A M G, BRUNEL J F, CHARKALUK E, et al. Effects of Sliding on Rolling Contact Fatigue of Railway Wheels［J］. Fatigue & Fracture of Engineering Materials & Structures, 2013, 36(6):515-525.
［3］DENG Song, HUA Lin, HAN Xinghui, et al. Investigation of Rolling Contact Fatigue Cracks in Ball Bearings［J］. International Journal of Fracture, 2014, 188(1):71-78.
［4］NAZIR M H, KHAN Z A, SAEED A. Experimental Analysis and Modelling of C-crack Propagation in Silicon Nitride Ball Bearing Element under Rolling Contact Fatigue［J］. Tribology International, 2018, 126:386-401.
［5］谢俊杰，柳小勤，伍星，等. 滚动轴承接触疲劳内部裂纹扩展有限元分析［J］.机械科学与技术, 2020, 39(3):350-355.
XIE Junjie, LIU Xiaoqin, WU Xing, et al. Finite Element Analysis of Internal Crack Propagation Induced by Contact Fatigue of Rolling Bearing［J］. Mechanical Science and Technology for Aerospace Engineering, 2020, 39(3):350-355.
［6］BELYTSCHKO T, BLACK T. Elastic Crack Growth in Finite Elements with Minimal Remeshing［J］. International Journal of Numerical Methods in Engineering, 1999, 45(5):601-620.
［7］MOS N, DOLBOW J, BELYTSCHKO T. A Finite Element Method for Crack Growth without Remeshing［J］. International Journal of Numerical Methods in Engineering, 1999, 46(1):131-150.
［8］BUDYN , ZI G, MOS N, et al. A Method for Multiple Crack Growth in Brittle Materials without Remeshing［J］. International Journal of Numerical Methods in Engineering, 2004, 61(10):1741-1770.
［9］MOTAMEDI D, MOHAMMADI S. Dynamic Analysis of Fixed Cracks in Composites by the Extended Finite Element Method［J］. Engineering Fracture Mechanics, 2010, 77(17):3373-3393.
［10］OOI GTC, 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.
［11］MORAD F, NIFFENEGGER M. A New Simulation Approach for Crack Initiation, Propagation and Arrest in Hollow Cylinders under Thermal Shock Based on XFEM［J］. Nuclear Engineering and Design, 2022, 386:111582
［12］李录贤，王铁军. 扩展有限元法（XFEM）及其应用［J］. 力学进展，2005，35(1)：5-20.
LI Luxian, WANG Tiejun. The Extended Finite Element Method and Its Applications—a Review［J］. Advances in Mechanics, 2005, 35(1):5-20.
［13］方修君，金锋. 基于ABAQUS平台的扩展有限元法［J］. 工程力学，2007，24(7)：6-10.
FANG Xiujun, JIN Feng. Extended Finite Element Method Based on ABAQUS［J］. Engineering Mechanics,2007, 24(7):6-10.
［14］余天堂. 模拟三维裂纹问题的扩展有限元法［J］. 岩土力学，2010, 31(10)：3280-3285.
YU Tiantang. Extended Finite Element Method for Modeling Three-dimensional Crack Problems［J］. Rock and Soil Mechanics, 2010, 31(10):3280-3285.
［15］王伟，付豪，邢林啸，等. 基于扩展有限元法的碳酸盐岩地热储层岩体裂缝扩展行为［J］. 地球科学，2021，46(10)：3509-3519.
WANG Wei, FU Hao, XING Linxiao, et al. Crack Propagation Behavior of Carbonatite Geothermal Reservoir Rock Mass Based on Extended Finite Element Method［J］. Earth Science, 2021, 46(10):3509-3519.
［16］杨恩光，杨立云，胡桓宁，等. 单轴压缩荷载下闭合裂纹扩展的试验和数值研究［J］. 岩土力学，2022, 43(1):613-621.
YANG Enguang, YANG Liyun, HU Huanning, et al. Experimental and Numerical Research on Propagation of Closed Cracks under Uniaxial Compression［J］. Rock and Soil Mechanics, 2022, 43(1):613-621.
［17］刘钰，赵国堂，曹毅杰，等. 整体温升作用下纵连板式无砟轨道宽窄接缝损伤演化研究［J］．北京交通大学学报，2021, 45(4):19-27.
LIU Yu, ZHAO Guotang, CAO Yijie, et al. Study on Damage Evolution of Wide and Narrow Joints in Longitudinally Connected Slab Ballastless Track under Load of Overall Temperature Rise［J］. Journal of Beijing Jiaotong University, 2021,45(4):19-27.
［18］许德涛，唐进元，周炜. 基于扩展有限元法的齿根裂纹扩展规律［J］. 中南大学学报(自然科学版)，2016, 47(8):2668-2675.
XU Detao, TANG Jinyuan ZHOU Wei. Tooth Root Crack Propagation Regularity Based on Extended Finite Element Method［J］.Journal of Central South University(Science and Technology), 2016, 47(8):2668-2675.
［19］WEI Yu, JIANG Yong. Fatigue Frature Analysis of Gear Teeth Using XFEM［J］. Transactions of Nonferrous Metals Society of China, 2019,29(10):2099-2108.
［20］杨夏炜，彭冲，马铁军，等. 高温合金线性摩擦焊接头疲劳裂纹扩展有限元分析［J］．航空学报，2022, 43(2):102-116.
YANG Xiawei, PENG Chong, MA Tiejun, et al. Finite Element Analysis of Fatigue Crack Growth of Linear Friction Welded Superalloy Joints［J］. Acta Aeronautica et Astronautica Sinica, 2022, 43(2):102-116.
［21］徐宇飞，胡殿印，毛建兴，等. 一种结合晶体塑性及扩展有限元的短裂纹扩展模拟方法［J］．中国有色金属学报，2022, 33(2):435-444.
XU Yufei, HU Dianyin, MAO Jianxing, et al. A Short Crack Growth Simulation Method Using Crystal Plasticity Combining with Extended Finite Element Method［J］. The Chinese Journal of Nonferrous Metals, 2022, 33(2):435-444.
［22］张行. 断裂与损伤力学［M］. 北京：北京航空航天大学出版社，2009.
ZHANG Xing. Fracture and Damage Mechanics［M］. Beijing:Beihang University Press, 2009.
［23］杨立云，王青成，王宇伟，等. 材料线弹性断裂力学的断裂准则研究进展［J］. 科技导报, 2020, 38(2):59-68.
YANG Liyun, WANG Qingcheng, WANG Yuwei, et al. Research Progress of Fracture Criteria in Linear Elastic Fracture Mechanics of Materials［J］. Science & Technology Review, 2020, 38(2):59-68.
［24］MELENK J M, BABUKA I. The Partition of Unity Finite Element Method:Basic Theory and Applications［J］. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1/4):289-314.
［25］DUARTE C A, ODEN J T. An H-P Adaptive Method Using Clouds［J］. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1/4):237-262.
［26］VENTURA G, BUDYN E, BELYTSCHKO T. Vector Level Sets for Description of Propagating Cracks in Finite Elements［J］. International Journal of Numerical Methods in Engineering, 2003, 58(10):1571-1592.
［27］STOLARSKA M, CHOPP D L. Modeling Thermal Fatigue Cracking in Integrated Circuits by Level Sets and the Extended Finite Element Method［J］. International Journal of Engineering Science, 2003, 41(20):2381-2410.
［28］金光来. 基于扩展有限元的沥青路面疲劳开裂行为的数值研究［D］. 南京：东南大学，2015.
JIN Guanglai. Numerical Analysis of Fatigue Crack Growth in Asphalt Pavement Based on Extended Finite Element Model［D］. Nanjing:Southeast University, 2015.
［29］WAGONER M P, BUTTLAR W G, PAULINO G H. Development of A Single-edge Notched Beam Test for Asphalt Concrete Mixtures［J］. Journal of Testing & Evaluation, 2005, 33(6):452-460.
［30］HARRIS T A, KOTZALAS M N. Rolling Bearing Analysis:Essential Concepts of Bearing Technology［M］. Boca Raton:Taylor & Francis, 2007.
［31］GUO W, CAO H R, ZI Y Y, et al. Material Analysis of the Fatigue Mechanism of Rollers in Tapered Roller Bearings［J］. Science China Technological Sciences, 2018, 61(7):1003-1011.
［32］GUO W, MA T Y, CAO H R, et al. Numerical Analysis of Rolling Contact Fatigue Crack Initiation Considering Material Microstructure［J］. Engineering Failure Analysis, 2022, 138:106394.
［33］勒迈特J. 损伤力学教程［M］. 倪金刚，陶春虎，译.北京：科学出版社，1996.
LEMAITRE J. A Course on Damage Mechanics［M］. NI Jingang, TAO Chunhu, Trans. Beijing:Science Press, 1996.

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